Search is not available for this dataset
text
string | meta
dict |
|---|---|
module Prelude.Variables where
open import Agda.Primitive
open import Agda.Builtin.Nat
open import Agda.Builtin.List
variable
ℓ ℓ₁ ℓ₂ ℓ₃ : Level
A B C : Set ℓ
F M : Set ℓ₁ → Set ℓ₂
x y z : A
xs ys zs : List A
n m : Nat
|
{
"alphanum_fraction": 0.6752136752,
"avg_line_length": 15.6,
"ext": "agda",
"hexsha": "bebf415b55c625313f7ca7702ca1a3cca81b4f3c",
"lang": "Agda",
"max_forks_count": 24,
"max_forks_repo_forks_event_max_datetime": "2021-04-22T06:10:41.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-03-12T18:03:45.000Z",
"max_forks_repo_head_hexsha": "da4fca7744d317b8843f2bc80a923972f65548d3",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "t-more/agda-prelude",
"max_forks_repo_path": "src/Prelude/Variables.agda",
"max_issues_count": 59,
"max_issues_repo_head_hexsha": "da4fca7744d317b8843f2bc80a923972f65548d3",
"max_issues_repo_issues_event_max_datetime": "2022-01-14T07:32:36.000Z",
"max_issues_repo_issues_event_min_datetime": "2016-02-09T05:36:44.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "t-more/agda-prelude",
"max_issues_repo_path": "src/Prelude/Variables.agda",
"max_line_length": 30,
"max_stars_count": 111,
"max_stars_repo_head_hexsha": "da4fca7744d317b8843f2bc80a923972f65548d3",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "t-more/agda-prelude",
"max_stars_repo_path": "src/Prelude/Variables.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-12T23:29:26.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-05T11:28:15.000Z",
"num_tokens": 93,
"size": 234
}
|
-- Solver for functors
{-# OPTIONS --without-K --safe #-}
open import Categories.Category
open import Categories.Functor renaming (id to idF)
module Experiment.Categories.Solver.MultiFunctor {o ℓ e} where
import Categories.Morphism.Reasoning as MR
open import Level
open import Relation.Binary using (Rel)
infixr 9 _:∘_
data Expr : (𝒞 : Category o ℓ e) → Rel (Category.Obj 𝒞) (suc (o ⊔ ℓ ⊔ e)) where
:id : ∀ {𝒞 A} → Expr 𝒞 A A
_:∘_ : ∀ {𝒞 A B C} → Expr 𝒞 B C → Expr 𝒞 A B → Expr 𝒞 A C
:F₁ : ∀ {𝒞 𝒟} (F : Functor 𝒟 𝒞) {A B} →
Expr 𝒟 A B → Expr 𝒞 (Functor.F₀ F A) (Functor.F₀ F B)
∥_∥ : ∀ {𝒞 A B} → 𝒞 [ A , B ] → Expr 𝒞 A B
-- Semantics
_⟦_⟧ : ∀ 𝒞 {A B} → Expr 𝒞 A B → 𝒞 [ A , B ]
𝒞 ⟦ :id ⟧ = Category.id 𝒞
𝒞 ⟦ e₁ :∘ e₂ ⟧ = 𝒞 [ 𝒞 ⟦ e₁ ⟧ ∘ 𝒞 ⟦ e₂ ⟧ ]
𝒞 ⟦ :F₁ F e ⟧ = Functor.F₁ F (_ ⟦ e ⟧)
𝒞 ⟦ ∥ f ∥ ⟧ = f
N∘ : ∀ (𝒞 𝒟 : Category o ℓ e) (F : Functor 𝒟 𝒞) {A B C} →
Expr 𝒟 B C → 𝒞 [ A , Functor.F₀ F B ] → 𝒞 [ A , Functor.F₀ F C ]
N∘ 𝒞 𝒟 F :id g = g
N∘ 𝒞 𝒟 F (e₁ :∘ e₂) g = N∘ 𝒞 𝒟 F e₁ (N∘ 𝒞 𝒟 F e₂ g)
N∘ 𝒞 𝒟 F (:F₁ {𝒟 = ℰ} G e) g = N∘ 𝒞 ℰ (F ∘F G) e g
N∘ 𝒞 𝒟 F ∥ f ∥ g = 𝒞 [ Functor.F₁ F f ∘ g ]
_⟦_⟧N : ∀ 𝒞 {A B} → Expr 𝒞 A B → 𝒞 [ A , B ]
𝒞 ⟦ e ⟧N = N∘ 𝒞 𝒞 idF e (Category.id 𝒞)
N∘≈⟦⟧ : ∀ 𝒞 𝒟 (F : Functor 𝒟 𝒞) {A B C}
(e : Expr 𝒟 B C) (g : 𝒞 [ A , Functor.F₀ F B ]) →
𝒞 [ N∘ 𝒞 𝒟 F e g ≈ 𝒞 [ Functor.F₁ F (𝒟 ⟦ e ⟧) ∘ g ] ]
N∘≈⟦⟧ 𝒞 𝒟 F :id g = begin
g ≈˘⟨ identityˡ ⟩
id ∘ g ≈˘⟨ identity ⟩∘⟨refl ⟩
F₁ (Category.id 𝒟) ∘ g ∎
where open Category 𝒞
open Functor F
open HomReasoning
N∘≈⟦⟧ 𝒞 𝒟 F (e₁ :∘ e₂) g = begin
N∘ 𝒞 𝒟 F e₁ (N∘ 𝒞 𝒟 F e₂ g) ≈⟨ N∘≈⟦⟧ 𝒞 𝒟 F e₁ (N∘ 𝒞 𝒟 F e₂ g) ⟩
F₁ (𝒟 ⟦ e₁ ⟧) ∘ N∘ 𝒞 𝒟 F e₂ g ≈⟨ pushʳ (N∘≈⟦⟧ 𝒞 𝒟 F e₂ g) ⟩
(F₁ (𝒟 ⟦ e₁ ⟧) ∘ F₁ (𝒟 ⟦ e₂ ⟧)) ∘ g ≈˘⟨ homomorphism ⟩∘⟨refl ⟩
F₁ (𝒟 [ 𝒟 ⟦ e₁ ⟧ ∘ 𝒟 ⟦ e₂ ⟧ ]) ∘ g ∎
where open Category 𝒞
open HomReasoning
open MR 𝒞
open Functor F
N∘≈⟦⟧ 𝒞 𝒟 F (:F₁ {𝒟 = ℰ} G e) g = N∘≈⟦⟧ 𝒞 ℰ (F ∘F G) e g
N∘≈⟦⟧ 𝒞 𝒟 F ∥ f ∥ g = Category.Equiv.refl 𝒞
⟦e⟧N≈⟦e⟧ : ∀ 𝒞 {A B} (e : Expr 𝒞 A B) → 𝒞 [ 𝒞 ⟦ e ⟧N ≈ 𝒞 ⟦ e ⟧ ]
⟦e⟧N≈⟦e⟧ 𝒞 e = N∘≈⟦⟧ 𝒞 𝒞 idF e id ○ identityʳ
where open Category 𝒞
open HomReasoning
solve : ∀ {𝒞 A B} (e₁ e₂ : Expr 𝒞 A B) →
𝒞 [ 𝒞 ⟦ e₁ ⟧N ≈ 𝒞 ⟦ e₂ ⟧N ] → 𝒞 [ 𝒞 ⟦ e₁ ⟧ ≈ 𝒞 ⟦ e₂ ⟧ ]
solve {𝒞 = 𝒞} e₁ e₂ eq = begin
𝒞 ⟦ e₁ ⟧ ≈˘⟨ ⟦e⟧N≈⟦e⟧ 𝒞 e₁ ⟩
𝒞 ⟦ e₁ ⟧N ≈⟨ eq ⟩
𝒞 ⟦ e₂ ⟧N ≈⟨ ⟦e⟧N≈⟦e⟧ 𝒞 e₂ ⟩
𝒞 ⟦ e₂ ⟧ ∎
where open Category 𝒞
open HomReasoning
∥-∥ : ∀ {𝒞 A B} {f : 𝒞 [ A , B ]} → Expr 𝒞 A B
∥-∥ {f = f} = ∥ f ∥
|
{
"alphanum_fraction": 0.4508104033,
"avg_line_length": 33.1625,
"ext": "agda",
"hexsha": "bac69bb2613253eedd7f3fe21189df2c008a76dc",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "37200ea91d34a6603d395d8ac81294068303f577",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "rei1024/agda-misc",
"max_forks_repo_path": "Experiment/Categories/Solver/MultiFunctor.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "37200ea91d34a6603d395d8ac81294068303f577",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "rei1024/agda-misc",
"max_issues_repo_path": "Experiment/Categories/Solver/MultiFunctor.agda",
"max_line_length": 79,
"max_stars_count": 3,
"max_stars_repo_head_hexsha": "37200ea91d34a6603d395d8ac81294068303f577",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "rei1024/agda-misc",
"max_stars_repo_path": "Experiment/Categories/Solver/MultiFunctor.agda",
"max_stars_repo_stars_event_max_datetime": "2020-04-21T00:03:43.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-04-07T17:49:42.000Z",
"num_tokens": 1618,
"size": 2653
}
|
-- Andreas, 2017-05-17, issue #2574 reported by G. Allais
open import Issue2574Import -- The imported module should be clickable.
open import Issue2574ImportBlank -- The imported module should be clickable.
|
{
"alphanum_fraction": 0.7557603687,
"avg_line_length": 43.4,
"ext": "agda",
"hexsha": "742bff859d73034454263bd8b447af4822457943",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cruhland/agda",
"max_forks_repo_path": "test/interaction/Issue2574.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cruhland/agda",
"max_issues_repo_path": "test/interaction/Issue2574.agda",
"max_line_length": 78,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cruhland/agda",
"max_stars_repo_path": "test/interaction/Issue2574.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 53,
"size": 217
}
|
-- Currently this test case is broken. Once Issue 3451 has been fixed
-- it should be moved to test/Fail (and this comment should be
-- removed).
-- The option --guardedness turns off sized types.
{-# OPTIONS --guardedness #-}
open import Agda.Builtin.Size
record Stream (A : Set) (i : Size) : Set where
coinductive
field
head : A
tail : {j : Size< i} → Stream A j
open Stream
postulate
destroy-guardedness : {A : Set} → A → A
repeat : ∀ {A i} → A → Stream A i
repeat x .head = x
repeat x .tail = destroy-guardedness (repeat x)
|
{
"alphanum_fraction": 0.664845173,
"avg_line_length": 21.96,
"ext": "agda",
"hexsha": "7196c668b4b77272b606c77f22dd1e6e15dfa7c1",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "2fa8ede09451d43647f918dbfb24ff7b27c52edc",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "phadej/agda",
"max_forks_repo_path": "test/Succeed/Issue1209-7.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "2fa8ede09451d43647f918dbfb24ff7b27c52edc",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "phadej/agda",
"max_issues_repo_path": "test/Succeed/Issue1209-7.agda",
"max_line_length": 69,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "2fa8ede09451d43647f918dbfb24ff7b27c52edc",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "phadej/agda",
"max_stars_repo_path": "test/Succeed/Issue1209-7.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 161,
"size": 549
}
|
module Class.MonadTrans where
open import Class.Monad
open import Level
record MonadTrans {a} (T : (Set a -> Set a) -> Set a -> Set a) : Set (suc a) where
field
embed : {A : Set a} {M : Set a -> Set a} {{_ : Monad M}} -> M A -> T M A
open MonadTrans {{...}} public
|
{
"alphanum_fraction": 0.5948905109,
"avg_line_length": 24.9090909091,
"ext": "agda",
"hexsha": "9b89f98a38ba6c28df2fc3351d0611d53617ca9e",
"lang": "Agda",
"max_forks_count": 2,
"max_forks_repo_forks_event_max_datetime": "2021-10-20T10:46:20.000Z",
"max_forks_repo_forks_event_min_datetime": "2019-06-27T23:12:48.000Z",
"max_forks_repo_head_hexsha": "62fa6f36e4555360d94041113749bbb6d291691c",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "WhatisRT/meta-cedille",
"max_forks_repo_path": "stdlib-exts/Class/MonadTrans.agda",
"max_issues_count": 10,
"max_issues_repo_head_hexsha": "62fa6f36e4555360d94041113749bbb6d291691c",
"max_issues_repo_issues_event_max_datetime": "2020-04-25T15:29:17.000Z",
"max_issues_repo_issues_event_min_datetime": "2019-06-13T17:44:43.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "WhatisRT/meta-cedille",
"max_issues_repo_path": "stdlib-exts/Class/MonadTrans.agda",
"max_line_length": 82,
"max_stars_count": 35,
"max_stars_repo_head_hexsha": "62fa6f36e4555360d94041113749bbb6d291691c",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "WhatisRT/meta-cedille",
"max_stars_repo_path": "stdlib-exts/Class/MonadTrans.agda",
"max_stars_repo_stars_event_max_datetime": "2021-10-12T22:59:10.000Z",
"max_stars_repo_stars_event_min_datetime": "2019-06-13T07:44:50.000Z",
"num_tokens": 90,
"size": 274
}
|
module Numeral.Natural.Relation.Order where
import Lvl
open import Functional
open import Logic
open import Logic.Propositional
open import Logic.Predicate
open import Numeral.Natural
open import Numeral.Natural.Oper
open import Relator.Equals
open import Relator.Equals.Proofs
open import Relator.Ordering
-- Inequalities/Comparisons
data _≤_ : ℕ → ℕ → Stmt{Lvl.𝟎} where
min : ∀{y} → (𝟎 ≤ y)
succ : ∀{x y} → (x ≤ y) → (𝐒(x) ≤ 𝐒(y))
_<_ : ℕ → ℕ → Stmt
_<_ a b = (𝐒(a) ≤ b)
open From-[≤][<] (_≤_) (_<_) public
|
{
"alphanum_fraction": 0.6897880539,
"avg_line_length": 21.625,
"ext": "agda",
"hexsha": "d4ed03d63167e37fa7c1fa1c4b65b6d1f2c4b4d3",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "Lolirofle/stuff-in-agda",
"max_forks_repo_path": "Numeral/Natural/Relation/Order.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "Lolirofle/stuff-in-agda",
"max_issues_repo_path": "Numeral/Natural/Relation/Order.agda",
"max_line_length": 43,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "Lolirofle/stuff-in-agda",
"max_stars_repo_path": "Numeral/Natural/Relation/Order.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-05T06:53:22.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-04-07T17:58:13.000Z",
"num_tokens": 183,
"size": 519
}
|
module Eq.ObsTheory where
open import Prelude
open import T
open import DynTheory
open import SubstTheory
open import Contexts
open import Eq.Defs
open import Eq.KleeneTheory
open ObservEq
---- Proofs about observational equivalence
-- observational equivalence being an equiv reln follows trivially from kleene equiv being one
obs-refl : ∀ {Γ} {A} → Reflexive (ObservEq Γ A)
obs-refl = obs (λ C → kleene-refl)
obs-sym : ∀ {Γ} {A} → Symmetric (ObservEq Γ A)
obs-sym eq = obs (λ C → kleene-sym (observe eq C))
obs-trans : ∀ {Γ} {A} → Transitive (ObservEq Γ A)
obs-trans eq1 eq2 = obs (λ C → kleene-trans (observe eq1 C) (observe eq2 C))
obs-is-equivalence : ∀{Γ} {A} → IsEquivalence (ObservEq Γ A)
obs-is-equivalence = record { refl_ = obs-refl
; sym_ = obs-sym
; trans_ = obs-trans }
obs-congruence : Congruence ObservEq
obs-congruence {e = e} {e' = e'} oeq C = obs help
where help : (C₁ : TCtx _ _ _ _) → KleeneEq (C₁ < C < e > >) (C₁ < C < e' > >)
help C' with observe oeq (C' << C >>)
... | keq = ID.coe2 KleeneEq (composing-commutes C' C e) (composing-commutes C' C e') keq
obs-consistent : Consistent ObservEq
obs-consistent oeq = observe oeq ∘
obs-is-con-congruence : IsConsistentCongruence ObservEq
obs-is-con-congruence = record { equiv = obs-is-equivalence
; cong = obs-congruence
; consistent = obs-consistent
}
-- Prove that observational equivalence is the coarsest consistent congruence.
-- That is, that it contains all other consistent congruences.
-- That is, if two terms are related by a consistent congruence, they are
-- observationally equivalence.
obs-is-coarsest : (R : TRel) → IsConsistentCongruence R →
{Γ : Ctx} {A : TTp} →
(R Γ A) ⊆ (ObservEq Γ A)
obs-is-coarsest R isCC eq = obs help
where help : (C : TCtx _ _ _ _) → KleeneEq (C < _ >) (C < _ >)
help C with (IsConsistentCongruence.cong isCC) eq C
... | eqC = (IsConsistentCongruence.consistent isCC) eqC
-- Produce a program context that is "equivalent" to a substitution.
-- Essentially the idea is, if we have a substitution
-- γ = e1/x1,...,en/xn, we produce the term
-- (λx1. ⋯ λxn. ∘) e1 ⋯ en
--
-- It took me a while of fiddling around before I came up with this
-- implementation based on composing contexts, but it works really nicely.
--
-- The earlier version that I got closest to making work placed the
-- terms we were substituting underneath other lambdas, which almost
-- works; since it requires weakening the terms, it means to prove
-- subst-ctx-respect-obs we would need to show that weakening preserves
-- observational equivalence. I don't know how to do this without using
-- that observational and logical equivalence coincide.
subst-ctx : ∀{Γ C} → (γ : TSubst Γ []) → (TCtx Γ C [] C)
subst-ctx {[]} γ = ∘
subst-ctx {A :: Γ} {C} γ with (subst-ctx {Γ} {A ⇒ C} (dropγ γ))
... | D = (D << Λ ∘ >>) $e (γ Z)
-- This would basically be the end of the world in call by value.
-- On paper, this proof goes:
--
-- Given some substitution γ[x -> e'], want to show that
-- (C << (λ x. ∘) >> e') < e > e'~>* γ[x -> e'](e), where C is the context constructed for γ.
-- We know that (C << (λ x. ∘) >> e') < e > = C << (λ x. e) >> e'.
-- By induction, we have that "C << (λ x. e) >> ~>* (λ x. γ(e))", and by compatability rules,
-- C << (λ x. e) >> e' ~>* (λ x. γ(e)) e'
-- Then, by beta, we have that (λ x. γ(e)) e' ~> γ([e'/x]e)).
subst-ctx-substs : ∀{Γ A} → (γ : TSubst Γ []) → (e : TExp Γ A) →
(subst-ctx γ) < e > ~>* ssubst γ e
subst-ctx-substs {[]} γ e = ID.coe1 (_~>*_ e) (symm (closed-subst γ e)) eval-refl
subst-ctx-substs {x :: Γ} γ e with subst-ctx-substs (dropγ γ) (Λ e)
... | recursive-eval with eval-compat (step-app-l {e₂ = γ Z}) recursive-eval
... | compat-eval with step-beta {e = ssubst (liftγ (dropγ γ)) e} {e' = γ Z}
... | step with eval-trans compat-eval (eval-step step)
... | eval with composing-commutes (subst-ctx (dropγ γ)) (Λ ∘) e
... | ctx-eq with (symm (subcomp (singγ (γ Z)) (liftγ (dropγ γ)) e) ≡≡ symm (subeq (drop-fix γ) e))
... | subst-eq = ID.coe2 (λ y z → (y $ γ Z) ~>* z) (symm ctx-eq) subst-eq eval
-- Straightforward extension of the above theorem to kleene equivalence at nat type.
subst-ctx-substs-eq : ∀{Γ} → (γ : TSubst Γ []) → (e : TExp Γ nat) →
(subst-ctx γ) < e > ≃ ssubst γ e
subst-ctx-substs-eq γ e with subst-ctx-substs γ e | kleene-refl {x = ssubst γ e}
... | eval | kleeneq n val E1 E2 = kleeneq n val (eval-trans eval E1) E2
-- Prove that observationally equivalent substitutions yield
-- contexts that are observationally equivalent when applied to a term.
subst-ctx-respect-obs : ∀{Γ} {A} (e : TExp Γ A) {γ γ' : TSubst Γ []} →
SubstRel (ObservEq []) Γ γ γ' →
[] ⊢ subst-ctx γ < e > ≅ subst-ctx γ' < e > :: A
subst-ctx-respect-obs {[]} e η = obs-refl
subst-ctx-respect-obs {B :: Γ} {A} e {γ} {γ'} η with
subst-ctx-respect-obs (Λ e) {dropγ γ} {dropγ γ'} (λ x → η (S x))
... | D-D'-equiv with obs-congruence D-D'-equiv (∘ $e γ Z)
... | cong1 with obs-congruence (η Z) ((subst-ctx (dropγ γ') < Λ e >) e$ ∘)
... | cong2 with obs-trans cong1 cong2
... | equiv =
ID.coe2 (ObservEq [] A)
(symm (resp (λ x → x $ γ Z) (composing-commutes (subst-ctx (dropγ γ)) (Λ ∘) e)))
(symm (resp (λ x → x $ γ' Z) (composing-commutes (subst-ctx (dropγ γ')) (Λ ∘) e)))
equiv
-- Applying a substitution to two obs equivalent terms yields observational equivalent output.
-- Takes advantage of substitution contexts.
substs-respect-obs-1 : ∀{Γ} {A} {e e' : TExp Γ A} {γ : TSubst Γ []} →
Γ ⊢ e ≅ e' :: A →
[] ⊢ ssubst γ e ≅ ssubst γ e' :: A
substs-respect-obs-1 {Γ} {A} {e} {e'} {γ} (obs observe) = obs help
where help : (C : TCtx [] A [] nat) → KleeneEq (C < ssubst γ e >) (C < ssubst γ e' >)
help C with observe (subst-ctx γ << weaken-closed-tctx C >>)
... | D-equiv with ID.coe2 KleeneEq
(composing-commutes (subst-ctx γ) (weaken-closed-tctx C) e)
(composing-commutes (subst-ctx γ) (weaken-closed-tctx C) e')
D-equiv
... | D-equiv2 with subst-ctx-substs-eq γ ((weaken-closed-tctx C) < e >) |
subst-ctx-substs-eq γ ((weaken-closed-tctx C) < e' >)
... | sub-equiv1 | sub-equiv2 with
kleene-trans (kleene-sym sub-equiv1) (kleene-trans D-equiv2 sub-equiv2)
... | equiv = ID.coe2 KleeneEq
(symm (subst-commutes-w-closed-tctx γ C e))
(symm (subst-commutes-w-closed-tctx γ C e')) equiv
-- Applying observationally equivalent substitutions a term
-- yields observational equivalent output.
-- Takes advantage of substitution contexts.
-- There is much in this proof that is similar to substs-respect-obs-1.
-- Maybe they could have been merged more?
substs-respect-obs-2 : ∀{Γ} {A} (e : TExp Γ A) {γ γ' : TSubst Γ []} →
SubstRel (ObservEq []) Γ γ γ' →
[] ⊢ ssubst γ e ≅ ssubst γ' e :: A
substs-respect-obs-2 {Γ} {A} e {γ} {γ'} η = obs help
where help : (C : TCtx [] A [] nat) → KleeneEq (C < ssubst γ e >) (C < ssubst γ' e >)
help C with subst-ctx-respect-obs (weaken-closed-tctx C < e >) η
... | oeq with obs-consistent oeq
... | keq with subst-ctx-substs-eq γ ((weaken-closed-tctx C) < e >) |
subst-ctx-substs-eq γ' ((weaken-closed-tctx C) < e >)
... | sub-equiv1 | sub-equiv2 with
kleene-trans (kleene-sym sub-equiv1) (kleene-trans keq sub-equiv2)
... | equiv = ID.coe2 KleeneEq
(symm (subst-commutes-w-closed-tctx γ C e))
(symm (subst-commutes-w-closed-tctx γ' C e)) equiv
-- Combine the two previous theorems.
substs-respect-obs : ∀{Γ} {A} {e e' : TExp Γ A} {γ γ' : TSubst Γ []} →
Γ ⊢ e ≅ e' :: A →
SubstRel (ObservEq []) Γ γ γ' →
[] ⊢ ssubst γ e ≅ ssubst γ' e' :: A
substs-respect-obs {Γ} {A} {e} {e'} {γ} {γ'} oeq η =
obs-trans (substs-respect-obs-2 e η) (substs-respect-obs-1 oeq)
|
{
"alphanum_fraction": 0.5859780379,
"avg_line_length": 50.2242424242,
"ext": "agda",
"hexsha": "00202b1aa54c41d5ae33cb52a5a4636e135adfad",
"lang": "Agda",
"max_forks_count": 3,
"max_forks_repo_forks_event_max_datetime": "2021-05-04T22:37:18.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-04-26T11:39:14.000Z",
"max_forks_repo_head_hexsha": "7412725cf27873b2b23f7e411a236a97dd99ef91",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "msullivan/godels-t",
"max_forks_repo_path": "Eq/ObsTheory.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "7412725cf27873b2b23f7e411a236a97dd99ef91",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "msullivan/godels-t",
"max_issues_repo_path": "Eq/ObsTheory.agda",
"max_line_length": 99,
"max_stars_count": 4,
"max_stars_repo_head_hexsha": "7412725cf27873b2b23f7e411a236a97dd99ef91",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "msullivan/godels-t",
"max_stars_repo_path": "Eq/ObsTheory.agda",
"max_stars_repo_stars_event_max_datetime": "2021-03-22T00:28:03.000Z",
"max_stars_repo_stars_event_min_datetime": "2016-12-25T01:52:57.000Z",
"num_tokens": 2736,
"size": 8287
}
|
{-# OPTIONS --without-K #-}
module function.fibration where
open import level
open import sum
open import equality.core
open import function.core
open import function.isomorphism.core
open import function.isomorphism.coherent
open import function.isomorphism.lift
open import function.isomorphism.univalence
open import function.isomorphism.utils
open import function.extensionality.core
open import function.extensionality.proof
open import function.overloading
open import hott.level.core
open import hott.equivalence.core
open import hott.equivalence.alternative
open import hott.univalence
open import sets.unit
Fibration : ∀ {i} j → Set i → Set _
Fibration j X = Σ (Set j) λ Y → Y → X
fib : ∀ {i j}{X : Set i}(Y : X → Set j)
→ Σ X Y → X
fib Y = proj₁
fib-iso : ∀ {i j}{X : Set i}{Y : X → Set j}
→ (x : X)
→ fib Y ⁻¹ x ≅ Y x
fib-iso {X = X}{Y = Y} x = begin
fib Y ⁻¹ x
≅⟨ refl≅ ⟩
( Σ (Σ X Y) λ { (x' , y)
→ x' ≡ x } )
≅⟨ Σ-assoc-iso ⟩
( Σ X λ x' → Y x' × x' ≡ x )
≅⟨ (Σ-ap-iso refl≅ λ x' → ×-comm) ⟩
( Σ X λ x' → x' ≡ x × Y x' )
≅⟨ sym≅ Σ-assoc-iso ⟩
( Σ (singleton' x) λ { (x' , _) → Y x' } )
≅⟨ Σ-ap-iso' (contr-⊤-iso (singl-contr' x)) (λ _ → refl≅) ⟩
( ⊤ × Y x )
≅⟨ ×-left-unit ⟩
Y x
∎
where open ≅-Reasoning
total-iso : ∀ {i j}{X : Set i}{Y : Set j}(p : Y → X)
→ (Σ X (_⁻¹_ p)) ≅ Y
total-iso {X = X}{Y = Y} p = begin
( Σ X λ x → (Σ Y λ y → p y ≡ x) )
≅⟨ Σ-comm-iso ⟩
( Σ Y λ y → (Σ X λ x → p y ≡ x) )
≅⟨ ( Σ-ap-iso refl≅ λ y → contr-⊤-iso (singl-contr (p y)) ) ⟩
(Y × ⊤)
≅⟨ ×-right-unit ⟩
Y
∎
where open ≅-Reasoning
fib-eq-iso : ∀ {i j}{X : Set i}{Y₁ Y₂ : Set j}
→ (p₁ : Y₁ → X) (p₂ : Y₂ → X)
→ _≡_ {A = Fibration _ X} (Y₁ , p₁) (Y₂ , p₂)
≅ ( Σ (Y₁ ≅' Y₂) λ q → p₁ ≡ p₂ ∘ apply q )
fib-eq-iso {i}{j}{X}{Y₁}{Y₂} p₁ p₂ = begin
_≡_ {A = Fibration _ X} (Y₁ , p₁) (Y₂ , p₂)
≅⟨ sym≅ Σ-split-iso ⟩
( Σ (Y₁ ≡ Y₂) λ q → subst (λ Y → Y → X) q p₁ ≡ p₂ )
≅⟨ ( Σ-ap-iso refl≅ λ q → lem q p₁ p₂ ) ⟩
( Σ (Y₁ ≡ Y₂) λ q → p₁ ≡ p₂ ∘ coerce q )
≅⟨ step ⟩
( Σ (Y₁ ≅' Y₂) λ q → p₁ ≡ p₂ ∘ apply q )
∎
where
open ≅-Reasoning
abstract
step : ( Σ (Y₁ ≡ Y₂) λ q → p₁ ≡ p₂ ∘ coerce q )
≅ ( Σ (Y₁ ≅' Y₂) λ q → p₁ ≡ p₂ ∘ apply q )
step = Σ-ap-iso (uni-iso ·≅ ≈⇔≅') λ q → refl≅
abstract
lem : {Y₁ Y₂ : Set j}(q : Y₁ ≡ Y₂)(p₁ : Y₁ → X)(p₂ : Y₂ → X)
→ (subst (λ Y → Y → X) q p₁ ≡ p₂)
≅ (p₁ ≡ p₂ ∘ coerce q)
lem refl p₁ p₂ = refl≅
fibration-iso : ∀ {i} j {X : Set i}
→ (Σ (Set (i ⊔ j)) λ Y → Y → X)
≅ (X → Set (i ⊔ j))
fibration-iso {i} j {X} = record
{ to = λ { (Y , p) x → p ⁻¹ x }
; from = λ P → (Σ X P , fib P)
; iso₁ = λ { (Y , p) → α Y p }
; iso₂ = λ P → funext λ x → ≅⇒≡ (fib-iso x) }
where
α : (Y : Set (i ⊔ j))(p : Y → X)
→ _≡_ {A = Σ (Set (i ⊔ j)) λ Y → Y → X}
(Σ X (_⁻¹_ p) , proj₁)
(Y , p)
α Y p = invert (fib-eq-iso proj₁ p)
( ≅⇒≅' (total-iso p)
, funext λ { (y , x , eq) → sym eq } )
family-eq-iso : ∀ {i j₁ j₂}{X : Set i}{Y₁ : X → Set j₁}{Y₂ : X → Set j₂}
→ (isom : Σ X Y₁ ≅ Σ X Y₂)
→ (∀ x y → proj₁ (apply≅ isom (x , y)) ≡ x)
→ (x : X) → Y₁ x ≅ Y₂ x
family-eq-iso {i}{j₁}{j₂}{X}{Y₁}{Y₂} isom comm x
= lift-iso _ (Y₁ x)
·≅ ≡⇒≅ (funext-inv eq' x)
·≅ sym≅ (lift-iso _ (Y₂ x))
where
open _≅_ isom
to-we : weak-equiv to
to-we = proj₂ (≅⇒≈ isom)
P₁ : X → Set (i ⊔ j₁ ⊔ j₂)
P₁ x = ↑ (i ⊔ j₂) (Y₁ x)
p₁ : Σ X P₁ → X
p₁ = proj₁
P₂ : X → Set (i ⊔ j₁ ⊔ j₂)
P₂ x = ↑ (i ⊔ j₁) (Y₂ x)
p₂ : Σ X P₂ → X
p₂ = proj₁
total : Σ X P₁ ≅ Σ X P₂
total = (Σ-ap-iso refl≅ λ x → sym≅ (lift-iso _ _))
·≅ isom
·≅ (Σ-ap-iso refl≅ λ x → lift-iso _ _)
comm' : (a : Σ X P₁) → p₁ a ≡ p₂ (apply total a)
comm' (x , lift u) = sym (comm x u)
eq' : P₁ ≡ P₂
eq' = iso⇒inj (sym≅ (fibration-iso (i ⊔ j₁ ⊔ j₂)))
(invert (fib-eq-iso p₁ p₂) (≅⇒≅' total , funext comm'))
fib-compose : ∀ {i j k}{X : Set i}{Y : Set j}{Z : Set k}
→ (f : X → Y)(g : Y → Z)(z : Z)
→ (g ∘' f) ⁻¹ z
≅ ( Σ (g ⁻¹ z) λ { (y , _) → f ⁻¹ y } )
fib-compose {X = X}{Y}{Z} f g z = begin
(g ∘' f) ⁻¹ z
≅⟨ refl≅ ⟩
( Σ X λ x → g (f x) ≡ z )
≅⟨ Σ-ap-iso refl≅ (λ _ → sym≅ ×-left-unit) ⟩
( Σ X λ x → ⊤ × g (f x) ≡ z)
≅⟨ ( Σ-ap-iso refl≅ λ x
→ Σ-ap-iso (sym≅ (contr-⊤-iso (singl-contr (f x))) ) λ _
→ refl≅ ) ⟩
( Σ X λ x → singleton (f x) × g (f x) ≡ z )
≅⟨ ( Σ-ap-iso refl≅ λ x → Σ-assoc-iso ) ⟩
( Σ X λ x → Σ Y λ y → (f x ≡ y) × (g (f x) ≡ z) )
≅⟨ ( Σ-ap-iso refl≅ λ x
→ Σ-ap-iso refl≅ λ y
→ Σ-ap-iso refl≅ λ p
→ ≡⇒≅ (ap (λ u → g u ≡ z) p) ) ⟩
( Σ X λ x → Σ Y λ y → (f x ≡ y) × (g y ≡ z) )
≅⟨ Σ-comm-iso ⟩
( Σ Y λ y → Σ X λ x → (f x ≡ y) × (g y ≡ z) )
≅⟨ ( Σ-ap-iso refl≅ λ y → sym≅ Σ-assoc-iso ) ⟩
( Σ Y λ y → (f ⁻¹ y) × (g y ≡ z) )
≅⟨ ( Σ-ap-iso refl≅ λ y → ×-comm ) ⟩
( Σ Y λ y → (g y ≡ z) × (f ⁻¹ y) )
≅⟨ sym≅ Σ-assoc-iso ⟩
( Σ (g ⁻¹ z) λ { (y , _) → f ⁻¹ y } )
∎
where open ≅-Reasoning
|
{
"alphanum_fraction": 0.4452526799,
"avg_line_length": 29.5141242938,
"ext": "agda",
"hexsha": "08cb22ca80e1b40111618ff7ecb70c571c58125f",
"lang": "Agda",
"max_forks_count": 4,
"max_forks_repo_forks_event_max_datetime": "2019-02-26T06:17:38.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-04-11T17:19:12.000Z",
"max_forks_repo_head_hexsha": "beebe176981953ab48f37de5eb74557cfc5402f4",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "HoTT/M-types",
"max_forks_repo_path": "function/fibration.agda",
"max_issues_count": 2,
"max_issues_repo_head_hexsha": "beebe176981953ab48f37de5eb74557cfc5402f4",
"max_issues_repo_issues_event_max_datetime": "2015-02-11T15:20:34.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-02-11T11:14:59.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "HoTT/M-types",
"max_issues_repo_path": "function/fibration.agda",
"max_line_length": 72,
"max_stars_count": 27,
"max_stars_repo_head_hexsha": "beebe176981953ab48f37de5eb74557cfc5402f4",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "HoTT/M-types",
"max_stars_repo_path": "function/fibration.agda",
"max_stars_repo_stars_event_max_datetime": "2022-01-09T07:26:57.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-04-14T15:47:03.000Z",
"num_tokens": 2548,
"size": 5224
}
|
{-# OPTIONS --without-K --rewriting #-}
open import HoTT
module Reflective where
record ReflectiveSubuniverse {ℓ} : Type (lsucc ℓ) where
field
P : Type ℓ → Type ℓ
R : Type ℓ → Type ℓ
η : (A : Type ℓ) → A → R A
-- replete : (A B : Type ℓ) → P A → A ≃ B → P B
|
{
"alphanum_fraction": 0.5282392027,
"avg_line_length": 17.7058823529,
"ext": "agda",
"hexsha": "536bb4c0703ef50be4afc2f2f6efddda5d2533ce",
"lang": "Agda",
"max_forks_count": 50,
"max_forks_repo_forks_event_max_datetime": "2022-02-14T03:03:25.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-10T01:48:08.000Z",
"max_forks_repo_head_hexsha": "66f800adef943afdf08c17b8ecfba67340fead5e",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "timjb/HoTT-Agda",
"max_forks_repo_path": "theorems/stash/modalities/Reflective.agda",
"max_issues_count": 31,
"max_issues_repo_head_hexsha": "66f800adef943afdf08c17b8ecfba67340fead5e",
"max_issues_repo_issues_event_max_datetime": "2021-10-03T19:15:25.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-03-05T20:09:00.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "timjb/HoTT-Agda",
"max_issues_repo_path": "theorems/stash/modalities/Reflective.agda",
"max_line_length": 57,
"max_stars_count": 294,
"max_stars_repo_head_hexsha": "66f800adef943afdf08c17b8ecfba67340fead5e",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "timjb/HoTT-Agda",
"max_stars_repo_path": "theorems/stash/modalities/Reflective.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-20T13:54:45.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T16:23:23.000Z",
"num_tokens": 107,
"size": 301
}
|
{-# OPTIONS --safe #-}
module Cubical.Categories.Morphism where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Sigma
open import Cubical.Categories.Category
private
variable
ℓ ℓ' : Level
-- C needs to be explicit for these definitions as Agda can't infer it
module _ (C : Category ℓ ℓ') where
open Category C
private
variable
x y z w : ob
isMonic : Hom[ x , y ] → Type (ℓ-max ℓ ℓ')
isMonic {x} {y} f =
∀ {z} {a a' : Hom[ z , x ]} → f ∘ a ≡ f ∘ a' → a ≡ a'
isEpic : (Hom[ x , y ]) → Type (ℓ-max ℓ ℓ')
isEpic {x} {y} g =
∀ {z} {b b' : Hom[ y , z ]} → b ∘ g ≡ b' ∘ g → b ≡ b'
-- A morphism is split monic if it has a *retraction*
isSplitMon : (Hom[ x , y ]) → Type ℓ'
isSplitMon {x} {y} f = ∃[ r ∈ Hom[ y , x ] ] r ∘ f ≡ id
-- A morphism is split epic if it has a *section*
isSplitEpi : (Hom[ x , y ]) → Type ℓ'
isSplitEpi {x} {y} g = ∃[ s ∈ Hom[ y , x ] ] g ∘ s ≡ id
record areInv (f : Hom[ x , y ]) (g : Hom[ y , x ]) : Type ℓ' where
field
sec : g ⋆ f ≡ id
ret : f ⋆ g ≡ id
record isIso (f : Hom[ x , y ]) : Type ℓ' where
field
inv : Hom[ y , x ]
sec : inv ⋆ f ≡ id
ret : f ⋆ inv ≡ id
-- C can be implicit here
module _ {C : Category ℓ ℓ'} where
open Category C
private
variable
x y z w : ob
open areInv
symAreInv : {f : Hom[ x , y ]} {g : Hom[ y , x ]} → areInv C f g → areInv C g f
sec (symAreInv x) = ret x
ret (symAreInv x) = sec x
-- equational reasoning with inverses
invMoveR : ∀ {f : Hom[ x , y ]} {g : Hom[ y , x ]} {h : Hom[ z , x ]} {k : Hom[ z , y ]}
→ areInv C f g
→ h ⋆ f ≡ k
→ h ≡ k ⋆ g
invMoveR {f = f} {g} {h} {k} ai p
= h
≡⟨ sym (⋆IdR _) ⟩
(h ⋆ id)
≡⟨ cong (h ⋆_) (sym (ai .ret)) ⟩
(h ⋆ (f ⋆ g))
≡⟨ sym (⋆Assoc _ _ _) ⟩
((h ⋆ f) ⋆ g)
≡⟨ cong (_⋆ g) p ⟩
k ⋆ g
∎
invMoveL : ∀ {f : Hom[ x , y ]} {g : Hom[ y , x ]} {h : Hom[ y , z ]} {k : Hom[ x , z ]}
→ areInv C f g
→ f ⋆ h ≡ k
→ h ≡ g ⋆ k
invMoveL {f = f} {g} {h} {k} ai p
= h
≡⟨ sym (⋆IdL _) ⟩
id ⋆ h
≡⟨ cong (_⋆ h) (sym (ai .sec)) ⟩
(g ⋆ f) ⋆ h
≡⟨ ⋆Assoc _ _ _ ⟩
g ⋆ (f ⋆ h)
≡⟨ cong (g ⋆_) p ⟩
(g ⋆ k)
∎
open isIso
isIso→areInv : ∀ {f : Hom[ x , y ]}
→ (isI : isIso C f)
→ areInv C f (isI .inv)
sec (isIso→areInv isI) = sec isI
ret (isIso→areInv isI) = ret isI
open CatIso
-- isIso agrees with CatIso
isIso→CatIso : ∀ {f : C [ x , y ]}
→ isIso C f
→ CatIso C x y
mor (isIso→CatIso {f = f} x) = f
inv (isIso→CatIso x) = inv x
sec (isIso→CatIso x) = sec x
ret (isIso→CatIso x) = ret x
CatIso→isIso : (cIso : CatIso C x y)
→ isIso C (cIso .mor)
inv (CatIso→isIso f) = inv f
sec (CatIso→isIso f) = sec f
ret (CatIso→isIso f) = ret f
CatIso→areInv : (cIso : CatIso C x y)
→ areInv C (cIso .mor) (cIso .inv)
CatIso→areInv cIso = isIso→areInv (CatIso→isIso cIso)
-- reverse of an iso is also an iso
symCatIso : ∀ {x y}
→ CatIso C x y
→ CatIso C y x
symCatIso (catiso mor inv sec ret) = catiso inv mor ret sec
|
{
"alphanum_fraction": 0.4812423124,
"avg_line_length": 25.0153846154,
"ext": "agda",
"hexsha": "0cf33a1c9392d9545951d1ec9b4b880a36d0851b",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "58f2d0dd07e51f8aa5b348a522691097b6695d1c",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "Seanpm2001-web/cubical",
"max_forks_repo_path": "Cubical/Categories/Morphism.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "58f2d0dd07e51f8aa5b348a522691097b6695d1c",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "Seanpm2001-web/cubical",
"max_issues_repo_path": "Cubical/Categories/Morphism.agda",
"max_line_length": 90,
"max_stars_count": 1,
"max_stars_repo_head_hexsha": "9acdecfa6437ec455568be4e5ff04849cc2bc13b",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "FernandoLarrain/cubical",
"max_stars_repo_path": "Cubical/Categories/Morphism.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-05T00:28:39.000Z",
"max_stars_repo_stars_event_min_datetime": "2022-03-05T00:28:39.000Z",
"num_tokens": 1397,
"size": 3252
}
|
------------------------------------------------------------------------
-- Pi with partiality algebra families as codomains
------------------------------------------------------------------------
{-# OPTIONS --erased-cubical --safe #-}
module Partiality-algebra.Pi where
open import Equality.Propositional.Cubical
open import Logical-equivalence using (_⇔_)
open import Prelude hiding (T)
open import H-level equality-with-J
open import H-level.Closure equality-with-J
open import Partiality-algebra as PA hiding (id; _∘_)
open Partiality-algebra-with
open Partiality-algebra
-- Applies an increasing sequence of functions to a value.
at-with :
∀ {a b p q} {A : Type a} {T : A → Type p} {B : A → Type b}
(P : (x : A) → Partiality-algebra-with (T x) q (B x)) →
let module P x = Partiality-algebra-with (P x) in
(∃ λ (f : ℕ → (x : A) → T x) →
∀ n x → P._⊑_ x (f n x) (f (suc n) x)) →
(x : A) → ∃ λ (f : ℕ → T x) →
∀ n → P._⊑_ x (f n) (f (suc n))
at-with _ s x = Σ-map (λ f n → f n x) (λ f n → f n x) s
-- Applies an increasing sequence of functions to a value.
at :
∀ {a b p q} {A : Type a} {B : A → Type b}
(P : (x : A) → Partiality-algebra p q (B x)) →
let module P x = Partiality-algebra (P x) in
(∃ λ (f : ℕ → (x : A) → P.T x) →
∀ n x → P._⊑_ x (f n x) (f (suc n) x)) →
(x : A) → ∃ λ (f : ℕ → P.T x) →
∀ n → P._⊑_ x (f n) (f (suc n))
at P = at-with (partiality-algebra-with ∘ P)
-- A kind of dependent function space from types to
-- Partiality-algebra-with families.
Π-with : ∀ {a b p q}
(A : Type a) {T : A → Type p} {B : A → Type b} →
((x : A) → Partiality-algebra-with (T x) q (B x)) →
Partiality-algebra-with
((x : A) → T x) (a ⊔ q) ((x : A) → B x)
_⊑_ (Π-with A P) = λ f g → ∀ x → _⊑_ (P x) (f x) (g x)
never (Π-with A P) = λ x → never (P x)
now (Π-with A P) = λ f x → now (P x) (f x)
⨆ (Π-with A P) = λ s x → ⨆ (P x) (at-with P s x)
antisymmetry (Π-with A P) = λ p q → ⟨ext⟩ λ x →
antisymmetry (P x) (p x) (q x)
T-is-set-unused (Π-with A P) = Π-closure ext 2 λ x →
T-is-set-unused (P x)
⊑-refl (Π-with A P) = λ f x → ⊑-refl (P x) (f x)
⊑-trans (Π-with A P) = λ f g x → ⊑-trans (P x) (f x) (g x)
never⊑ (Π-with A P) = λ f x → never⊑ (P x) (f x)
upper-bound (Π-with A P) = λ s n x →
upper-bound (P x) (at-with P s x) n
least-upper-bound (Π-with A P) = λ s ub is-ub x →
least-upper-bound
(P x) (at-with P s x) (ub x)
(λ n → is-ub n x)
⊑-propositional (Π-with A P) = Π-closure ext 1 λ x →
⊑-propositional (P x)
-- A kind of dependent function space from types to partiality algebra
-- families.
Π : ∀ {a b p q} →
(A : Type a) {B : A → Type b} →
((x : A) → Partiality-algebra p q (B x)) →
Partiality-algebra (a ⊔ p) (a ⊔ q) ((x : A) → B x)
T (Π A P) = (x : A) → T (P x)
partiality-algebra-with (Π A P) = Π-with A (partiality-algebra-with ∘ P)
|
{
"alphanum_fraction": 0.4632194521,
"avg_line_length": 39.6219512195,
"ext": "agda",
"hexsha": "51b846fc8b7482af8edb13c7d637ab4d4c4de900",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "f69749280969f9093e5e13884c6feb0ad2506eae",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "nad/partiality-monad",
"max_forks_repo_path": "src/Partiality-algebra/Pi.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "f69749280969f9093e5e13884c6feb0ad2506eae",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "nad/partiality-monad",
"max_issues_repo_path": "src/Partiality-algebra/Pi.agda",
"max_line_length": 72,
"max_stars_count": 2,
"max_stars_repo_head_hexsha": "f69749280969f9093e5e13884c6feb0ad2506eae",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "nad/partiality-monad",
"max_stars_repo_path": "src/Partiality-algebra/Pi.agda",
"max_stars_repo_stars_event_max_datetime": "2020-07-03T08:56:08.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-05-21T22:59:18.000Z",
"num_tokens": 1145,
"size": 3249
}
|
-- {-# OPTIONS -v tc.with.strip:40 #-}
module Issue824 where
record R : Set where
data D : Set → Set₁ where
d : ∀ {A} → D A → D A
postulate
d′ : D R
data P : R → D R → Set₁ where
p : {x : R} {y : D R} → P x y → P x (d y)
Foo : P _ (d d′) → Set₁
Foo (p _) with Set
Foo (p _) | _ = Set
-- Bug.agda:18,1-19,20
-- Inaccessible (dotted) patterns from the parent clause must also be
-- inaccessible in the with clause, when checking the pattern
-- {.Bug.recCon-NOT-PRINTED},
-- when checking that the clause
-- Foo (p _) with unit
-- Foo (p _) | _ = Set
-- has type P (record {}) (d d′) → Set₁
-- See also issue 635 and issue 665.
-- Andreas, 2013-03-21: should work now.
|
{
"alphanum_fraction": 0.6029411765,
"avg_line_length": 21.935483871,
"ext": "agda",
"hexsha": "46981a99b235dde0518c79379937da892a2d52ef",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cruhland/agda",
"max_forks_repo_path": "test/Succeed/Issue824.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cruhland/agda",
"max_issues_repo_path": "test/Succeed/Issue824.agda",
"max_line_length": 69,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cruhland/agda",
"max_stars_repo_path": "test/Succeed/Issue824.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 241,
"size": 680
}
|
------------------------------------------------------------------------
-- Call-by-value (CBV) reduction in pure type systems (PTS)
------------------------------------------------------------------------
module Pts.Reduction.Cbv where
open import Data.Fin.Substitution
open import Data.Fin.Substitution.ExtraLemmas
open import Data.Star using (map; gmap)
import Relation.Binary.EquivalenceClosure as EqClos
import Relation.Binary.PropositionalEquality as PropEq
open import Relation.Binary.Reduction
open import Pts.Syntax
open import Pts.Reduction.Full as Full hiding (reduction)
-- All remaining submodules are parametrized by a given set of sorts.
module _ {Sort : Set} where
open Syntax Sort
open Substitution Sort using (_[_])
----------------------------------------------------------------------
-- Call-by-value (CBV) reduction and equivalence relations
-- Untyped values with up to n free variables.
data Val {n} : Term n → Set where
sort : ∀ s → Val (sort s) -- sort
Π : ∀ a b → Val (Π a b) -- dependent product
ƛ : ∀ a b → Val (ƛ a b) -- abstraction
infixl 9 _·₁_ _·₂_
infix 5 _→v_
-- One-step CBV reduction.
data _→v_ {n} : Term n → Term n → Set where
cont : ∀ a b {c} (v : Val c) → (ƛ a b) · c →v b [ c ]
_·₁_ : ∀ {a₁ a₂} → a₁ →v a₂ → ∀ b → a₁ · b →v a₂ · b
_·₂_ : ∀ {a b₁ b₂} (v : Val a) → b₁ →v b₂ → a · b₁ →v a · b₂
reduction : Reduction Term
reduction = record { _→1_ = _→v_ }
-- CBV reduction and equivalence.
open Reduction reduction public renaming (_→*_ to _→v*_; _↔_ to _≡v_)
----------------------------------------------------------------------
-- Substitutions in CBV reductions/equivalence
--
-- The applications _/→v_, _/→v*_ and _/≡v_ below may be considered
-- substitution lemmas, i.e. they establish the commutativity of the
-- respective reductions/equivalence with substitutions.
-- Application of generic substitutions to the
-- reductions/equivalence.
record CbvSubstApp {T} (l : Lift T Term) : Set where
open Lift l
open SubstApp Sort l
open PropEq hiding ([_])
-- Substitutions commute.
field /-sub-↑ : ∀ {m n} a b (σ : Sub T m n) →
a [ b ] / σ ≡ (a / σ ↑) [ b / σ ]
infixl 8 _/Val_ _/→v_
-- Application of substitutions preserves values.
_/Val_ : ∀ {m n a} → Val a → (σ : Sub T m n) → Val (a / σ)
sort s /Val σ = sort s
Π a b /Val σ = Π (a / σ) (b / σ ↑)
ƛ a b /Val σ = ƛ (a / σ) (b / σ ↑)
-- Substitution commutes with one-step reduction.
_/→v_ : ∀ {m n a b} → a →v b → (σ : Sub T m n) → a / σ →v b / σ
cont a b c /→v σ =
subst (_→v_ _) (sym (/-sub-↑ b _ σ)) (cont (a / σ) (b / σ ↑) (c /Val σ))
a₁→a₂ ·₁ b /→v σ = (a₁→a₂ /→v σ) ·₁ (b / σ)
a ·₂ b₁→b₂ /→v σ = (a /Val σ) ·₂ (b₁→b₂ /→v σ)
redSubstApp : RedSubstApp reduction (record { _/_ = _/_ })
redSubstApp = record { _/→1_ = _/→v_ }
open RedSubstApp redSubstApp public
hiding (_/→1_) renaming (_/→*_ to _/→v*_; _/↔_ to _/≡v_)
-- Term substitutions in reductions/equivalences.
module CbvSubstitution where
open Substitution Sort
using (termSubst; weaken; sub-commutes; varLiftSubLemmas)
-- Application of renamings to reductions/equivalences.
varSubstApp : CbvSubstApp (TermSubst.varLift termSubst)
varSubstApp = record { /-sub-↑ = /-sub-↑ }
where open LiftSubLemmas varLiftSubLemmas
private module V = CbvSubstApp varSubstApp
-- Weakening of one-step CBV reductions.
weaken-→v : ∀ {n} {a b : Term n} → a →v b → weaken a →v weaken b
weaken-→v a→b = a→b V./→v VarSubst.wk
-- Weakening of CBV reductions.
weaken-→v* : ∀ {n} {a b : Term n} → a →v* b → weaken a →v* weaken b
weaken-→v* = gmap weaken weaken-→v
-- Weakening of equivalences.
weaken-≡v : ∀ {n} {a b : Term n} → a ≡v b → weaken a ≡v weaken b
weaken-≡v = EqClos.gmap weaken weaken-→v
-- Application of term substitutions to reductions/equivalences.
termSubstApp : CbvSubstApp (TermSubst.termLift termSubst)
termSubstApp = record { /-sub-↑ = λ a _ _ → sub-commutes a }
open CbvSubstApp termSubstApp public
----------------------------------------------------------------------
-- Properties of the CBV reductions/equivalence
-- Inclusions.
→v⇒→v* = →1⇒→* reduction
→v*⇒≡v = →*⇒↔ reduction
→v⇒≡v = →1⇒↔ reduction
-- CBV reduction is a preorder.
→v*-predorder = →*-predorder reduction
-- Preorder reasoning for CBV reduction.
module →v*-Reasoning = →*-Reasoning reduction
-- Terms together with CBV equivalence form a setoid.
≡v-setoid = ↔-setoid reduction
-- Equational reasoning for CBV equivalence.
module ≡v-Reasoning = ↔-Reasoning reduction
----------------------------------------------------------------------
-- Relationships between CBV reduction and full β-reduction
-- One-step CBV reduction implies one-step β-reduction.
→v⇒→β : ∀ {n} {a b : Term n} → a →v b → a →β b
→v⇒→β (cont a b c) = cont a b _
→v⇒→β (a₁→a₂ ·₁ b) = →v⇒→β a₁→a₂ ·₁ b
→v⇒→β (a ·₂ b₁→b₂) = _ ·₂ →v⇒→β b₁→b₂
-- CBV reduction implies parallel reduction.
→v*⇒→β* : ∀ {n} {a b : Term n} → a →v* b → a →β* b
→v*⇒→β* = map →v⇒→β
-- CBV equivalence implies parallel equivalence.
≡v⇒≡p : ∀ {n} {a b : Term n} → a ≡v b → a ≡β b
≡v⇒≡p = EqClos.map →v⇒→β
|
{
"alphanum_fraction": 0.5599480327,
"avg_line_length": 34.987012987,
"ext": "agda",
"hexsha": "4ece549f0d9ed7a25f7a6603588bddaf73564e1d",
"lang": "Agda",
"max_forks_count": 4,
"max_forks_repo_forks_event_max_datetime": "2019-08-11T23:28:33.000Z",
"max_forks_repo_forks_event_min_datetime": "2017-08-20T10:29:44.000Z",
"max_forks_repo_head_hexsha": "d701c2688e4a88eb81bdd9d458f9a2fcf81d5a43",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "asr/pts-agda",
"max_forks_repo_path": "src/Pts/Reduction/Cbv.agda",
"max_issues_count": 1,
"max_issues_repo_head_hexsha": "d701c2688e4a88eb81bdd9d458f9a2fcf81d5a43",
"max_issues_repo_issues_event_max_datetime": "2017-08-21T16:01:50.000Z",
"max_issues_repo_issues_event_min_datetime": "2017-08-21T14:48:09.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "asr/pts-agda",
"max_issues_repo_path": "src/Pts/Reduction/Cbv.agda",
"max_line_length": 78,
"max_stars_count": 21,
"max_stars_repo_head_hexsha": "d701c2688e4a88eb81bdd9d458f9a2fcf81d5a43",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "asr/pts-agda",
"max_stars_repo_path": "src/Pts/Reduction/Cbv.agda",
"max_stars_repo_stars_event_max_datetime": "2021-08-31T10:47:57.000Z",
"max_stars_repo_stars_event_min_datetime": "2016-05-13T12:11:10.000Z",
"num_tokens": 1841,
"size": 5388
}
|
module LocalVsImportedModuleClash where
X = TODO--This-shouldn't-happen-if-the-scope-checker-does-it's-job
|
{
"alphanum_fraction": 0.7981651376,
"avg_line_length": 21.8,
"ext": "agda",
"hexsha": "00f19139db5e95ac11ea6765d5bce948f511bafd",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cruhland/agda",
"max_forks_repo_path": "test/Fail/LocalVsImportedModuleClash.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cruhland/agda",
"max_issues_repo_path": "test/Fail/LocalVsImportedModuleClash.agda",
"max_line_length": 66,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cruhland/agda",
"max_stars_repo_path": "test/Fail/LocalVsImportedModuleClash.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 33,
"size": 109
}
|
{-# OPTIONS --without-K --safe #-}
module Categories.NaturalTransformation.NaturalIsomorphism.Equivalence where
-- a certain notion of equivalence between Natural Isomorphisms.
open import Level
open import Data.Product using (_×_; _,_; map; zip)
open import Relation.Binary using (IsEquivalence)
open import Categories.Category
open import Categories.Functor using (Functor)
open import Categories.NaturalTransformation.NaturalIsomorphism hiding (_≃_)
open import Categories.NaturalTransformation.Equivalence
open NaturalIsomorphism
private
variable
o ℓ e o′ ℓ′ e′ : Level
C D : Category o ℓ e
infix 4 _≅_
_≅_ : ∀ {F G : Functor C D} → (α β : NaturalIsomorphism F G) → Set _
α ≅ β = F⇒G α ≃ F⇒G β × F⇐G α ≃ F⇐G β
≅-isEquivalence : ∀ {F G : Functor C D} → IsEquivalence (_≅_ {F = F} {G = G})
≅-isEquivalence {D = D} {F = F} {G = G} = record
{ refl = H.refl , H.refl
; sym = map (λ z → H.sym z) (λ z → H.sym z) -- eta expansion needed
; trans = zip (λ a b → H.trans a b) λ a b → H.trans a b -- ditto
}
where module H = Category.HomReasoning D
|
{
"alphanum_fraction": 0.6828358209,
"avg_line_length": 33.5,
"ext": "agda",
"hexsha": "3a21fd58d9283c62191600b3e4d0210c3f235824",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "58e5ec015781be5413bdf968f7ec4fdae0ab4b21",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "MirceaS/agda-categories",
"max_forks_repo_path": "src/Categories/NaturalTransformation/NaturalIsomorphism/Equivalence.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "58e5ec015781be5413bdf968f7ec4fdae0ab4b21",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "MirceaS/agda-categories",
"max_issues_repo_path": "src/Categories/NaturalTransformation/NaturalIsomorphism/Equivalence.agda",
"max_line_length": 77,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "58e5ec015781be5413bdf968f7ec4fdae0ab4b21",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "MirceaS/agda-categories",
"max_stars_repo_path": "src/Categories/NaturalTransformation/NaturalIsomorphism/Equivalence.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 354,
"size": 1072
}
|
{-# OPTIONS --safe #-}
module Cubical.Algebra.Group.Instances.DiffInt where
open import Cubical.HITs.SetQuotients
open import Cubical.Foundations.Prelude
open import Cubical.Data.Int.MoreInts.DiffInt renaming (ℤ to ℤType ; _+_ to _+ℤ_ ; _-_ to _-ℤ_)
open import Cubical.Algebra.Group.Base
open import Cubical.Algebra.Semigroup.Base
open import Cubical.Algebra.Monoid.Base
open GroupStr
ℤ-isGroup : IsGroup {G = ℤType} ([ 0 , 0 ]) (_+ℤ_) (-ℤ_)
IsSemigroup.is-set (IsMonoid.isSemigroup (IsGroup.isMonoid ℤ-isGroup)) = ℤ-isSet
IsSemigroup.assoc (IsMonoid.isSemigroup (IsGroup.isMonoid ℤ-isGroup)) = +ℤ-assoc
IsMonoid.identity (IsGroup.isMonoid ℤ-isGroup) = λ x → (zero-identityʳ 0 x , zero-identityˡ 0 x)
IsGroup.inverse ℤ-isGroup = λ x → (-ℤ-invʳ x , -ℤ-invˡ x)
ℤ : Group₀
fst ℤ = ℤType
1g (snd ℤ) = [ 0 , 0 ]
_·_ (snd ℤ) = _+ℤ_
inv (snd ℤ) = -ℤ_
isGroup (snd ℤ) = ℤ-isGroup
|
{
"alphanum_fraction": 0.722095672,
"avg_line_length": 35.12,
"ext": "agda",
"hexsha": "f9fd62d140f794d4abc8e3d95194cf98918d6e2a",
"lang": "Agda",
"max_forks_count": 134,
"max_forks_repo_forks_event_max_datetime": "2022-03-23T16:22:13.000Z",
"max_forks_repo_forks_event_min_datetime": "2018-11-16T06:11:03.000Z",
"max_forks_repo_head_hexsha": "58f2d0dd07e51f8aa5b348a522691097b6695d1c",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "Seanpm2001-web/cubical",
"max_forks_repo_path": "Cubical/Algebra/Group/Instances/DiffInt.agda",
"max_issues_count": 584,
"max_issues_repo_head_hexsha": "58f2d0dd07e51f8aa5b348a522691097b6695d1c",
"max_issues_repo_issues_event_max_datetime": "2022-03-30T12:09:17.000Z",
"max_issues_repo_issues_event_min_datetime": "2018-10-15T09:49:02.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "Seanpm2001-web/cubical",
"max_issues_repo_path": "Cubical/Algebra/Group/Instances/DiffInt.agda",
"max_line_length": 97,
"max_stars_count": 301,
"max_stars_repo_head_hexsha": "9acdecfa6437ec455568be4e5ff04849cc2bc13b",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "FernandoLarrain/cubical",
"max_stars_repo_path": "Cubical/Algebra/Group/Instances/DiffInt.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-24T02:10:47.000Z",
"max_stars_repo_stars_event_min_datetime": "2018-10-17T18:00:24.000Z",
"num_tokens": 332,
"size": 878
}
|
open import Common.Size
postulate
A : Set
f : Size → A
-- k' < k < j <= i + 2 =/=> ∃ l < i
test : ∀ i (j : Size< (↑ ↑ ↑ i)) (k : Size< j) (k' : Size< k) → Size → Set → (((l : Size< i) → A) → A) → A
test i j k k' _ _ ret = ret λ l → f l
|
{
"alphanum_fraction": 0.4338842975,
"avg_line_length": 24.2,
"ext": "agda",
"hexsha": "e8ab94c35738b9dbc95c4424446f70b24138da39",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2019-03-05T20:02:38.000Z",
"max_forks_repo_forks_event_min_datetime": "2019-03-05T20:02:38.000Z",
"max_forks_repo_head_hexsha": "231d6ad8e77b67ff8c4b1cb35a6c31ccd988c3e9",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "Agda-zh/agda",
"max_forks_repo_path": "test/Fail/Issue1523d.agda",
"max_issues_count": 3,
"max_issues_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_issues_repo_issues_event_max_datetime": "2019-04-01T19:39:26.000Z",
"max_issues_repo_issues_event_min_datetime": "2018-11-14T15:31:44.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "shlevy/agda",
"max_issues_repo_path": "test/Fail/Issue1523d.agda",
"max_line_length": 106,
"max_stars_count": 3,
"max_stars_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "shlevy/agda",
"max_stars_repo_path": "test/Fail/Issue1523d.agda",
"max_stars_repo_stars_event_max_datetime": "2015-12-07T20:14:00.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-03-28T14:51:03.000Z",
"num_tokens": 109,
"size": 242
}
|
module RTP where
open import RTN public
{-
data Bool : Set where
False : Bool
True : Bool
-}
postulate
Int : Set
String : Set
Float : Set
Char : Set
{-# BUILTIN FLOAT Float #-}
{-# BUILTIN STRING String #-}
{-# BUILTIN CHAR Char #-}
-- postulate primShowBool : Bool -> String
postulate primShowInt : Int -> String
postulate primShowChar : Char -> String
postulate primStringAppend : String -> String -> String
postulate primStringReverse : String -> String
-- postulate primStringToList : String -> List Char
-- postulate primStringFromList
-- Int stuff
postulate primIntZero : Int
postulate primIntOne : Int
postulate primIntSucc : Int -> Int
postulate primNatToInt : Nat -> Int
postulate primIntToNat : Int -> Nat
postulate primIntAdd : Int -> Int -> Int
postulate primIntSub : Int -> Int -> Int
postulate primIntMul : Int -> Int -> Int
postulate primIntDiv : Int -> Int -> Int
postulate primIntMod : Int -> Int -> Int
|
{
"alphanum_fraction": 0.6630218688,
"avg_line_length": 23.3953488372,
"ext": "agda",
"hexsha": "d381f6a5bcd6c99a716a888f8b8dccaa24029a63",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2022-03-12T11:35:18.000Z",
"max_forks_repo_forks_event_min_datetime": "2022-03-12T11:35:18.000Z",
"max_forks_repo_head_hexsha": "477c8c37f948e6038b773409358fd8f38395f827",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "larrytheliquid/agda",
"max_forks_repo_path": "src/rts/RTP.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "477c8c37f948e6038b773409358fd8f38395f827",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "larrytheliquid/agda",
"max_issues_repo_path": "src/rts/RTP.agda",
"max_line_length": 57,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "477c8c37f948e6038b773409358fd8f38395f827",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "larrytheliquid/agda",
"max_stars_repo_path": "src/rts/RTP.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 285,
"size": 1006
}
|
open import Agda.Primitive using (lzero; lsuc; _⊔_; Level)
open import Relation.Binary.PropositionalEquality using (_≡_; refl; subst)
open import Relation.Binary using (Setoid)
-- A formalization of raw syntax
module Syntax where
-- Syntactic classes
data ObjectClass : Set where
Ty Tm : ObjectClass
data Class : Set where
obj : ObjectClass → Class
EqTy EqTm : Class
-- Variable context shape
infixl 6 _⊕_
data VShape : Set where
𝟘 : VShape
𝟙 : VShape
_⊕_ : VShape → VShape → VShape
data var : VShape → Set where
var-here : var 𝟙
var-left : ∀ {γ δ} → var γ → var (γ ⊕ δ)
var-right : ∀ {γ δ} → var δ → var (γ ⊕ δ)
-- Metavariable context shapes
infixl 9 _⊕ᵐᵛ_
data MShape : Set where
𝟘ᵐᵛ : MShape
𝟙ᵐᵛ : ∀ (cl : Class) (γ : VShape) → MShape
_⊕ᵐᵛ_ : MShape → MShape → MShape
infix 8 [_,_]∈_
data [_,_]∈_ : Class → VShape → MShape → Set where
mv-here : ∀ cl γ → [ cl , γ ]∈ 𝟙ᵐᵛ cl γ
mv-left : ∀ {𝕂 𝕄} cl γ → [ cl , γ ]∈ 𝕂 → [ cl , γ ]∈ 𝕂 ⊕ᵐᵛ 𝕄
mv-right : ∀ {𝕂 𝕄} cl γ → [ cl , γ ]∈ 𝕄 → [ cl , γ ]∈ 𝕂 ⊕ᵐᵛ 𝕄
-- Symbol signature
record Signature : Set₁ where
field
symb : ObjectClass → Set -- a set of symbol names, one for each class
symb-arg : ∀ {cl} → symb cl → MShape
-- Expressions
module Expression (𝕊 : Signature) where
open Signature 𝕊
data Expr : Class → (𝕄 : MShape) → (γ : VShape) → Set
Arg : ∀ (cl : Class) (𝕄 : MShape) (γ : VShape) (δ : VShape) → Set
Arg cl 𝕄 γ δ = Expr cl 𝕄 (γ ⊕ δ)
ExprObj : ∀ (cl : ObjectClass) (𝕄 : MShape) (γ : VShape) → Set
ExprObj cl = Expr (obj cl)
ExprTm = ExprObj Tm
ExprTy = ExprObj Ty
data Expr where
expr-var : ∀ {𝕄} {γ} (x : var γ) → ExprTm 𝕄 γ
expr-symb : ∀ {cl 𝕄 γ} (S : symb cl) →
(es : ∀ {clⁱ γⁱ} (i : [ clⁱ , γⁱ ]∈ symb-arg S) → Arg clⁱ 𝕄 γ γⁱ) →
ExprObj cl 𝕄 γ
expr-meta : ∀ {cl 𝕄 γ} {γᴹ} (M : [ obj cl , γᴹ ]∈ 𝕄) → (ts : ∀ (i : var γᴹ) → ExprTm 𝕄 γ) → ExprObj cl 𝕄 γ
expr-eqty : ∀ {γ} {𝕄} → Expr EqTy 𝕄 γ
expr-eqtm : ∀ {γ} {𝕄} → Expr EqTm 𝕄 γ
expr-meta-generic : ∀ {𝕄} {cl} {γ γᴹ} (M : [ cl , γᴹ ]∈ 𝕄) → Arg cl 𝕄 γ γᴹ
expr-meta-generic {cl = obj _} M = expr-meta M (λ i → expr-var (var-right i))
expr-meta-generic {cl = EqTy} M = expr-eqty
expr-meta-generic {cl = EqTm} M = expr-eqtm
-- Syntactic equality
module Equality {𝕊 : Signature} where
open Signature 𝕊
open Expression 𝕊
infix 4 _≈_
data _≈_ : ∀ {cl 𝕄 γ} → Expr cl 𝕄 γ → Expr cl 𝕄 γ → Set where
≈-≡ : ∀ {cl 𝕄 γ} {t u : Expr cl 𝕄 γ} (ξ : t ≡ u) → t ≈ u
≈-symb : ∀ {cl 𝕄 γ} {S : symb cl} →
{ds es : ∀ {cⁱ γⁱ} (i : [ cⁱ , γⁱ ]∈ symb-arg S) → Arg cⁱ 𝕄 γ γⁱ}
(ξ : ∀ {cⁱ γⁱ} (i : [ cⁱ , γⁱ ]∈ symb-arg S) → ds i ≈ es i) → expr-symb S ds ≈ expr-symb S es
≈-meta : ∀ {cl 𝕄 γ} {γᴹ} {M : [ obj cl , γᴹ ]∈ 𝕄} → {ts us : ∀ (i : var γᴹ) → ExprTm 𝕄 γ}
(ξ : ∀ i → ts i ≈ us i) → expr-meta M ts ≈ expr-meta M us
≈-refl : ∀ {cl 𝕄 γ} {t : Expr cl 𝕄 γ} → t ≈ t
≈-refl = ≈-≡ refl
≈-eqty : ∀ {𝕄 γ} {s t : Expr EqTy 𝕄 γ} → s ≈ t
≈-eqty {s = expr-eqty} {t = expr-eqty} = ≈-refl
≈-eqtm : ∀ {𝕄 γ} {s t : Expr EqTm 𝕄 γ} → s ≈ t
≈-eqtm {s = expr-eqtm} {t = expr-eqtm} = ≈-refl
≈-sym : ∀ {cl 𝕄 γ} {t u : Expr cl 𝕄 γ} → t ≈ u → u ≈ t
≈-sym (≈-≡ refl) = ≈-≡ refl
≈-sym (≈-symb ε) = ≈-symb (λ i → ≈-sym (ε i))
≈-sym (≈-meta ε) = ≈-meta (λ i → ≈-sym (ε i))
≈-trans : ∀ {cl 𝕄 γ} {t u v : Expr cl 𝕄 γ} → t ≈ u → u ≈ v → t ≈ v
≈-trans (≈-≡ refl) ξ = ξ
≈-trans (≈-symb ζ) (≈-≡ refl) = ≈-symb ζ
≈-trans (≈-symb ζ) (≈-symb ξ) = ≈-symb (λ i → ≈-trans (ζ i) (ξ i))
≈-trans (≈-meta ζ) (≈-≡ refl) = ≈-meta ζ
≈-trans (≈-meta ζ) (≈-meta ξ) = ≈-meta (λ i → ≈-trans (ζ i) (ξ i))
-- the setoid of expressions
Expr-setoid : ∀ (cl : Class) (𝕄 : MShape) (γ : VShape) → Setoid lzero lzero
Expr-setoid cl 𝕄 γ =
record
{ Carrier = Expr cl 𝕄 γ
; _≈_ = _≈_
; isEquivalence = record { refl = ≈-refl ; sym = ≈-sym ; trans = ≈-trans }
}
infix 4 _%_≈_
_%_≈_ : ∀ (𝕊 : Signature) {cl 𝕄 γ} → (t u : Expression.Expr 𝕊 cl 𝕄 γ) → Set
_%_≈_ 𝕊 = Equality._≈_ {𝕊 = 𝕊}
|
{
"alphanum_fraction": 0.5024538444,
"avg_line_length": 31.2335766423,
"ext": "agda",
"hexsha": "aa2d0cc7e01fac4fc5512ce86b1377cc01333d77",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "9b634d284a0ec5108c68489575194cd573f38908",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "andrejbauer/dependent-type-theory-syntax",
"max_forks_repo_path": "src/Syntax.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "9b634d284a0ec5108c68489575194cd573f38908",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "andrejbauer/dependent-type-theory-syntax",
"max_issues_repo_path": "src/Syntax.agda",
"max_line_length": 112,
"max_stars_count": 7,
"max_stars_repo_head_hexsha": "9b634d284a0ec5108c68489575194cd573f38908",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "andrejbauer/dependent-type-theory-syntax",
"max_stars_repo_path": "src/Syntax.agda",
"max_stars_repo_stars_event_max_datetime": "2021-10-14T01:48:00.000Z",
"max_stars_repo_stars_event_min_datetime": "2021-05-25T11:14:42.000Z",
"num_tokens": 2033,
"size": 4279
}
|
-- 2011-10-01 Andreas
module EtaContractIrrelevant where
import Common.Level
data _≡_ {a}{A : Set a}(x : A) : A → Set where
refl : x ≡ x
subst : ∀ {a b}{A : Set a}(P : A → Set b){x y : A} → x ≡ y → P x → P y
subst P refl x = x
postulate
Val : Set
Pred = Val → Set
fam : Pred → Set1
fam A = {a : Val} → .(A a) → Pred
postulate
π : (A : Pred)(F : fam A) → Pred
πCong : {A A' : Pred}(A≡A' : A ≡ A') →
{F : fam A }
{F' : fam A'}
(F≡F' : (λ {a} Aa → F {a = a} Aa)
≡ (λ {a} Aa → F' {a = a} (subst (λ A → A a) A≡A' Aa))) →
π A F ≡ π A' F'
πCong refl refl = refl
-- needs eta-contraction for irrelevant functions F F'
|
{
"alphanum_fraction": 0.5085271318,
"avg_line_length": 20.8064516129,
"ext": "agda",
"hexsha": "f289589a76bd8053bcf072f33e72c1c0812766f7",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "aa10ae6a29dc79964fe9dec2de07b9df28b61ed5",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "asr/agda-kanso",
"max_forks_repo_path": "test/succeed/EtaContractIrrelevant.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "aa10ae6a29dc79964fe9dec2de07b9df28b61ed5",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "asr/agda-kanso",
"max_issues_repo_path": "test/succeed/EtaContractIrrelevant.agda",
"max_line_length": 70,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "aa10ae6a29dc79964fe9dec2de07b9df28b61ed5",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "asr/agda-kanso",
"max_stars_repo_path": "test/succeed/EtaContractIrrelevant.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 287,
"size": 645
}
|
------------------------------------------------------------------------
-- Termination
------------------------------------------------------------------------
{-# OPTIONS --sized-types #-}
open import Prelude
module Delay-monad.Termination {a} {A : Type a} where
open import Equality.Propositional
open import Logical-equivalence using (_⇔_)
open import Prelude.Size
open import Bijection equality-with-J using (_↔_)
open import Double-negation equality-with-J
open import Monad equality-with-J
open import Delay-monad
open import Delay-monad.Bisimilarity hiding (_∎; step-≡ˡ)
-- Termination predicates.
Terminates : Size → Delay A ∞ → A → Type a
Terminates i x y = [ i ] now y ≈ x
infix 4 _⇓_
_⇓_ : Delay A ∞ → A → Type a
_⇓_ = Terminates ∞
-- Terminates i is pointwise isomorphic to Terminates ∞.
--
-- Note that Terminates carves out an "inductive fragment" of [_]_≈_:
-- the only "coinductive" constructor, later, does not target
-- Terminates.
Terminates↔⇓ : ∀ {i x y} → Terminates i x y ↔ x ⇓ y
Terminates↔⇓ = record
{ surjection = record
{ logical-equivalence = record
{ to = to
; from = from _
}
; right-inverse-of = to∘from
}
; left-inverse-of = from∘to
}
where
to : ∀ {i x y} → Terminates i x y → x ⇓ y
to now = now
to (laterʳ p) = laterʳ (to p)
from : ∀ i {x y} → x ⇓ y → Terminates i x y
from _ now = now
from _ (laterʳ p) = laterʳ (from _ p)
to∘from : ∀ {i x y} (p : x ⇓ y) → to (from i p) ≡ p
to∘from now = refl
to∘from (laterʳ p) = cong laterʳ (to∘from p)
from∘to : ∀ {i x y} (p : Terminates i x y) → from i (to p) ≡ p
from∘to now = refl
from∘to (laterʳ p) = cong laterʳ (from∘to p)
-- The termination relation respects weak bisimilarity.
--
-- This function cannot be made size-preserving in its second argument
-- (unless A is uninhabited), see Delay-monad.Bisimilarity.Negative.
⇓-respects-≈ : ∀ {i x y z} →
Terminates i x z → x ≈ y → Terminates i y z
⇓-respects-≈ = transitive-≈-now
-- If a computation does not terminate, then it is weakly bisimilar
-- to never.
¬⇓→⇑ : ∀ {i} x → ¬ (∃ λ y → x ⇓ y) → [ i ] never ≈ x
¬⇓→⇑ (now x) ¬⇓ = ⊥-elim (¬⇓ (_ , now))
¬⇓→⇑ (later x) ¬⇓ = later λ { .force → ¬⇓→⇑ _ (¬⇓ ∘ Σ-map id laterʳ) }
-- In the double-negation monad every computation is weakly
-- bisimilar to either never or now something.
¬¬[⇑⊎⇓] : ∀ x → ¬¬ (never ≈ x ⊎ ∃ λ y → x ⇓ y)
¬¬[⇑⊎⇓] x = [ inj₂ , inj₁ ∘ ¬⇓→⇑ _ ] ⟨$⟩ excluded-middle
-- If A is a set, then the termination predicate is propositional.
Terminates-propositional :
Is-set A → ∀ {i x y} → Is-proposition (Terminates i x y)
Terminates-propositional A-set {i} = λ p q → irr p q refl
where
irr :
∀ {x y y′}
(p : [ i ] now y ≈ x)
(q : [ i ] now y′ ≈ x)
(y≡y′ : y ≡ y′) →
subst (([ i ]_≈ x) ∘ now) y≡y′ p ≡ q
irr (laterʳ p) (laterʳ q) refl = cong laterʳ (irr p q refl)
irr {y = y} now now y≡y =
subst (([ i ]_≈ now y) ∘ now) y≡y now ≡⟨ cong (λ eq → subst (([ i ]_≈ now y) ∘ now) eq _) (A-set y≡y refl) ⟩
subst (([ i ]_≈ now y) ∘ now) refl now ≡⟨⟩
now ∎
-- If x terminates with y and z, then y is equal to z.
termination-value-unique :
∀ {i x y z} → Terminates i x y → Terminates i x z → y ≡ z
termination-value-unique now now = refl
termination-value-unique (laterʳ p) (laterʳ q) =
termination-value-unique p q
-- If A is a set, then ∃ λ y → x ⇓ y is propositional.
∃-Terminates-propositional :
Is-set A → ∀ {i x} → Is-proposition (∃ (Terminates i x))
∃-Terminates-propositional A-set (y₁ , x⇓y₁) (y₂ , x⇓y₂) =
Σ-≡,≡→≡
(termination-value-unique x⇓y₁ x⇓y₂)
(Terminates-propositional A-set _ _)
|
{
"alphanum_fraction": 0.5641846811,
"avg_line_length": 30.7131147541,
"ext": "agda",
"hexsha": "90a9c56d4e5697ac2e2f0caaedc335263a2d64cd",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "495f9996673d0f1f34ce202902daaa6c39f8925e",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "nad/delay-monad",
"max_forks_repo_path": "src/Delay-monad/Termination.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "495f9996673d0f1f34ce202902daaa6c39f8925e",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "nad/delay-monad",
"max_issues_repo_path": "src/Delay-monad/Termination.agda",
"max_line_length": 114,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "495f9996673d0f1f34ce202902daaa6c39f8925e",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "nad/delay-monad",
"max_stars_repo_path": "src/Delay-monad/Termination.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 1410,
"size": 3747
}
|
-- Module shadowing using generated modules for records and datatypes
module Issue260a where
module D where
data D : Set where
|
{
"alphanum_fraction": 0.8046875,
"avg_line_length": 21.3333333333,
"ext": "agda",
"hexsha": "8e7d1d6e7e3d0848dcb3d8c605adc5d3622baeeb",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "231d6ad8e77b67ff8c4b1cb35a6c31ccd988c3e9",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "Agda-zh/agda",
"max_forks_repo_path": "test/Fail/Issue260a.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "shlevy/agda",
"max_issues_repo_path": "test/Fail/Issue260a.agda",
"max_line_length": 69,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "shlevy/agda",
"max_stars_repo_path": "test/Fail/Issue260a.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 29,
"size": 128
}
|
interleaved mutual
data Nat : Set
record IsNat (n : Nat) : Set
isNat : (n : Nat) → IsNat n
|
{
"alphanum_fraction": 0.612244898,
"avg_line_length": 16.3333333333,
"ext": "agda",
"hexsha": "8469fbf473a80fe1dea33927f712d7b86720d5fa",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cruhland/agda",
"max_forks_repo_path": "test/Fail/Issue2858-missing.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cruhland/agda",
"max_issues_repo_path": "test/Fail/Issue2858-missing.agda",
"max_line_length": 30,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cruhland/agda",
"max_stars_repo_path": "test/Fail/Issue2858-missing.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 37,
"size": 98
}
|
module string-thms where
open import bool
open import eq
open import string
postulate
=string-refl : (s : string) → s =string s ≡ tt
=string-to-≡ : (a b : string) → a =string b ≡ tt → a ≡ b
≡string-to-= : (a b : string) → a ≡ b → a =string b ≡ tt
≡string-to-= a .a refl = =string-refl a
|
{
"alphanum_fraction": 0.612244898,
"avg_line_length": 22.6153846154,
"ext": "agda",
"hexsha": "ac56c512f083fde31f78af97642aa795494fdc3b",
"lang": "Agda",
"max_forks_count": 17,
"max_forks_repo_forks_event_max_datetime": "2021-11-28T20:13:21.000Z",
"max_forks_repo_forks_event_min_datetime": "2018-12-03T22:38:15.000Z",
"max_forks_repo_head_hexsha": "f3f0261904577e930bd7646934f756679a6cbba6",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "rfindler/ial",
"max_forks_repo_path": "string-thms.agda",
"max_issues_count": 8,
"max_issues_repo_head_hexsha": "f3f0261904577e930bd7646934f756679a6cbba6",
"max_issues_repo_issues_event_max_datetime": "2022-03-22T03:43:34.000Z",
"max_issues_repo_issues_event_min_datetime": "2018-07-09T22:53:38.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "rfindler/ial",
"max_issues_repo_path": "string-thms.agda",
"max_line_length": 58,
"max_stars_count": 29,
"max_stars_repo_head_hexsha": "f3f0261904577e930bd7646934f756679a6cbba6",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "rfindler/ial",
"max_stars_repo_path": "string-thms.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-04T15:05:12.000Z",
"max_stars_repo_stars_event_min_datetime": "2019-02-06T13:09:31.000Z",
"num_tokens": 111,
"size": 294
}
|
{-# OPTIONS --without-K #-}
module hott.truncation.core where
open import sum
open import equality
open import function.core
open import function.fibration
open import function.extensionality
open import function.isomorphism
open import sets.nat.core
open import hott.equivalence
open import hott.level.core
open import hott.level.closure
module _ {i j i' j'}{A : Set i}{A' : Set i'}
{B : A → Set j}{B' : A' → Set j'}
(f : A → A')
(g : (a : A) → B a → B' (f a)) where
private
E E' : Set _
E = Σ A B
E' = Σ A' B'
p : E → A
p = proj₁
p' : E' → A'
p' = proj₁
t : E → E'
t (a , b) = (f a , g a b)
module _ (f-equiv : weak-equiv f)
(t-equiv : weak-equiv t) where
private
φ : A ≅ A'
φ = ≈⇒≅ (f , f-equiv)
τ : E ≅ E'
τ = ≈⇒≅ (t , t-equiv)
lem : (a : A)(e : E) → (p e ≡ a) ≅ (p' (t e) ≡ f a)
lem a e = iso≡ φ
fib-equiv : (a : A) → B a ≅ B' (f a)
fib-equiv a = sym≅ (fib-iso a) ·≅ Σ-ap-iso τ (lem a) ·≅ fib-iso (f a)
postulate
Trunc : ∀ {i} → ℕ → Set i → Set i
Trunc-level : ∀ {i} n {X : Set i} → h n (Trunc n X)
[_] : ∀ {i n} {X : Set i} → X → Trunc n X
Trunc-ext : ∀ {i j} n (X : Set i)(Y : Set j)
→ (Trunc n X → Y) → X → Y
Trunc-ext n X Y f x = f [ x ]
postulate
Trunc-univ : ∀ {i j} n (X : Set i)(Y : Set j) → h n Y
→ weak-equiv (Trunc-ext n X Y)
Trunc-elim-iso : ∀ {i j} n (X : Set i)(Y : Set j) → h n Y
→ (Trunc n X → Y) ≅ (X → Y)
Trunc-elim-iso n X Y hY = ≈⇒≅ (Trunc-ext n X Y , Trunc-univ n X Y hY)
Trunc-elim : ∀ {i j} n (X : Set i)(Y : Set j) → h n Y
→ (X → Y) → (Trunc n X → Y)
Trunc-elim n X Y hY = invert (Trunc-elim-iso n X Y hY)
Trunc-elim-β : ∀ {i j} n (X : Set i)(Y : Set j)(hY : h n Y)
→ (f : X → Y)(x : X)
→ Trunc-elim n X Y hY f [ x ] ≡ f x
Trunc-elim-β n X Y hY f x = funext-inv (_≅_.iso₂ (Trunc-elim-iso n X Y hY) f) x
module _ {i j} n {X : Set i} (Y : Trunc n X → Set j)
(hY : (x : Trunc n X) → h n (Y x)) where
private
Z : Set _
Z = Σ (Trunc n X) Y
hZ : h n Z
hZ = Σ-level (Trunc-level n) hY
Sec₂ : ∀ {k}{A : Set k} → (A → Trunc n X) → Set _
Sec₂ {A = A} r = (x : A) → Y (r x)
Sec : ∀ {k} → Set k → Set _
Sec A = Σ (A → Trunc n X) Sec₂
τ : Sec (Trunc n X) ≅ Sec X
τ = sym≅ ΠΣ-swap-iso ·≅ Trunc-elim-iso n X Z hZ ·≅ ΠΣ-swap-iso
ψ : (r : Trunc n X → Trunc n X)
→ (Sec₂ r) ≅ Sec₂ (r ∘ [_])
ψ = fib-equiv {A = Trunc n X → Trunc n X}{A' = X → Trunc n X}{B = Sec₂} {B' = Sec₂}
(Trunc-ext n X (Trunc n X)) (λ r g x → g [ x ])
(Trunc-univ n X (Trunc n X) (Trunc-level n))
(proj₂ (≅⇒≈ τ))
Trunc-dep-iso : Sec₂ (λ x → x) ≅ Sec₂ [_]
Trunc-dep-iso = ψ (λ x → x)
Trunc-dep-elim : ((x : X) → Y [ x ]) → (x : Trunc n X) → Y x
Trunc-dep-elim = invert Trunc-dep-iso
Trunc-dep-elim-β : (d : ((x : X) → Y [ x ]))
→ (x : X) → Trunc-dep-elim d [ x ] ≡ d x
Trunc-dep-elim-β d = funext-inv (_≅_.iso₂ Trunc-dep-iso d)
|
{
"alphanum_fraction": 0.475848564,
"avg_line_length": 27.8545454545,
"ext": "agda",
"hexsha": "1d848ff41537a68a0c30fc42e08bad375583e2a3",
"lang": "Agda",
"max_forks_count": 4,
"max_forks_repo_forks_event_max_datetime": "2019-05-04T19:31:00.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-02-02T12:17:00.000Z",
"max_forks_repo_head_hexsha": "bbbc3bfb2f80ad08c8e608cccfa14b83ea3d258c",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "pcapriotti/agda-base",
"max_forks_repo_path": "src/hott/truncation/core.agda",
"max_issues_count": 4,
"max_issues_repo_head_hexsha": "bbbc3bfb2f80ad08c8e608cccfa14b83ea3d258c",
"max_issues_repo_issues_event_max_datetime": "2016-10-26T11:57:26.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-02-02T14:32:16.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "pcapriotti/agda-base",
"max_issues_repo_path": "src/hott/truncation/core.agda",
"max_line_length": 87,
"max_stars_count": 20,
"max_stars_repo_head_hexsha": "bbbc3bfb2f80ad08c8e608cccfa14b83ea3d258c",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "pcapriotti/agda-base",
"max_stars_repo_path": "src/hott/truncation/core.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-01T11:25:54.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-06-12T12:20:17.000Z",
"num_tokens": 1322,
"size": 3064
}
|
module Human.Humanity where
-- Use agda-prelude instead of agda-stdlib?
open import Human.JS public
open import Human.Unit public
open import Human.Nat public
open import Human.List public
open import Human.Bool public
open import Human.String public
open import Human.IO public
open import Human.Float public
open import Human.Int public
Lazy : ∀ (A : Set) → Set
Lazy A = Unit → A
then:_ : ∀ {A : Set} → A → Lazy A
then: a = λ x → a
else:_ : ∀ {A : Set} → A → Lazy A
else: a = λ x → a
if : ∀ {A : Set} → Bool → Lazy A → Lazy A → A
if true t f = t unit
if false t f = f unit
init-to : ∀ {A : Set} → Nat → A → (Nat → A → A) → A
init-to zero x fn = x
init-to (suc i) x fn = init-to i (fn zero x) (λ i → fn (suc i))
{-# COMPILE JS init-to = A => n => x => fn => { for (var i = 0, l = n.toJSValue(); i < l; ++i) x = fn(agdaRTS.primIntegerFromString(String(i)))(x); return x; } #-}
syntax init-to m x (λ i → b) = init x for i to m do: b
init-from-to : ∀ {A : Set} → Nat → A → Nat → (Nat → A → A) → A
init-from-to n x m f = init-to (m - n) x (λ i x → f (n + i) x)
syntax init-from-to n x m (λ i → b) = init x for i from n to m do: b
for-to : Nat → (Nat → IO Unit) → IO Unit
for-to zero act = return unit
for-to (suc n) act = act zero >> for-to n (λ i → act (suc i))
syntax for-from-to n m (λ i → b) = for i from n to m do: b
for-from-to : Nat → Nat → (Nat → IO Unit) → IO Unit
for-from-to n m f = for-to (m - n) (λ i → f (n + i))
syntax for-to m (λ i → b) = for i to m do: b
_++_ : String → String → String
_++_ = primStringAppend
show : Nat → String
show zero = "Z"
show (suc n) = "S" ++ show n
Program : Set
Program = Lazy (IO Unit)
_f+_ : Float → Float → Float
_f+_ = primFloatPlus
|
{
"alphanum_fraction": 0.5913348946,
"avg_line_length": 26.6875,
"ext": "agda",
"hexsha": "0bc67cac4dcae8e189789bb14f93897d84f532e2",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "b509eb4c4014605facfb4ee5c807cd07753d4477",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "MaisaMilena/JuiceMaker",
"max_forks_repo_path": "src/Human/Humanity.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "b509eb4c4014605facfb4ee5c807cd07753d4477",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "MaisaMilena/JuiceMaker",
"max_issues_repo_path": "src/Human/Humanity.agda",
"max_line_length": 163,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "b509eb4c4014605facfb4ee5c807cd07753d4477",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "MaisaMilena/JuiceMaker",
"max_stars_repo_path": "src/Human/Humanity.agda",
"max_stars_repo_stars_event_max_datetime": "2020-11-28T05:46:27.000Z",
"max_stars_repo_stars_event_min_datetime": "2019-03-29T17:35:20.000Z",
"num_tokens": 608,
"size": 1708
}
|
------------------------------------------------------------------------
-- The Agda standard library
--
-- Interleavings of lists using setoid equality
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Relation.Binary using (Setoid)
module Data.List.Relation.Ternary.Interleaving.Setoid {c ℓ} (S : Setoid c ℓ) where
open import Level using (_⊔_)
open import Data.List.Base as List using (List; []; _∷_)
open import Data.List.Relation.Ternary.Interleaving.Properties
import Data.List.Relation.Ternary.Interleaving as General
open Setoid S renaming (Carrier to A)
------------------------------------------------------------------------
-- Definition
Interleaving : List A → List A → List A → Set (c ⊔ ℓ)
Interleaving = General.Interleaving _≈_ _≈_
------------------------------------------------------------------------
-- Re-export the basic combinators
open General hiding (Interleaving) public
|
{
"alphanum_fraction": 0.5245901639,
"avg_line_length": 33.6551724138,
"ext": "agda",
"hexsha": "7a7e4c38af2e24f3ef077ae25f59374ec6aef65e",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2021-11-04T06:54:45.000Z",
"max_forks_repo_forks_event_min_datetime": "2021-11-04T06:54:45.000Z",
"max_forks_repo_head_hexsha": "0debb886eb5dbcd38dbeebd04b34cf9d9c5e0e71",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "omega12345/agda-mode",
"max_forks_repo_path": "test/asset/agda-stdlib-1.0/Data/List/Relation/Ternary/Interleaving/Setoid.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "0debb886eb5dbcd38dbeebd04b34cf9d9c5e0e71",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "omega12345/agda-mode",
"max_issues_repo_path": "test/asset/agda-stdlib-1.0/Data/List/Relation/Ternary/Interleaving/Setoid.agda",
"max_line_length": 82,
"max_stars_count": 5,
"max_stars_repo_head_hexsha": "0debb886eb5dbcd38dbeebd04b34cf9d9c5e0e71",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "omega12345/agda-mode",
"max_stars_repo_path": "test/asset/agda-stdlib-1.0/Data/List/Relation/Ternary/Interleaving/Setoid.agda",
"max_stars_repo_stars_event_max_datetime": "2020-10-10T21:41:32.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-10-07T12:07:53.000Z",
"num_tokens": 194,
"size": 976
}
|
-- Andreas, 2015-12-29
record ⊤ : Set where
data P : ⊤ → Set where
c : P record{}
test : (x : ⊤) (p : P x) → Set
test _ c with ⊤
test _ y | z = ⊤
-- Expected error: with-clause pattern mismatch.
-- The error should be printed nicely, like:
--
-- With clause pattern x is not an instance of its parent pattern
-- record {}
-- when checking that the clause
-- test c with Set
-- test x y | z = ⊤
-- has type (x : ⊤) → P x → Set
|
{
"alphanum_fraction": 0.6087962963,
"avg_line_length": 20.5714285714,
"ext": "agda",
"hexsha": "b3e9cfe766c17d3341a72036ac13263a61d73d61",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "c0ae7d20728b15d7da4efff6ffadae6fe4590016",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "redfish64/autonomic-agda",
"max_forks_repo_path": "test/Fail/WithClausePatternMismatch.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "c0ae7d20728b15d7da4efff6ffadae6fe4590016",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "redfish64/autonomic-agda",
"max_issues_repo_path": "test/Fail/WithClausePatternMismatch.agda",
"max_line_length": 65,
"max_stars_count": 3,
"max_stars_repo_head_hexsha": "c0ae7d20728b15d7da4efff6ffadae6fe4590016",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "redfish64/autonomic-agda",
"max_stars_repo_path": "test/Fail/WithClausePatternMismatch.agda",
"max_stars_repo_stars_event_max_datetime": "2015-12-07T20:14:00.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-03-28T14:51:03.000Z",
"num_tokens": 142,
"size": 432
}
|
{-
Product of structures S and T: X ↦ S X × T X
-}
{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Structures.Product where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Transport
open import Cubical.Foundations.Univalence
open import Cubical.Foundations.Path
open import Cubical.Foundations.SIP
open import Cubical.Data.Sigma
private
variable
ℓ ℓ₁ ℓ₁' ℓ₂ ℓ₂' : Level
ProductStructure : (S₁ : Type ℓ → Type ℓ₁) (S₂ : Type ℓ → Type ℓ₂)
→ Type ℓ → Type (ℓ-max ℓ₁ ℓ₂)
ProductStructure S₁ S₂ X = S₁ X × S₂ X
ProductEquivStr :
{S₁ : Type ℓ → Type ℓ₁} (ι₁ : StrEquiv S₁ ℓ₁')
{S₂ : Type ℓ → Type ℓ₂} (ι₂ : StrEquiv S₂ ℓ₂')
→ StrEquiv (ProductStructure S₁ S₂) (ℓ-max ℓ₁' ℓ₂')
ProductEquivStr ι₁ ι₂ (X , s₁ , s₂) (Y , t₁ , t₂) f =
(ι₁ (X , s₁) (Y , t₁) f) × (ι₂ (X , s₂) (Y , t₂) f)
productUnivalentStr :
{S₁ : Type ℓ → Type ℓ₁} (ι₁ : StrEquiv S₁ ℓ₁') (θ₁ : UnivalentStr S₁ ι₁)
{S₂ : Type ℓ → Type ℓ₂} (ι₂ : StrEquiv S₂ ℓ₂') (θ₂ : UnivalentStr S₂ ι₂)
→ UnivalentStr (ProductStructure S₁ S₂) (ProductEquivStr ι₁ ι₂)
productUnivalentStr {S₁ = S₁} ι₁ θ₁ {S₂} ι₂ θ₂ {X , s₁ , s₂} {Y , t₁ , t₂} e =
compEquiv (Σ-cong-equiv (θ₁ e) (λ _ → θ₂ e)) ΣPath≃PathΣ
productEquivAction :
{S₁ : Type ℓ → Type ℓ₁} (α₁ : EquivAction S₁)
{S₂ : Type ℓ → Type ℓ₂} (α₂ : EquivAction S₂)
→ EquivAction (ProductStructure S₁ S₂)
productEquivAction α₁ α₂ e = Σ-cong-equiv (α₁ e) (λ _ → α₂ e)
productTransportStr :
{S₁ : Type ℓ → Type ℓ₁} (α₁ : EquivAction S₁) (τ₁ : TransportStr α₁)
{S₂ : Type ℓ → Type ℓ₂} (α₂ : EquivAction S₂) (τ₂ : TransportStr α₂)
→ TransportStr (productEquivAction α₁ α₂)
productTransportStr _ τ₁ _ τ₂ e (s₁ , s₂) = ΣPathP (τ₁ e s₁ , τ₂ e s₂)
|
{
"alphanum_fraction": 0.6711111111,
"avg_line_length": 35.2941176471,
"ext": "agda",
"hexsha": "f9df3681868fd4561d9f99bf2bc12f618bed65f7",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "fd8059ec3eed03f8280b4233753d00ad123ffce8",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "dan-iel-lee/cubical",
"max_forks_repo_path": "Cubical/Structures/Product.agda",
"max_issues_count": 1,
"max_issues_repo_head_hexsha": "fd8059ec3eed03f8280b4233753d00ad123ffce8",
"max_issues_repo_issues_event_max_datetime": "2022-01-27T02:07:48.000Z",
"max_issues_repo_issues_event_min_datetime": "2022-01-27T02:07:48.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "dan-iel-lee/cubical",
"max_issues_repo_path": "Cubical/Structures/Product.agda",
"max_line_length": 78,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "fd8059ec3eed03f8280b4233753d00ad123ffce8",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "dan-iel-lee/cubical",
"max_stars_repo_path": "Cubical/Structures/Product.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 760,
"size": 1800
}
|
{-# OPTIONS --safe --experimental-lossy-unification #-}
module Cubical.Algebra.Group.EilenbergMacLane.WedgeConnectivity where
open import Cubical.Algebra.Group.EilenbergMacLane.Base
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Algebra.Group.Base
open import Cubical.HITs.Truncation as Trunc renaming (rec to trRec; elim to trElim)
open import Cubical.HITs.EilenbergMacLane1
open import Cubical.Algebra.AbGroup.Base
open import Cubical.Data.Empty
renaming (rec to ⊥-rec)
open import Cubical.Data.Nat
open import Cubical.HITs.Susp
{-
This file contains a direct construction of the wedge connectivity lemma for EM
spaces. This direct construction gives nicer reductions and computes better than
the more general theorem. The main results are in the module "wedgeConEM" at the
end of this file.
-}
private
variable ℓ ℓ' ℓ'' : Level
-- One of the base cases, stated separately to avoid termination issues
wedgeConFun' : (G : AbGroup ℓ) (H : AbGroup ℓ') (n : ℕ)
→ {A : EM-raw G (suc n) → EM-raw H (suc zero) → Type ℓ''}
→ ((x : _) (y : _) → isOfHLevel (suc n + suc zero) (A x y))
→ (f : (x : _) → A ptEM-raw x)
→ (g : (x : _) → A x ptEM-raw)
→ f ptEM-raw ≡ g ptEM-raw
→ (x : _) (y : _) → A x y
wedgeConFun'ᵣ : (G : AbGroup ℓ) (H : AbGroup ℓ') (n : ℕ)
→ {A : EM-raw G (suc n) → EM-raw H (suc zero) → Type ℓ''}
→ (hLev : ((x : _) (y : _) → isOfHLevel (suc n + suc zero) (A x y)))
→ (f : (x : _) → A ptEM-raw x)
→ (g : (x : _) → A x ptEM-raw)
→ (p : f ptEM-raw ≡ g ptEM-raw)
→ (x : _) → wedgeConFun' G H n hLev f g p x ptEM-raw ≡ g x
wedgeConFun' G H zero {A = A} hlev f g p =
elimSet _ (λ _ → isSetΠ λ _ → hlev _ _) f mainpath
where
I→A : (x : fst G) → (i : I) → A (emloop x i) embase
I→A x i =
hcomp (λ k → λ {(i = i0) → p (~ k) ; (i = i1) → p (~ k)})
(g (emloop x i))
SquareP2 : (x : _) (z : _)
→ SquareP (λ i j → A (emloop x i) (emloop z j))
(cong f (emloop z)) (cong f (emloop z))
(λ i → I→A x i) λ i → I→A x i
SquareP2 x z =
toPathP (isOfHLevelPathP' 1 (λ _ _ → hlev _ _ _ _) _ _ _ _)
CubeP2 : (x : _) (g h : _)
→ PathP (λ k → PathP (λ j → PathP (λ i → A (emloop x i) (emcomp g h j k))
(f (emcomp g h j k)) (f (emcomp g h j k)))
(λ i → SquareP2 x g i k) λ i → SquareP2 x ((snd (AbGroup→Group H) GroupStr.· g) h) i k)
(λ _ i → I→A x i) λ j i → SquareP2 x h i j
CubeP2 x g h = toPathP (isOfHLevelPathP' 1 (isOfHLevelPathP 2 (hlev _ _) _ _) _ _ _ _)
mainpath : (x : _) → PathP (λ i → (y : EM₁ (AbGroup→Group H)) → A (emloop x i) y) f f
mainpath x i embase = I→A x i
mainpath x i (emloop z j) = SquareP2 x z i j
mainpath x i (emcomp g h j k) = CubeP2 x g h k j i
mainpath x i (emsquash y z p q r s j k' l) = mega i j k' l
where
mega :
PathP (λ i → PathP (λ j → PathP (λ k →
PathP (λ l → A (emloop x i) (emsquash y z p q r s j k l))
(mainpath x i y)
(mainpath x i z))
(λ l → mainpath x i (p l))
λ l → mainpath x i (q l))
(λ k l → mainpath x i (r k l))
λ k l → mainpath x i (s k l))
(λ j mainpath l → f (emsquash y z p q r s j mainpath l))
λ j mainpath l → f (emsquash y z p q r s j mainpath l)
mega =
toPathP (isOfHLevelPathP' 1
(isOfHLevelPathP 2 (isOfHLevelPathP 2 (hlev _ _) _ _) _ _) _ _ _ _)
wedgeConFun' G H (suc n) {A = A} hLev f g p north y = f y
wedgeConFun' G H (suc n) {A = A} hLev f g p south y = subst (λ x → A x y) (merid ptEM-raw) (f y)
wedgeConFun' G H (suc n) {A = A} hLev f g p (merid a i) y = mainₗ a y i
module _ where
llem₁ : g south ≡ subst (λ x₁ → A x₁ ptEM-raw) (merid ptEM-raw) (f ptEM-raw)
llem₁ = (λ i → transp (λ j → A (merid ptEM-raw (j ∨ ~ i)) ptEM-raw) (~ i) (g (merid ptEM-raw (~ i))))
∙ cong (subst (λ x₁ → A x₁ ptEM-raw) (merid ptEM-raw)) (sym p)
llem₁' :
Square
(λ i → transp (λ j → A (merid ptEM-raw (i ∨ j)) ptEM-raw) i (g (merid ptEM-raw i))) refl
(cong (subst (λ x → A x ptEM-raw) (merid ptEM-raw)) (sym p)) llem₁
llem₁' i j =
hcomp (λ k → λ { (i = i0) → transp (λ z → A (merid ptEM-raw (j ∨ z)) ptEM-raw) j
(g (merid ptEM-raw j))
; (i = i1) → subst (λ x₁ → A x₁ ptEM-raw) (merid ptEM-raw) (p (~ k))
; (j = i0) → (subst (λ x → A x ptEM-raw) (merid ptEM-raw)) (p (~ k ∨ ~ i))})
(transp (λ k → A (merid ptEM-raw (k ∨ ~ i ∧ j)) ptEM-raw) (~ i ∧ j) (g (merid ptEM-raw (~ i ∧ j))))
llem₂ : (λ i₁ → transp (λ j → A (merid ptEM-raw (i₁ ∧ j)) ptEM-raw) (~ i₁) (f ptEM-raw))
≡ (λ i₁ → hcomp (λ k → λ { (i₁ = i0) → p (~ k) ; (i₁ = i1) → llem₁ k })
(g (merid ptEM-raw i₁)))
llem₂ i j =
hcomp (λ k → λ { (i = i0) → transp (λ j₁ → A (merid ptEM-raw (j ∧ j₁)) ptEM-raw) (~ j) (p (~ k))
; (j = i0) → p (~ k)
; (j = i1) → llem₁' k i})
(transp (λ k → A (merid ptEM-raw ((i ∨ k) ∧ j)) ptEM-raw) (i ∨ ~ j) (g (merid ptEM-raw (i ∧ j))))
mainₗ : (a : _) (y : _)
→ PathP (λ i → A (merid a i) y) (f y) (subst (λ x → A x y) (merid ptEM-raw) (f y))
mainₗ =
wedgeConFun' G H n
(λ _ _ → isOfHLevelPathP' (suc (n + 1)) (hLev _ _) _ _)
(λ x i → transp (λ j → A (merid ptEM-raw (i ∧ j)) x) (~ i) (f x))
(λ x i → hcomp (λ k → λ { (i = i0) → p (~ k)
; (i = i1) → llem₁ k})
(g (merid x i)))
llem₂
mainP : (y : _)
→ mainₗ y ptEM-raw
≡ λ i → hcomp (λ k → λ { (i = i0) → p (~ k)
; (i = i1) → llem₁ k})
(g (merid y i))
mainP y =
wedgeConFun'ᵣ G H n
(λ _ _ → isOfHLevelPathP' (suc (n + 1)) (hLev _ _) _ _)
(λ x i → transp (λ j → A (merid ptEM-raw (i ∧ j)) x) (~ i) (f x))
(λ x i → hcomp (λ k → λ { (i = i0) → p (~ k)
; (i = i1) → llem₁ k})
(g (merid x i)))
llem₂ y
wedgeConFun'ᵣ G H zero {A = A} hLev f g p =
elimProp _ (λ _ → hLev _ _ _ _) p
wedgeConFun'ᵣ G H (suc n) {A = A} hLev f g p north = p
wedgeConFun'ᵣ G H (suc n) {A = A} hLev f g p south = sym (llem₁ G H n hLev f g p ptEM-raw i0 ptEM-raw)
wedgeConFun'ᵣ G H (suc n) {A = A} hLev f g p (merid a i) k = P k i
where
llem : _
llem i j =
hcomp (λ k → λ { (i = i1) → g (merid a j)
; (j = i0) → p (i ∨ ~ k)
; (j = i1) → llem₁ G H n hLev f g p ptEM-raw i0 ptEM-raw (~ i ∧ k)})
(g (merid a j))
P : PathP (λ k → PathP (λ i → A (merid a i) ptEM-raw)
(p k) (llem₁ G H n hLev f g p ptEM-raw i0 ptEM-raw (~ k)))
(λ i → mainₗ G H n hLev f g p a i ptEM-raw a ptEM-raw i) λ i → g (merid a i)
P = mainP G H n hLev f g p a i0 ptEM-raw a ◁ llem
-- Here, the actual stuff gets proved. However an additional natural number is stuck into the context
-- to convince the termination checker
private
wedgeConFun : (G : AbGroup ℓ) (H : AbGroup ℓ')
(k n m : ℕ) → (n + m ≡ k) → {A : EM-raw G (suc n) → EM-raw H (suc m) → Type ℓ''}
→ ((x : _) (y : _) → isOfHLevel (suc n + suc m) (A x y))
→ (f : (x : _) → A ptEM-raw x)
→ (g : (x : _) → A x ptEM-raw)
→ f ptEM-raw ≡ g ptEM-raw
→ (x : _) (y : _) → A x y
wedgeconLeft : (G : AbGroup ℓ) (H : AbGroup ℓ') (k n m : ℕ) (P : n + m ≡ k)
{A : EM-raw G (suc n) → EM-raw H (suc m) → Type ℓ''}
→ (hLev : ((x : _) (y : _) → isOfHLevel (suc n + suc m) (A x y)))
→ (f : (x : _) → A ptEM-raw x)
→ (g : (x : _) → A x ptEM-raw)
→ (p : f ptEM-raw ≡ g ptEM-raw)
→ (x : _) → wedgeConFun G H k n m P hLev f g p ptEM-raw x ≡ f x
wedgeconRight : (G : AbGroup ℓ) (H : AbGroup ℓ')
(k n m : ℕ) (P : n + m ≡ k) {A : EM-raw G (suc n) → EM-raw H (suc m) → Type ℓ''}
→ (hLev : ((x : _) (y : _) → isOfHLevel (suc n + suc m) (A x y)))
→ (f : (x : _) → A ptEM-raw x)
→ (g : (x : _) → A x ptEM-raw)
→ (p : f ptEM-raw ≡ g ptEM-raw)
→ (x : _) → wedgeConFun G H k n m P hLev f g p x ptEM-raw ≡ g x
wedgeConFun G H k n zero P {A = A} hLev f g p = wedgeConFun' G H n hLev f g p
wedgeConFun G H k zero (suc m) P {A = A} hLev f g p x y =
wedgeConFun' H G (suc m) {A = λ x y → A y x}
(λ x y → subst (λ n → isOfHLevel (2 + n) (A y x)) (+-comm 1 m) (hLev y x))
g f (sym p) y x
wedgeConFun G H l (suc n) (suc m) P {A = A} hlev f g p north y = f y
wedgeConFun G H l (suc n) (suc m) P {A = A} hlev f g p south y = subst (λ x → A x y) (merid ptEM-raw) (f y)
wedgeConFun G H zero (suc n) (suc m) P {A = A} hlev f g p (merid a i) y = ⊥-path i
where
⊥-path : PathP (λ i → A (merid a i) y) (f y) (subst (λ x → A x y) (merid ptEM-raw) (f y))
⊥-path = ⊥-rec (snotz P)
wedgeConFun G H (suc l) (suc n) (suc m) P {A = A} hlev f g p (merid a i) y = mmain a y i
module _ where
llem₃ : g south ≡ (subst (λ x → A x ptEM-raw) (merid ptEM-raw) (f ptEM-raw))
llem₃ = ((λ i → transp (λ j → A (merid ptEM-raw (~ i ∨ j)) ptEM-raw) (~ i) (g (merid ptEM-raw (~ i)))))
∙ cong (subst (λ x → A x ptEM-raw) (merid ptEM-raw)) (sym p)
llem₃' :
Square
(λ i → transp (λ j → A (merid ptEM-raw (~ i ∨ j)) ptEM-raw) (~ i) (g (merid ptEM-raw (~ i))))
(refl {x = subst (λ x → A x ptEM-raw) (merid ptEM-raw) (f ptEM-raw)})
llem₃
((cong (transport (λ z → A (merid ptEM-raw z) ptEM-raw)) (sym p)))
llem₃' i j =
hcomp (λ k → λ { (i = i0) → transp (λ j₁ → A (merid ptEM-raw (~ j ∨ j₁)) ptEM-raw) (~ j) (g (merid ptEM-raw (~ j)))
; (i = i1) → subst (λ x → A x ptEM-raw) (merid ptEM-raw) (p (~ k))
; (j = i1) → cong (transport (λ z → A (merid ptEM-raw z) ptEM-raw)) (sym p) (i ∧ k)})
(transp (λ j₁ → A (merid ptEM-raw ((~ j ∧ ~ i) ∨ j₁)) ptEM-raw) (~ j ∧ ~ i) (g (merid ptEM-raw (~ j ∧ ~ i))))
llem₄ : (λ i₁ → transp (λ j → A (merid ptEM-raw (j ∧ i₁)) ptEM-raw) (~ i₁) (f ptEM-raw))
≡ (λ i₁ → hcomp (λ k → λ { (i₁ = i0) → p (~ k) ; (i₁ = i1) → llem₃ k })
(g (merid ptEM-raw i₁)))
llem₄ i j =
hcomp (λ k → λ { (i = i0) → transp (λ z → A (merid ptEM-raw (z ∧ j)) ptEM-raw) (~ j) (p (~ k))
; (j = i0) → p (~ k)
; (j = i1) → llem₃' k (~ i)})
(transp (λ z → A (merid ptEM-raw ((i ∨ z) ∧ j)) ptEM-raw) (i ∨ ~ j) (g (merid ptEM-raw (i ∧ j))))
mmain : (a : _) (y : _)
→ PathP (λ i → A (merid a i) y) (f y)
(subst (λ x → A x y) (merid ptEM-raw) (f y))
mmain =
wedgeConFun G H l n (suc m) (cong predℕ P)
(λ _ _ → isOfHLevelPathP' (suc (n + (suc (suc m)))) (hlev _ _) _ _)
(λ x i → transp (λ j → A (merid ptEM-raw (j ∧ i)) x) (~ i) (f x))
(λ y i → hcomp (λ k → λ { (i = i0) → p (~ k)
; (i = i1) → llem₃ k})
(g (merid y i)))
llem₄
mainR : (x : _) → mmain x ptEM-raw
≡ λ i → hcomp (λ k → λ { (i = i0) → p (~ k)
; (i = i1) → llem₃ k})
(g (merid x i))
mainR x =
wedgeconRight G H l n (suc m) (cong predℕ P)
(λ _ _ → isOfHLevelPathP' (suc (n + (suc (suc m)))) (hlev _ _) _ _)
(λ x i → transp (λ j → A (merid ptEM-raw (j ∧ i)) x) (~ i) (f x))
(λ y i → hcomp (λ k → λ { (i = i0) → p (~ k)
; (i = i1) → llem₃ k})
(g (merid y i)))
llem₄ x
wedgeconLeft G H k zero zero P {A = A} hLev f g p _ = refl
wedgeconLeft G H k (suc n) zero P {A = A} hLev f g p _ = refl
wedgeconLeft G H k zero (suc m) P {A = A} hLev f g p x =
wedgeConFun'ᵣ H G (suc m)
(λ x₁ y →
subst (λ n → (x₂ y₁ : A y x₁) → isOfHLevel (suc n) (x₂ ≡ y₁))
(+-comm 1 m) (hLev y x₁))
g f (λ i → p (~ i)) x
wedgeconLeft G H k (suc n) (suc m) P {A = A} hLev f g p _ = refl
wedgeconRight G H k n zero P {A = A} hLev f g p = wedgeConFun'ᵣ G H n hLev f g p
wedgeconRight G H k zero (suc m) P {A = A} hLev f g p _ = refl
wedgeconRight G H zero (suc n) (suc m) P {A = A} hLev f g p x = ⊥-rec (snotz P)
wedgeconRight G H l (suc n) (suc m) P {A = A} hLev f g p north = p
wedgeconRight G H l (suc n) (suc m) P {A = A} hLev f g p south =
sym (llem₃ G H _ n m refl hLev f g p ptEM-raw i0 ptEM-raw)
wedgeconRight G H (suc l) (suc n) (suc m) P {A = A} hLev f g p (merid a i) k =
help k i
where
llem : _
llem i j =
hcomp (λ k → λ { (i = i1) → g (merid a j)
; (j = i0) → p (i ∨ ~ k)
; (j = i1) → llem₃ G H l n m P hLev f g p ptEM-raw i0 ptEM-raw (~ i ∧ k)})
(g (merid a j))
help : PathP (λ k → PathP (λ i → A (merid a i) ptEM-raw)
(p k) (llem₃ G H l n m P hLev f g p ptEM-raw i0 ptEM-raw (~ k)))
(λ i → mmain G H l n m P hLev f g p a i north a north i) (cong g (merid a))
help = mainR G H l n m P hLev f g p a i0 ptEM-raw a ◁ llem
module wedgeConEM (G : AbGroup ℓ) (H : AbGroup ℓ') (n m : ℕ)
{A : EM-raw G (suc n) → EM-raw H (suc m) → Type ℓ''}
(hLev : ((x : _) (y : _) → isOfHLevel (suc n + suc m) (A x y)))
(f : (x : _) → A ptEM-raw x)
(g : (x : _) → A x ptEM-raw)
(p : f ptEM-raw ≡ g ptEM-raw) where
fun : (x : EM-raw G (suc n)) (y : EM-raw H (suc m)) → A x y
fun = wedgeConFun G H (n + m) n m refl hLev f g p
left : (x : EM-raw H (suc m)) → fun ptEM-raw x ≡ f x
left = wedgeconLeft G H (n + m) n m refl hLev f g p
right : (x : EM-raw G (suc n)) → fun x ptEM-raw ≡ g x
right = wedgeconRight G H (n + m) n m refl hLev f g p
|
{
"alphanum_fraction": 0.4651550981,
"avg_line_length": 50.2727272727,
"ext": "agda",
"hexsha": "1a9ae3a272fbd5aafc260206d65287f215888be2",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "58c0b83bb0fed0dc683f3d29b1709effe51c1689",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "thomas-lamiaux/cubical",
"max_forks_repo_path": "Cubical/Algebra/Group/EilenbergMacLane/WedgeConnectivity.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "58c0b83bb0fed0dc683f3d29b1709effe51c1689",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "thomas-lamiaux/cubical",
"max_issues_repo_path": "Cubical/Algebra/Group/EilenbergMacLane/WedgeConnectivity.agda",
"max_line_length": 122,
"max_stars_count": 1,
"max_stars_repo_head_hexsha": "58c0b83bb0fed0dc683f3d29b1709effe51c1689",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "thomas-lamiaux/cubical",
"max_stars_repo_path": "Cubical/Algebra/Group/EilenbergMacLane/WedgeConnectivity.agda",
"max_stars_repo_stars_event_max_datetime": "2021-10-31T17:32:49.000Z",
"max_stars_repo_stars_event_min_datetime": "2021-10-31T17:32:49.000Z",
"num_tokens": 5863,
"size": 14378
}
|
-- Andreas, 2014-10-23
-- If you must, you can split on a shadowed hidden var...
data ℕ : Set where
zero : ℕ
suc : ℕ → ℕ
f : {n n : ℕ} → Set₁
f = Set
where
g : {n n : ℕ} → Set → Set
g _ = {!.n!}
|
{
"alphanum_fraction": 0.5142857143,
"avg_line_length": 15,
"ext": "agda",
"hexsha": "9feaf4e701b89bf44d65d3876ed5e829d209c7e5",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "c0ae7d20728b15d7da4efff6ffadae6fe4590016",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "redfish64/autonomic-agda",
"max_forks_repo_path": "test/interaction/Issue1325b.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "c0ae7d20728b15d7da4efff6ffadae6fe4590016",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "redfish64/autonomic-agda",
"max_issues_repo_path": "test/interaction/Issue1325b.agda",
"max_line_length": 57,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "c0ae7d20728b15d7da4efff6ffadae6fe4590016",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "redfish64/autonomic-agda",
"max_stars_repo_path": "test/interaction/Issue1325b.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 88,
"size": 210
}
|
{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import LibraBFT.Base.Types
import LibraBFT.Impl.Consensus.ConsensusTypes.Block as Block
import LibraBFT.Impl.Consensus.ConsensusTypes.QuorumCert as QuorumCert
open import LibraBFT.ImplShared.Base.Types
open import LibraBFT.ImplShared.Consensus.Types
open import Optics.All
open import Util.Hash
open import Util.Prelude
module LibraBFT.Impl.Consensus.LedgerRecoveryData where
postulate -- TODO-2: compareX, sortBy, findIndex, deleteAt, find
compareX : (Epoch × Round) → (Epoch × Round) → Ordering
sortBy : (Block → Block → Ordering) → List Block → List Block
findIndex : (Block → Bool) → List Block → Maybe ℕ
deleteAt : ℕ → List Block → List Block
find : (QuorumCert → Bool) → List QuorumCert -> Maybe QuorumCert
findRoot : List Block → List QuorumCert → LedgerRecoveryData
→ Either ErrLog (RootInfo × List Block × List QuorumCert)
findRoot blocks0 quorumCerts0 (LedgerRecoveryData∙new storageLedger) = do
(rootId , (blocks1 , quorumCerts)) ←
if storageLedger ^∙ liEndsEpoch
then (do
genesis ← Block.makeGenesisBlockFromLedgerInfo storageLedger
let genesisQC = QuorumCert.certificateForGenesisFromLedgerInfo storageLedger (genesis ^∙ bId)
pure (genesis ^∙ bId , (genesis ∷ blocks0 , genesisQC ∷ quorumCerts0)))
else
pure (storageLedger ^∙ liConsensusBlockId , (blocks0 , quorumCerts0))
let sorter : Block → Block → Ordering
sorter bl br = compareX (bl ^∙ bEpoch , bl ^∙ bRound) (br ^∙ bEpoch , br ^∙ bRound)
sortedBlocks = sortBy sorter blocks1
rootIdx ← maybeS
(findIndex (λ x → x ^∙ bId == rootId) sortedBlocks)
(Left fakeErr) -- ["unable to find root", show rootId]
(pure ∘ id)
rootBlock ← maybeS
(sortedBlocks !? rootIdx)
(Left fakeErr) -- ["sortedBlocks !? rootIdx"]
(pure ∘ id)
let blocks = deleteAt rootIdx sortedBlocks
rootQuorumCert ← maybeS
(find (λ x → x ^∙ qcCertifiedBlock ∙ biId == rootBlock ^∙ bId) quorumCerts)
(Left fakeErr) -- ["No QC found for root", show rootId]
(pure ∘ id)
rootLedgerInfo ← maybeS
(find (λ x → x ^∙ qcCommitInfo ∙ biId == rootBlock ^∙ bId) quorumCerts)
(Left fakeErr) -- ["No LI found for root", show rootId]
(pure ∘ id)
pure (RootInfo∙new rootBlock rootQuorumCert rootLedgerInfo , blocks , quorumCerts)
{-
where
here t = "LedgerRecoveryData":"findRoot":t
deleteAt idx xs = lft ++ tail rgt where (lft, rgt) = splitAt idx xs
tail = \case [] -> []; (_:xs) -> xs
-}
|
{
"alphanum_fraction": 0.6699716714,
"avg_line_length": 44.8253968254,
"ext": "agda",
"hexsha": "ff05293907015c90b7dfbf1e93b2a4cd5a6aecf6",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "a4674fc473f2457fd3fe5123af48253cfb2404ef",
"max_forks_repo_licenses": [
"UPL-1.0"
],
"max_forks_repo_name": "LaudateCorpus1/bft-consensus-agda",
"max_forks_repo_path": "src/LibraBFT/Impl/Consensus/LedgerRecoveryData.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "a4674fc473f2457fd3fe5123af48253cfb2404ef",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"UPL-1.0"
],
"max_issues_repo_name": "LaudateCorpus1/bft-consensus-agda",
"max_issues_repo_path": "src/LibraBFT/Impl/Consensus/LedgerRecoveryData.agda",
"max_line_length": 111,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "a4674fc473f2457fd3fe5123af48253cfb2404ef",
"max_stars_repo_licenses": [
"UPL-1.0"
],
"max_stars_repo_name": "LaudateCorpus1/bft-consensus-agda",
"max_stars_repo_path": "src/LibraBFT/Impl/Consensus/LedgerRecoveryData.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 851,
"size": 2824
}
|
{-# OPTIONS --without-K --safe #-}
-- a categorical (i.e. non-skeletal) version of Lawvere Theory,
-- as per https://ncatlab.org/nlab/show/Lawvere+theory
module Categories.Theory.Lawvere where
open import Data.Nat using (ℕ)
open import Data.Product using (Σ; _,_)
open import Level
open import Categories.Category.Cartesian.Structure
open import Categories.Category using (Category; _[_,_])
open import Categories.Category.Instance.Setoids
open import Categories.Category.Monoidal.Instance.Setoids using (Setoids-CartesianCategory)
open import Categories.Category.Product
open import Categories.Functor using (Functor; _∘F_) renaming (id to idF)
open import Categories.Functor.Cartesian
open import Categories.Functor.Cartesian.Properties
import Categories.Morphism as Mor
open import Categories.NaturalTransformation using (NaturalTransformation)
private
variable
o ℓ e o′ ℓ′ e′ o″ ℓ″ e″ : Level
record FiniteProduct (o ℓ e : Level) : Set (suc (o ⊔ ℓ ⊔ e)) where
field
T : CartesianCategory o ℓ e
module T = CartesianCategory T
open Mor T.U
field
generic : T.Obj
field
obj-iso-to-generic-power : ∀ x → Σ ℕ (λ n → x ≅ T.power generic n)
record LT-Hom (T₁ : FiniteProduct o ℓ e) (T₂ : FiniteProduct o′ ℓ′ e′) : Set (o ⊔ ℓ ⊔ e ⊔ o′ ⊔ ℓ′ ⊔ e′) where
private
module T₁ = FiniteProduct T₁
module T₂ = FiniteProduct T₂
field
cartF : CartesianF T₁.T T₂.T
module cartF = CartesianF cartF
LT-id : {A : FiniteProduct o ℓ e} → LT-Hom A A
LT-id = record { cartF = idF-CartesianF _ }
LT-∘ : {A : FiniteProduct o ℓ e} {B : FiniteProduct o′ ℓ′ e′} {C : FiniteProduct o″ ℓ″ e″} →
LT-Hom B C → LT-Hom A B → LT-Hom A C
LT-∘ G H = record { cartF = ∘-CartesianF (cartF G) (cartF H) }
where open LT-Hom
record T-Algebra (FP : FiniteProduct o ℓ e) : Set (o ⊔ ℓ ⊔ e ⊔ suc (ℓ′ ⊔ e′)) where
private
module FP = FiniteProduct FP
field
cartF : CartesianF FP.T (Setoids-CartesianCategory ℓ′ e′)
module cartF = CartesianF cartF
mod : Functor FP.T.U (Setoids ℓ′ e′)
mod = cartF.F
|
{
"alphanum_fraction": 0.6932876041,
"avg_line_length": 29.5797101449,
"ext": "agda",
"hexsha": "9ab04215902086144c88112aa3616eac5c15994b",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2021-11-04T06:54:45.000Z",
"max_forks_repo_forks_event_min_datetime": "2021-11-04T06:54:45.000Z",
"max_forks_repo_head_hexsha": "7672b7a3185ae77467cc30e05dbe50b36ff2af8a",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "bblfish/agda-categories",
"max_forks_repo_path": "src/Categories/Theory/Lawvere.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "7672b7a3185ae77467cc30e05dbe50b36ff2af8a",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "bblfish/agda-categories",
"max_issues_repo_path": "src/Categories/Theory/Lawvere.agda",
"max_line_length": 109,
"max_stars_count": 5,
"max_stars_repo_head_hexsha": "7672b7a3185ae77467cc30e05dbe50b36ff2af8a",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "bblfish/agda-categories",
"max_stars_repo_path": "src/Categories/Theory/Lawvere.agda",
"max_stars_repo_stars_event_max_datetime": "2020-10-10T21:41:32.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-10-07T12:07:53.000Z",
"num_tokens": 657,
"size": 2041
}
|
{-# OPTIONS --without-K --safe #-}
module Data.Maybe.Base where
open import Level
data Maybe (A : Type a) : Type a where
nothing : Maybe A
just : A → Maybe A
maybe : {B : Maybe A → Type b} → B nothing → ((x : A) → B (just x)) → (x : Maybe A) → B x
maybe b f nothing = b
maybe b f (just x) = f x
mapMaybe : (A → B) → Maybe A → Maybe B
mapMaybe f nothing = nothing
mapMaybe f (just x) = just (f x)
infixr 2 _|?_
_|?_ : Maybe A → A → A
nothing |? x = x
just x |? _ = x
|
{
"alphanum_fraction": 0.5755693582,
"avg_line_length": 21,
"ext": "agda",
"hexsha": "8d62b5fe992895f60b313067cd9abef750feb427",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2021-11-11T12:30:21.000Z",
"max_forks_repo_forks_event_min_datetime": "2021-11-11T12:30:21.000Z",
"max_forks_repo_head_hexsha": "97a3aab1282b2337c5f43e2cfa3fa969a94c11b7",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "oisdk/agda-playground",
"max_forks_repo_path": "Data/Maybe/Base.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "97a3aab1282b2337c5f43e2cfa3fa969a94c11b7",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "oisdk/agda-playground",
"max_issues_repo_path": "Data/Maybe/Base.agda",
"max_line_length": 89,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "97a3aab1282b2337c5f43e2cfa3fa969a94c11b7",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "oisdk/agda-playground",
"max_stars_repo_path": "Data/Maybe/Base.agda",
"max_stars_repo_stars_event_max_datetime": "2021-11-16T08:11:34.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-09-11T17:45:41.000Z",
"num_tokens": 173,
"size": 483
}
|
{-# OPTIONS --cubical --safe #-}
-- First and second species counterpoint
module Counterpoint where
open import Data.Bool using (Bool; true; false; if_then_else_; _∨_; _∧_; not)
open import Data.Fin using (Fin; #_)
open import Data.Integer using (+_)
open import Data.List using (List; []; _∷_; mapMaybe; map; zip; _++_; concatMap)
open import Data.Maybe using (Maybe; just; nothing)
open import Data.Nat using (suc; _+_; _<ᵇ_; compare; _∸_; ℕ; zero) renaming (_≡ᵇ_ to _==_)
open import Data.Product using (_×_; _,_; proj₁; proj₂; uncurry)
open import Data.Vec using ([]; _∷_; Vec; lookup; drop; reverse)
open import Function using (_∘_)
open import Relation.Binary.PropositionalEquality using (_≡_; refl)
open import Music
open import Note
open import Pitch
open import Interval
open import Util using (pairs)
------------------------------------------------
-- First species
-- Beginning must be the 1st, 5th, or 8th
data BeginningError : Set where
not158 : PitchInterval → BeginningError
checkBeginning : PitchInterval → Maybe BeginningError
checkBeginning pi@(_ , i) =
if ((i == per1) ∨ (i == per5) ∨ (i == per8))
then nothing
else just (not158 pi)
------------------------------------------------
-- Intervals in middle bars must be consonant and non-unison
data IntervalError : Set where
dissonant : Upi → IntervalError
unison : Pitch → IntervalError
intervalCheck : PitchInterval → Maybe IntervalError
intervalCheck (p , i) with isConsonant i | isUnison i
intervalCheck (p , i) | false | _ = just (dissonant i)
intervalCheck (p , i) | _ | true = just (unison p)
intervalCheck (p , i) | _ | _ = nothing
checkIntervals : List PitchInterval → List IntervalError
checkIntervals = mapMaybe intervalCheck
------------------------------------------------
-- Perfect intervals must not approached by parallel or similar motion
data Motion : Set where
contrary : Motion
parallel : Motion
similar : Motion
oblique : Motion
motion : PitchInterval → PitchInterval → Motion
motion (p , i) (q , j) =
let p' = p + i; q' = q + j
in if i == j then parallel
else (if (p == q) ∨ (p' == q') then oblique
else (if p <ᵇ q then (if p' <ᵇ q' then similar else contrary)
else (if p' <ᵇ q' then contrary else similar)))
data MotionError : Set where
parallel : PitchInterval → PitchInterval → MotionError
similar : PitchInterval → PitchInterval → MotionError
motionCheck : PitchInterval → PitchInterval → Maybe MotionError
motionCheck i1 i2 with motion i1 i2 | isPerfect (proj₂ i2)
motionCheck i1 i2 | contrary | _ = nothing
motionCheck i1 i2 | oblique | _ = nothing
motionCheck i1 i2 | parallel | false = nothing
motionCheck i1 i2 | parallel | true = just (parallel i1 i2)
motionCheck i1 i2 | similar | false = nothing
motionCheck i1 i2 | similar | true = just (similar i1 i2)
checkMotion : List PitchInterval → List MotionError
checkMotion = mapMaybe (uncurry motionCheck) ∘ pairs
------------------------------------------------
-- Ending must be the 1st or 8th approached by a cadence
data EndingError : Set where
not18 : PitchInterval → EndingError
not27 : PitchInterval → EndingError
tooShort : List PitchInterval → EndingError
endingCheck : PitchInterval → PitchInterval → Maybe EndingError
endingCheck pi1@(p , i) (q , 0) =
if ((p + 1 == q) ∧ (i == min3)) then nothing else just (not27 pi1)
endingCheck pi1@(p , i) (q , 12) =
if ((q + 2 == p) ∧ (i == maj6) ∨ (p + 1 == q) ∧ (i == min10))
then nothing
else just (not27 pi1)
endingCheck pi1 pi2 =
just (not18 pi2)
checkEnding : List PitchInterval → PitchInterval → Maybe EndingError
checkEnding [] _ = just (tooShort [])
checkEnding (p ∷ []) q = endingCheck p q
checkEnding (p ∷ ps) q = checkEnding ps q
------------------------------------------------
-- Correct first species counterpoint
record FirstSpecies : Set where
constructor firstSpecies
field
firstBar : PitchInterval
middleBars : List PitchInterval
lastBar : PitchInterval
beginningOk : checkBeginning firstBar ≡ nothing
intervalsOk : checkIntervals middleBars ≡ []
motionOk : checkMotion (firstBar ∷ middleBars) ≡ []
-- no need to include the last bar,
-- since endingOK guarantees contrary motion in the ending
endingOk : checkEnding middleBars lastBar ≡ nothing
------------------------------------------------
-- Second Species
PitchInterval2 : Set
PitchInterval2 = Pitch × Upi × Upi
strongBeat : PitchInterval2 → PitchInterval
strongBeat (p , i , _) = p , i
weakBeat : PitchInterval2 → PitchInterval
weakBeat (p , _ , i) = p , i
expandPitchInterval2 : PitchInterval2 → List PitchInterval
expandPitchInterval2 (p , i , j) = (p , i) ∷ (p , j) ∷ []
expandPitchIntervals2 : List PitchInterval2 → List PitchInterval
expandPitchIntervals2 = concatMap expandPitchInterval2
------------------------------------------------
-- Beginning must be the 5th or 8th
data BeginningError2 : Set where
not58 : PitchInterval → BeginningError2
checkBeginning2 : PitchInterval → Maybe BeginningError2
checkBeginning2 pi@(_ , i) =
if ((i == per5) ∨ (i == per8))
then nothing
else just (not58 pi)
checkEnding2 : List PitchInterval2 → PitchInterval → Maybe EndingError
checkEnding2 [] _ = just (tooShort [])
checkEnding2 (p ∷ []) q = endingCheck (weakBeat p) q
checkEnding2 (_ ∷ p ∷ ps) q = checkEnding2 (p ∷ ps) q
------------------------------------------------
-- Strong beats must be consonant and non-unison
checkStrongBeats : List PitchInterval2 → List IntervalError
checkStrongBeats = checkIntervals ∘ map strongBeat
------------------------------------------------
-- Weak beats may be dissonant or unison
checkWeakBeat : PitchInterval2 → Pitch → Maybe IntervalError
checkWeakBeat (p , i , j) q with isConsonant j | isUnison j
checkWeakBeat (p , i , j) q | false | _ =
if isPassingTone (secondPitch (p , i)) (secondPitch (p , j)) q
then nothing
else just (dissonant j)
checkWeakBeat (p , i , j) q | _ | true =
if isOppositeStep (secondPitch (p , i)) (secondPitch (p , j)) q
then nothing
else just (unison p)
checkWeakBeat (p , i , j) q | _ | _ =
nothing
checkWeakBeats : List PitchInterval2 → Pitch → List IntervalError
checkWeakBeats [] p = []
checkWeakBeats pis@(_ ∷ qis) p =
mapMaybe (uncurry checkWeakBeat)
(zip pis
(map (λ {(q , i , j) → proj₂ (pitchIntervalToPitchPair (q , i))}) qis ++ (p ∷ [])))
------------------------------------------------
-- Perfect intervals on strong beats must not be approached by parallel or similar motion
checkMotion2 : List PitchInterval → List MotionError
checkMotion2 [] = []
checkMotion2 (_ ∷ []) = []
checkMotion2 (p ∷ q ∷ ps) = checkMotion (p ∷ q ∷ []) ++ checkMotion2 ps
------------------------------------------------
-- Correct second species counterpoint
record SecondSpecies : Set where
constructor secondSpecies
field
firstBar : PitchInterval -- require counterpont to start with a rest, which is preferred
middleBars : List PitchInterval2
lastBar : PitchInterval -- require counterpoint to end with only a single whole note, which is preferred
beginningOk : checkBeginning2 firstBar ≡ nothing
strongBeatsOk : checkStrongBeats middleBars ≡ []
weakBeatsOk : checkWeakBeats middleBars (secondPitch lastBar) ≡ []
motionOk : checkMotion2 (firstBar ∷ (expandPitchIntervals2 middleBars)) ≡ []
endingOk : checkEnding2 middleBars lastBar ≡ nothing
|
{
"alphanum_fraction": 0.6375049039,
"avg_line_length": 35.9014084507,
"ext": "agda",
"hexsha": "211d10afce5b8e5ebb7a24f17ae2bb8fc67eb27d",
"lang": "Agda",
"max_forks_count": 3,
"max_forks_repo_forks_event_max_datetime": "2020-11-10T04:04:40.000Z",
"max_forks_repo_forks_event_min_datetime": "2019-01-12T17:02:36.000Z",
"max_forks_repo_head_hexsha": "04896c61b603d46011b7d718fcb47dd756e66021",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "halfaya/MusicTools",
"max_forks_repo_path": "agda/Counterpoint.agda",
"max_issues_count": 1,
"max_issues_repo_head_hexsha": "04896c61b603d46011b7d718fcb47dd756e66021",
"max_issues_repo_issues_event_max_datetime": "2020-11-17T00:58:55.000Z",
"max_issues_repo_issues_event_min_datetime": "2020-11-13T01:26:20.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "halfaya/MusicTools",
"max_issues_repo_path": "agda/Counterpoint.agda",
"max_line_length": 114,
"max_stars_count": 28,
"max_stars_repo_head_hexsha": "04896c61b603d46011b7d718fcb47dd756e66021",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "halfaya/MusicTools",
"max_stars_repo_path": "agda/Counterpoint.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-04T18:04:07.000Z",
"max_stars_repo_stars_event_min_datetime": "2017-04-21T09:08:52.000Z",
"num_tokens": 2063,
"size": 7647
}
|
{-# OPTIONS --rewriting #-}
open import Agda.Builtin.Equality
open import Agda.Builtin.Equality.Rewrite
open import Agda.Builtin.Unit
postulate
A : Set
a : A
f : {X : Set} → X → A
g : {X : Set} → A → X
rew-fg : {X : Set} (a : A) → f (g {X} a) ≡ a
{-# REWRITE rew-fg #-}
test : f tt ≡ a
test = refl
|
{
"alphanum_fraction": 0.575562701,
"avg_line_length": 18.2941176471,
"ext": "agda",
"hexsha": "c822bf0bd547bb24aaa580453cf6bcff01b253f2",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "98c9382a59f707c2c97d75919e389fc2a783ac75",
"max_forks_repo_licenses": [
"BSD-2-Clause"
],
"max_forks_repo_name": "KDr2/agda",
"max_forks_repo_path": "test/Fail/Issue5923.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "98c9382a59f707c2c97d75919e389fc2a783ac75",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"BSD-2-Clause"
],
"max_issues_repo_name": "KDr2/agda",
"max_issues_repo_path": "test/Fail/Issue5923.agda",
"max_line_length": 46,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "98c9382a59f707c2c97d75919e389fc2a783ac75",
"max_stars_repo_licenses": [
"BSD-2-Clause"
],
"max_stars_repo_name": "KDr2/agda",
"max_stars_repo_path": "test/Fail/Issue5923.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 121,
"size": 311
}
|
module VecFlip where
open import AgdaPrelude
goodNil : Vec Nat Zero
goodNil = Nil Nat
badNil : Vec Zero Nat
badNil = Nil Nat
|
{
"alphanum_fraction": 0.7519379845,
"avg_line_length": 11.7272727273,
"ext": "agda",
"hexsha": "38a1878175f00ef820335c837ec4e5664ee4b579",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "64a1b4c6632153d75cba540f7c91f40b49375e2f",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "JoeyEremondi/lambda-pi-constraint",
"max_forks_repo_path": "thesisExamples/VecFlip.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "64a1b4c6632153d75cba540f7c91f40b49375e2f",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "JoeyEremondi/lambda-pi-constraint",
"max_issues_repo_path": "thesisExamples/VecFlip.agda",
"max_line_length": 23,
"max_stars_count": 16,
"max_stars_repo_head_hexsha": "64a1b4c6632153d75cba540f7c91f40b49375e2f",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "JoeyEremondi/lambda-pi-constraint",
"max_stars_repo_path": "thesisExamples/VecFlip.agda",
"max_stars_repo_stars_event_max_datetime": "2021-02-05T20:21:46.000Z",
"max_stars_repo_stars_event_min_datetime": "2017-03-16T11:14:56.000Z",
"num_tokens": 38,
"size": 129
}
|
{-# OPTIONS --without-K --rewriting #-}
open import HoTT
module groups.HomSequence where
infix 15 _⊣|ᴳ
infixr 10 _→⟨_⟩ᴳ_
data HomSequence {i} : (G : Group i) (H : Group i) → Type (lsucc i) where
_⊣|ᴳ : (G : Group i) → HomSequence G G
_→⟨_⟩ᴳ_ : (G : Group i) {H K : Group i}
→ (G →ᴳ H) → HomSequence H K
→ HomSequence G K
HomSeq-++ : ∀ {i} {G H K : Group i}
→ HomSequence G H → HomSequence H K → HomSequence G K
HomSeq-++ (_ ⊣|ᴳ) seq = seq
HomSeq-++ (_ →⟨ φ ⟩ᴳ seq₁) seq₂ = _ →⟨ φ ⟩ᴳ HomSeq-++ seq₁ seq₂
HomSeq-snoc : ∀ {i} {G H K : Group i}
→ HomSequence G H → (H →ᴳ K) → HomSequence G K
HomSeq-snoc seq φ = HomSeq-++ seq (_ →⟨ φ ⟩ᴳ _ ⊣|ᴳ)
{- maps between two hom sequences -}
infix 15 _↓|ᴳ
infixr 10 _↓⟨_⟩ᴳ_
data HomSeqMap {i₀ i₁} : {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
→ HomSequence G₀ H₀ → HomSequence G₁ H₁
→ (G₀ →ᴳ G₁) → (H₀ →ᴳ H₁) → Type (lsucc (lmax i₀ i₁)) where
_↓|ᴳ : {G₀ : Group i₀} {G₁ : Group i₁} (ξ : G₀ →ᴳ G₁) → HomSeqMap (G₀ ⊣|ᴳ) (G₁ ⊣|ᴳ) ξ ξ
_↓⟨_⟩ᴳ_ : {G₀ H₀ K₀ : Group i₀} {G₁ H₁ K₁ : Group i₁}
→ {φ : G₀ →ᴳ H₀} {seq₀ : HomSequence H₀ K₀}
→ {ψ : G₁ →ᴳ H₁} {seq₁ : HomSequence H₁ K₁}
→ (ξG : G₀ →ᴳ G₁) {ξH : H₀ →ᴳ H₁} {ξK : K₀ →ᴳ K₁}
→ CommSquareᴳ φ ψ ξG ξH
→ HomSeqMap seq₀ seq₁ ξH ξK
→ HomSeqMap (G₀ →⟨ φ ⟩ᴳ seq₀) (G₁ →⟨ ψ ⟩ᴳ seq₁) ξG ξK
HomSeqMap-snoc : ∀ {i₀ i₁} {G₀ H₀ K₀ : Group i₀} {G₁ H₁ K₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{φ₀ : H₀ →ᴳ K₀} {φ₁ : H₁ →ᴳ K₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁} {ξK : K₀ →ᴳ K₁}
→ HomSeqMap seq₀ seq₁ ξG ξH
→ CommSquareᴳ φ₀ φ₁ ξH ξK
→ HomSeqMap (HomSeq-snoc seq₀ φ₀) (HomSeq-snoc seq₁ φ₁) ξG ξK
HomSeqMap-snoc (ξG ↓|ᴳ) □ = ξG ↓⟨ □ ⟩ᴳ _ ↓|ᴳ
HomSeqMap-snoc (ξG ↓⟨ □₁ ⟩ᴳ seq) □₂ = ξG ↓⟨ □₁ ⟩ᴳ HomSeqMap-snoc seq □₂
{- equivalences between two hom sequences -}
is-seqᴳ-equiv : ∀ {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁}
→ HomSeqMap seq₀ seq₁ ξG ξH
→ Type (lmax i₀ i₁)
is-seqᴳ-equiv (ξ ↓|ᴳ) = is-equiv (GroupHom.f ξ)
is-seqᴳ-equiv (ξ ↓⟨ _ ⟩ᴳ seq) = is-equiv (GroupHom.f ξ) × is-seqᴳ-equiv seq
is-seqᴳ-equiv-snoc : ∀ {i₀ i₁} {G₀ H₀ K₀ : Group i₀} {G₁ H₁ K₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{φ₀ : H₀ →ᴳ K₀} {φ₁ : H₁ →ᴳ K₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁} {ξK : K₀ →ᴳ K₁}
{seq-map : HomSeqMap seq₀ seq₁ ξG ξH}
{cs : CommSquareᴳ φ₀ φ₁ ξH ξK}
→ is-seqᴳ-equiv seq-map → is-equiv (GroupHom.f ξK)
→ is-seqᴳ-equiv (HomSeqMap-snoc seq-map cs)
is-seqᴳ-equiv-snoc {seq-map = ξG ↓|ᴳ} ξG-is-equiv ξH-is-equiv = ξG-is-equiv , ξH-is-equiv
is-seqᴳ-equiv-snoc {seq-map = ξG ↓⟨ _ ⟩ᴳ seq} (ξG-is-equiv , seq-is-equiv) ξH-is-equiv =
ξG-is-equiv , is-seqᴳ-equiv-snoc seq-is-equiv ξH-is-equiv
private
is-seqᴳ-equiv-head : ∀ {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁}
{seq-map : HomSeqMap seq₀ seq₁ ξG ξH}
→ is-seqᴳ-equiv seq-map → is-equiv (GroupHom.f ξG)
is-seqᴳ-equiv-head {seq-map = ξ ↓|ᴳ} ise = ise
is-seqᴳ-equiv-head {seq-map = ξ ↓⟨ _ ⟩ᴳ _} ise = fst ise
is-seqᴳ-equiv-last : ∀ {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁}
{seq-map : HomSeqMap seq₀ seq₁ ξG ξH}
→ is-seqᴳ-equiv seq-map → is-equiv (GroupHom.f ξH)
is-seqᴳ-equiv-last {seq-map = ξ ↓|ᴳ} ise = ise
is-seqᴳ-equiv-last {seq-map = _ ↓⟨ _ ⟩ᴳ rest} (_ , rest-ise) = is-seqᴳ-equiv-last rest-ise
module is-seqᴳ-equiv {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁}
{seq-map : HomSeqMap seq₀ seq₁ ξG ξH}
(seq-map-is-equiv : is-seqᴳ-equiv seq-map) where
head = is-seqᴳ-equiv-head seq-map-is-equiv
last = is-seqᴳ-equiv-last seq-map-is-equiv
HomSeqEquiv : ∀ {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
(seq₀ : HomSequence G₀ H₀) (seq₁ : HomSequence G₁ H₁)
(ξG : G₀ →ᴳ G₁) (ξH : H₀ →ᴳ H₁) → Type (lsucc (lmax i₀ i₁))
HomSeqEquiv seq₀ seq₁ ξG ξH = Σ (HomSeqMap seq₀ seq₁ ξG ξH) is-seqᴳ-equiv
HomSeqEquiv-inverse : ∀ {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁}
(equiv : HomSeqEquiv seq₀ seq₁ ξG ξH)
→ HomSeqEquiv seq₁ seq₀
(GroupIso.g-hom (ξG , is-seqᴳ-equiv-head (snd equiv)))
(GroupIso.g-hom (ξH , is-seqᴳ-equiv-last (snd equiv)))
HomSeqEquiv-inverse ((ξ ↓|ᴳ) , ξ-ise) =
(GroupIso.g-hom (ξ , ξ-ise) ↓|ᴳ) , is-equiv-inverse ξ-ise
HomSeqEquiv-inverse ((ξ ↓⟨ □ ⟩ᴳ rest) , (ξ-ise , rest-ise)) =
(GroupIso.g-hom (ξ , ξ-ise)
↓⟨ CommSquareᴳ-inverse-v □ ξ-ise (is-seqᴳ-equiv-head rest-ise) ⟩ᴳ
fst rest-inverse-equiv) ,
is-equiv-inverse ξ-ise , snd rest-inverse-equiv
where
rest-inverse-equiv = HomSeqEquiv-inverse (rest , rest-ise)
{- Doesn't seem useful.
infix 15 _↕|ᴳ
infixr 10 _↕⟨_⟩ᴳ_
_↕|ᴳ : ∀ {i} {G₀ G₁ : Group i} (iso : G₀ ≃ᴳ G₁)
→ HomSeqEquiv (G₀ ⊣|ᴳ) (G₁ ⊣|ᴳ) (fst iso) (fst iso)
iso ↕|ᴳ = (fst iso ↓|ᴳ) , snd iso
_↕⟨_⟩ᴳ_ : ∀ {i} {G₀ G₁ H₀ H₁ K₀ K₁ : Group i}
→ {φ : G₀ →ᴳ H₀} {seq₀ : HomSequence H₀ K₀}
→ {ψ : G₁ →ᴳ H₁} {seq₁ : HomSequence H₁ K₁}
→ (isoG : G₀ ≃ᴳ G₁) {isoH : H₀ ≃ᴳ H₁} {isoK : K₀ ≃ᴳ K₁}
→ HomCommSquare φ ψ (fst isoG) (fst isoH)
→ HomSeqEquiv seq₀ seq₁ (fst isoH) (fst isoK)
→ HomSeqEquiv (G₀ →⟨ φ ⟩ᴳ seq₀) (G₁ →⟨ ψ ⟩ᴳ seq₁) (fst isoG) (fst isoK)
(ξG , hG-is-equiv) ↕⟨ sqr ⟩ᴳ (seq-map , seq-map-is-equiv) =
(ξG ↓⟨ sqr ⟩ᴳ seq-map) , hG-is-equiv , seq-map-is-equiv
-}
private
hom-seq-map-index-type : ∀ {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁}
→ ℕ → HomSeqMap seq₀ seq₁ ξG ξH → Type (lmax i₀ i₁)
hom-seq-map-index-type _ (_ ↓|ᴳ) = Lift ⊤
hom-seq-map-index-type O (_↓⟨_⟩ᴳ_ {φ = φ} {ψ = ψ} ξG {ξH} _ _)
= CommSquareᴳ φ ψ ξG ξH
hom-seq-map-index-type (S n) (_ ↓⟨ _ ⟩ᴳ seq-map)
= hom-seq-map-index-type n seq-map
abstract
hom-seq-map-index : ∀ {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁}
(n : ℕ) (seq-map : HomSeqMap seq₀ seq₁ ξG ξH)
→ hom-seq-map-index-type n seq-map
hom-seq-map-index _ (_ ↓|ᴳ) = lift tt
hom-seq-map-index O (_ ↓⟨ □ ⟩ᴳ _) = □
hom-seq-map-index (S n) (_ ↓⟨ _ ⟩ᴳ seq-map)
= hom-seq-map-index n seq-map
private
hom-seq-equiv-index-type : ∀ {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁}
→ ℕ → HomSeqMap seq₀ seq₁ ξG ξH → Type (lmax i₀ i₁)
hom-seq-equiv-index-type {ξG = ξG} O _ = is-equiv (GroupHom.f ξG)
hom-seq-equiv-index-type (S _) (_ ↓|ᴳ) = Lift ⊤
hom-seq-equiv-index-type (S n) (_ ↓⟨ _ ⟩ᴳ seq-map)
= hom-seq-equiv-index-type n seq-map
abstract
hom-seq-equiv-index : ∀ {i₀ i₁} {G₀ H₀ : Group i₀} {G₁ H₁ : Group i₁}
{seq₀ : HomSequence G₀ H₀} {seq₁ : HomSequence G₁ H₁}
{ξG : G₀ →ᴳ G₁} {ξH : H₀ →ᴳ H₁}
(n : ℕ) (seq-equiv : HomSeqEquiv seq₀ seq₁ ξG ξH)
→ hom-seq-equiv-index-type n (fst seq-equiv)
hom-seq-equiv-index O (seq-map , ise) = is-seqᴳ-equiv-head ise
hom-seq-equiv-index (S _) ((_ ↓|ᴳ) , _) = lift tt
hom-seq-equiv-index (S n) ((_ ↓⟨ _ ⟩ᴳ seq-map) , ise)
= hom-seq-equiv-index n (seq-map , snd ise)
|
{
"alphanum_fraction": 0.5927419355,
"avg_line_length": 40.4347826087,
"ext": "agda",
"hexsha": "57a8b8e2c0920ed035bb69bc78b745728dcca12c",
"lang": "Agda",
"max_forks_count": 50,
"max_forks_repo_forks_event_max_datetime": "2022-02-14T03:03:25.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-10T01:48:08.000Z",
"max_forks_repo_head_hexsha": "66f800adef943afdf08c17b8ecfba67340fead5e",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "timjb/HoTT-Agda",
"max_forks_repo_path": "theorems/groups/HomSequence.agda",
"max_issues_count": 31,
"max_issues_repo_head_hexsha": "66f800adef943afdf08c17b8ecfba67340fead5e",
"max_issues_repo_issues_event_max_datetime": "2021-10-03T19:15:25.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-03-05T20:09:00.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "timjb/HoTT-Agda",
"max_issues_repo_path": "theorems/groups/HomSequence.agda",
"max_line_length": 92,
"max_stars_count": 294,
"max_stars_repo_head_hexsha": "66f800adef943afdf08c17b8ecfba67340fead5e",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "timjb/HoTT-Agda",
"max_stars_repo_path": "theorems/groups/HomSequence.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-20T13:54:45.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T16:23:23.000Z",
"num_tokens": 3765,
"size": 7440
}
|
------------------------------------------------------------------------------
-- Conversion rules for inequalities
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module LTC-PCF.Data.Nat.Inequalities.ConversionRules where
open import Common.FOL.Relation.Binary.EqReasoning
open import LTC-PCF.Base
open import LTC-PCF.Data.Nat.Inequalities
------------------------------------------------------------------------------
private
-- Before to prove some properties for lt it is convenient
-- to descompose the behavior of the function step by step.
-- Initially, we define the possible states (lt-s₁,
-- lt-s₂, ...). Then we write down the proof for
-- the execution step from the state p to the state q, e.g.
--
-- proof₁→proof₂ : ∀ m n → lt-s₂ m n → lt-s₃ m n.
-- The terms lt-00, lt-0S, lt-S0 and lt-SS show the use of the
-- states lt-s₁, lt-s₂, ..., and the proofs associated with the
-- execution steps.
----------------------------------------------------------------------
-- The steps of lt.
-- Initially, the conversion rule fix-eq is applied.
lt-s₁ : D → D → D
lt-s₁ m n = lth (fix lth) · m · n
-- First argument application.
lt-s₂ : D → D
lt-s₂ m = lam (λ n →
if (iszero₁ n)
then false
else (if (iszero₁ m)
then true
else (fix lth · pred₁ m · pred₁ n)))
-- Second argument application.
lt-s₃ : D → D → D
lt-s₃ m n = if (iszero₁ n)
then false
else (if (iszero₁ m)
then true
else (fix lth · pred₁ m · pred₁ n))
-- Reduction iszero₁ n ≡ b.
lt-s₄ : D → D → D → D
lt-s₄ m n b = if b
then false
else (if (iszero₁ m)
then true
else (fix lth · pred₁ m · pred₁ n))
-- Reduction iszero₁ n ≡ true.
-- It should be
-- lt-s₅ : D → D → D
-- lt-s₅ m n = false
-- but we do not give a name to this step.
-- Reduction iszero₁ n ≡ false.
lt-s₅ : D → D → D
lt-s₅ m n = if (iszero₁ m) then true else (fix lth · pred₁ m · pred₁ n)
-- Reduction iszero₁ m ≡ b.
lt-s₆ : D → D → D → D
lt-s₆ m n b = if b then true else (fix lth · pred₁ m · pred₁ n)
-- Reduction iszero₁ m ≡ true.
-- It should be
-- lt-s₇ : D → D → D
-- lt-s₇ m n = true
-- but we do not give a name to this step.
-- Reduction iszero₁ m ≡ false.
lt-s₇ : D → D → D
lt-s₇ m n = fix lth · pred₁ m · pred₁ n
-- Reduction pred₁ (succ m) ≡ m.
lt-s₈ : D → D → D
lt-s₈ m n = fix lth · m · pred₁ n
-- Reduction pred₁ (succ n) ≡ n.
lt-s₉ : D → D → D
lt-s₉ m n = fix lth · m · n
----------------------------------------------------------------------
-- The execution steps
{-
To prove the execution steps, e.g.
proof₃→proof₄ : ∀ m n → lt-s₃ m n → lt-s₄ m n)
we usually need to prove that
C [m] ≡ C [n] (1)
given that
m ≡ n, (2)
where (2) is a conversion rule usually.
We prove (1) using
subst : ∀ {x y} (A : D → Set) → x ≡ y → A x → A y
where
• P is given by λ t → C [m] ≡ C [t],
• x ≡ y is given m ≡ n and
• P x is given by C [m] ≡ C [m] (i.e. refl).
-}
-- Application of the conversion rule fix-eq.
proof₀₋₁ : ∀ m n → fix lth · m · n ≡ lt-s₁ m n
proof₀₋₁ m n = subst (λ x → x · m · n ≡ lth (fix lth) · m · n)
(sym (fix-eq lth))
refl
-- Application of the first argument.
proof₁₋₂ : ∀ m n → lt-s₁ m n ≡ lt-s₂ m · n
proof₁₋₂ m n = subst (λ x → x · n ≡ lt-s₂ m · n)
(sym (beta lt-s₂ m))
refl
-- Application of the second argument.
proof₂₋₃ : ∀ m n → lt-s₂ m · n ≡ lt-s₃ m n
proof₂₋₃ m n = beta (lt-s₃ m) n
-- Reduction iszero n ≡ b using that proof.
proof₃₋₄ : ∀ m n b → iszero₁ n ≡ b → lt-s₃ m n ≡ lt-s₄ m n b
proof₃₋₄ m n .(iszero₁ n) refl = refl
-- Reduction of iszero₁ n ≡ true using the conversion rule if-true.
proof₄₊ : ∀ m n → lt-s₄ m n true ≡ false
proof₄₊ m n = if-true false
-- Reduction of iszero₁ n ≡ false ... using the conversion rule
-- if-false.
proof₄₋₅ : ∀ m n → lt-s₄ m n false ≡ lt-s₅ m n
proof₄₋₅ m n = if-false (lt-s₅ m n)
-- Reduction iszero₁ m ≡ b using that proof.
proof₅₋₆ : ∀ m n b → iszero₁ m ≡ b → lt-s₅ m n ≡ lt-s₆ m n b
proof₅₋₆ m n .(iszero₁ m) refl = refl
-- Reduction of iszero₁ m ≡ true using the conversion rule if-true.
proof₆₊ : ∀ m n → lt-s₆ m n true ≡ true
proof₆₊ m n = if-true true
-- Reduction of iszero₁ m ≡ false ... using the conversion rule
-- if-false.
proof₆₋₇ : ∀ m n → lt-s₆ m n false ≡ lt-s₇ m n
proof₆₋₇ m n = if-false (lt-s₇ m n)
-- Reduction pred (succ m) ≡ m using the conversion rule pred-S.
proof₇₋₈ : ∀ m n → lt-s₇ (succ₁ m) n ≡ lt-s₈ m n
proof₇₋₈ m n = subst (λ x → lt-s₈ x n ≡ lt-s₈ m n)
(sym (pred-S m))
refl
-- Reduction pred (succ n) ≡ n using the conversion rule pred-S.
proof₈₋₉ : ∀ m n → lt-s₈ m (succ₁ n) ≡ lt-s₉ m n
proof₈₋₉ m n = subst (λ x → lt-s₉ m x ≡ lt-s₉ m n)
(sym (pred-S n))
refl
------------------------------------------------------------------------------
private
X≮0 : ∀ n → n ≮ zero
X≮0 n = fix lth · n · zero ≡⟨ proof₀₋₁ n zero ⟩
lt-s₁ n zero ≡⟨ proof₁₋₂ n zero ⟩
lt-s₂ n · zero ≡⟨ proof₂₋₃ n zero ⟩
lt-s₃ n zero ≡⟨ proof₃₋₄ n zero true iszero-0 ⟩
lt-s₄ n zero true ≡⟨ proof₄₊ n zero ⟩
false ∎
lt-00 : zero ≮ zero
lt-00 = X≮0 zero
lt-0S : ∀ n → zero < succ₁ n
lt-0S n =
fix lth · zero · (succ₁ n) ≡⟨ proof₀₋₁ zero (succ₁ n) ⟩
lt-s₁ zero (succ₁ n) ≡⟨ proof₁₋₂ zero (succ₁ n) ⟩
lt-s₂ zero · (succ₁ n) ≡⟨ proof₂₋₃ zero (succ₁ n) ⟩
lt-s₃ zero (succ₁ n) ≡⟨ proof₃₋₄ zero (succ₁ n) false (iszero-S n) ⟩
lt-s₄ zero (succ₁ n) false ≡⟨ proof₄₋₅ zero (succ₁ n) ⟩
lt-s₅ zero (succ₁ n) ≡⟨ proof₅₋₆ zero (succ₁ n) true iszero-0 ⟩
lt-s₆ zero (succ₁ n) true ≡⟨ proof₆₊ zero (succ₁ n) ⟩
true ∎
lt-S0 : ∀ n → succ₁ n ≮ zero
lt-S0 n = X≮0 (succ₁ n)
lt-SS : ∀ m n → lt (succ₁ m) (succ₁ n) ≡ lt m n
lt-SS m n =
fix lth · (succ₁ m) · (succ₁ n) ≡⟨ proof₀₋₁ (succ₁ m) (succ₁ n) ⟩
lt-s₁ (succ₁ m) (succ₁ n) ≡⟨ proof₁₋₂ (succ₁ m) (succ₁ n) ⟩
lt-s₂ (succ₁ m) · (succ₁ n) ≡⟨ proof₂₋₃ (succ₁ m) (succ₁ n) ⟩
lt-s₃ (succ₁ m) (succ₁ n) ≡⟨ proof₃₋₄ (succ₁ m) (succ₁ n) false (iszero-S n) ⟩
lt-s₄ (succ₁ m) (succ₁ n) false ≡⟨ proof₄₋₅ (succ₁ m) (succ₁ n) ⟩
lt-s₅ (succ₁ m) (succ₁ n) ≡⟨ proof₅₋₆ (succ₁ m) (succ₁ n) false (iszero-S m) ⟩
lt-s₆ (succ₁ m) (succ₁ n) false ≡⟨ proof₆₋₇ (succ₁ m) (succ₁ n) ⟩
lt-s₇ (succ₁ m) (succ₁ n) ≡⟨ proof₇₋₈ m (succ₁ n) ⟩
lt-s₈ m (succ₁ n) ≡⟨ proof₈₋₉ m n ⟩
lt-s₉ m n ∎
|
{
"alphanum_fraction": 0.4847649249,
"avg_line_length": 32.6711711712,
"ext": "agda",
"hexsha": "912056fc1d84ae0339931ae237fc7032f4a1e9d6",
"lang": "Agda",
"max_forks_count": 3,
"max_forks_repo_forks_event_max_datetime": "2018-03-14T08:50:00.000Z",
"max_forks_repo_forks_event_min_datetime": "2016-09-19T14:18:30.000Z",
"max_forks_repo_head_hexsha": "2fc9f2b81052a2e0822669f02036c5750371b72d",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "asr/fotc",
"max_forks_repo_path": "src/fot/LTC-PCF/Data/Nat/Inequalities/ConversionRules.agda",
"max_issues_count": 2,
"max_issues_repo_head_hexsha": "2fc9f2b81052a2e0822669f02036c5750371b72d",
"max_issues_repo_issues_event_max_datetime": "2017-01-01T14:34:26.000Z",
"max_issues_repo_issues_event_min_datetime": "2016-10-12T17:28:16.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "asr/fotc",
"max_issues_repo_path": "src/fot/LTC-PCF/Data/Nat/Inequalities/ConversionRules.agda",
"max_line_length": 87,
"max_stars_count": 11,
"max_stars_repo_head_hexsha": "2fc9f2b81052a2e0822669f02036c5750371b72d",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "asr/fotc",
"max_stars_repo_path": "src/fot/LTC-PCF/Data/Nat/Inequalities/ConversionRules.agda",
"max_stars_repo_stars_event_max_datetime": "2021-09-12T16:09:54.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-09-03T20:53:42.000Z",
"num_tokens": 2687,
"size": 7253
}
|
--{-# OPTIONS --with-K #-}
open import Data
open import Data.Tuple using (_⨯_ ; _,_)
open import Logic.Predicate
import Lvl
open import Syntax.Number
import Type as Meta
-- `Constants` is the type of all possible constant terms.
-- `Sort` is a subset of `Constants` that indicate the sorts of the type system (the types of types).
-- `Axioms` pairs constant terms with types.
-- `Rules` pairs product terms with types.
module Formalization.PureTypeSystem (Constants : Meta.Type{0}) where -- TODO: I don't really have a reference for any of the definitions so they may be incorrect
open import Numeral.Natural
open import Numeral.Finite
private variable ℓ ℓ₁ ℓ₂ ℓ₃ : Lvl.Level
private variable d d₁ d₂ d₃ : ℕ
data Term : ℕ → Meta.Type{0} where
Apply : Term(d) → Term(d) → Term(d)
Abstract : Term(d) → Term(𝐒(d)) → Term(d)
Var : 𝕟(d) → Term(d)
Constant : Constants → Term(d)
Product : Term(d) → Term(𝐒(d)) → Term(d)
Expression : Meta.Type{0}
Expression = Term(0)
module VarNumeralSyntax where
-- Syntax for writing Var as a numeral.
instance
Term-from-ℕ : ∀{N} → Numeral(Term(N))
Numeral.restriction-ℓ ( Term-from-ℕ {N} ) = Numeral.restriction-ℓ ( 𝕟-from-ℕ {N} )
Numeral.restriction ( Term-from-ℕ {N} ) = Numeral.restriction ( 𝕟-from-ℕ {N} )
num ⦃ Term-from-ℕ {N} ⦄ (n) ⦃ proof ⦄ = Var(num n)
module ExplicitLambdaSyntax where
open VarNumeralSyntax public
infixr 100 𝜆[_::_] Π[_::_]
infixl 101 _←_
pattern 𝜆[_::_] d type expr = Term.Abstract{d} type expr
pattern Π[_::_] d type expr = Term.Product{d} type expr
pattern _←_ a b = Term.Apply a b
module _ where
var-𝐒 : Term(d) → Term(𝐒(d))
var-𝐒 (Apply f x) = Apply (var-𝐒(f)) (var-𝐒(x))
var-𝐒 (Abstract{d} type body) = Abstract{𝐒(d)} (var-𝐒 type) (var-𝐒(body))
var-𝐒 (Var{𝐒(d)} n) = Var{𝐒(𝐒(d))} (𝐒(n))
var-𝐒 (Constant c) = Constant c
var-𝐒 (Product a b) = Product (var-𝐒 a) (var-𝐒 b)
substituteVar0 : Term(d) → Term(𝐒(d)) → Term(d)
substituteVar0 val (Apply f x) = Apply (substituteVar0 val f) (substituteVar0 val x)
substituteVar0 val (Abstract type body) = Abstract (substituteVar0 val type) (substituteVar0 (var-𝐒 val) body)
substituteVar0 val (Var 𝟎) = val
substituteVar0 val (Var(𝐒 i)) = Var i
substituteVar0 val (Constant c) = Constant c
substituteVar0 val (Product a b) = Product (substituteVar0 val a) (substituteVar0 (var-𝐒 val) b)
open import Relator.Equals
private variable x y : Term(d)
substituteVar0-var-𝐒 : (substituteVar0 y (var-𝐒 x) ≡ x)
substituteVar0-var-𝐒 {d}{y}{Apply f x}
rewrite substituteVar0-var-𝐒 {d}{y}{f}
rewrite substituteVar0-var-𝐒 {d}{y}{x}
= [≡]-intro
substituteVar0-var-𝐒 {d}{y}{Abstract t x}
rewrite substituteVar0-var-𝐒 {d}{y}{t}
rewrite substituteVar0-var-𝐒 {𝐒 d}{var-𝐒 y}{x}
= [≡]-intro
substituteVar0-var-𝐒 {_}{_}{Var 𝟎} = [≡]-intro
substituteVar0-var-𝐒 {_}{_}{Var(𝐒 _)} = [≡]-intro
substituteVar0-var-𝐒 {_}{_}{Constant c} = [≡]-intro
substituteVar0-var-𝐒 {d}{y}{Product t x}
rewrite substituteVar0-var-𝐒 {d}{y}{t}
rewrite substituteVar0-var-𝐒 {𝐒 d}{var-𝐒 y}{x}
= [≡]-intro
{-# REWRITE substituteVar0-var-𝐒 #-}
module _ where
-- postulate _β⥈*_ : Term(d) → Term(d) → Meta.Type{0}
open import Relator.ReflexiveTransitiveClosure
private variable f g x y : Term(d)
-- β-reduction (beta) with its compatible closure over `Apply`.
-- Reduces a term of form `f(x)` to `f[0 ≔ x]`.
data _β⇴_ : Term(d₁) → Term(d₂) → Meta.Type{1} where
β : ∀{f : Term(𝐒(d))}{x ty : Term(d)} → (Apply(Abstract ty (f))(x) β⇴ substituteVar0(x)(f))
cong-applyₗ : (f β⇴ g) → (Apply f(x) β⇴ Apply g(x))
cong-applyᵣ : (x β⇴ y) → (Apply f(x) β⇴ Apply f(y))
_β⇴*_ : Term(d) → Term(d) → Meta.Type
_β⇴*_ = ReflexiveTransitiveClosure(_β⇴_)
_β⥈_ : Term(d) → Term(d) → Meta.Type
_β⥈_ = SymmetricClosure(_β⇴_)
_β⥈*_ : Term(d) → Term(d) → Meta.Type
_β⥈*_ = ReflexiveTransitiveClosure(_β⥈_)
{-
module _ where
open import Data.Boolean
open import Data.Boolean.Stmt
open import Data.Option
import Data.Option.Functions as Option
open import Logic.Propositional
open import Functional
private variable T A B : Meta.Type{ℓ}
private variable x : A
private variable y : B
private variable m m₁ m₂ : T
private variable f : A → B
open import Relator.Equals
record MapContainer (A : Meta.Type{ℓ₁}) (B : A → Meta.Type{ℓ₂}) (Map : Meta.Type{ℓ₃}) : Meta.Type{Lvl.𝐒(ℓ₁) Lvl.⊔ Lvl.𝐒(ℓ₂) Lvl.⊔ ℓ₃} where
field
∅ : Map
has : A → Map → Bool
get : (a : A) → Map → Option(B(a))
set : (a : A) → B(a) → Map → Map
unset : A → Map → Map
union : Map → Map → Map
-- map : (B → B) → (Map → Map)
_⊆_ : Map → Map → Meta.Type{0}
_≡ₘ_ : Map → Map → Meta.Type{0}
field
get-of-∅ : (get x ∅ ≡ None)
get-has : (Option.isSome(get x m) ≡ has x m)
get-of-set : (get x (set x y m) ≡ Some(y))
get-of-unset : (get x (unset x m) ≡ None)
get-of-union : (get x (union m₁ m₂) ≡ (get x m₁) Option.Same.orᵣ (get x m₂))
-- get-of-map : (get x (map f m) ≡ Option.map f(get x m))
submap-get : (m₁ ⊆ m₂) ↔ (∀{x} → (IsFalse(has x m₁) ∨ (get x m₁ ≡ get x m₂)))
equiv-get : (m₁ ≡ₘ m₂) ↔ (∀{x} → (get x m₁ ≡ get x m₂))
-}
open import Numeral.CoordinateVector
open import Type.Dependent
module Typing
(Sort : ∀{d} → Term(d) → Meta.Type{0})
(Axioms : Constants → Expression → Meta.Type{0})
(Rules : ∀{d₁ d₂ d₃} → ∃(Sort{d₁}) → ∃(Sort{d₂}) → ∃(Sort{d₃}) → Meta.Type{0})
where
data Context : ℕ → Meta.Type{0} where
∅ : Context(𝟎)
_⊱_ : Context(d) → Term(d) → Context(𝐒(d))
get : (i : 𝕟(𝐒(d))) → Context(𝐒(d)) → Term(d)
get 𝟎 (_ ⊱ x) = x
get {𝐒 _} (𝐒 i) (l ⊱ _) = var-𝐒(get i l)
private variable A A₁ A₂ B B₁ B₂ F F₁ F₂ X X₁ X₂ BX T T₁ T₂ : Term(d)
private variable c : Constants
private variable i i₁ i₂ : 𝕟(d)
private variable s s₁ s₂ s₃ : ∃(Sort)
private variable Γ Δ : Context(d)
-- Subtyping rules.
_<:_ = _β⥈*_
open import Data.Option
open import Relator.Equals
-- Typing rules. (TODO: I think there are some issues with the depth indexing)
data _⊢_::_ : Context(d₁) → Term(d₂) → Term(d₃) → Meta.Type{1} where
constants : (Axioms c A) → (Γ ⊢ (Constant{d₂} c) :: A)
variables : (Γ ⊢ (get i Γ) :: ([∃]-witness s)) → (Γ ⊢ (Var i) :: (get i Γ))
weakening : (Γ ⊢ B :: ([∃]-witness s)) → (Γ ⊢ X :: A) → ((Γ ⊱ B) ⊢ X :: A)
product : (Rules s₁ s₂ s₃) → (Γ ⊢ A :: ([∃]-witness s₁)) → ((Γ ⊱ A) ⊢ B :: ([∃]-witness s₂)) → (Γ ⊢ (Product A B) :: ([∃]-witness s₃))
application : (Γ ⊢ F :: Product A B) → (Γ ⊢ X :: A) → (Γ ⊢ Apply F X :: substituteVar0 X B)
abstraction : (Γ ⊢ (Product A B) :: ([∃]-witness s)) → ((Γ ⊱ A) ⊢ F :: B) → (Γ ⊢ (Abstract A F) :: (Product A B))
-- conversion : (Γ ⊢ B :: Constant([∃]-witness s)) → (A <: B) → (Γ ⊢ X :: A) → (Γ ⊢ X :: B)
{-
3: 6
4: 7
0: 3
1: 4
𝕟-to-ℕ (Wrapping.[−] i₁) ≡ 𝕟-to-ℕ (Wrapping.[−] i₂)
-}
data _≡d_ : Term(d₁) → Term(d₂) → Meta.Type{0} where
application : (F₁ ≡d F₂) → (X₁ ≡d X₂) → (Apply F₁ X₁ ≡d Apply F₂ X₂)
abstraction : (T₁ ≡d T₂) → (B₁ ≡d B₂) → Abstract T₁ B₁ ≡d Abstract T₂ B₂
var-left : (Var{𝐒(d₁)} {!d₁ −₀ d₂!} ≡d Var{𝐒(d₂)} 𝟎)
var-right : (Var{𝐒(d₁)} 𝟎 ≡d Var{𝐒(d₂)} {!d₁ −₀ d₂!})
var-step : (Var i₁ ≡d Var i₂) → (Var(𝐒(i₁)) ≡d Var(𝐒(i₂)))
constant : Constant{d₁} c ≡d Constant{d₂} c
product : (A₁ ≡d A₂) → (B₁ ≡d B₂) → Product A₁ B₁ ≡d Product A₂ B₂
open import Logic.Propositional
open import Syntax.Function
open import Type.Dependent.Functions
-- typing-substitution : ((set Var0 B (Γ ∪ Δ)) ⊢ A :: B) → ((Γ ∪ map(\(intro e p) → {!substituteVar0 X p!}) Δ) ⊢ (substituteVar0 X A) :: (substituteVar0 X B))
import Data.Either as Either
open import Logic.Classical
module _
⦃ classical-sort : ∀{d}{c} → Classical(Sort{d} c) ⦄
-- (axioms-term-or-sort : ∀{A B} → (Axioms A B) → (Sort(B) ∨ ∃(d ↦ ∃{Obj = ∃(Sort{d})}(s ↦ Γ ⊢ B :: ([∃]-witness s)))))
where
sort-substituteVar0 : Sort(X) → Sort(A) → Sort(substituteVar0 X A)
sort-substituteVar0 {A = Apply F X} _ sort-A = {!!}
sort-substituteVar0 {A = Abstract T B} _ sort-A = {!!}
sort-substituteVar0 {A = Var 𝟎} sort-X sort-A = sort-X
sort-substituteVar0 {A = Var (𝐒 i)} _ sort-A = {!!}
sort-substituteVar0 {A = Constant c} _ sort-A = {!sort-A!}
sort-substituteVar0 {A = Product A B} _ sort-A = {!!}
-- When a term has a type, the type is either a sort or its type is a sort.
type-is-term-or-sort : (Γ ⊢ A :: B) → (Sort(B) ∨ ∃{Obj = ∃(d ↦ ∃(Sort{d}))}(s ↦ Γ ⊢ B :: ([∃]-witness([∃]-proof s))))
type-is-term-or-sort (constants {c} axiom) = {!!}
type-is-term-or-sort (variables {s = s} ty) = [∨]-introᵣ ([∃]-intro ([∃]-intro _ ⦃ s ⦄) ⦃ ty ⦄)
type-is-term-or-sort (weakening{s = s} pre post) = Either.mapRight ([∃]-map-proof (weakening{s = s} pre)) (type-is-term-or-sort post)
type-is-term-or-sort (product{s₃ = s₃} r a b) = [∨]-introₗ ([∃]-proof s₃)
type-is-term-or-sort (application {F = F} ab a) = {!!}
type-is-term-or-sort (abstraction{s = s} ab f) = [∨]-introᵣ ([∃]-intro ([∃]-intro _ ⦃ s ⦄) ⦃ ab ⦄)
{-type-is-term-or-sort (constants {c} axiom) = ? -- axioms-term-or-sort axiom
type-is-term-or-sort (variables {s = s} ty) = [∨]-introᵣ {!!}
type-is-term-or-sort (product{s₃ = s₃} r a b) = [∨]-introₗ ([∃]-proof s₃)
type-is-term-or-sort (application {F = Apply F F₁} ab a) = {!!}
type-is-term-or-sort (application {F = Abstract F F₁} (abstraction ab ab₁) a) = {!!}
type-is-term-or-sort (application {F = Constant x} ab a) = {!!}
type-is-term-or-sort (application {F = Product F F₁} ab a) = {!!}
type-is-term-or-sort (abstraction{s = s} ab f) = [∨]-introᵣ ([∃]-intro s ⦃ ab ⦄)
-}
-- A supermap of the context have the same typings.
-- typing-supercontext : (Γ ⊆ Δ) → ((Γ ⊢ A :: B) → (Δ ⊢ A :: B))
-- TODO: Confluence, subject reduction
open import Data.Option.Equiv.Id
open import Data.Option.Proofs
open import Relator.Equals.Proofs
open import Structure.Function
open import Structure.Function.Domain hiding (Constant)
open import Structure.Relator.Properties
open import Structure.Setoid.Uniqueness
open import Syntax.Transitivity
instance
Constant-injective : Injective(Constant{d})
Injective.proof Constant-injective [≡]-intro = [≡]-intro
instance
Var-injective : Injective(Var{d})
Injective.proof Var-injective [≡]-intro = [≡]-intro
Productₗ-injective : ∀{ty₁ ty₂}{f₁ f₂} → (Product{d} ty₁ f₁ ≡ Product{d} ty₂ f₂) → (ty₁ ≡ ty₂)
Productₗ-injective [≡]-intro = [≡]-intro
Productᵣ-injective : ∀{ty₁ ty₂}{f₁ f₂} → (Product{d} ty₁ f₁ ≡ Product{d} ty₂ f₂) → (f₁ ≡ f₂) -- TODO: Here is an example of what axiom K does. If one had `Product ty f₁ ≡ Product ty f₂` instead, then it cannot pattern match on the identity because of `ty` being the same on both sides.
Productᵣ-injective [≡]-intro = [≡]-intro
Applyₗ-injective : ∀{f₁ f₂}{x₁ x₂} → (Apply{d} f₁ x₁ ≡ Apply{d} f₂ x₂) → (f₁ ≡ f₂)
Applyₗ-injective [≡]-intro = [≡]-intro
Applyᵣ-injective : ∀{f₁ f₂}{x₁ x₂} → (Apply{d} f₁ x₁ ≡ Apply{d} f₂ x₂) → (x₁ ≡ x₂)
Applyᵣ-injective [≡]-intro = [≡]-intro
Abstractₗ-injective : ∀{T₁ T₂}{body₁ body₂} → (Abstract{d} T₁ body₁ ≡ Abstract{d} T₂ body₂) → (T₁ ≡ T₂)
Abstractₗ-injective [≡]-intro = [≡]-intro
Abstractᵣ-injective : ∀{T₁ T₂}{body₁ body₂} → (Abstract{d} T₁ body₁ ≡ Abstract{d} T₂ body₂) → (body₁ ≡ body₂)
Abstractᵣ-injective [≡]-intro = [≡]-intro
open import Functional
open import Logic.Predicate.Equiv
import Structure.Relator.Function.Multi as Relator
open import Structure.Operator
-- Every typable term have an unique type when all constants and products also have an unique type.
{-typing-uniqueness : Relator.Names.Function(1)(Axioms) → (∀{d₁ d₂ d₃ : ℕ} → Relator.Names.Function(2) ⦃ [≡∃]-equiv ⦄ ⦃ [≡∃]-equiv ⦄ ⦃ [≡∃]-equiv ⦄ (Rules{d₁}{d₂}{d₃})) → Unique(Γ ⊢ X ::_)
typing-uniqueness ax rul (constants px) (constants py) = ax [≡]-intro px py
typing-uniqueness ax rul (variables _ pix) (variables _ piy) = injective(Some) (transitivity(_≡_) (symmetry(_≡_) pix) piy)
typing-uniqueness ax rul (product rx px px₁) (product ry py py₁)
rewrite typing-uniqueness ax rul px py
= rul (typing-uniqueness ax rul px py) (typing-uniqueness ax rul px₁ py₁) rx ry
typing-uniqueness ax rul (application px px₁) (application py py₁) = congruence₁(substituteVar0 _) (Productᵣ-injective (typing-uniqueness ax rul px py))
typing-uniqueness ax rul (abstraction px px₁) (abstraction py py₁)
= congruence₁(Product _) {!!} -- (typing-uniqueness ax rul px₁ {!!})
-- typing-uniqueness {𝐒 d} ax rul {x}{y} px (conversion py x₁ py₁) rewrite typing-uniqueness ax rul px py₁ = {!x!}
-- typing-uniqueness {𝐒 d} ax rul (conversion px x px₁) py = {!!}
-}
{-
typing-uniqueness : Relator.Names.Function(1)(Axioms) → (∀{d₁ d₂ d₃ : ℕ} → Relator.Names.Function(2) ⦃ [≡∃]-equiv ⦄ ⦃ [≡∃]-equiv ⦄ ⦃ [≡∃]-equiv ⦄ (Rules{d₁}{d₂}{d₃})) → (∀{d : ℕ} → Relator.Names.Function(2)(_⊢_::_ {d = d}))
typing-uniqueness ax rul gam exp (constants px) (constants py) = ax (injective(Constant) exp) px py
typing-uniqueness ax rul {x = Γ₁}{y = Γ₂} gam exp {y₁} {y₂} (variables _ pix) (variables _ piy) = injective(Some) $
Some y₁ 🝖[ _≡_ ]-[ pix ]-sym
get _ Γ₁ 🝖[ _≡_ ]-[ congruence₂(get) (injective(Var) exp) gam ]
get _ Γ₂ 🝖[ _≡_ ]-[ piy ]
Some y₂ 🝖-end
typing-uniqueness ax rul gam exp (product rx px px₁) (product ry py py₁) = rul XY AB rx ry where
XY = typing-uniqueness ax rul gam (Productₗ-injective exp) px py
AB = typing-uniqueness ax rul (congruence₃(push) (Productₗ-injective exp) XY gam) (Productᵣ-injective exp) px₁ py₁
typing-uniqueness ax rul gam exp (application px px₁) (application py py₁) = congruence₂(substituteVar0) (Applyᵣ-injective exp) (Productᵣ-injective (typing-uniqueness ax rul gam (Applyₗ-injective exp) px py))
typing-uniqueness ax rul gam exp (abstraction px px₁) (abstraction py py₁) = congruence₂(Product) {!!} {!!} where
X₁X₂ = Abstractₗ-injective exp
AB : _
Y₁Y₂ : _
Y₁Y₂ = typing-uniqueness ax rul (congruence₃(push) X₁X₂ AB gam) (Abstractᵣ-injective exp) px₁ py₁
AB = typing-uniqueness ax rul gam (congruence₂(Product) X₁X₂ Y₁Y₂) px py
-- congruence₂(Product) (Abstractₗ-injective exp) (typing-uniqueness ax rul (congruence₃(push) (Abstractₗ-injective exp) (typing-uniqueness ax rul gam {!!} px py) gam) (Abstractᵣ-injective exp) px₁ py₁)
-}
|
{
"alphanum_fraction": 0.6075992157,
"avg_line_length": 45.6512345679,
"ext": "agda",
"hexsha": "b29cde43fc6a772c743963eff0a040b91a658476",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "Lolirofle/stuff-in-agda",
"max_forks_repo_path": "Formalization/PureTypeSystem.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "Lolirofle/stuff-in-agda",
"max_issues_repo_path": "Formalization/PureTypeSystem.agda",
"max_line_length": 287,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "Lolirofle/stuff-in-agda",
"max_stars_repo_path": "Formalization/PureTypeSystem.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-05T06:53:22.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-04-07T17:58:13.000Z",
"num_tokens": 5740,
"size": 14791
}
|
------------------------------------------------------------------------
-- Vectors
------------------------------------------------------------------------
module Data.Vec where
open import Data.Nat
open import Data.Fin using (Fin; zero; suc)
open import Data.List as List using (List)
open import Data.Product using (_×_; _,_)
------------------------------------------------------------------------
-- Types
infixr 5 _∷_
data Vec (a : Set) : ℕ → Set where
[] : Vec a zero
_∷_ : ∀ {n} (x : a) (xs : Vec a n) → Vec a (suc n)
infix 4 _∈_ _[_]=_
data _∈_ {a : Set} : a → {n : ℕ} → Vec a n → Set where
here : ∀ {n} {x} {xs : Vec a n} → x ∈ x ∷ xs
there : ∀ {n} {x y} {xs : Vec a n} (x∈xs : x ∈ xs) → x ∈ y ∷ xs
data _[_]=_ {a : Set} : {n : ℕ} → Vec a n → Fin n → a → Set where
here : ∀ {n} {x} {xs : Vec a n} → x ∷ xs [ zero ]= x
there : ∀ {n} {i} {x y} {xs : Vec a n}
(xs[i]=x : xs [ i ]= x) → y ∷ xs [ suc i ]= x
------------------------------------------------------------------------
-- Some operations
head : ∀ {a n} → Vec a (1 + n) → a
head (x ∷ xs) = x
tail : ∀ {a n} → Vec a (1 + n) → Vec a n
tail (x ∷ xs) = xs
[_] : ∀ {a} → a → Vec a 1
[ x ] = x ∷ []
infixr 5 _++_
_++_ : ∀ {a m n} → Vec a m → Vec a n → Vec a (m + n)
[] ++ ys = ys
(x ∷ xs) ++ ys = x ∷ (xs ++ ys)
map : ∀ {a b n} → (a → b) → Vec a n → Vec b n
map f [] = []
map f (x ∷ xs) = f x ∷ map f xs
zipWith : ∀ {a b c n}
→ (a → b → c) → Vec a n → Vec b n → Vec c n
zipWith _⊕_ [] [] = []
zipWith _⊕_ (x ∷ xs) (y ∷ ys) = (x ⊕ y) ∷ zipWith _⊕_ xs ys
zip : ∀ {a b n} → Vec a n → Vec b n → Vec (a × b) n
zip = zipWith _,_
replicate : ∀ {a n} → a → Vec a n
replicate {n = zero} x = []
replicate {n = suc n} x = x ∷ replicate x
foldr : ∀ {a} (b : ℕ → Set) {m}
→ (∀ {n} → a → b n → b (suc n))
→ b zero
→ Vec a m → b m
foldr b _⊕_ n [] = n
foldr b _⊕_ n (x ∷ xs) = x ⊕ foldr b _⊕_ n xs
foldr₁ : ∀ {a : Set} {m}
→ (a → a → a) → Vec a (suc m) → a
foldr₁ _⊕_ (x ∷ []) = x
foldr₁ _⊕_ (x ∷ y ∷ ys) = x ⊕ foldr₁ _⊕_ (y ∷ ys)
foldl : ∀ {a : Set} (b : ℕ → Set) {m}
→ (∀ {n} → b n → a → b (suc n))
→ b zero
→ Vec a m → b m
foldl b _⊕_ n [] = n
foldl b _⊕_ n (x ∷ xs) = foldl (λ n → b (suc n)) _⊕_ (n ⊕ x) xs
foldl₁ : ∀ {a : Set} {m}
→ (a → a → a) → Vec a (suc m) → a
foldl₁ _⊕_ (x ∷ xs) = foldl _ _⊕_ x xs
concat : ∀ {a m n} → Vec (Vec a m) n → Vec a (n * m)
concat [] = []
concat (xs ∷ xss) = xs ++ concat xss
infixr 5 _++'_
data SplitAt {a : Set} (m : ℕ) {n : ℕ} : Vec a (m + n) → Set where
_++'_ : (xs : Vec a m) (ys : Vec a n) → SplitAt m (xs ++ ys)
splitAt : ∀ {a} m {n} (xs : Vec a (m + n)) → SplitAt m xs
splitAt zero xs = [] ++' xs
splitAt (suc m) (x ∷ xs) with splitAt m xs
splitAt (suc m) (x ∷ .(ys ++ zs)) | ys ++' zs = (x ∷ ys) ++' zs
take : ∀ {a} m {n} → Vec a (m + n) → Vec a m
take m xs with splitAt m xs
take m .(xs ++ ys) | xs ++' ys = xs
drop : ∀ {a} m {n} → Vec a (m + n) → Vec a n
drop m xs with splitAt m xs
drop m .(xs ++ ys) | xs ++' ys = ys
data Group {a : Set} (n k : ℕ) : Vec a (n * k) → Set where
concat' : (xss : Vec (Vec a k) n) → Group n k (concat xss)
group : ∀ {a} n k (xs : Vec a (n * k)) → Group n k xs
group zero k [] = concat' []
group (suc n) k xs with splitAt k xs
group (suc n) k .(ys ++ zs) | ys ++' zs with group n k zs
group (suc n) k .(ys ++ concat zss) | ys ++' ._ | concat' zss = concat' (ys ∷ zss)
reverse : ∀ {a n} → Vec a n → Vec a n
reverse {a} = foldl (Vec a) (λ rev x → x ∷ rev) []
sum : ∀ {n} → Vec ℕ n → ℕ
sum = foldr _ _+_ 0
toList : ∀ {a n} → Vec a n → List a
toList [] = List.[]
toList (x ∷ xs) = List._∷_ x (toList xs)
fromList : ∀ {a} → (xs : List a) → Vec a (List.length xs)
fromList List.[] = []
fromList (List._∷_ x xs) = x ∷ fromList xs
-- Snoc.
infixl 5 _∷ʳ_
_∷ʳ_ : ∀ {a n} → Vec a n → a → Vec a (1 + n)
[] ∷ʳ y = [ y ]
(x ∷ xs) ∷ʳ y = x ∷ (xs ∷ʳ y)
infixl 5 _∷ʳ'_
data InitLast {a : Set} (n : ℕ) : Vec a (1 + n) → Set where
_∷ʳ'_ : (xs : Vec a n) (x : a) → InitLast n (xs ∷ʳ x)
initLast : ∀ {a n} (xs : Vec a (1 + n)) → InitLast n xs
initLast {n = zero} (x ∷ []) = [] ∷ʳ' x
initLast {n = suc n} (x ∷ xs) with initLast xs
initLast {n = suc n} (x ∷ .(ys ∷ʳ y)) | ys ∷ʳ' y = (x ∷ ys) ∷ʳ' y
init : ∀ {a n} → Vec a (1 + n) → Vec a n
init xs with initLast xs
init .(ys ∷ʳ y) | ys ∷ʳ' y = ys
last : ∀ {a n} → Vec a (1 + n) → a
last xs with initLast xs
last .(ys ∷ʳ y) | ys ∷ʳ' y = y
infixl 1 _>>=_
_>>=_ : ∀ {A B m n} → Vec A m → (A → Vec B n) → Vec B (m * n)
xs >>= f = concat (map f xs)
infixl 4 _⊛_
_⊛_ : ∀ {A B m n} → Vec (A → B) m → Vec A n → Vec B (m * n)
fs ⊛ xs = fs >>= λ f → map f xs
-- Interleaves the two vectors.
infixr 5 _⋎_
_⋎_ : ∀ {A m n} → Vec A m → Vec A n → Vec A (m +⋎ n)
[] ⋎ ys = ys
(x ∷ xs) ⋎ ys = x ∷ (ys ⋎ xs)
lookup : ∀ {a n} → Fin n → Vec a n → a
lookup zero (x ∷ xs) = x
lookup (suc i) (x ∷ xs) = lookup i xs
-- Update.
infixl 6 _[_]≔_
_[_]≔_ : ∀ {A n} → Vec A n → Fin n → A → Vec A n
[] [ () ]≔ y
(x ∷ xs) [ zero ]≔ y = y ∷ xs
(x ∷ xs) [ suc i ]≔ y = x ∷ xs [ i ]≔ y
-- Generates a vector containing all elements in Fin n. This function
-- is not placed in Data.Fin since Data.Vec depends on Data.Fin.
allFin : ∀ n → Vec (Fin n) n
allFin zero = []
allFin (suc n) = zero ∷ map suc (allFin n)
|
{
"alphanum_fraction": 0.4362870743,
"avg_line_length": 27.7258883249,
"ext": "agda",
"hexsha": "36c8ec8952128f49758918322d6f40d3647d6f99",
"lang": "Agda",
"max_forks_count": 3,
"max_forks_repo_forks_event_max_datetime": "2022-03-12T11:54:10.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-07-21T16:37:58.000Z",
"max_forks_repo_head_hexsha": "8ef786b40e4a9ab274c6103dc697dcb658cf3db3",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "isabella232/Lemmachine",
"max_forks_repo_path": "vendor/stdlib/src/Data/Vec.agda",
"max_issues_count": 1,
"max_issues_repo_head_hexsha": "8ef786b40e4a9ab274c6103dc697dcb658cf3db3",
"max_issues_repo_issues_event_max_datetime": "2022-03-12T12:17:51.000Z",
"max_issues_repo_issues_event_min_datetime": "2022-03-12T12:17:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "larrytheliquid/Lemmachine",
"max_issues_repo_path": "vendor/stdlib/src/Data/Vec.agda",
"max_line_length": 82,
"max_stars_count": 56,
"max_stars_repo_head_hexsha": "8ef786b40e4a9ab274c6103dc697dcb658cf3db3",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "isabella232/Lemmachine",
"max_stars_repo_path": "vendor/stdlib/src/Data/Vec.agda",
"max_stars_repo_stars_event_max_datetime": "2021-12-21T17:02:19.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-20T02:11:42.000Z",
"num_tokens": 2369,
"size": 5462
}
|
module bool where
open import level
----------------------------------------------------------------------
-- datatypes
----------------------------------------------------------------------
open import unit
open import empty
data 𝔹 : Set where
tt : 𝔹
ff : 𝔹
-- this is an alias for Mac users who cannot see blackboard b.
bool : Set
bool = 𝔹
{-# BUILTIN BOOL 𝔹 #-}
{-# BUILTIN TRUE tt #-}
{-# BUILTIN FALSE ff #-}
----------------------------------------------------------------------
-- syntax
----------------------------------------------------------------------
infix 7 ~_
infix 6 _xor_ _nand_
infixr 6 _&&_
infixr 5 _||_
infix 4 if_then_else_ if*_then_else_
infixr 4 _imp_
----------------------------------------------------------------------
-- operations
----------------------------------------------------------------------
toSet : 𝔹 → Set
toSet tt = ⊤
toSet ff = ⊥
-- not
~_ : 𝔹 → 𝔹
~ tt = ff
~ ff = tt
-- and
_&&_ : 𝔹 → 𝔹 → 𝔹
tt && b = b
ff && b = ff
-- or
_||_ : 𝔹 → 𝔹 → 𝔹
tt || b = tt
ff || b = b
if_then_else_ : ∀ {ℓ} {A : Set ℓ} → 𝔹 → A → A → A
if tt then y else z = y
if ff then y else z = z
if*_then_else_ : ∀ {ℓ} {A B : Set ℓ} → (b : 𝔹) → A → B → if b then A else B
if* tt then a else b = a
if* ff then a else b = b
_xor_ : 𝔹 → 𝔹 → 𝔹
tt xor ff = tt
ff xor tt = tt
tt xor tt = ff
ff xor ff = ff
-- implication
_imp_ : 𝔹 → 𝔹 → 𝔹
tt imp b2 = b2
ff imp b2 = tt
-- also called the Sheffer stroke
_nand_ : 𝔹 → 𝔹 → 𝔹
tt nand tt = ff
tt nand ff = tt
ff nand tt = tt
ff nand ff = tt
_nor_ : 𝔹 → 𝔹 → 𝔹
x nor y = ~ (x || y)
|
{
"alphanum_fraction": 0.4137931034,
"avg_line_length": 18,
"ext": "agda",
"hexsha": "25d7538e286c3cf4c80e556eb74caf62b8e9e273",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "b33c6a59d664aed46cac8ef77d34313e148fecc2",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "heades/AUGL",
"max_forks_repo_path": "bool.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "b33c6a59d664aed46cac8ef77d34313e148fecc2",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "heades/AUGL",
"max_issues_repo_path": "bool.agda",
"max_line_length": 75,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "b33c6a59d664aed46cac8ef77d34313e148fecc2",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "heades/AUGL",
"max_stars_repo_path": "bool.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 527,
"size": 1566
}
|
{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import homotopy.PushoutSplit
module cw.cohomology.CofiberGrid {i j k}
{A : Type i} {B : Type j} {C : Type k}
(f : A → B) (g : B → C) where
{-
A -------> B -----------> C
| | _/|
| | _/ |
| | __.D_ |
v v .--' | `-.v
1 ------> B/A ------|-> C/A
| | |
| v |
| __.E_ |
v .--' `-.v
1 ---------> C/B
-}
open import cw.cohomology.GridMap f g
private
B-to-B/A : B → B/A
B-to-B/A = cfcod' f
D-span : Span
D-span = span B/A C B B-to-B/A g
D : Type (lmax i (lmax j k))
D = Pushout D-span
private
module VSplit = PushoutRSplit (λ _ → tt) f g
module C/AToD = VSplit.Split
C/A-to-D : C/A → D
C/A-to-D = C/AToD.f
B/A-to-D : B/A → D
B/A-to-D = left
private
E : Type (lmax i (lmax j k))
E = Cofiber B/A-to-D
private
module HSplit = PushoutLSplit B-to-B/A (λ _ → tt) g
module C/BToE = HSplit.Split
C/B-to-E : C/B → E
C/B-to-E = C/BToE.f
private
module DToC/B = HSplit.Inner
D-to-C/B : D → C/B
D-to-C/B = DToC/B.f
D-to-E : D → E
D-to-E = cfcod
C/A-to-D-to-C/B : ∀ c/a → D-to-C/B (C/A-to-D c/a) == C/A-to-C/B c/a
C/A-to-D-to-C/B = Cofiber-elim
idp
(λ c → idp)
(λ a → ↓-='-in' $ ! $
ap (D-to-C/B ∘ C/A-to-D) (glue a)
=⟨ ap-∘ D-to-C/B C/A-to-D (glue a) ⟩
ap D-to-C/B (ap C/A-to-D (glue a))
=⟨ C/AToD.glue-β a |in-ctx ap D-to-C/B ⟩
ap D-to-C/B (ap left (glue a) ∙ glue (f a))
=⟨ ap-∙ D-to-C/B (ap left (glue a)) (glue (f a)) ⟩
ap D-to-C/B (ap left (glue a)) ∙ ap D-to-C/B (glue (f a))
=⟨ ap2 _∙_ (∘-ap D-to-C/B left (glue a)) (DToC/B.glue-β (f a)) ⟩
ap (λ _ → cfbase) (glue a) ∙ glue (f a)
=⟨ ap-cst cfbase (glue a) |in-ctx _∙ glue (f a) ⟩
glue (f a)
=⟨ ! $ C/AToC/B.glue-β a ⟩
ap C/A-to-C/B (glue a)
=∎)
D-to-C/B-to-E : ∀ d → C/B-to-E (D-to-C/B d) == D-to-E d
D-to-C/B-to-E = HSplit.split-inner
{- The public interface -}
C/A-to-C/B-comm-square : CommSquare C/A-to-C/B D-to-E C/A-to-D C/B-to-E
C/A-to-C/B-comm-square = comm-sqr λ c/a → ap C/B-to-E (! (C/A-to-D-to-C/B c/a))
∙ D-to-C/B-to-E (C/A-to-D c/a)
B/A-to-C/A-comm-square : CommSquare B/A-to-C/A B/A-to-D (idf B/A) C/A-to-D
B/A-to-C/A-comm-square = comm-sqr VSplit.split-inner
C/A-to-D-is-equiv : is-equiv C/A-to-D
C/A-to-D-is-equiv = snd VSplit.split-equiv
C/B-to-E-is-equiv : is-equiv C/B-to-E
C/B-to-E-is-equiv = snd HSplit.split-equiv
|
{
"alphanum_fraction": 0.4516479536,
"avg_line_length": 27.8888888889,
"ext": "agda",
"hexsha": "46da7b9fea7bba3bb37d5d1ca2c4c7b73fd5497f",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2018-12-26T21:31:57.000Z",
"max_forks_repo_forks_event_min_datetime": "2018-12-26T21:31:57.000Z",
"max_forks_repo_head_hexsha": "e7d663b63d89f380ab772ecb8d51c38c26952dbb",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "mikeshulman/HoTT-Agda",
"max_forks_repo_path": "theorems/cw/cohomology/CofiberGrid.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "e7d663b63d89f380ab772ecb8d51c38c26952dbb",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "mikeshulman/HoTT-Agda",
"max_issues_repo_path": "theorems/cw/cohomology/CofiberGrid.agda",
"max_line_length": 81,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "e7d663b63d89f380ab772ecb8d51c38c26952dbb",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "mikeshulman/HoTT-Agda",
"max_stars_repo_path": "theorems/cw/cohomology/CofiberGrid.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 1084,
"size": 2761
}
|
{-# OPTIONS --without-K --safe #-}
open import Categories.Category
module Categories.Diagram.Pullback.Limit {o ℓ e} (C : Category o ℓ e) where
open import Data.Product using (∃₂; _,_)
open import Function using (_$_)
open import Categories.Category.Instance.Span
open import Categories.Functor
open import Categories.Diagram.Pullback C
open import Categories.Morphism.Reasoning C as MR hiding (center)
import Relation.Binary.PropositionalEquality as ≡
import Categories.Category.Construction.Cones as Con
import Categories.Diagram.Limit as Lim
private
module C = Category C
module Span = Category Span
open Category C
variable
X Y Z : Obj
f g h : X ⇒ Y
open HomReasoning
module _ {F : Functor Span.op C} where
open Functor F
open Lim F
open Con F
private
W = F₀ center
A = F₀ left
B = F₀ right
A⇒W : A ⇒ W
A⇒W = F₁ span-arrˡ
B⇒W : B ⇒ W
B⇒W = F₁ span-arrʳ
limit⇒pullback : Limit → Pullback A⇒W B⇒W
limit⇒pullback lim = record
{ p₁ = proj left
; p₂ = proj right
; commute = trans (limit-commute span-arrˡ) (sym (limit-commute span-arrʳ))
; universal = universal
; unique = commute′
; p₁∘universal≈h₁ = commute
; p₂∘universal≈h₂ = commute
}
where open Limit lim
universal : A⇒W ∘ f ≈ B⇒W ∘ g → dom f ⇒ apex
universal {f = f} {g = g} eq = rep $ record
{ apex = record
{ ψ = λ { center → B⇒W ∘ g
; left → f
; right → g
}
; commute = λ { {center} {center} span-id → elimˡ identity
; {left} {center} span-arrˡ → eq
; {left} {left} span-id → elimˡ identity
; {right} {center} span-arrʳ → refl
; {right} {right} span-id → elimˡ identity
}
}
}
proj-center : proj center ≈ B⇒W ∘ proj right
proj-center = sym (limit-commute span-arrʳ)
commute′ : ∀ {eq : A⇒W ∘ f ≈ B⇒W ∘ g} → proj left ∘ h ≈ f → proj right ∘ h ≈ g → h ≈ universal eq
commute′ {f = f} {g = g} {h = h} {eq = eq} eq₁ eq₂ = sym $ terminal.!-unique $ record
{ arr = h
; commute = λ { {center} → begin
proj center ∘ h ≈⟨ pushˡ proj-center ⟩
B⇒W ∘ proj right ∘ h ≈⟨ refl⟩∘⟨ eq₂ ⟩
B⇒W ∘ g ∎
; {left} → eq₁
; {right} → eq₂
}
}
module _ (p : Pullback f g) where
open Pullback p
pullback⇒limit-F : Functor Span.op C
pullback⇒limit-F = record
{ F₀ = λ { center → cod f
; left → dom f
; right → dom g
}
; F₁ = λ { {center} {.center} span-id → C.id
; {left} {.left} span-id → C.id
; {right} {.right} span-id → C.id
; {.left} {.center} span-arrˡ → f
; {.right} {.center} span-arrʳ → g
}
; identity = λ { {center} → refl
; {left} → refl
; {right} → refl
}
; homomorphism = λ { {center} {.center} {.center} {span-id} {span-id} → sym identityˡ
; {left} {.left} {.left} {span-id} {span-id} → sym identityˡ
; {right} {.right} {.right} {span-id} {span-id} → sym identityˡ
; {.left} {.left} {.center} {span-id} {span-arrˡ} → sym identityʳ
; {.right} {.right} {.center} {span-id} {span-arrʳ} → sym identityʳ
; {.left} {.center} {.center} {span-arrˡ} {span-id} → sym identityˡ
; {.right} {.center} {.center} {span-arrʳ} {span-id} → sym identityˡ
}
; F-resp-≈ = λ { {center} {.center} {span-id} {.span-id} ≡.refl → refl
; {left} {.left} {span-id} {.span-id} ≡.refl → refl
; {right} {.right} {span-id} {.span-id} ≡.refl → refl
; {.left} {.center} {span-arrˡ} {.span-arrˡ} ≡.refl → refl
; {.right} {.center} {span-arrʳ} {.span-arrʳ} ≡.refl → refl
}
}
open Functor pullback⇒limit-F
open Lim pullback⇒limit-F
open Con pullback⇒limit-F
pullback⇒limit : Limit
pullback⇒limit = record
{ terminal = record
{ ⊤ = ⊤
; ! = !
; !-unique = !-unique
}
}
where ⊤ : Cone
⊤ = record
{ apex = record
{ ψ = λ { center → g ∘ p₂
; left → p₁
; right → p₂
}
; commute = λ { {center} {.center} span-id → identityˡ
; {left} {.left} span-id → identityˡ
; {right} {.right} span-id → identityˡ
; {.left} {.center} span-arrˡ → commute
; {.right} {.center} span-arrʳ → refl
}
}
}
! : ∀ {A : Cone} → Cone⇒ A ⊤
! {A} = record
{ arr = universal commute′
; commute = λ { {center} → begin
(g ∘ p₂) ∘ universal _ ≈⟨ pullʳ p₂∘universal≈h₂ ⟩
g ∘ A.ψ right ≈⟨ A.commute span-arrʳ ⟩
A.ψ center ∎
; {left} → p₁∘universal≈h₁
; {right} → p₂∘universal≈h₂
}
}
where module A = Cone A
commute′ = trans (A.commute span-arrˡ) (sym (A.commute span-arrʳ))
!-unique : ∀ {A : Cone} (h : Cone⇒ A ⊤) → Cones [ ! ≈ h ]
!-unique {A} h = sym (unique h.commute h.commute)
where module h = Cone⇒ h
|
{
"alphanum_fraction": 0.4214651312,
"avg_line_length": 37.2142857143,
"ext": "agda",
"hexsha": "1b68b6e9854f17f1d4bf742f00868318c4856593",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "58e5ec015781be5413bdf968f7ec4fdae0ab4b21",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "MirceaS/agda-categories",
"max_forks_repo_path": "src/Categories/Diagram/Pullback/Limit.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "58e5ec015781be5413bdf968f7ec4fdae0ab4b21",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "MirceaS/agda-categories",
"max_issues_repo_path": "src/Categories/Diagram/Pullback/Limit.agda",
"max_line_length": 107,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "58e5ec015781be5413bdf968f7ec4fdae0ab4b21",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "MirceaS/agda-categories",
"max_stars_repo_path": "src/Categories/Diagram/Pullback/Limit.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 1831,
"size": 6252
}
|
{-# OPTIONS --without-K --safe #-}
module Dodo.Binary.Domain where
-- Stdlib imports
open import Level using (Level; _⊔_)
open import Function.Base using (flip; _∘_)
open import Data.Product using (_×_; _,_; ∃; ∃-syntax; proj₁; proj₂)
open import Data.Sum using (_⊎_; inj₁; inj₂; swap)
open import Relation.Unary using (Pred; _∈_; _∉_)
open import Relation.Binary using (Rel; REL)
-- Local imports
open import Dodo.Unary.Equality
open import Dodo.Unary.Union
open import Dodo.Binary.Equality
open import Dodo.Binary.Composition
-- # Definitions
-- | The domain of the binary relation
dom : ∀ {a b ℓ : Level} {A : Set a} {B : Set b}
→ REL A B ℓ
--------------
→ Pred A (b ⊔ ℓ)
dom R x = ∃[ y ] (R x y)
-- | The co-domain (or range) of the binary relation
--
--
-- # Design decision: Not range
--
-- It is somewhat arbitrary what constitutes the /co-domain/ of a binary relation,
-- and how it differs from its /range/. Usually, the /co-domain/ denotes the set of
-- /possible/ outputs of a function, while the /range/ denotes the set of /actual/
-- outputs. When considering functions, the /domain/ is a set of /independent/ variables,
-- while the /co-domain/ is the set variables that are /dependent/ on the domain.
--
-- However, when considering /relations/ (as opposed to mere functions), this dependency
-- is (usually) absent; Or could be inverted, where the domain "depends on" the codomain.
-- Under such interpretation, distinguishing co-domain from range is rather arbitrary.
codom : ∀ {a b ℓ : Level} {A : Set a} {B : Set b}
→ REL A B ℓ
--------------
→ Pred B (a ⊔ ℓ)
codom R y = ∃[ x ] (R x y)
-- | The domain and co-domain of the binary relation
--
-- Conventionally named after: Union (of) Domain (and) Range
udr : ∀ {a ℓ : Level} {A : Set a}
→ Rel A ℓ
--------------
→ Pred A (a ⊔ ℓ)
udr R = dom R ∪₁ codom R
-- # Operations
-- ## Operations: dom / codom / udr
-- | Weakens an element of a relation's domain to an element of its udr.
--
-- Note that Agda is unable to infer `R` from `x ∈ dom R`.
-- (As `R` may be beta-reduced inside the latter, I think)
dom⇒udr : ∀ {a ℓ : Level} {A : Set a} (R : Rel A ℓ) {x : A} → x ∈ dom R → x ∈ udr R
dom⇒udr _ = inj₁
-- | Weakens an element of a relation's co-domain to an element of its udr.
--
-- Note that Agda is unable to infer `R` from `x ∈ dom R`.
-- (As `R` may be beta-reduced inside the latter, I think)
codom⇒udr : ∀ {a ℓ : Level} {A : Set a} (R : Rel A ℓ) {x : A} → x ∈ codom R → x ∈ udr R
codom⇒udr _ = inj₂
module _ {a b ℓ : Level} {A : Set a} {B : Set b} where
-- | Takes an inhabitant of `R x y` as proof that `x` is in the domain of `R`.
--
-- Note that `R` must be provided /explicitly/, as it may not always be inferred
-- from its applied type.
take-dom : (R : REL A B ℓ) → {x : A} {y : B} → R x y → x ∈ dom R
take-dom R {x} {y} Rxy = (y , Rxy)
-- | Takes an inhabitant of `R x y` as proof that `y` is in the co-domain of `R`.
--
-- Note that `R` must be provided /explicitly/, as it may not always be inferred
-- from its applied type.
take-codom : (R : REL A B ℓ) → {x : A} {y : B} → R x y → y ∈ codom R
take-codom R {x} {y} Rxy = (x , Rxy)
module _ {a ℓ : Level} {A : Set a} where
-- | Takes an inhabitant of `R x y` as proof that `x` is in the udr of `R`.
--
-- Note that `R` must be provided /explicitly/, as it may not always be inferred
-- from its applied type.
take-udrˡ : (R : Rel A ℓ) → {x y : A} → R x y → x ∈ udr R
take-udrˡ R Rxy = dom⇒udr R (take-dom R Rxy)
-- | Takes an inhabitant of `R x y` as proof that `y` is in the udr of `R`.
--
-- Note that `R` must be provided /explicitly/, as it may not always be inferred
-- from its applied type.
take-udrʳ : (R : Rel A ℓ) → {x y : A} → R x y → y ∈ udr R
take-udrʳ R Rxy = codom⇒udr R (take-codom R Rxy)
module _ {a b ℓ₁ ℓ₂ : Level} {A : Set a} {B : Set b}
{P : REL A B ℓ₁} {Q : REL A B ℓ₂} where
dom-preserves-⊆ : P ⊆₂ Q → dom P ⊆₁ dom Q
dom-preserves-⊆ P⊆Q = ⊆: λ{x (y , Pxy) → (y , un-⊆₂ P⊆Q x y Pxy)}
codom-preserves-⊆ : P ⊆₂ Q → codom P ⊆₁ codom Q
codom-preserves-⊆ P⊆Q = ⊆: λ{y (x , Pxy) → (x , un-⊆₂ P⊆Q x y Pxy)}
module _ {a ℓ₁ ℓ₂ : Level} {A : Set a}
{P : Rel A ℓ₁} {Q : Rel A ℓ₂} where
udr-preserves-⊆ : P ⊆₂ Q → udr P ⊆₁ udr Q
udr-preserves-⊆ P⊆Q = ⊆: lemma
where
lemma : udr P ⊆₁' udr Q
lemma x (inj₁ x∈dom) = dom⇒udr Q (⊆₁-apply (dom-preserves-⊆ P⊆Q) x∈dom)
lemma y (inj₂ y∈codom) = codom⇒udr Q (⊆₁-apply (codom-preserves-⊆ P⊆Q) y∈codom)
module _ {a ℓ₁ ℓ₂ : Level} {A : Set a}
{P : Rel A ℓ₁} {Q : Rel A ℓ₂} where
udr-combine-⨾ : udr (P ⨾ Q) ⊆₁ udr P ∪₁ udr Q
udr-combine-⨾ = ⊆: lemma
where
lemma : udr (P ⨾ Q) ⊆₁' (udr P ∪₁ udr Q)
lemma _ (inj₁ (a , (Pxb ⨾[ b ]⨾ Qba))) = inj₁ (inj₁ (b , Pxb))
lemma _ (inj₂ (a , (Pab ⨾[ b ]⨾ Qbx))) = inj₂ (inj₂ (b , Qbx))
module _ {a ℓ : Level} {A : Set a}
{P : Rel A ℓ} where
udr-flip : udr P ⇔₁ udr (flip P)
udr-flip = ⇔: (λ _ → swap) (λ _ → swap)
dom-flip : dom P ⇔₁ codom (flip P)
dom-flip = ⇔: (λ _ z → z) (λ _ z → z)
codom-flip : codom P ⇔₁ dom (flip P)
codom-flip = ⇔: (λ _ z → z) (λ _ z → z)
|
{
"alphanum_fraction": 0.575399061,
"avg_line_length": 34.5779220779,
"ext": "agda",
"hexsha": "0d476b138830272ac95d524c889a8b74621e8089",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "376f0ccee1e1aa31470890e494bcb534324f598a",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "sourcedennis/agda-dodo",
"max_forks_repo_path": "src/Dodo/Binary/Domain.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "376f0ccee1e1aa31470890e494bcb534324f598a",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "sourcedennis/agda-dodo",
"max_issues_repo_path": "src/Dodo/Binary/Domain.agda",
"max_line_length": 90,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "376f0ccee1e1aa31470890e494bcb534324f598a",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "sourcedennis/agda-dodo",
"max_stars_repo_path": "src/Dodo/Binary/Domain.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 2040,
"size": 5325
}
|
{-# OPTIONS --without-K --safe #-}
module Dodo.Binary.Empty where
-- Stdlib imports
open import Level using (Level; _⊔_)
open import Relation.Nullary using (¬_)
open import Relation.Binary using (REL; Rel)
-- # Definitions
-- | A predicate stating no inhabitants exist for the given relation
Empty₂ : ∀ {a b ℓ : Level} {A : Set a} {B : Set b} → REL A B ℓ → Set (a ⊔ b ⊔ ℓ)
Empty₂ {A = A} {B = B} r = ∀ (x : A) (y : B) → ¬ r x y
-- | Negation of a binary relation
¬₂_ : ∀ {a b ℓ : Level} {A : Set a} {B : Set b} → REL A B ℓ → REL A B ℓ
¬₂_ r x y = ¬ r x y
|
{
"alphanum_fraction": 0.5971479501,
"avg_line_length": 28.05,
"ext": "agda",
"hexsha": "acad012e76533aa6a9d123270fae82e4407d9498",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "376f0ccee1e1aa31470890e494bcb534324f598a",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "sourcedennis/agda-dodo",
"max_forks_repo_path": "src/Dodo/Binary/Empty.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "376f0ccee1e1aa31470890e494bcb534324f598a",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "sourcedennis/agda-dodo",
"max_issues_repo_path": "src/Dodo/Binary/Empty.agda",
"max_line_length": 80,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "376f0ccee1e1aa31470890e494bcb534324f598a",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "sourcedennis/agda-dodo",
"max_stars_repo_path": "src/Dodo/Binary/Empty.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 200,
"size": 561
}
|
module Text.Greek.SBLGNT.Heb where
open import Data.List
open import Text.Greek.Bible
open import Text.Greek.Script
open import Text.Greek.Script.Unicode
ΠΡΟΣ-ΕΒΡΑΙΟΥΣ : List (Word)
ΠΡΟΣ-ΕΒΡΑΙΟΥΣ =
word (Π ∷ ο ∷ ∙λ ∷ υ ∷ μ ∷ ε ∷ ρ ∷ ῶ ∷ ς ∷ []) "Heb.1.1"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.1"
∷ word (π ∷ ο ∷ ∙λ ∷ υ ∷ τ ∷ ρ ∷ ό ∷ π ∷ ω ∷ ς ∷ []) "Heb.1.1"
∷ word (π ∷ ά ∷ ∙λ ∷ α ∷ ι ∷ []) "Heb.1.1"
∷ word (ὁ ∷ []) "Heb.1.1"
∷ word (θ ∷ ε ∷ ὸ ∷ ς ∷ []) "Heb.1.1"
∷ word (∙λ ∷ α ∷ ∙λ ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.1.1"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.1.1"
∷ word (π ∷ α ∷ τ ∷ ρ ∷ ά ∷ σ ∷ ι ∷ ν ∷ []) "Heb.1.1"
∷ word (ἐ ∷ ν ∷ []) "Heb.1.1"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.1.1"
∷ word (π ∷ ρ ∷ ο ∷ φ ∷ ή ∷ τ ∷ α ∷ ι ∷ ς ∷ []) "Heb.1.1"
∷ word (ἐ ∷ π ∷ []) "Heb.1.2"
∷ word (ἐ ∷ σ ∷ χ ∷ ά ∷ τ ∷ ο ∷ υ ∷ []) "Heb.1.2"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.1.2"
∷ word (ἡ ∷ μ ∷ ε ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.1.2"
∷ word (τ ∷ ο ∷ ύ ∷ τ ∷ ω ∷ ν ∷ []) "Heb.1.2"
∷ word (ἐ ∷ ∙λ ∷ ά ∷ ∙λ ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.1.2"
∷ word (ἡ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.1.2"
∷ word (ἐ ∷ ν ∷ []) "Heb.1.2"
∷ word (υ ∷ ἱ ∷ ῷ ∷ []) "Heb.1.2"
∷ word (ὃ ∷ ν ∷ []) "Heb.1.2"
∷ word (ἔ ∷ θ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.1.2"
∷ word (κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ό ∷ μ ∷ ο ∷ ν ∷ []) "Heb.1.2"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.1.2"
∷ word (δ ∷ ι ∷ []) "Heb.1.2"
∷ word (ο ∷ ὗ ∷ []) "Heb.1.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.2"
∷ word (ἐ ∷ π ∷ ο ∷ ί ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.1.2"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.1.2"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ ς ∷ []) "Heb.1.2"
∷ word (ὃ ∷ ς ∷ []) "Heb.1.3"
∷ word (ὢ ∷ ν ∷ []) "Heb.1.3"
∷ word (ἀ ∷ π ∷ α ∷ ύ ∷ γ ∷ α ∷ σ ∷ μ ∷ α ∷ []) "Heb.1.3"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.1.3"
∷ word (δ ∷ ό ∷ ξ ∷ η ∷ ς ∷ []) "Heb.1.3"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.3"
∷ word (χ ∷ α ∷ ρ ∷ α ∷ κ ∷ τ ∷ ὴ ∷ ρ ∷ []) "Heb.1.3"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.1.3"
∷ word (ὑ ∷ π ∷ ο ∷ σ ∷ τ ∷ ά ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.1.3"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.1.3"
∷ word (φ ∷ έ ∷ ρ ∷ ω ∷ ν ∷ []) "Heb.1.3"
∷ word (τ ∷ ε ∷ []) "Heb.1.3"
∷ word (τ ∷ ὰ ∷ []) "Heb.1.3"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.1.3"
∷ word (τ ∷ ῷ ∷ []) "Heb.1.3"
∷ word (ῥ ∷ ή ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.1.3"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.1.3"
∷ word (δ ∷ υ ∷ ν ∷ ά ∷ μ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.1.3"
∷ word (δ ∷ ι ∷ []) "Heb.1.3"
∷ word (α ∷ ὑ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.1.3"
∷ word (κ ∷ α ∷ θ ∷ α ∷ ρ ∷ ι ∷ σ ∷ μ ∷ ὸ ∷ ν ∷ []) "Heb.1.3"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.1.3"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.1.3"
∷ word (π ∷ ο ∷ ι ∷ η ∷ σ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.1.3"
∷ word (ἐ ∷ κ ∷ ά ∷ θ ∷ ι ∷ σ ∷ ε ∷ ν ∷ []) "Heb.1.3"
∷ word (ἐ ∷ ν ∷ []) "Heb.1.3"
∷ word (δ ∷ ε ∷ ξ ∷ ι ∷ ᾷ ∷ []) "Heb.1.3"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.1.3"
∷ word (μ ∷ ε ∷ γ ∷ α ∷ ∙λ ∷ ω ∷ σ ∷ ύ ∷ ν ∷ η ∷ ς ∷ []) "Heb.1.3"
∷ word (ἐ ∷ ν ∷ []) "Heb.1.3"
∷ word (ὑ ∷ ψ ∷ η ∷ ∙λ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.1.3"
∷ word (τ ∷ ο ∷ σ ∷ ο ∷ ύ ∷ τ ∷ ῳ ∷ []) "Heb.1.4"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ω ∷ ν ∷ []) "Heb.1.4"
∷ word (γ ∷ ε ∷ ν ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.1.4"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.1.4"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ω ∷ ν ∷ []) "Heb.1.4"
∷ word (ὅ ∷ σ ∷ ῳ ∷ []) "Heb.1.4"
∷ word (δ ∷ ι ∷ α ∷ φ ∷ ο ∷ ρ ∷ ώ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.1.4"
∷ word (π ∷ α ∷ ρ ∷ []) "Heb.1.4"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.1.4"
∷ word (κ ∷ ε ∷ κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ό ∷ μ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.1.4"
∷ word (ὄ ∷ ν ∷ ο ∷ μ ∷ α ∷ []) "Heb.1.4"
∷ word (Τ ∷ ί ∷ ν ∷ ι ∷ []) "Heb.1.5"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.1.5"
∷ word (ε ∷ ἶ ∷ π ∷ έ ∷ ν ∷ []) "Heb.1.5"
∷ word (π ∷ ο ∷ τ ∷ ε ∷ []) "Heb.1.5"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.1.5"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ω ∷ ν ∷ []) "Heb.1.5"
∷ word (Υ ∷ ἱ ∷ ό ∷ ς ∷ []) "Heb.1.5"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.1.5"
∷ word (ε ∷ ἶ ∷ []) "Heb.1.5"
∷ word (σ ∷ ύ ∷ []) "Heb.1.5"
∷ word (ἐ ∷ γ ∷ ὼ ∷ []) "Heb.1.5"
∷ word (σ ∷ ή ∷ μ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.1.5"
∷ word (γ ∷ ε ∷ γ ∷ έ ∷ ν ∷ ν ∷ η ∷ κ ∷ ά ∷ []) "Heb.1.5"
∷ word (σ ∷ ε ∷ []) "Heb.1.5"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.5"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.1.5"
∷ word (Ἐ ∷ γ ∷ ὼ ∷ []) "Heb.1.5"
∷ word (ἔ ∷ σ ∷ ο ∷ μ ∷ α ∷ ι ∷ []) "Heb.1.5"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.1.5"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.1.5"
∷ word (π ∷ α ∷ τ ∷ έ ∷ ρ ∷ α ∷ []) "Heb.1.5"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.5"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.1.5"
∷ word (ἔ ∷ σ ∷ τ ∷ α ∷ ι ∷ []) "Heb.1.5"
∷ word (μ ∷ ο ∷ ι ∷ []) "Heb.1.5"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.1.5"
∷ word (υ ∷ ἱ ∷ ό ∷ ν ∷ []) "Heb.1.5"
∷ word (ὅ ∷ τ ∷ α ∷ ν ∷ []) "Heb.1.6"
∷ word (δ ∷ ὲ ∷ []) "Heb.1.6"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.1.6"
∷ word (ε ∷ ἰ ∷ σ ∷ α ∷ γ ∷ ά ∷ γ ∷ ῃ ∷ []) "Heb.1.6"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.1.6"
∷ word (π ∷ ρ ∷ ω ∷ τ ∷ ό ∷ τ ∷ ο ∷ κ ∷ ο ∷ ν ∷ []) "Heb.1.6"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.1.6"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.1.6"
∷ word (ο ∷ ἰ ∷ κ ∷ ο ∷ υ ∷ μ ∷ έ ∷ ν ∷ η ∷ ν ∷ []) "Heb.1.6"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.1.6"
∷ word (Κ ∷ α ∷ ὶ ∷ []) "Heb.1.6"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ κ ∷ υ ∷ ν ∷ η ∷ σ ∷ ά ∷ τ ∷ ω ∷ σ ∷ α ∷ ν ∷ []) "Heb.1.6"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.1.6"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.1.6"
∷ word (ἄ ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ο ∷ ι ∷ []) "Heb.1.6"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.1.6"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.7"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.1.7"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.1.7"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.1.7"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.1.7"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.1.7"
∷ word (Ὁ ∷ []) "Heb.1.7"
∷ word (π ∷ ο ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.1.7"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.1.7"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.1.7"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.1.7"
∷ word (π ∷ ν ∷ ε ∷ ύ ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.1.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.7"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.1.7"
∷ word (∙λ ∷ ε ∷ ι ∷ τ ∷ ο ∷ υ ∷ ρ ∷ γ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.1.7"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.1.7"
∷ word (π ∷ υ ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.1.7"
∷ word (φ ∷ ∙λ ∷ ό ∷ γ ∷ α ∷ []) "Heb.1.7"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.1.8"
∷ word (δ ∷ ὲ ∷ []) "Heb.1.8"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.1.8"
∷ word (υ ∷ ἱ ∷ ό ∷ ν ∷ []) "Heb.1.8"
∷ word (Ὁ ∷ []) "Heb.1.8"
∷ word (θ ∷ ρ ∷ ό ∷ ν ∷ ο ∷ ς ∷ []) "Heb.1.8"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.1.8"
∷ word (ὁ ∷ []) "Heb.1.8"
∷ word (θ ∷ ε ∷ ὸ ∷ ς ∷ []) "Heb.1.8"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.1.8"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.1.8"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ []) "Heb.1.8"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.1.8"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ ο ∷ ς ∷ []) "Heb.1.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.8"
∷ word (ἡ ∷ []) "Heb.1.8"
∷ word (ῥ ∷ ά ∷ β ∷ δ ∷ ο ∷ ς ∷ []) "Heb.1.8"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.1.8"
∷ word (ε ∷ ὐ ∷ θ ∷ ύ ∷ τ ∷ η ∷ τ ∷ ο ∷ ς ∷ []) "Heb.1.8"
∷ word (ῥ ∷ ά ∷ β ∷ δ ∷ ο ∷ ς ∷ []) "Heb.1.8"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.1.8"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.1.8"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.1.8"
∷ word (ἠ ∷ γ ∷ ά ∷ π ∷ η ∷ σ ∷ α ∷ ς ∷ []) "Heb.1.9"
∷ word (δ ∷ ι ∷ κ ∷ α ∷ ι ∷ ο ∷ σ ∷ ύ ∷ ν ∷ η ∷ ν ∷ []) "Heb.1.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.9"
∷ word (ἐ ∷ μ ∷ ί ∷ σ ∷ η ∷ σ ∷ α ∷ ς ∷ []) "Heb.1.9"
∷ word (ἀ ∷ ν ∷ ο ∷ μ ∷ ί ∷ α ∷ ν ∷ []) "Heb.1.9"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.1.9"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.1.9"
∷ word (ἔ ∷ χ ∷ ρ ∷ ι ∷ σ ∷ έ ∷ ν ∷ []) "Heb.1.9"
∷ word (σ ∷ ε ∷ []) "Heb.1.9"
∷ word (ὁ ∷ []) "Heb.1.9"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.1.9"
∷ word (ὁ ∷ []) "Heb.1.9"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.1.9"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.1.9"
∷ word (ἔ ∷ ∙λ ∷ α ∷ ι ∷ ο ∷ ν ∷ []) "Heb.1.9"
∷ word (ἀ ∷ γ ∷ α ∷ ∙λ ∷ ∙λ ∷ ι ∷ ά ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.1.9"
∷ word (π ∷ α ∷ ρ ∷ ὰ ∷ []) "Heb.1.9"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.1.9"
∷ word (μ ∷ ε ∷ τ ∷ ό ∷ χ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.1.9"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.1.9"
∷ word (κ ∷ α ∷ ί ∷ []) "Heb.1.10"
∷ word (Σ ∷ ὺ ∷ []) "Heb.1.10"
∷ word (κ ∷ α ∷ τ ∷ []) "Heb.1.10"
∷ word (ἀ ∷ ρ ∷ χ ∷ ά ∷ ς ∷ []) "Heb.1.10"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ε ∷ []) "Heb.1.10"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.1.10"
∷ word (γ ∷ ῆ ∷ ν ∷ []) "Heb.1.10"
∷ word (ἐ ∷ θ ∷ ε ∷ μ ∷ ε ∷ ∙λ ∷ ί ∷ ω ∷ σ ∷ α ∷ ς ∷ []) "Heb.1.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.10"
∷ word (ἔ ∷ ρ ∷ γ ∷ α ∷ []) "Heb.1.10"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.1.10"
∷ word (χ ∷ ε ∷ ι ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.1.10"
∷ word (σ ∷ ο ∷ ύ ∷ []) "Heb.1.10"
∷ word (ε ∷ ἰ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.1.10"
∷ word (ο ∷ ἱ ∷ []) "Heb.1.10"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ο ∷ ί ∷ []) "Heb.1.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὶ ∷ []) "Heb.1.11"
∷ word (ἀ ∷ π ∷ ο ∷ ∙λ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.1.11"
∷ word (σ ∷ ὺ ∷ []) "Heb.1.11"
∷ word (δ ∷ ὲ ∷ []) "Heb.1.11"
∷ word (δ ∷ ι ∷ α ∷ μ ∷ έ ∷ ν ∷ ε ∷ ι ∷ ς ∷ []) "Heb.1.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.11"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.1.11"
∷ word (ὡ ∷ ς ∷ []) "Heb.1.11"
∷ word (ἱ ∷ μ ∷ ά ∷ τ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.1.11"
∷ word (π ∷ α ∷ ∙λ ∷ α ∷ ι ∷ ω ∷ θ ∷ ή ∷ σ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.1.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.12"
∷ word (ὡ ∷ σ ∷ ε ∷ ὶ ∷ []) "Heb.1.12"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ β ∷ ό ∷ ∙λ ∷ α ∷ ι ∷ ο ∷ ν ∷ []) "Heb.1.12"
∷ word (ἑ ∷ ∙λ ∷ ί ∷ ξ ∷ ε ∷ ι ∷ ς ∷ []) "Heb.1.12"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ύ ∷ ς ∷ []) "Heb.1.12"
∷ word (ὡ ∷ ς ∷ []) "Heb.1.12"
∷ word (ἱ ∷ μ ∷ ά ∷ τ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.1.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.12"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ α ∷ γ ∷ ή ∷ σ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.1.12"
∷ word (σ ∷ ὺ ∷ []) "Heb.1.12"
∷ word (δ ∷ ὲ ∷ []) "Heb.1.12"
∷ word (ὁ ∷ []) "Heb.1.12"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.1.12"
∷ word (ε ∷ ἶ ∷ []) "Heb.1.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.1.12"
∷ word (τ ∷ ὰ ∷ []) "Heb.1.12"
∷ word (ἔ ∷ τ ∷ η ∷ []) "Heb.1.12"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.1.12"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.1.12"
∷ word (ἐ ∷ κ ∷ ∙λ ∷ ε ∷ ί ∷ ψ ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.1.12"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.1.13"
∷ word (τ ∷ ί ∷ ν ∷ α ∷ []) "Heb.1.13"
∷ word (δ ∷ ὲ ∷ []) "Heb.1.13"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.1.13"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ω ∷ ν ∷ []) "Heb.1.13"
∷ word (ε ∷ ἴ ∷ ρ ∷ η ∷ κ ∷ έ ∷ ν ∷ []) "Heb.1.13"
∷ word (π ∷ ο ∷ τ ∷ ε ∷ []) "Heb.1.13"
∷ word (Κ ∷ ά ∷ θ ∷ ο ∷ υ ∷ []) "Heb.1.13"
∷ word (ἐ ∷ κ ∷ []) "Heb.1.13"
∷ word (δ ∷ ε ∷ ξ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.1.13"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.1.13"
∷ word (ἕ ∷ ω ∷ ς ∷ []) "Heb.1.13"
∷ word (ἂ ∷ ν ∷ []) "Heb.1.13"
∷ word (θ ∷ ῶ ∷ []) "Heb.1.13"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.1.13"
∷ word (ἐ ∷ χ ∷ θ ∷ ρ ∷ ο ∷ ύ ∷ ς ∷ []) "Heb.1.13"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.1.13"
∷ word (ὑ ∷ π ∷ ο ∷ π ∷ ό ∷ δ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.1.13"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.1.13"
∷ word (π ∷ ο ∷ δ ∷ ῶ ∷ ν ∷ []) "Heb.1.13"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.1.13"
∷ word (ο ∷ ὐ ∷ χ ∷ ὶ ∷ []) "Heb.1.14"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.1.14"
∷ word (ε ∷ ἰ ∷ σ ∷ ὶ ∷ ν ∷ []) "Heb.1.14"
∷ word (∙λ ∷ ε ∷ ι ∷ τ ∷ ο ∷ υ ∷ ρ ∷ γ ∷ ι ∷ κ ∷ ὰ ∷ []) "Heb.1.14"
∷ word (π ∷ ν ∷ ε ∷ ύ ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.1.14"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.1.14"
∷ word (δ ∷ ι ∷ α ∷ κ ∷ ο ∷ ν ∷ ί ∷ α ∷ ν ∷ []) "Heb.1.14"
∷ word (ἀ ∷ π ∷ ο ∷ σ ∷ τ ∷ ε ∷ ∙λ ∷ ∙λ ∷ ό ∷ μ ∷ ε ∷ ν ∷ α ∷ []) "Heb.1.14"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.1.14"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.1.14"
∷ word (μ ∷ έ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.1.14"
∷ word (κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ο ∷ μ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.1.14"
∷ word (σ ∷ ω ∷ τ ∷ η ∷ ρ ∷ ί ∷ α ∷ ν ∷ []) "Heb.1.14"
∷ word (Δ ∷ ι ∷ ὰ ∷ []) "Heb.2.1"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.2.1"
∷ word (δ ∷ ε ∷ ῖ ∷ []) "Heb.2.1"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ σ ∷ σ ∷ ο ∷ τ ∷ έ ∷ ρ ∷ ω ∷ ς ∷ []) "Heb.2.1"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ έ ∷ χ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.2.1"
∷ word (ἡ ∷ μ ∷ ᾶ ∷ ς ∷ []) "Heb.2.1"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.2.1"
∷ word (ἀ ∷ κ ∷ ο ∷ υ ∷ σ ∷ θ ∷ ε ∷ ῖ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.2.1"
∷ word (μ ∷ ή ∷ π ∷ ο ∷ τ ∷ ε ∷ []) "Heb.2.1"
∷ word (π ∷ α ∷ ρ ∷ α ∷ ρ ∷ υ ∷ ῶ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.2.1"
∷ word (ε ∷ ἰ ∷ []) "Heb.2.2"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.2.2"
∷ word (ὁ ∷ []) "Heb.2.2"
∷ word (δ ∷ ι ∷ []) "Heb.2.2"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ω ∷ ν ∷ []) "Heb.2.2"
∷ word (∙λ ∷ α ∷ ∙λ ∷ η ∷ θ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.2.2"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ς ∷ []) "Heb.2.2"
∷ word (ἐ ∷ γ ∷ έ ∷ ν ∷ ε ∷ τ ∷ ο ∷ []) "Heb.2.2"
∷ word (β ∷ έ ∷ β ∷ α ∷ ι ∷ ο ∷ ς ∷ []) "Heb.2.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.2"
∷ word (π ∷ ᾶ ∷ σ ∷ α ∷ []) "Heb.2.2"
∷ word (π ∷ α ∷ ρ ∷ ά ∷ β ∷ α ∷ σ ∷ ι ∷ ς ∷ []) "Heb.2.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.2"
∷ word (π ∷ α ∷ ρ ∷ α ∷ κ ∷ ο ∷ ὴ ∷ []) "Heb.2.2"
∷ word (ἔ ∷ ∙λ ∷ α ∷ β ∷ ε ∷ ν ∷ []) "Heb.2.2"
∷ word (ἔ ∷ ν ∷ δ ∷ ι ∷ κ ∷ ο ∷ ν ∷ []) "Heb.2.2"
∷ word (μ ∷ ι ∷ σ ∷ θ ∷ α ∷ π ∷ ο ∷ δ ∷ ο ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.2.2"
∷ word (π ∷ ῶ ∷ ς ∷ []) "Heb.2.3"
∷ word (ἡ ∷ μ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.2.3"
∷ word (ἐ ∷ κ ∷ φ ∷ ε ∷ υ ∷ ξ ∷ ό ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.2.3"
∷ word (τ ∷ η ∷ ∙λ ∷ ι ∷ κ ∷ α ∷ ύ ∷ τ ∷ η ∷ ς ∷ []) "Heb.2.3"
∷ word (ἀ ∷ μ ∷ ε ∷ ∙λ ∷ ή ∷ σ ∷ α ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.2.3"
∷ word (σ ∷ ω ∷ τ ∷ η ∷ ρ ∷ ί ∷ α ∷ ς ∷ []) "Heb.2.3"
∷ word (ἥ ∷ τ ∷ ι ∷ ς ∷ []) "Heb.2.3"
∷ word (ἀ ∷ ρ ∷ χ ∷ ὴ ∷ ν ∷ []) "Heb.2.3"
∷ word (∙λ ∷ α ∷ β ∷ ο ∷ ῦ ∷ σ ∷ α ∷ []) "Heb.2.3"
∷ word (∙λ ∷ α ∷ ∙λ ∷ ε ∷ ῖ ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.2.3"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.2.3"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.2.3"
∷ word (κ ∷ υ ∷ ρ ∷ ί ∷ ο ∷ υ ∷ []) "Heb.2.3"
∷ word (ὑ ∷ π ∷ ὸ ∷ []) "Heb.2.3"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.2.3"
∷ word (ἀ ∷ κ ∷ ο ∷ υ ∷ σ ∷ ά ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.2.3"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.2.3"
∷ word (ἡ ∷ μ ∷ ᾶ ∷ ς ∷ []) "Heb.2.3"
∷ word (ἐ ∷ β ∷ ε ∷ β ∷ α ∷ ι ∷ ώ ∷ θ ∷ η ∷ []) "Heb.2.3"
∷ word (σ ∷ υ ∷ ν ∷ ε ∷ π ∷ ι ∷ μ ∷ α ∷ ρ ∷ τ ∷ υ ∷ ρ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.2.4"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.2.4"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.2.4"
∷ word (σ ∷ η ∷ μ ∷ ε ∷ ί ∷ ο ∷ ι ∷ ς ∷ []) "Heb.2.4"
∷ word (τ ∷ ε ∷ []) "Heb.2.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.4"
∷ word (τ ∷ έ ∷ ρ ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.2.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.4"
∷ word (π ∷ ο ∷ ι ∷ κ ∷ ί ∷ ∙λ ∷ α ∷ ι ∷ ς ∷ []) "Heb.2.4"
∷ word (δ ∷ υ ∷ ν ∷ ά ∷ μ ∷ ε ∷ σ ∷ ι ∷ ν ∷ []) "Heb.2.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.4"
∷ word (π ∷ ν ∷ ε ∷ ύ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.2.4"
∷ word (ἁ ∷ γ ∷ ί ∷ ο ∷ υ ∷ []) "Heb.2.4"
∷ word (μ ∷ ε ∷ ρ ∷ ι ∷ σ ∷ μ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.2.4"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.2.4"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.2.4"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.2.4"
∷ word (θ ∷ έ ∷ ∙λ ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.2.4"
∷ word (Ο ∷ ὐ ∷ []) "Heb.2.5"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.2.5"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ο ∷ ι ∷ ς ∷ []) "Heb.2.5"
∷ word (ὑ ∷ π ∷ έ ∷ τ ∷ α ∷ ξ ∷ ε ∷ ν ∷ []) "Heb.2.5"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.2.5"
∷ word (ο ∷ ἰ ∷ κ ∷ ο ∷ υ ∷ μ ∷ έ ∷ ν ∷ η ∷ ν ∷ []) "Heb.2.5"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.2.5"
∷ word (μ ∷ έ ∷ ∙λ ∷ ∙λ ∷ ο ∷ υ ∷ σ ∷ α ∷ ν ∷ []) "Heb.2.5"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.2.5"
∷ word (ἧ ∷ ς ∷ []) "Heb.2.5"
∷ word (∙λ ∷ α ∷ ∙λ ∷ ο ∷ ῦ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.2.5"
∷ word (δ ∷ ι ∷ ε ∷ μ ∷ α ∷ ρ ∷ τ ∷ ύ ∷ ρ ∷ α ∷ τ ∷ ο ∷ []) "Heb.2.6"
∷ word (δ ∷ έ ∷ []) "Heb.2.6"
∷ word (π ∷ ο ∷ ύ ∷ []) "Heb.2.6"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.2.6"
∷ word (∙λ ∷ έ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.2.6"
∷ word (Τ ∷ ί ∷ []) "Heb.2.6"
∷ word (ἐ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.2.6"
∷ word (ἄ ∷ ν ∷ θ ∷ ρ ∷ ω ∷ π ∷ ο ∷ ς ∷ []) "Heb.2.6"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.2.6"
∷ word (μ ∷ ι ∷ μ ∷ ν ∷ ῄ ∷ σ ∷ κ ∷ ῃ ∷ []) "Heb.2.6"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.2.6"
∷ word (ἢ ∷ []) "Heb.2.6"
∷ word (υ ∷ ἱ ∷ ὸ ∷ ς ∷ []) "Heb.2.6"
∷ word (ἀ ∷ ν ∷ θ ∷ ρ ∷ ώ ∷ π ∷ ο ∷ υ ∷ []) "Heb.2.6"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.2.6"
∷ word (ἐ ∷ π ∷ ι ∷ σ ∷ κ ∷ έ ∷ π ∷ τ ∷ ῃ ∷ []) "Heb.2.6"
∷ word (α ∷ ὐ ∷ τ ∷ ό ∷ ν ∷ []) "Heb.2.6"
∷ word (ἠ ∷ ∙λ ∷ ά ∷ τ ∷ τ ∷ ω ∷ σ ∷ α ∷ ς ∷ []) "Heb.2.7"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.2.7"
∷ word (β ∷ ρ ∷ α ∷ χ ∷ ύ ∷ []) "Heb.2.7"
∷ word (τ ∷ ι ∷ []) "Heb.2.7"
∷ word (π ∷ α ∷ ρ ∷ []) "Heb.2.7"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.2.7"
∷ word (δ ∷ ό ∷ ξ ∷ ῃ ∷ []) "Heb.2.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.7"
∷ word (τ ∷ ι ∷ μ ∷ ῇ ∷ []) "Heb.2.7"
∷ word (ἐ ∷ σ ∷ τ ∷ ε ∷ φ ∷ ά ∷ ν ∷ ω ∷ σ ∷ α ∷ ς ∷ []) "Heb.2.7"
∷ word (α ∷ ὐ ∷ τ ∷ ό ∷ ν ∷ []) "Heb.2.7"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.2.8"
∷ word (ὑ ∷ π ∷ έ ∷ τ ∷ α ∷ ξ ∷ α ∷ ς ∷ []) "Heb.2.8"
∷ word (ὑ ∷ π ∷ ο ∷ κ ∷ ά ∷ τ ∷ ω ∷ []) "Heb.2.8"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.2.8"
∷ word (π ∷ ο ∷ δ ∷ ῶ ∷ ν ∷ []) "Heb.2.8"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.2.8"
∷ word (ἐ ∷ ν ∷ []) "Heb.2.8"
∷ word (τ ∷ ῷ ∷ []) "Heb.2.8"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.2.8"
∷ word (ὑ ∷ π ∷ ο ∷ τ ∷ ά ∷ ξ ∷ α ∷ ι ∷ []) "Heb.2.8"
∷ word (τ ∷ ὰ ∷ []) "Heb.2.8"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.2.8"
∷ word (ο ∷ ὐ ∷ δ ∷ ὲ ∷ ν ∷ []) "Heb.2.8"
∷ word (ἀ ∷ φ ∷ ῆ ∷ κ ∷ ε ∷ ν ∷ []) "Heb.2.8"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.2.8"
∷ word (ἀ ∷ ν ∷ υ ∷ π ∷ ό ∷ τ ∷ α ∷ κ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.2.8"
∷ word (ν ∷ ῦ ∷ ν ∷ []) "Heb.2.8"
∷ word (δ ∷ ὲ ∷ []) "Heb.2.8"
∷ word (ο ∷ ὔ ∷ π ∷ ω ∷ []) "Heb.2.8"
∷ word (ὁ ∷ ρ ∷ ῶ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.2.8"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.2.8"
∷ word (τ ∷ ὰ ∷ []) "Heb.2.8"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.2.8"
∷ word (ὑ ∷ π ∷ ο ∷ τ ∷ ε ∷ τ ∷ α ∷ γ ∷ μ ∷ έ ∷ ν ∷ α ∷ []) "Heb.2.8"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.2.9"
∷ word (δ ∷ ὲ ∷ []) "Heb.2.9"
∷ word (β ∷ ρ ∷ α ∷ χ ∷ ύ ∷ []) "Heb.2.9"
∷ word (τ ∷ ι ∷ []) "Heb.2.9"
∷ word (π ∷ α ∷ ρ ∷ []) "Heb.2.9"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.2.9"
∷ word (ἠ ∷ ∙λ ∷ α ∷ τ ∷ τ ∷ ω ∷ μ ∷ έ ∷ ν ∷ ο ∷ ν ∷ []) "Heb.2.9"
∷ word (β ∷ ∙λ ∷ έ ∷ π ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.2.9"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ν ∷ []) "Heb.2.9"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.2.9"
∷ word (τ ∷ ὸ ∷ []) "Heb.2.9"
∷ word (π ∷ ά ∷ θ ∷ η ∷ μ ∷ α ∷ []) "Heb.2.9"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.2.9"
∷ word (θ ∷ α ∷ ν ∷ ά ∷ τ ∷ ο ∷ υ ∷ []) "Heb.2.9"
∷ word (δ ∷ ό ∷ ξ ∷ ῃ ∷ []) "Heb.2.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.9"
∷ word (τ ∷ ι ∷ μ ∷ ῇ ∷ []) "Heb.2.9"
∷ word (ἐ ∷ σ ∷ τ ∷ ε ∷ φ ∷ α ∷ ν ∷ ω ∷ μ ∷ έ ∷ ν ∷ ο ∷ ν ∷ []) "Heb.2.9"
∷ word (ὅ ∷ π ∷ ω ∷ ς ∷ []) "Heb.2.9"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.2.9"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.2.9"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.2.9"
∷ word (π ∷ α ∷ ν ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.2.9"
∷ word (γ ∷ ε ∷ ύ ∷ σ ∷ η ∷ τ ∷ α ∷ ι ∷ []) "Heb.2.9"
∷ word (θ ∷ α ∷ ν ∷ ά ∷ τ ∷ ο ∷ υ ∷ []) "Heb.2.9"
∷ word (Ἔ ∷ π ∷ ρ ∷ ε ∷ π ∷ ε ∷ ν ∷ []) "Heb.2.10"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.2.10"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.2.10"
∷ word (δ ∷ ι ∷ []) "Heb.2.10"
∷ word (ὃ ∷ ν ∷ []) "Heb.2.10"
∷ word (τ ∷ ὰ ∷ []) "Heb.2.10"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.2.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.10"
∷ word (δ ∷ ι ∷ []) "Heb.2.10"
∷ word (ο ∷ ὗ ∷ []) "Heb.2.10"
∷ word (τ ∷ ὰ ∷ []) "Heb.2.10"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.2.10"
∷ word (π ∷ ο ∷ ∙λ ∷ ∙λ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.2.10"
∷ word (υ ∷ ἱ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.2.10"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.2.10"
∷ word (δ ∷ ό ∷ ξ ∷ α ∷ ν ∷ []) "Heb.2.10"
∷ word (ἀ ∷ γ ∷ α ∷ γ ∷ ό ∷ ν ∷ τ ∷ α ∷ []) "Heb.2.10"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.2.10"
∷ word (ἀ ∷ ρ ∷ χ ∷ η ∷ γ ∷ ὸ ∷ ν ∷ []) "Heb.2.10"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.2.10"
∷ word (σ ∷ ω ∷ τ ∷ η ∷ ρ ∷ ί ∷ α ∷ ς ∷ []) "Heb.2.10"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.2.10"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.2.10"
∷ word (π ∷ α ∷ θ ∷ η ∷ μ ∷ ά ∷ τ ∷ ω ∷ ν ∷ []) "Heb.2.10"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ῶ ∷ σ ∷ α ∷ ι ∷ []) "Heb.2.10"
∷ word (ὅ ∷ []) "Heb.2.11"
∷ word (τ ∷ ε ∷ []) "Heb.2.11"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.2.11"
∷ word (ἁ ∷ γ ∷ ι ∷ ά ∷ ζ ∷ ω ∷ ν ∷ []) "Heb.2.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.11"
∷ word (ο ∷ ἱ ∷ []) "Heb.2.11"
∷ word (ἁ ∷ γ ∷ ι ∷ α ∷ ζ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.2.11"
∷ word (ἐ ∷ ξ ∷ []) "Heb.2.11"
∷ word (ἑ ∷ ν ∷ ὸ ∷ ς ∷ []) "Heb.2.11"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.2.11"
∷ word (δ ∷ ι ∷ []) "Heb.2.11"
∷ word (ἣ ∷ ν ∷ []) "Heb.2.11"
∷ word (α ∷ ἰ ∷ τ ∷ ί ∷ α ∷ ν ∷ []) "Heb.2.11"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.2.11"
∷ word (ἐ ∷ π ∷ α ∷ ι ∷ σ ∷ χ ∷ ύ ∷ ν ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.2.11"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.2.11"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.2.11"
∷ word (κ ∷ α ∷ ∙λ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.2.11"
∷ word (∙λ ∷ έ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.2.12"
∷ word (Ἀ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ῶ ∷ []) "Heb.2.12"
∷ word (τ ∷ ὸ ∷ []) "Heb.2.12"
∷ word (ὄ ∷ ν ∷ ο ∷ μ ∷ ά ∷ []) "Heb.2.12"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.2.12"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.2.12"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.2.12"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.2.12"
∷ word (ἐ ∷ ν ∷ []) "Heb.2.12"
∷ word (μ ∷ έ ∷ σ ∷ ῳ ∷ []) "Heb.2.12"
∷ word (ἐ ∷ κ ∷ κ ∷ ∙λ ∷ η ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.2.12"
∷ word (ὑ ∷ μ ∷ ν ∷ ή ∷ σ ∷ ω ∷ []) "Heb.2.12"
∷ word (σ ∷ ε ∷ []) "Heb.2.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.13"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.2.13"
∷ word (Ἐ ∷ γ ∷ ὼ ∷ []) "Heb.2.13"
∷ word (ἔ ∷ σ ∷ ο ∷ μ ∷ α ∷ ι ∷ []) "Heb.2.13"
∷ word (π ∷ ε ∷ π ∷ ο ∷ ι ∷ θ ∷ ὼ ∷ ς ∷ []) "Heb.2.13"
∷ word (ἐ ∷ π ∷ []) "Heb.2.13"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.2.13"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.13"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.2.13"
∷ word (Ἰ ∷ δ ∷ ο ∷ ὺ ∷ []) "Heb.2.13"
∷ word (ἐ ∷ γ ∷ ὼ ∷ []) "Heb.2.13"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.13"
∷ word (τ ∷ ὰ ∷ []) "Heb.2.13"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ί ∷ α ∷ []) "Heb.2.13"
∷ word (ἅ ∷ []) "Heb.2.13"
∷ word (μ ∷ ο ∷ ι ∷ []) "Heb.2.13"
∷ word (ἔ ∷ δ ∷ ω ∷ κ ∷ ε ∷ ν ∷ []) "Heb.2.13"
∷ word (ὁ ∷ []) "Heb.2.13"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.2.13"
∷ word (Ἐ ∷ π ∷ ε ∷ ὶ ∷ []) "Heb.2.14"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.2.14"
∷ word (τ ∷ ὰ ∷ []) "Heb.2.14"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ί ∷ α ∷ []) "Heb.2.14"
∷ word (κ ∷ ε ∷ κ ∷ ο ∷ ι ∷ ν ∷ ώ ∷ ν ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.2.14"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.2.14"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.14"
∷ word (σ ∷ α ∷ ρ ∷ κ ∷ ό ∷ ς ∷ []) "Heb.2.14"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.14"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.2.14"
∷ word (π ∷ α ∷ ρ ∷ α ∷ π ∷ ∙λ ∷ η ∷ σ ∷ ί ∷ ω ∷ ς ∷ []) "Heb.2.14"
∷ word (μ ∷ ε ∷ τ ∷ έ ∷ σ ∷ χ ∷ ε ∷ ν ∷ []) "Heb.2.14"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.2.14"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.2.14"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.2.14"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.2.14"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.2.14"
∷ word (θ ∷ α ∷ ν ∷ ά ∷ τ ∷ ο ∷ υ ∷ []) "Heb.2.14"
∷ word (κ ∷ α ∷ τ ∷ α ∷ ρ ∷ γ ∷ ή ∷ σ ∷ ῃ ∷ []) "Heb.2.14"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.2.14"
∷ word (τ ∷ ὸ ∷ []) "Heb.2.14"
∷ word (κ ∷ ρ ∷ ά ∷ τ ∷ ο ∷ ς ∷ []) "Heb.2.14"
∷ word (ἔ ∷ χ ∷ ο ∷ ν ∷ τ ∷ α ∷ []) "Heb.2.14"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.2.14"
∷ word (θ ∷ α ∷ ν ∷ ά ∷ τ ∷ ο ∷ υ ∷ []) "Heb.2.14"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ []) "Heb.2.14"
∷ word (ἔ ∷ σ ∷ τ ∷ ι ∷ []) "Heb.2.14"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.2.14"
∷ word (δ ∷ ι ∷ ά ∷ β ∷ ο ∷ ∙λ ∷ ο ∷ ν ∷ []) "Heb.2.14"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.15"
∷ word (ἀ ∷ π ∷ α ∷ ∙λ ∷ ∙λ ∷ ά ∷ ξ ∷ ῃ ∷ []) "Heb.2.15"
∷ word (τ ∷ ο ∷ ύ ∷ τ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.2.15"
∷ word (ὅ ∷ σ ∷ ο ∷ ι ∷ []) "Heb.2.15"
∷ word (φ ∷ ό ∷ β ∷ ῳ ∷ []) "Heb.2.15"
∷ word (θ ∷ α ∷ ν ∷ ά ∷ τ ∷ ο ∷ υ ∷ []) "Heb.2.15"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.2.15"
∷ word (π ∷ α ∷ ν ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.2.15"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.2.15"
∷ word (ζ ∷ ῆ ∷ ν ∷ []) "Heb.2.15"
∷ word (ἔ ∷ ν ∷ ο ∷ χ ∷ ο ∷ ι ∷ []) "Heb.2.15"
∷ word (ἦ ∷ σ ∷ α ∷ ν ∷ []) "Heb.2.15"
∷ word (δ ∷ ο ∷ υ ∷ ∙λ ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.2.15"
∷ word (ο ∷ ὐ ∷ []) "Heb.2.16"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.2.16"
∷ word (δ ∷ ή ∷ π ∷ ο ∷ υ ∷ []) "Heb.2.16"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ω ∷ ν ∷ []) "Heb.2.16"
∷ word (ἐ ∷ π ∷ ι ∷ ∙λ ∷ α ∷ μ ∷ β ∷ ά ∷ ν ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.2.16"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.2.16"
∷ word (σ ∷ π ∷ έ ∷ ρ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.2.16"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ὰ ∷ μ ∷ []) "Heb.2.16"
∷ word (ἐ ∷ π ∷ ι ∷ ∙λ ∷ α ∷ μ ∷ β ∷ ά ∷ ν ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.2.16"
∷ word (ὅ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.2.17"
∷ word (ὤ ∷ φ ∷ ε ∷ ι ∷ ∙λ ∷ ε ∷ ν ∷ []) "Heb.2.17"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.2.17"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.2.17"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.2.17"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.2.17"
∷ word (ὁ ∷ μ ∷ ο ∷ ι ∷ ω ∷ θ ∷ ῆ ∷ ν ∷ α ∷ ι ∷ []) "Heb.2.17"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.2.17"
∷ word (ἐ ∷ ∙λ ∷ ε ∷ ή ∷ μ ∷ ω ∷ ν ∷ []) "Heb.2.17"
∷ word (γ ∷ έ ∷ ν ∷ η ∷ τ ∷ α ∷ ι ∷ []) "Heb.2.17"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.2.17"
∷ word (π ∷ ι ∷ σ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.2.17"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.2.17"
∷ word (τ ∷ ὰ ∷ []) "Heb.2.17"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.2.17"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.2.17"
∷ word (θ ∷ ε ∷ ό ∷ ν ∷ []) "Heb.2.17"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.2.17"
∷ word (τ ∷ ὸ ∷ []) "Heb.2.17"
∷ word (ἱ ∷ ∙λ ∷ ά ∷ σ ∷ κ ∷ ε ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.2.17"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.2.17"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.2.17"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.2.17"
∷ word (∙λ ∷ α ∷ ο ∷ ῦ ∷ []) "Heb.2.17"
∷ word (ἐ ∷ ν ∷ []) "Heb.2.18"
∷ word (ᾧ ∷ []) "Heb.2.18"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.2.18"
∷ word (π ∷ έ ∷ π ∷ ο ∷ ν ∷ θ ∷ ε ∷ ν ∷ []) "Heb.2.18"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.2.18"
∷ word (π ∷ ε ∷ ι ∷ ρ ∷ α ∷ σ ∷ θ ∷ ε ∷ ί ∷ ς ∷ []) "Heb.2.18"
∷ word (δ ∷ ύ ∷ ν ∷ α ∷ τ ∷ α ∷ ι ∷ []) "Heb.2.18"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.2.18"
∷ word (π ∷ ε ∷ ι ∷ ρ ∷ α ∷ ζ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ ς ∷ []) "Heb.2.18"
∷ word (β ∷ ο ∷ η ∷ θ ∷ ῆ ∷ σ ∷ α ∷ ι ∷ []) "Heb.2.18"
∷ word (Ὅ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.3.1"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ο ∷ ὶ ∷ []) "Heb.3.1"
∷ word (ἅ ∷ γ ∷ ι ∷ ο ∷ ι ∷ []) "Heb.3.1"
∷ word (κ ∷ ∙λ ∷ ή ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.3.1"
∷ word (ἐ ∷ π ∷ ο ∷ υ ∷ ρ ∷ α ∷ ν ∷ ί ∷ ο ∷ υ ∷ []) "Heb.3.1"
∷ word (μ ∷ έ ∷ τ ∷ ο ∷ χ ∷ ο ∷ ι ∷ []) "Heb.3.1"
∷ word (κ ∷ α ∷ τ ∷ α ∷ ν ∷ ο ∷ ή ∷ σ ∷ α ∷ τ ∷ ε ∷ []) "Heb.3.1"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.3.1"
∷ word (ἀ ∷ π ∷ ό ∷ σ ∷ τ ∷ ο ∷ ∙λ ∷ ο ∷ ν ∷ []) "Heb.3.1"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.3.1"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ έ ∷ α ∷ []) "Heb.3.1"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.3.1"
∷ word (ὁ ∷ μ ∷ ο ∷ ∙λ ∷ ο ∷ γ ∷ ί ∷ α ∷ ς ∷ []) "Heb.3.1"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.3.1"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ν ∷ []) "Heb.3.1"
∷ word (π ∷ ι ∷ σ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.3.2"
∷ word (ὄ ∷ ν ∷ τ ∷ α ∷ []) "Heb.3.2"
∷ word (τ ∷ ῷ ∷ []) "Heb.3.2"
∷ word (π ∷ ο ∷ ι ∷ ή ∷ σ ∷ α ∷ ν ∷ τ ∷ ι ∷ []) "Heb.3.2"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.3.2"
∷ word (ὡ ∷ ς ∷ []) "Heb.3.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.3.2"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ ῆ ∷ ς ∷ []) "Heb.3.2"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.2"
∷ word (τ ∷ ῷ ∷ []) "Heb.3.2"
∷ word (ο ∷ ἴ ∷ κ ∷ ῳ ∷ []) "Heb.3.2"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.3.2"
∷ word (π ∷ ∙λ ∷ ε ∷ ί ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.3.3"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.3.3"
∷ word (ο ∷ ὗ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.3.3"
∷ word (δ ∷ ό ∷ ξ ∷ η ∷ ς ∷ []) "Heb.3.3"
∷ word (π ∷ α ∷ ρ ∷ ὰ ∷ []) "Heb.3.3"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ ῆ ∷ ν ∷ []) "Heb.3.3"
∷ word (ἠ ∷ ξ ∷ ί ∷ ω ∷ τ ∷ α ∷ ι ∷ []) "Heb.3.3"
∷ word (κ ∷ α ∷ θ ∷ []) "Heb.3.3"
∷ word (ὅ ∷ σ ∷ ο ∷ ν ∷ []) "Heb.3.3"
∷ word (π ∷ ∙λ ∷ ε ∷ ί ∷ ο ∷ ν ∷ α ∷ []) "Heb.3.3"
∷ word (τ ∷ ι ∷ μ ∷ ὴ ∷ ν ∷ []) "Heb.3.3"
∷ word (ἔ ∷ χ ∷ ε ∷ ι ∷ []) "Heb.3.3"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.3.3"
∷ word (ο ∷ ἴ ∷ κ ∷ ο ∷ υ ∷ []) "Heb.3.3"
∷ word (ὁ ∷ []) "Heb.3.3"
∷ word (κ ∷ α ∷ τ ∷ α ∷ σ ∷ κ ∷ ε ∷ υ ∷ ά ∷ σ ∷ α ∷ ς ∷ []) "Heb.3.3"
∷ word (α ∷ ὐ ∷ τ ∷ ό ∷ ν ∷ []) "Heb.3.3"
∷ word (π ∷ ᾶ ∷ ς ∷ []) "Heb.3.4"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.3.4"
∷ word (ο ∷ ἶ ∷ κ ∷ ο ∷ ς ∷ []) "Heb.3.4"
∷ word (κ ∷ α ∷ τ ∷ α ∷ σ ∷ κ ∷ ε ∷ υ ∷ ά ∷ ζ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.3.4"
∷ word (ὑ ∷ π ∷ ό ∷ []) "Heb.3.4"
∷ word (τ ∷ ι ∷ ν ∷ ο ∷ ς ∷ []) "Heb.3.4"
∷ word (ὁ ∷ []) "Heb.3.4"
∷ word (δ ∷ ὲ ∷ []) "Heb.3.4"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.3.4"
∷ word (κ ∷ α ∷ τ ∷ α ∷ σ ∷ κ ∷ ε ∷ υ ∷ ά ∷ σ ∷ α ∷ ς ∷ []) "Heb.3.4"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.3.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.3.5"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ ῆ ∷ ς ∷ []) "Heb.3.5"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.3.5"
∷ word (π ∷ ι ∷ σ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.3.5"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.5"
∷ word (ὅ ∷ ∙λ ∷ ῳ ∷ []) "Heb.3.5"
∷ word (τ ∷ ῷ ∷ []) "Heb.3.5"
∷ word (ο ∷ ἴ ∷ κ ∷ ῳ ∷ []) "Heb.3.5"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.3.5"
∷ word (ὡ ∷ ς ∷ []) "Heb.3.5"
∷ word (θ ∷ ε ∷ ρ ∷ ά ∷ π ∷ ω ∷ ν ∷ []) "Heb.3.5"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.3.5"
∷ word (μ ∷ α ∷ ρ ∷ τ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.3.5"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.3.5"
∷ word (∙λ ∷ α ∷ ∙λ ∷ η ∷ θ ∷ η ∷ σ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.3.5"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.3.6"
∷ word (δ ∷ ὲ ∷ []) "Heb.3.6"
∷ word (ὡ ∷ ς ∷ []) "Heb.3.6"
∷ word (υ ∷ ἱ ∷ ὸ ∷ ς ∷ []) "Heb.3.6"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.3.6"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.3.6"
∷ word (ο ∷ ἶ ∷ κ ∷ ο ∷ ν ∷ []) "Heb.3.6"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.3.6"
∷ word (ὅ ∷ ς ∷ []) "Heb.3.6"
∷ word (ο ∷ ἶ ∷ κ ∷ ό ∷ ς ∷ []) "Heb.3.6"
∷ word (ἐ ∷ σ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.3.6"
∷ word (ἡ ∷ μ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.3.6"
∷ word (ἐ ∷ ὰ ∷ ν ∷ []) "Heb.3.6"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.3.6"
∷ word (π ∷ α ∷ ρ ∷ ρ ∷ η ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.3.6"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.3.6"
∷ word (τ ∷ ὸ ∷ []) "Heb.3.6"
∷ word (κ ∷ α ∷ ύ ∷ χ ∷ η ∷ μ ∷ α ∷ []) "Heb.3.6"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.3.6"
∷ word (ἐ ∷ ∙λ ∷ π ∷ ί ∷ δ ∷ ο ∷ ς ∷ []) "Heb.3.6"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ σ ∷ χ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.3.6"
∷ word (Δ ∷ ι ∷ ό ∷ []) "Heb.3.7"
∷ word (κ ∷ α ∷ θ ∷ ὼ ∷ ς ∷ []) "Heb.3.7"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.3.7"
∷ word (τ ∷ ὸ ∷ []) "Heb.3.7"
∷ word (π ∷ ν ∷ ε ∷ ῦ ∷ μ ∷ α ∷ []) "Heb.3.7"
∷ word (τ ∷ ὸ ∷ []) "Heb.3.7"
∷ word (ἅ ∷ γ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.3.7"
∷ word (Σ ∷ ή ∷ μ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.3.7"
∷ word (ἐ ∷ ὰ ∷ ν ∷ []) "Heb.3.7"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.3.7"
∷ word (φ ∷ ω ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.3.7"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.3.7"
∷ word (ἀ ∷ κ ∷ ο ∷ ύ ∷ σ ∷ η ∷ τ ∷ ε ∷ []) "Heb.3.7"
∷ word (μ ∷ ὴ ∷ []) "Heb.3.8"
∷ word (σ ∷ κ ∷ ∙λ ∷ η ∷ ρ ∷ ύ ∷ ν ∷ η ∷ τ ∷ ε ∷ []) "Heb.3.8"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.3.8"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ ς ∷ []) "Heb.3.8"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.3.8"
∷ word (ὡ ∷ ς ∷ []) "Heb.3.8"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.8"
∷ word (τ ∷ ῷ ∷ []) "Heb.3.8"
∷ word (π ∷ α ∷ ρ ∷ α ∷ π ∷ ι ∷ κ ∷ ρ ∷ α ∷ σ ∷ μ ∷ ῷ ∷ []) "Heb.3.8"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.3.8"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.3.8"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.3.8"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.3.8"
∷ word (π ∷ ε ∷ ι ∷ ρ ∷ α ∷ σ ∷ μ ∷ ο ∷ ῦ ∷ []) "Heb.3.8"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.8"
∷ word (τ ∷ ῇ ∷ []) "Heb.3.8"
∷ word (ἐ ∷ ρ ∷ ή ∷ μ ∷ ῳ ∷ []) "Heb.3.8"
∷ word (ο ∷ ὗ ∷ []) "Heb.3.9"
∷ word (ἐ ∷ π ∷ ε ∷ ί ∷ ρ ∷ α ∷ σ ∷ α ∷ ν ∷ []) "Heb.3.9"
∷ word (ο ∷ ἱ ∷ []) "Heb.3.9"
∷ word (π ∷ α ∷ τ ∷ έ ∷ ρ ∷ ε ∷ ς ∷ []) "Heb.3.9"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.3.9"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.9"
∷ word (δ ∷ ο ∷ κ ∷ ι ∷ μ ∷ α ∷ σ ∷ ί ∷ ᾳ ∷ []) "Heb.3.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.3.9"
∷ word (ε ∷ ἶ ∷ δ ∷ ο ∷ ν ∷ []) "Heb.3.9"
∷ word (τ ∷ ὰ ∷ []) "Heb.3.9"
∷ word (ἔ ∷ ρ ∷ γ ∷ α ∷ []) "Heb.3.9"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.3.9"
∷ word (τ ∷ ε ∷ σ ∷ σ ∷ ε ∷ ρ ∷ ά ∷ κ ∷ ο ∷ ν ∷ τ ∷ α ∷ []) "Heb.3.10"
∷ word (ἔ ∷ τ ∷ η ∷ []) "Heb.3.10"
∷ word (δ ∷ ι ∷ ὸ ∷ []) "Heb.3.10"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ώ ∷ χ ∷ θ ∷ ι ∷ σ ∷ α ∷ []) "Heb.3.10"
∷ word (τ ∷ ῇ ∷ []) "Heb.3.10"
∷ word (γ ∷ ε ∷ ν ∷ ε ∷ ᾷ ∷ []) "Heb.3.10"
∷ word (τ ∷ α ∷ ύ ∷ τ ∷ ῃ ∷ []) "Heb.3.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.3.10"
∷ word (ε ∷ ἶ ∷ π ∷ ο ∷ ν ∷ []) "Heb.3.10"
∷ word (Ἀ ∷ ε ∷ ὶ ∷ []) "Heb.3.10"
∷ word (π ∷ ∙λ ∷ α ∷ ν ∷ ῶ ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.3.10"
∷ word (τ ∷ ῇ ∷ []) "Heb.3.10"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ ᾳ ∷ []) "Heb.3.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὶ ∷ []) "Heb.3.10"
∷ word (δ ∷ ὲ ∷ []) "Heb.3.10"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.3.10"
∷ word (ἔ ∷ γ ∷ ν ∷ ω ∷ σ ∷ α ∷ ν ∷ []) "Heb.3.10"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.3.10"
∷ word (ὁ ∷ δ ∷ ο ∷ ύ ∷ ς ∷ []) "Heb.3.10"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.3.10"
∷ word (ὡ ∷ ς ∷ []) "Heb.3.11"
∷ word (ὤ ∷ μ ∷ ο ∷ σ ∷ α ∷ []) "Heb.3.11"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.11"
∷ word (τ ∷ ῇ ∷ []) "Heb.3.11"
∷ word (ὀ ∷ ρ ∷ γ ∷ ῇ ∷ []) "Heb.3.11"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.3.11"
∷ word (Ε ∷ ἰ ∷ []) "Heb.3.11"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ∙λ ∷ ε ∷ ύ ∷ σ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.3.11"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.3.11"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.3.11"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ π ∷ α ∷ υ ∷ σ ∷ ί ∷ ν ∷ []) "Heb.3.11"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.3.11"
∷ word (β ∷ ∙λ ∷ έ ∷ π ∷ ε ∷ τ ∷ ε ∷ []) "Heb.3.12"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ο ∷ ί ∷ []) "Heb.3.12"
∷ word (μ ∷ ή ∷ π ∷ ο ∷ τ ∷ ε ∷ []) "Heb.3.12"
∷ word (ἔ ∷ σ ∷ τ ∷ α ∷ ι ∷ []) "Heb.3.12"
∷ word (ἔ ∷ ν ∷ []) "Heb.3.12"
∷ word (τ ∷ ι ∷ ν ∷ ι ∷ []) "Heb.3.12"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.3.12"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ []) "Heb.3.12"
∷ word (π ∷ ο ∷ ν ∷ η ∷ ρ ∷ ὰ ∷ []) "Heb.3.12"
∷ word (ἀ ∷ π ∷ ι ∷ σ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.3.12"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.12"
∷ word (τ ∷ ῷ ∷ []) "Heb.3.12"
∷ word (ἀ ∷ π ∷ ο ∷ σ ∷ τ ∷ ῆ ∷ ν ∷ α ∷ ι ∷ []) "Heb.3.12"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.3.12"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.3.12"
∷ word (ζ ∷ ῶ ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.3.12"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.3.13"
∷ word (π ∷ α ∷ ρ ∷ α ∷ κ ∷ α ∷ ∙λ ∷ ε ∷ ῖ ∷ τ ∷ ε ∷ []) "Heb.3.13"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.3.13"
∷ word (κ ∷ α ∷ θ ∷ []) "Heb.3.13"
∷ word (ἑ ∷ κ ∷ ά ∷ σ ∷ τ ∷ η ∷ ν ∷ []) "Heb.3.13"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.3.13"
∷ word (ἄ ∷ χ ∷ ρ ∷ ι ∷ ς ∷ []) "Heb.3.13"
∷ word (ο ∷ ὗ ∷ []) "Heb.3.13"
∷ word (τ ∷ ὸ ∷ []) "Heb.3.13"
∷ word (Σ ∷ ή ∷ μ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.3.13"
∷ word (κ ∷ α ∷ ∙λ ∷ ε ∷ ῖ ∷ τ ∷ α ∷ ι ∷ []) "Heb.3.13"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.3.13"
∷ word (μ ∷ ὴ ∷ []) "Heb.3.13"
∷ word (σ ∷ κ ∷ ∙λ ∷ η ∷ ρ ∷ υ ∷ ν ∷ θ ∷ ῇ ∷ []) "Heb.3.13"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.3.13"
∷ word (ἐ ∷ ξ ∷ []) "Heb.3.13"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.3.13"
∷ word (ἀ ∷ π ∷ ά ∷ τ ∷ ῃ ∷ []) "Heb.3.13"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.3.13"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.3.13"
∷ word (μ ∷ έ ∷ τ ∷ ο ∷ χ ∷ ο ∷ ι ∷ []) "Heb.3.14"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.3.14"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.3.14"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.3.14"
∷ word (γ ∷ ε ∷ γ ∷ ό ∷ ν ∷ α ∷ μ ∷ ε ∷ ν ∷ []) "Heb.3.14"
∷ word (ἐ ∷ ά ∷ ν ∷ π ∷ ε ∷ ρ ∷ []) "Heb.3.14"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.3.14"
∷ word (ἀ ∷ ρ ∷ χ ∷ ὴ ∷ ν ∷ []) "Heb.3.14"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.3.14"
∷ word (ὑ ∷ π ∷ ο ∷ σ ∷ τ ∷ ά ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.3.14"
∷ word (μ ∷ έ ∷ χ ∷ ρ ∷ ι ∷ []) "Heb.3.14"
∷ word (τ ∷ έ ∷ ∙λ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.3.14"
∷ word (β ∷ ε ∷ β ∷ α ∷ ί ∷ α ∷ ν ∷ []) "Heb.3.14"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ σ ∷ χ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.3.14"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.15"
∷ word (τ ∷ ῷ ∷ []) "Heb.3.15"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.3.15"
∷ word (Σ ∷ ή ∷ μ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.3.15"
∷ word (ἐ ∷ ὰ ∷ ν ∷ []) "Heb.3.15"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.3.15"
∷ word (φ ∷ ω ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.3.15"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.3.15"
∷ word (ἀ ∷ κ ∷ ο ∷ ύ ∷ σ ∷ η ∷ τ ∷ ε ∷ []) "Heb.3.15"
∷ word (Μ ∷ ὴ ∷ []) "Heb.3.15"
∷ word (σ ∷ κ ∷ ∙λ ∷ η ∷ ρ ∷ ύ ∷ ν ∷ η ∷ τ ∷ ε ∷ []) "Heb.3.15"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.3.15"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ ς ∷ []) "Heb.3.15"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.3.15"
∷ word (ὡ ∷ ς ∷ []) "Heb.3.15"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.15"
∷ word (τ ∷ ῷ ∷ []) "Heb.3.15"
∷ word (π ∷ α ∷ ρ ∷ α ∷ π ∷ ι ∷ κ ∷ ρ ∷ α ∷ σ ∷ μ ∷ ῷ ∷ []) "Heb.3.15"
∷ word (τ ∷ ί ∷ ν ∷ ε ∷ ς ∷ []) "Heb.3.16"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.3.16"
∷ word (ἀ ∷ κ ∷ ο ∷ ύ ∷ σ ∷ α ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.3.16"
∷ word (π ∷ α ∷ ρ ∷ ε ∷ π ∷ ί ∷ κ ∷ ρ ∷ α ∷ ν ∷ α ∷ ν ∷ []) "Heb.3.16"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ []) "Heb.3.16"
∷ word (ο ∷ ὐ ∷ []) "Heb.3.16"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.3.16"
∷ word (ο ∷ ἱ ∷ []) "Heb.3.16"
∷ word (ἐ ∷ ξ ∷ ε ∷ ∙λ ∷ θ ∷ ό ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.3.16"
∷ word (ἐ ∷ ξ ∷ []) "Heb.3.16"
∷ word (Α ∷ ἰ ∷ γ ∷ ύ ∷ π ∷ τ ∷ ο ∷ υ ∷ []) "Heb.3.16"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.3.16"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ έ ∷ ω ∷ ς ∷ []) "Heb.3.16"
∷ word (τ ∷ ί ∷ σ ∷ ι ∷ ν ∷ []) "Heb.3.17"
∷ word (δ ∷ ὲ ∷ []) "Heb.3.17"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ώ ∷ χ ∷ θ ∷ ι ∷ σ ∷ ε ∷ ν ∷ []) "Heb.3.17"
∷ word (τ ∷ ε ∷ σ ∷ σ ∷ ε ∷ ρ ∷ ά ∷ κ ∷ ο ∷ ν ∷ τ ∷ α ∷ []) "Heb.3.17"
∷ word (ἔ ∷ τ ∷ η ∷ []) "Heb.3.17"
∷ word (ο ∷ ὐ ∷ χ ∷ ὶ ∷ []) "Heb.3.17"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.3.17"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ή ∷ σ ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.3.17"
∷ word (ὧ ∷ ν ∷ []) "Heb.3.17"
∷ word (τ ∷ ὰ ∷ []) "Heb.3.17"
∷ word (κ ∷ ῶ ∷ ∙λ ∷ α ∷ []) "Heb.3.17"
∷ word (ἔ ∷ π ∷ ε ∷ σ ∷ ε ∷ ν ∷ []) "Heb.3.17"
∷ word (ἐ ∷ ν ∷ []) "Heb.3.17"
∷ word (τ ∷ ῇ ∷ []) "Heb.3.17"
∷ word (ἐ ∷ ρ ∷ ή ∷ μ ∷ ῳ ∷ []) "Heb.3.17"
∷ word (τ ∷ ί ∷ σ ∷ ι ∷ ν ∷ []) "Heb.3.18"
∷ word (δ ∷ ὲ ∷ []) "Heb.3.18"
∷ word (ὤ ∷ μ ∷ ο ∷ σ ∷ ε ∷ ν ∷ []) "Heb.3.18"
∷ word (μ ∷ ὴ ∷ []) "Heb.3.18"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ∙λ ∷ ε ∷ ύ ∷ σ ∷ ε ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.3.18"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.3.18"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.3.18"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ π ∷ α ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.3.18"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.3.18"
∷ word (ε ∷ ἰ ∷ []) "Heb.3.18"
∷ word (μ ∷ ὴ ∷ []) "Heb.3.18"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.3.18"
∷ word (ἀ ∷ π ∷ ε ∷ ι ∷ θ ∷ ή ∷ σ ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.3.18"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.3.19"
∷ word (β ∷ ∙λ ∷ έ ∷ π ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.3.19"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.3.19"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.3.19"
∷ word (ἠ ∷ δ ∷ υ ∷ ν ∷ ή ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.3.19"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ∙λ ∷ θ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.3.19"
∷ word (δ ∷ ι ∷ []) "Heb.3.19"
∷ word (ἀ ∷ π ∷ ι ∷ σ ∷ τ ∷ ί ∷ α ∷ ν ∷ []) "Heb.3.19"
∷ word (Φ ∷ ο ∷ β ∷ η ∷ θ ∷ ῶ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.4.1"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.4.1"
∷ word (μ ∷ ή ∷ π ∷ ο ∷ τ ∷ ε ∷ []) "Heb.4.1"
∷ word (κ ∷ α ∷ τ ∷ α ∷ ∙λ ∷ ε ∷ ι ∷ π ∷ ο ∷ μ ∷ έ ∷ ν ∷ η ∷ ς ∷ []) "Heb.4.1"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.4.1"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ∙λ ∷ θ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.4.1"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.4.1"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.4.1"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ π ∷ α ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.4.1"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.4.1"
∷ word (δ ∷ ο ∷ κ ∷ ῇ ∷ []) "Heb.4.1"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.4.1"
∷ word (ἐ ∷ ξ ∷ []) "Heb.4.1"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.4.1"
∷ word (ὑ ∷ σ ∷ τ ∷ ε ∷ ρ ∷ η ∷ κ ∷ έ ∷ ν ∷ α ∷ ι ∷ []) "Heb.4.1"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.2"
∷ word (γ ∷ ά ∷ ρ ∷ []) "Heb.4.2"
∷ word (ἐ ∷ σ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.4.2"
∷ word (ε ∷ ὐ ∷ η ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ι ∷ σ ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ []) "Heb.4.2"
∷ word (κ ∷ α ∷ θ ∷ ά ∷ π ∷ ε ∷ ρ ∷ []) "Heb.4.2"
∷ word (κ ∷ ἀ ∷ κ ∷ ε ∷ ῖ ∷ ν ∷ ο ∷ ι ∷ []) "Heb.4.2"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ []) "Heb.4.2"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.4.2"
∷ word (ὠ ∷ φ ∷ έ ∷ ∙λ ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.4.2"
∷ word (ὁ ∷ []) "Heb.4.2"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ς ∷ []) "Heb.4.2"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.4.2"
∷ word (ἀ ∷ κ ∷ ο ∷ ῆ ∷ ς ∷ []) "Heb.4.2"
∷ word (ἐ ∷ κ ∷ ε ∷ ί ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.4.2"
∷ word (μ ∷ ὴ ∷ []) "Heb.4.2"
∷ word (σ ∷ υ ∷ γ ∷ κ ∷ ε ∷ κ ∷ ε ∷ ρ ∷ α ∷ σ ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.4.2"
∷ word (τ ∷ ῇ ∷ []) "Heb.4.2"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.4.2"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.4.2"
∷ word (ἀ ∷ κ ∷ ο ∷ ύ ∷ σ ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.4.2"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ρ ∷ χ ∷ ό ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.4.3"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.4.3"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.4.3"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ π ∷ α ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.4.3"
∷ word (ο ∷ ἱ ∷ []) "Heb.4.3"
∷ word (π ∷ ι ∷ σ ∷ τ ∷ ε ∷ ύ ∷ σ ∷ α ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.4.3"
∷ word (κ ∷ α ∷ θ ∷ ὼ ∷ ς ∷ []) "Heb.4.3"
∷ word (ε ∷ ἴ ∷ ρ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.4.3"
∷ word (Ὡ ∷ ς ∷ []) "Heb.4.3"
∷ word (ὤ ∷ μ ∷ ο ∷ σ ∷ α ∷ []) "Heb.4.3"
∷ word (ἐ ∷ ν ∷ []) "Heb.4.3"
∷ word (τ ∷ ῇ ∷ []) "Heb.4.3"
∷ word (ὀ ∷ ρ ∷ γ ∷ ῇ ∷ []) "Heb.4.3"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.4.3"
∷ word (Ε ∷ ἰ ∷ []) "Heb.4.3"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ∙λ ∷ ε ∷ ύ ∷ σ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.4.3"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.4.3"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.4.3"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ π ∷ α ∷ υ ∷ σ ∷ ί ∷ ν ∷ []) "Heb.4.3"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.4.3"
∷ word (κ ∷ α ∷ ί ∷ τ ∷ ο ∷ ι ∷ []) "Heb.4.3"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.4.3"
∷ word (ἔ ∷ ρ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.4.3"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.4.3"
∷ word (κ ∷ α ∷ τ ∷ α ∷ β ∷ ο ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.4.3"
∷ word (κ ∷ ό ∷ σ ∷ μ ∷ ο ∷ υ ∷ []) "Heb.4.3"
∷ word (γ ∷ ε ∷ ν ∷ η ∷ θ ∷ έ ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.4.3"
∷ word (ε ∷ ἴ ∷ ρ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.4.4"
∷ word (γ ∷ ά ∷ ρ ∷ []) "Heb.4.4"
∷ word (π ∷ ο ∷ υ ∷ []) "Heb.4.4"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.4.4"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.4.4"
∷ word (ἑ ∷ β ∷ δ ∷ ό ∷ μ ∷ η ∷ ς ∷ []) "Heb.4.4"
∷ word (ο ∷ ὕ ∷ τ ∷ ω ∷ ς ∷ []) "Heb.4.4"
∷ word (Κ ∷ α ∷ ὶ ∷ []) "Heb.4.4"
∷ word (κ ∷ α ∷ τ ∷ έ ∷ π ∷ α ∷ υ ∷ σ ∷ ε ∷ ν ∷ []) "Heb.4.4"
∷ word (ὁ ∷ []) "Heb.4.4"
∷ word (θ ∷ ε ∷ ὸ ∷ ς ∷ []) "Heb.4.4"
∷ word (ἐ ∷ ν ∷ []) "Heb.4.4"
∷ word (τ ∷ ῇ ∷ []) "Heb.4.4"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ ᾳ ∷ []) "Heb.4.4"
∷ word (τ ∷ ῇ ∷ []) "Heb.4.4"
∷ word (ἑ ∷ β ∷ δ ∷ ό ∷ μ ∷ ῃ ∷ []) "Heb.4.4"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.4.4"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.4.4"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.4.4"
∷ word (ἔ ∷ ρ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.4.4"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.4.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.5"
∷ word (ἐ ∷ ν ∷ []) "Heb.4.5"
∷ word (τ ∷ ο ∷ ύ ∷ τ ∷ ῳ ∷ []) "Heb.4.5"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.4.5"
∷ word (Ε ∷ ἰ ∷ []) "Heb.4.5"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ∙λ ∷ ε ∷ ύ ∷ σ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.4.5"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.4.5"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.4.5"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ π ∷ α ∷ υ ∷ σ ∷ ί ∷ ν ∷ []) "Heb.4.5"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.4.5"
∷ word (ἐ ∷ π ∷ ε ∷ ὶ ∷ []) "Heb.4.6"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.4.6"
∷ word (ἀ ∷ π ∷ ο ∷ ∙λ ∷ ε ∷ ί ∷ π ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.4.6"
∷ word (τ ∷ ι ∷ ν ∷ ὰ ∷ ς ∷ []) "Heb.4.6"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ∙λ ∷ θ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.4.6"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.4.6"
∷ word (α ∷ ὐ ∷ τ ∷ ή ∷ ν ∷ []) "Heb.4.6"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.6"
∷ word (ο ∷ ἱ ∷ []) "Heb.4.6"
∷ word (π ∷ ρ ∷ ό ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.4.6"
∷ word (ε ∷ ὐ ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ι ∷ σ ∷ θ ∷ έ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.4.6"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.4.6"
∷ word (ε ∷ ἰ ∷ σ ∷ ῆ ∷ ∙λ ∷ θ ∷ ο ∷ ν ∷ []) "Heb.4.6"
∷ word (δ ∷ ι ∷ []) "Heb.4.6"
∷ word (ἀ ∷ π ∷ ε ∷ ί ∷ θ ∷ ε ∷ ι ∷ α ∷ ν ∷ []) "Heb.4.6"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.4.7"
∷ word (τ ∷ ι ∷ ν ∷ ὰ ∷ []) "Heb.4.7"
∷ word (ὁ ∷ ρ ∷ ί ∷ ζ ∷ ε ∷ ι ∷ []) "Heb.4.7"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.4.7"
∷ word (Σ ∷ ή ∷ μ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.4.7"
∷ word (ἐ ∷ ν ∷ []) "Heb.4.7"
∷ word (Δ ∷ α ∷ υ ∷ ὶ ∷ δ ∷ []) "Heb.4.7"
∷ word (∙λ ∷ έ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.4.7"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.4.7"
∷ word (τ ∷ ο ∷ σ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.4.7"
∷ word (χ ∷ ρ ∷ ό ∷ ν ∷ ο ∷ ν ∷ []) "Heb.4.7"
∷ word (κ ∷ α ∷ θ ∷ ὼ ∷ ς ∷ []) "Heb.4.7"
∷ word (π ∷ ρ ∷ ο ∷ ε ∷ ί ∷ ρ ∷ η ∷ τ ∷ α ∷ ι ∷ []) "Heb.4.7"
∷ word (Σ ∷ ή ∷ μ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.4.7"
∷ word (ἐ ∷ ὰ ∷ ν ∷ []) "Heb.4.7"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.4.7"
∷ word (φ ∷ ω ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.4.7"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.4.7"
∷ word (ἀ ∷ κ ∷ ο ∷ ύ ∷ σ ∷ η ∷ τ ∷ ε ∷ []) "Heb.4.7"
∷ word (μ ∷ ὴ ∷ []) "Heb.4.7"
∷ word (σ ∷ κ ∷ ∙λ ∷ η ∷ ρ ∷ ύ ∷ ν ∷ η ∷ τ ∷ ε ∷ []) "Heb.4.7"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.4.7"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ ς ∷ []) "Heb.4.7"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.4.7"
∷ word (ε ∷ ἰ ∷ []) "Heb.4.8"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.4.8"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.4.8"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ς ∷ []) "Heb.4.8"
∷ word (κ ∷ α ∷ τ ∷ έ ∷ π ∷ α ∷ υ ∷ σ ∷ ε ∷ ν ∷ []) "Heb.4.8"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.4.8"
∷ word (ἂ ∷ ν ∷ []) "Heb.4.8"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.4.8"
∷ word (ἄ ∷ ∙λ ∷ ∙λ ∷ η ∷ ς ∷ []) "Heb.4.8"
∷ word (ἐ ∷ ∙λ ∷ ά ∷ ∙λ ∷ ε ∷ ι ∷ []) "Heb.4.8"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.4.8"
∷ word (τ ∷ α ∷ ῦ ∷ τ ∷ α ∷ []) "Heb.4.8"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.4.8"
∷ word (ἄ ∷ ρ ∷ α ∷ []) "Heb.4.9"
∷ word (ἀ ∷ π ∷ ο ∷ ∙λ ∷ ε ∷ ί ∷ π ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.4.9"
∷ word (σ ∷ α ∷ β ∷ β ∷ α ∷ τ ∷ ι ∷ σ ∷ μ ∷ ὸ ∷ ς ∷ []) "Heb.4.9"
∷ word (τ ∷ ῷ ∷ []) "Heb.4.9"
∷ word (∙λ ∷ α ∷ ῷ ∷ []) "Heb.4.9"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.4.9"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.4.9"
∷ word (ὁ ∷ []) "Heb.4.10"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.4.10"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ∙λ ∷ θ ∷ ὼ ∷ ν ∷ []) "Heb.4.10"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.4.10"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.4.10"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ π ∷ α ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.4.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.4.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.10"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.4.10"
∷ word (κ ∷ α ∷ τ ∷ έ ∷ π ∷ α ∷ υ ∷ σ ∷ ε ∷ ν ∷ []) "Heb.4.10"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.4.10"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.4.10"
∷ word (ἔ ∷ ρ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.4.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.4.10"
∷ word (ὥ ∷ σ ∷ π ∷ ε ∷ ρ ∷ []) "Heb.4.10"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.4.10"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.4.10"
∷ word (ἰ ∷ δ ∷ ί ∷ ω ∷ ν ∷ []) "Heb.4.10"
∷ word (ὁ ∷ []) "Heb.4.10"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.4.10"
∷ word (σ ∷ π ∷ ο ∷ υ ∷ δ ∷ ά ∷ σ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.4.11"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.4.11"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ∙λ ∷ θ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.4.11"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.4.11"
∷ word (ἐ ∷ κ ∷ ε ∷ ί ∷ ν ∷ η ∷ ν ∷ []) "Heb.4.11"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.4.11"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ π ∷ α ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.4.11"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.4.11"
∷ word (μ ∷ ὴ ∷ []) "Heb.4.11"
∷ word (ἐ ∷ ν ∷ []) "Heb.4.11"
∷ word (τ ∷ ῷ ∷ []) "Heb.4.11"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.4.11"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.4.11"
∷ word (ὑ ∷ π ∷ ο ∷ δ ∷ ε ∷ ί ∷ γ ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.4.11"
∷ word (π ∷ έ ∷ σ ∷ ῃ ∷ []) "Heb.4.11"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.4.11"
∷ word (ἀ ∷ π ∷ ε ∷ ι ∷ θ ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.4.11"
∷ word (Ζ ∷ ῶ ∷ ν ∷ []) "Heb.4.12"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.4.12"
∷ word (ὁ ∷ []) "Heb.4.12"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ς ∷ []) "Heb.4.12"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.4.12"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.4.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.12"
∷ word (ἐ ∷ ν ∷ ε ∷ ρ ∷ γ ∷ ὴ ∷ ς ∷ []) "Heb.4.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.12"
∷ word (τ ∷ ο ∷ μ ∷ ώ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ς ∷ []) "Heb.4.12"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.4.12"
∷ word (π ∷ ᾶ ∷ σ ∷ α ∷ ν ∷ []) "Heb.4.12"
∷ word (μ ∷ ά ∷ χ ∷ α ∷ ι ∷ ρ ∷ α ∷ ν ∷ []) "Heb.4.12"
∷ word (δ ∷ ί ∷ σ ∷ τ ∷ ο ∷ μ ∷ ο ∷ ν ∷ []) "Heb.4.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.12"
∷ word (δ ∷ ι ∷ ϊ ∷ κ ∷ ν ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.4.12"
∷ word (ἄ ∷ χ ∷ ρ ∷ ι ∷ []) "Heb.4.12"
∷ word (μ ∷ ε ∷ ρ ∷ ι ∷ σ ∷ μ ∷ ο ∷ ῦ ∷ []) "Heb.4.12"
∷ word (ψ ∷ υ ∷ χ ∷ ῆ ∷ ς ∷ []) "Heb.4.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.12"
∷ word (π ∷ ν ∷ ε ∷ ύ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.4.12"
∷ word (ἁ ∷ ρ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.4.12"
∷ word (τ ∷ ε ∷ []) "Heb.4.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.12"
∷ word (μ ∷ υ ∷ ε ∷ ∙λ ∷ ῶ ∷ ν ∷ []) "Heb.4.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.12"
∷ word (κ ∷ ρ ∷ ι ∷ τ ∷ ι ∷ κ ∷ ὸ ∷ ς ∷ []) "Heb.4.12"
∷ word (ἐ ∷ ν ∷ θ ∷ υ ∷ μ ∷ ή ∷ σ ∷ ε ∷ ω ∷ ν ∷ []) "Heb.4.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.12"
∷ word (ἐ ∷ ν ∷ ν ∷ ο ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.4.12"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ ς ∷ []) "Heb.4.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.13"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.4.13"
∷ word (ἔ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.4.13"
∷ word (κ ∷ τ ∷ ί ∷ σ ∷ ι ∷ ς ∷ []) "Heb.4.13"
∷ word (ἀ ∷ φ ∷ α ∷ ν ∷ ὴ ∷ ς ∷ []) "Heb.4.13"
∷ word (ἐ ∷ ν ∷ ώ ∷ π ∷ ι ∷ ο ∷ ν ∷ []) "Heb.4.13"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.4.13"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.4.13"
∷ word (δ ∷ ὲ ∷ []) "Heb.4.13"
∷ word (γ ∷ υ ∷ μ ∷ ν ∷ ὰ ∷ []) "Heb.4.13"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.13"
∷ word (τ ∷ ε ∷ τ ∷ ρ ∷ α ∷ χ ∷ η ∷ ∙λ ∷ ι ∷ σ ∷ μ ∷ έ ∷ ν ∷ α ∷ []) "Heb.4.13"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.4.13"
∷ word (ὀ ∷ φ ∷ θ ∷ α ∷ ∙λ ∷ μ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.4.13"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.4.13"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.4.13"
∷ word (ὃ ∷ ν ∷ []) "Heb.4.13"
∷ word (ἡ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.4.13"
∷ word (ὁ ∷ []) "Heb.4.13"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ς ∷ []) "Heb.4.13"
∷ word (Ἔ ∷ χ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.4.14"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.4.14"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ έ ∷ α ∷ []) "Heb.4.14"
∷ word (μ ∷ έ ∷ γ ∷ α ∷ ν ∷ []) "Heb.4.14"
∷ word (δ ∷ ι ∷ ε ∷ ∙λ ∷ η ∷ ∙λ ∷ υ ∷ θ ∷ ό ∷ τ ∷ α ∷ []) "Heb.4.14"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.4.14"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ο ∷ ύ ∷ ς ∷ []) "Heb.4.14"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ν ∷ []) "Heb.4.14"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.4.14"
∷ word (υ ∷ ἱ ∷ ὸ ∷ ν ∷ []) "Heb.4.14"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.4.14"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.4.14"
∷ word (κ ∷ ρ ∷ α ∷ τ ∷ ῶ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.4.14"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.4.14"
∷ word (ὁ ∷ μ ∷ ο ∷ ∙λ ∷ ο ∷ γ ∷ ί ∷ α ∷ ς ∷ []) "Heb.4.14"
∷ word (ο ∷ ὐ ∷ []) "Heb.4.15"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.4.15"
∷ word (ἔ ∷ χ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.4.15"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ έ ∷ α ∷ []) "Heb.4.15"
∷ word (μ ∷ ὴ ∷ []) "Heb.4.15"
∷ word (δ ∷ υ ∷ ν ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.4.15"
∷ word (σ ∷ υ ∷ μ ∷ π ∷ α ∷ θ ∷ ῆ ∷ σ ∷ α ∷ ι ∷ []) "Heb.4.15"
∷ word (τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.4.15"
∷ word (ἀ ∷ σ ∷ θ ∷ ε ∷ ν ∷ ε ∷ ί ∷ α ∷ ι ∷ ς ∷ []) "Heb.4.15"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.4.15"
∷ word (π ∷ ε ∷ π ∷ ε ∷ ι ∷ ρ ∷ α ∷ σ ∷ μ ∷ έ ∷ ν ∷ ο ∷ ν ∷ []) "Heb.4.15"
∷ word (δ ∷ ὲ ∷ []) "Heb.4.15"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.4.15"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.4.15"
∷ word (κ ∷ α ∷ θ ∷ []) "Heb.4.15"
∷ word (ὁ ∷ μ ∷ ο ∷ ι ∷ ό ∷ τ ∷ η ∷ τ ∷ α ∷ []) "Heb.4.15"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.4.15"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.4.15"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ρ ∷ χ ∷ ώ ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.4.16"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.4.16"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.4.16"
∷ word (π ∷ α ∷ ρ ∷ ρ ∷ η ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.4.16"
∷ word (τ ∷ ῷ ∷ []) "Heb.4.16"
∷ word (θ ∷ ρ ∷ ό ∷ ν ∷ ῳ ∷ []) "Heb.4.16"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.4.16"
∷ word (χ ∷ ά ∷ ρ ∷ ι ∷ τ ∷ ο ∷ ς ∷ []) "Heb.4.16"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.4.16"
∷ word (∙λ ∷ ά ∷ β ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.4.16"
∷ word (ἔ ∷ ∙λ ∷ ε ∷ ο ∷ ς ∷ []) "Heb.4.16"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.4.16"
∷ word (χ ∷ ά ∷ ρ ∷ ι ∷ ν ∷ []) "Heb.4.16"
∷ word (ε ∷ ὕ ∷ ρ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.4.16"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.4.16"
∷ word (ε ∷ ὔ ∷ κ ∷ α ∷ ι ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.4.16"
∷ word (β ∷ ο ∷ ή ∷ θ ∷ ε ∷ ι ∷ α ∷ ν ∷ []) "Heb.4.16"
∷ word (Π ∷ ᾶ ∷ ς ∷ []) "Heb.5.1"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.5.1"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.5.1"
∷ word (ἐ ∷ ξ ∷ []) "Heb.5.1"
∷ word (ἀ ∷ ν ∷ θ ∷ ρ ∷ ώ ∷ π ∷ ω ∷ ν ∷ []) "Heb.5.1"
∷ word (∙λ ∷ α ∷ μ ∷ β ∷ α ∷ ν ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.5.1"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.5.1"
∷ word (ἀ ∷ ν ∷ θ ∷ ρ ∷ ώ ∷ π ∷ ω ∷ ν ∷ []) "Heb.5.1"
∷ word (κ ∷ α ∷ θ ∷ ί ∷ σ ∷ τ ∷ α ∷ τ ∷ α ∷ ι ∷ []) "Heb.5.1"
∷ word (τ ∷ ὰ ∷ []) "Heb.5.1"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.5.1"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.5.1"
∷ word (θ ∷ ε ∷ ό ∷ ν ∷ []) "Heb.5.1"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.5.1"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ῃ ∷ []) "Heb.5.1"
∷ word (δ ∷ ῶ ∷ ρ ∷ ά ∷ []) "Heb.5.1"
∷ word (τ ∷ ε ∷ []) "Heb.5.1"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.1"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.5.1"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.5.1"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.5.1"
∷ word (μ ∷ ε ∷ τ ∷ ρ ∷ ι ∷ ο ∷ π ∷ α ∷ θ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.5.2"
∷ word (δ ∷ υ ∷ ν ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.5.2"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.5.2"
∷ word (ἀ ∷ γ ∷ ν ∷ ο ∷ ο ∷ ῦ ∷ σ ∷ ι ∷ []) "Heb.5.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.2"
∷ word (π ∷ ∙λ ∷ α ∷ ν ∷ ω ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ ς ∷ []) "Heb.5.2"
∷ word (ἐ ∷ π ∷ ε ∷ ὶ ∷ []) "Heb.5.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.2"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.5.2"
∷ word (π ∷ ε ∷ ρ ∷ ί ∷ κ ∷ ε ∷ ι ∷ τ ∷ α ∷ ι ∷ []) "Heb.5.2"
∷ word (ἀ ∷ σ ∷ θ ∷ έ ∷ ν ∷ ε ∷ ι ∷ α ∷ ν ∷ []) "Heb.5.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.3"
∷ word (δ ∷ ι ∷ []) "Heb.5.3"
∷ word (α ∷ ὐ ∷ τ ∷ ὴ ∷ ν ∷ []) "Heb.5.3"
∷ word (ὀ ∷ φ ∷ ε ∷ ί ∷ ∙λ ∷ ε ∷ ι ∷ []) "Heb.5.3"
∷ word (κ ∷ α ∷ θ ∷ ὼ ∷ ς ∷ []) "Heb.5.3"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.5.3"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.5.3"
∷ word (∙λ ∷ α ∷ ο ∷ ῦ ∷ []) "Heb.5.3"
∷ word (ο ∷ ὕ ∷ τ ∷ ω ∷ ς ∷ []) "Heb.5.3"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.3"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.5.3"
∷ word (α ∷ ὑ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.5.3"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.5.3"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.5.3"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.5.3"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.4"
∷ word (ο ∷ ὐ ∷ χ ∷ []) "Heb.5.4"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ῷ ∷ []) "Heb.5.4"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.5.4"
∷ word (∙λ ∷ α ∷ μ ∷ β ∷ ά ∷ ν ∷ ε ∷ ι ∷ []) "Heb.5.4"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.5.4"
∷ word (τ ∷ ι ∷ μ ∷ ή ∷ ν ∷ []) "Heb.5.4"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.5.4"
∷ word (κ ∷ α ∷ ∙λ ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.5.4"
∷ word (ὑ ∷ π ∷ ὸ ∷ []) "Heb.5.4"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.5.4"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.5.4"
∷ word (κ ∷ α ∷ θ ∷ ώ ∷ σ ∷ π ∷ ε ∷ ρ ∷ []) "Heb.5.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.4"
∷ word (Ἀ ∷ α ∷ ρ ∷ ώ ∷ ν ∷ []) "Heb.5.4"
∷ word (Ο ∷ ὕ ∷ τ ∷ ω ∷ ς ∷ []) "Heb.5.5"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.5"
∷ word (ὁ ∷ []) "Heb.5.5"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.5.5"
∷ word (ο ∷ ὐ ∷ χ ∷ []) "Heb.5.5"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.5.5"
∷ word (ἐ ∷ δ ∷ ό ∷ ξ ∷ α ∷ σ ∷ ε ∷ ν ∷ []) "Heb.5.5"
∷ word (γ ∷ ε ∷ ν ∷ η ∷ θ ∷ ῆ ∷ ν ∷ α ∷ ι ∷ []) "Heb.5.5"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ έ ∷ α ∷ []) "Heb.5.5"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ []) "Heb.5.5"
∷ word (ὁ ∷ []) "Heb.5.5"
∷ word (∙λ ∷ α ∷ ∙λ ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.5.5"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.5.5"
∷ word (α ∷ ὐ ∷ τ ∷ ό ∷ ν ∷ []) "Heb.5.5"
∷ word (Υ ∷ ἱ ∷ ό ∷ ς ∷ []) "Heb.5.5"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.5.5"
∷ word (ε ∷ ἶ ∷ []) "Heb.5.5"
∷ word (σ ∷ ύ ∷ []) "Heb.5.5"
∷ word (ἐ ∷ γ ∷ ὼ ∷ []) "Heb.5.5"
∷ word (σ ∷ ή ∷ μ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.5.5"
∷ word (γ ∷ ε ∷ γ ∷ έ ∷ ν ∷ ν ∷ η ∷ κ ∷ ά ∷ []) "Heb.5.5"
∷ word (σ ∷ ε ∷ []) "Heb.5.5"
∷ word (κ ∷ α ∷ θ ∷ ὼ ∷ ς ∷ []) "Heb.5.6"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.6"
∷ word (ἐ ∷ ν ∷ []) "Heb.5.6"
∷ word (ἑ ∷ τ ∷ έ ∷ ρ ∷ ῳ ∷ []) "Heb.5.6"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.5.6"
∷ word (Σ ∷ ὺ ∷ []) "Heb.5.6"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.5.6"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.5.6"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.5.6"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ []) "Heb.5.6"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.5.6"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.5.6"
∷ word (τ ∷ ά ∷ ξ ∷ ι ∷ ν ∷ []) "Heb.5.6"
∷ word (Μ ∷ ε ∷ ∙λ ∷ χ ∷ ι ∷ σ ∷ έ ∷ δ ∷ ε ∷ κ ∷ []) "Heb.5.6"
∷ word (ὃ ∷ ς ∷ []) "Heb.5.7"
∷ word (ἐ ∷ ν ∷ []) "Heb.5.7"
∷ word (τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.5.7"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ι ∷ ς ∷ []) "Heb.5.7"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.5.7"
∷ word (σ ∷ α ∷ ρ ∷ κ ∷ ὸ ∷ ς ∷ []) "Heb.5.7"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.5.7"
∷ word (δ ∷ ε ∷ ή ∷ σ ∷ ε ∷ ι ∷ ς ∷ []) "Heb.5.7"
∷ word (τ ∷ ε ∷ []) "Heb.5.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.7"
∷ word (ἱ ∷ κ ∷ ε ∷ τ ∷ η ∷ ρ ∷ ί ∷ α ∷ ς ∷ []) "Heb.5.7"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.5.7"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.5.7"
∷ word (δ ∷ υ ∷ ν ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.5.7"
∷ word (σ ∷ ῴ ∷ ζ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.5.7"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.5.7"
∷ word (ἐ ∷ κ ∷ []) "Heb.5.7"
∷ word (θ ∷ α ∷ ν ∷ ά ∷ τ ∷ ο ∷ υ ∷ []) "Heb.5.7"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.5.7"
∷ word (κ ∷ ρ ∷ α ∷ υ ∷ γ ∷ ῆ ∷ ς ∷ []) "Heb.5.7"
∷ word (ἰ ∷ σ ∷ χ ∷ υ ∷ ρ ∷ ᾶ ∷ ς ∷ []) "Heb.5.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.7"
∷ word (δ ∷ α ∷ κ ∷ ρ ∷ ύ ∷ ω ∷ ν ∷ []) "Heb.5.7"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ν ∷ έ ∷ γ ∷ κ ∷ α ∷ ς ∷ []) "Heb.5.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.7"
∷ word (ε ∷ ἰ ∷ σ ∷ α ∷ κ ∷ ο ∷ υ ∷ σ ∷ θ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.5.7"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.5.7"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.5.7"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ α ∷ β ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.5.7"
∷ word (κ ∷ α ∷ ί ∷ π ∷ ε ∷ ρ ∷ []) "Heb.5.8"
∷ word (ὢ ∷ ν ∷ []) "Heb.5.8"
∷ word (υ ∷ ἱ ∷ ό ∷ ς ∷ []) "Heb.5.8"
∷ word (ἔ ∷ μ ∷ α ∷ θ ∷ ε ∷ ν ∷ []) "Heb.5.8"
∷ word (ἀ ∷ φ ∷ []) "Heb.5.8"
∷ word (ὧ ∷ ν ∷ []) "Heb.5.8"
∷ word (ἔ ∷ π ∷ α ∷ θ ∷ ε ∷ ν ∷ []) "Heb.5.8"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.5.8"
∷ word (ὑ ∷ π ∷ α ∷ κ ∷ ο ∷ ή ∷ ν ∷ []) "Heb.5.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.9"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ω ∷ θ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.5.9"
∷ word (ἐ ∷ γ ∷ έ ∷ ν ∷ ε ∷ τ ∷ ο ∷ []) "Heb.5.9"
∷ word (π ∷ ᾶ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.5.9"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.5.9"
∷ word (ὑ ∷ π ∷ α ∷ κ ∷ ο ∷ ύ ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.5.9"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.5.9"
∷ word (α ∷ ἴ ∷ τ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.5.9"
∷ word (σ ∷ ω ∷ τ ∷ η ∷ ρ ∷ ί ∷ α ∷ ς ∷ []) "Heb.5.9"
∷ word (α ∷ ἰ ∷ ω ∷ ν ∷ ί ∷ ο ∷ υ ∷ []) "Heb.5.9"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ α ∷ γ ∷ ο ∷ ρ ∷ ε ∷ υ ∷ θ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.5.10"
∷ word (ὑ ∷ π ∷ ὸ ∷ []) "Heb.5.10"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.5.10"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.5.10"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.5.10"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.5.10"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.5.10"
∷ word (τ ∷ ά ∷ ξ ∷ ι ∷ ν ∷ []) "Heb.5.10"
∷ word (Μ ∷ ε ∷ ∙λ ∷ χ ∷ ι ∷ σ ∷ έ ∷ δ ∷ ε ∷ κ ∷ []) "Heb.5.10"
∷ word (Π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.5.11"
∷ word (ο ∷ ὗ ∷ []) "Heb.5.11"
∷ word (π ∷ ο ∷ ∙λ ∷ ὺ ∷ ς ∷ []) "Heb.5.11"
∷ word (ἡ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.5.11"
∷ word (ὁ ∷ []) "Heb.5.11"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ς ∷ []) "Heb.5.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.11"
∷ word (δ ∷ υ ∷ σ ∷ ε ∷ ρ ∷ μ ∷ ή ∷ ν ∷ ε ∷ υ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.5.11"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.5.11"
∷ word (ἐ ∷ π ∷ ε ∷ ὶ ∷ []) "Heb.5.11"
∷ word (ν ∷ ω ∷ θ ∷ ρ ∷ ο ∷ ὶ ∷ []) "Heb.5.11"
∷ word (γ ∷ ε ∷ γ ∷ ό ∷ ν ∷ α ∷ τ ∷ ε ∷ []) "Heb.5.11"
∷ word (τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.5.11"
∷ word (ἀ ∷ κ ∷ ο ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.5.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.12"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.5.12"
∷ word (ὀ ∷ φ ∷ ε ∷ ί ∷ ∙λ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.5.12"
∷ word (ε ∷ ἶ ∷ ν ∷ α ∷ ι ∷ []) "Heb.5.12"
∷ word (δ ∷ ι ∷ δ ∷ ά ∷ σ ∷ κ ∷ α ∷ ∙λ ∷ ο ∷ ι ∷ []) "Heb.5.12"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.5.12"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.5.12"
∷ word (χ ∷ ρ ∷ ό ∷ ν ∷ ο ∷ ν ∷ []) "Heb.5.12"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.5.12"
∷ word (χ ∷ ρ ∷ ε ∷ ί ∷ α ∷ ν ∷ []) "Heb.5.12"
∷ word (ἔ ∷ χ ∷ ε ∷ τ ∷ ε ∷ []) "Heb.5.12"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.5.12"
∷ word (δ ∷ ι ∷ δ ∷ ά ∷ σ ∷ κ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.5.12"
∷ word (ὑ ∷ μ ∷ ᾶ ∷ ς ∷ []) "Heb.5.12"
∷ word (τ ∷ ι ∷ ν ∷ ὰ ∷ []) "Heb.5.12"
∷ word (τ ∷ ὰ ∷ []) "Heb.5.12"
∷ word (σ ∷ τ ∷ ο ∷ ι ∷ χ ∷ ε ∷ ῖ ∷ α ∷ []) "Heb.5.12"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.5.12"
∷ word (ἀ ∷ ρ ∷ χ ∷ ῆ ∷ ς ∷ []) "Heb.5.12"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.5.12"
∷ word (∙λ ∷ ο ∷ γ ∷ ί ∷ ω ∷ ν ∷ []) "Heb.5.12"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.5.12"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.5.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.12"
∷ word (γ ∷ ε ∷ γ ∷ ό ∷ ν ∷ α ∷ τ ∷ ε ∷ []) "Heb.5.12"
∷ word (χ ∷ ρ ∷ ε ∷ ί ∷ α ∷ ν ∷ []) "Heb.5.12"
∷ word (ἔ ∷ χ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.5.12"
∷ word (γ ∷ ά ∷ ∙λ ∷ α ∷ κ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.5.12"
∷ word (ο ∷ ὐ ∷ []) "Heb.5.12"
∷ word (σ ∷ τ ∷ ε ∷ ρ ∷ ε ∷ ᾶ ∷ ς ∷ []) "Heb.5.12"
∷ word (τ ∷ ρ ∷ ο ∷ φ ∷ ῆ ∷ ς ∷ []) "Heb.5.12"
∷ word (π ∷ ᾶ ∷ ς ∷ []) "Heb.5.13"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.5.13"
∷ word (ὁ ∷ []) "Heb.5.13"
∷ word (μ ∷ ε ∷ τ ∷ έ ∷ χ ∷ ω ∷ ν ∷ []) "Heb.5.13"
∷ word (γ ∷ ά ∷ ∙λ ∷ α ∷ κ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.5.13"
∷ word (ἄ ∷ π ∷ ε ∷ ι ∷ ρ ∷ ο ∷ ς ∷ []) "Heb.5.13"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ υ ∷ []) "Heb.5.13"
∷ word (δ ∷ ι ∷ κ ∷ α ∷ ι ∷ ο ∷ σ ∷ ύ ∷ ν ∷ η ∷ ς ∷ []) "Heb.5.13"
∷ word (ν ∷ ή ∷ π ∷ ι ∷ ο ∷ ς ∷ []) "Heb.5.13"
∷ word (γ ∷ ά ∷ ρ ∷ []) "Heb.5.13"
∷ word (ἐ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.5.13"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ί ∷ ω ∷ ν ∷ []) "Heb.5.14"
∷ word (δ ∷ έ ∷ []) "Heb.5.14"
∷ word (ἐ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.5.14"
∷ word (ἡ ∷ []) "Heb.5.14"
∷ word (σ ∷ τ ∷ ε ∷ ρ ∷ ε ∷ ὰ ∷ []) "Heb.5.14"
∷ word (τ ∷ ρ ∷ ο ∷ φ ∷ ή ∷ []) "Heb.5.14"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.5.14"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.5.14"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.5.14"
∷ word (ἕ ∷ ξ ∷ ι ∷ ν ∷ []) "Heb.5.14"
∷ word (τ ∷ ὰ ∷ []) "Heb.5.14"
∷ word (α ∷ ἰ ∷ σ ∷ θ ∷ η ∷ τ ∷ ή ∷ ρ ∷ ι ∷ α ∷ []) "Heb.5.14"
∷ word (γ ∷ ε ∷ γ ∷ υ ∷ μ ∷ ν ∷ α ∷ σ ∷ μ ∷ έ ∷ ν ∷ α ∷ []) "Heb.5.14"
∷ word (ἐ ∷ χ ∷ ό ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.5.14"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.5.14"
∷ word (δ ∷ ι ∷ ά ∷ κ ∷ ρ ∷ ι ∷ σ ∷ ι ∷ ν ∷ []) "Heb.5.14"
∷ word (κ ∷ α ∷ ∙λ ∷ ο ∷ ῦ ∷ []) "Heb.5.14"
∷ word (τ ∷ ε ∷ []) "Heb.5.14"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.5.14"
∷ word (κ ∷ α ∷ κ ∷ ο ∷ ῦ ∷ []) "Heb.5.14"
∷ word (Δ ∷ ι ∷ ὸ ∷ []) "Heb.6.1"
∷ word (ἀ ∷ φ ∷ έ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.6.1"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.6.1"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.1"
∷ word (ἀ ∷ ρ ∷ χ ∷ ῆ ∷ ς ∷ []) "Heb.6.1"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.6.1"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.6.1"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ν ∷ []) "Heb.6.1"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.6.1"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.6.1"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ό ∷ τ ∷ η ∷ τ ∷ α ∷ []) "Heb.6.1"
∷ word (φ ∷ ε ∷ ρ ∷ ώ ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.6.1"
∷ word (μ ∷ ὴ ∷ []) "Heb.6.1"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.6.1"
∷ word (θ ∷ ε ∷ μ ∷ έ ∷ ∙λ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.6.1"
∷ word (κ ∷ α ∷ τ ∷ α ∷ β ∷ α ∷ ∙λ ∷ ∙λ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.6.1"
∷ word (μ ∷ ε ∷ τ ∷ α ∷ ν ∷ ο ∷ ί ∷ α ∷ ς ∷ []) "Heb.6.1"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.6.1"
∷ word (ν ∷ ε ∷ κ ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.6.1"
∷ word (ἔ ∷ ρ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.6.1"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.1"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.6.1"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.6.1"
∷ word (θ ∷ ε ∷ ό ∷ ν ∷ []) "Heb.6.1"
∷ word (β ∷ α ∷ π ∷ τ ∷ ι ∷ σ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.6.2"
∷ word (δ ∷ ι ∷ δ ∷ α ∷ χ ∷ ὴ ∷ ν ∷ []) "Heb.6.2"
∷ word (ἐ ∷ π ∷ ι ∷ θ ∷ έ ∷ σ ∷ ε ∷ ώ ∷ ς ∷ []) "Heb.6.2"
∷ word (τ ∷ ε ∷ []) "Heb.6.2"
∷ word (χ ∷ ε ∷ ι ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.6.2"
∷ word (ἀ ∷ ν ∷ α ∷ σ ∷ τ ∷ ά ∷ σ ∷ ε ∷ ώ ∷ ς ∷ []) "Heb.6.2"
∷ word (τ ∷ ε ∷ []) "Heb.6.2"
∷ word (ν ∷ ε ∷ κ ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.6.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.2"
∷ word (κ ∷ ρ ∷ ί ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.6.2"
∷ word (α ∷ ἰ ∷ ω ∷ ν ∷ ί ∷ ο ∷ υ ∷ []) "Heb.6.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.3"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.6.3"
∷ word (π ∷ ο ∷ ι ∷ ή ∷ σ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.6.3"
∷ word (ἐ ∷ ά ∷ ν ∷ π ∷ ε ∷ ρ ∷ []) "Heb.6.3"
∷ word (ἐ ∷ π ∷ ι ∷ τ ∷ ρ ∷ έ ∷ π ∷ ῃ ∷ []) "Heb.6.3"
∷ word (ὁ ∷ []) "Heb.6.3"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.6.3"
∷ word (Ἀ ∷ δ ∷ ύ ∷ ν ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.6.4"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.6.4"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.6.4"
∷ word (ἅ ∷ π ∷ α ∷ ξ ∷ []) "Heb.6.4"
∷ word (φ ∷ ω ∷ τ ∷ ι ∷ σ ∷ θ ∷ έ ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.6.4"
∷ word (γ ∷ ε ∷ υ ∷ σ ∷ α ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.6.4"
∷ word (τ ∷ ε ∷ []) "Heb.6.4"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.4"
∷ word (δ ∷ ω ∷ ρ ∷ ε ∷ ᾶ ∷ ς ∷ []) "Heb.6.4"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.4"
∷ word (ἐ ∷ π ∷ ο ∷ υ ∷ ρ ∷ α ∷ ν ∷ ί ∷ ο ∷ υ ∷ []) "Heb.6.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.4"
∷ word (μ ∷ ε ∷ τ ∷ ό ∷ χ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.6.4"
∷ word (γ ∷ ε ∷ ν ∷ η ∷ θ ∷ έ ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.6.4"
∷ word (π ∷ ν ∷ ε ∷ ύ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.6.4"
∷ word (ἁ ∷ γ ∷ ί ∷ ο ∷ υ ∷ []) "Heb.6.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.5"
∷ word (κ ∷ α ∷ ∙λ ∷ ὸ ∷ ν ∷ []) "Heb.6.5"
∷ word (γ ∷ ε ∷ υ ∷ σ ∷ α ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.6.5"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.6.5"
∷ word (ῥ ∷ ῆ ∷ μ ∷ α ∷ []) "Heb.6.5"
∷ word (δ ∷ υ ∷ ν ∷ ά ∷ μ ∷ ε ∷ ι ∷ ς ∷ []) "Heb.6.5"
∷ word (τ ∷ ε ∷ []) "Heb.6.5"
∷ word (μ ∷ έ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.6.5"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ ο ∷ ς ∷ []) "Heb.6.5"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.6"
∷ word (π ∷ α ∷ ρ ∷ α ∷ π ∷ ε ∷ σ ∷ ό ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.6.6"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.6.6"
∷ word (ἀ ∷ ν ∷ α ∷ κ ∷ α ∷ ι ∷ ν ∷ ί ∷ ζ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.6.6"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.6.6"
∷ word (μ ∷ ε ∷ τ ∷ ά ∷ ν ∷ ο ∷ ι ∷ α ∷ ν ∷ []) "Heb.6.6"
∷ word (ἀ ∷ ν ∷ α ∷ σ ∷ τ ∷ α ∷ υ ∷ ρ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.6.6"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.6.6"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.6.6"
∷ word (υ ∷ ἱ ∷ ὸ ∷ ν ∷ []) "Heb.6.6"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.6.6"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.6.6"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.6"
∷ word (π ∷ α ∷ ρ ∷ α ∷ δ ∷ ε ∷ ι ∷ γ ∷ μ ∷ α ∷ τ ∷ ί ∷ ζ ∷ ο ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.6.6"
∷ word (γ ∷ ῆ ∷ []) "Heb.6.7"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.6.7"
∷ word (ἡ ∷ []) "Heb.6.7"
∷ word (π ∷ ι ∷ ο ∷ ῦ ∷ σ ∷ α ∷ []) "Heb.6.7"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.6.7"
∷ word (ἐ ∷ π ∷ []) "Heb.6.7"
∷ word (α ∷ ὐ ∷ τ ∷ ῆ ∷ ς ∷ []) "Heb.6.7"
∷ word (ἐ ∷ ρ ∷ χ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.6.7"
∷ word (π ∷ ο ∷ ∙λ ∷ ∙λ ∷ ά ∷ κ ∷ ι ∷ ς ∷ []) "Heb.6.7"
∷ word (ὑ ∷ ε ∷ τ ∷ ό ∷ ν ∷ []) "Heb.6.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.7"
∷ word (τ ∷ ί ∷ κ ∷ τ ∷ ο ∷ υ ∷ σ ∷ α ∷ []) "Heb.6.7"
∷ word (β ∷ ο ∷ τ ∷ ά ∷ ν ∷ η ∷ ν ∷ []) "Heb.6.7"
∷ word (ε ∷ ὔ ∷ θ ∷ ε ∷ τ ∷ ο ∷ ν ∷ []) "Heb.6.7"
∷ word (ἐ ∷ κ ∷ ε ∷ ί ∷ ν ∷ ο ∷ ι ∷ ς ∷ []) "Heb.6.7"
∷ word (δ ∷ ι ∷ []) "Heb.6.7"
∷ word (ο ∷ ὓ ∷ ς ∷ []) "Heb.6.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.7"
∷ word (γ ∷ ε ∷ ω ∷ ρ ∷ γ ∷ ε ∷ ῖ ∷ τ ∷ α ∷ ι ∷ []) "Heb.6.7"
∷ word (μ ∷ ε ∷ τ ∷ α ∷ ∙λ ∷ α ∷ μ ∷ β ∷ ά ∷ ν ∷ ε ∷ ι ∷ []) "Heb.6.7"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ ο ∷ γ ∷ ί ∷ α ∷ ς ∷ []) "Heb.6.7"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.6.7"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.6.7"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.6.7"
∷ word (ἐ ∷ κ ∷ φ ∷ έ ∷ ρ ∷ ο ∷ υ ∷ σ ∷ α ∷ []) "Heb.6.8"
∷ word (δ ∷ ὲ ∷ []) "Heb.6.8"
∷ word (ἀ ∷ κ ∷ ά ∷ ν ∷ θ ∷ α ∷ ς ∷ []) "Heb.6.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.8"
∷ word (τ ∷ ρ ∷ ι ∷ β ∷ ό ∷ ∙λ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.6.8"
∷ word (ἀ ∷ δ ∷ ό ∷ κ ∷ ι ∷ μ ∷ ο ∷ ς ∷ []) "Heb.6.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.8"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ ρ ∷ α ∷ ς ∷ []) "Heb.6.8"
∷ word (ἐ ∷ γ ∷ γ ∷ ύ ∷ ς ∷ []) "Heb.6.8"
∷ word (ἧ ∷ ς ∷ []) "Heb.6.8"
∷ word (τ ∷ ὸ ∷ []) "Heb.6.8"
∷ word (τ ∷ έ ∷ ∙λ ∷ ο ∷ ς ∷ []) "Heb.6.8"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.6.8"
∷ word (κ ∷ α ∷ ῦ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.6.8"
∷ word (Π ∷ ε ∷ π ∷ ε ∷ ί ∷ σ ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.6.9"
∷ word (δ ∷ ὲ ∷ []) "Heb.6.9"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.6.9"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.6.9"
∷ word (ἀ ∷ γ ∷ α ∷ π ∷ η ∷ τ ∷ ο ∷ ί ∷ []) "Heb.6.9"
∷ word (τ ∷ ὰ ∷ []) "Heb.6.9"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ σ ∷ σ ∷ ο ∷ ν ∷ α ∷ []) "Heb.6.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.9"
∷ word (ἐ ∷ χ ∷ ό ∷ μ ∷ ε ∷ ν ∷ α ∷ []) "Heb.6.9"
∷ word (σ ∷ ω ∷ τ ∷ η ∷ ρ ∷ ί ∷ α ∷ ς ∷ []) "Heb.6.9"
∷ word (ε ∷ ἰ ∷ []) "Heb.6.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.9"
∷ word (ο ∷ ὕ ∷ τ ∷ ω ∷ ς ∷ []) "Heb.6.9"
∷ word (∙λ ∷ α ∷ ∙λ ∷ ο ∷ ῦ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.6.9"
∷ word (ο ∷ ὐ ∷ []) "Heb.6.10"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.6.10"
∷ word (ἄ ∷ δ ∷ ι ∷ κ ∷ ο ∷ ς ∷ []) "Heb.6.10"
∷ word (ὁ ∷ []) "Heb.6.10"
∷ word (θ ∷ ε ∷ ὸ ∷ ς ∷ []) "Heb.6.10"
∷ word (ἐ ∷ π ∷ ι ∷ ∙λ ∷ α ∷ θ ∷ έ ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.6.10"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.6.10"
∷ word (ἔ ∷ ρ ∷ γ ∷ ο ∷ υ ∷ []) "Heb.6.10"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.6.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.10"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.10"
∷ word (ἀ ∷ γ ∷ ά ∷ π ∷ η ∷ ς ∷ []) "Heb.6.10"
∷ word (ἧ ∷ ς ∷ []) "Heb.6.10"
∷ word (ἐ ∷ ν ∷ ε ∷ δ ∷ ε ∷ ί ∷ ξ ∷ α ∷ σ ∷ θ ∷ ε ∷ []) "Heb.6.10"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.6.10"
∷ word (τ ∷ ὸ ∷ []) "Heb.6.10"
∷ word (ὄ ∷ ν ∷ ο ∷ μ ∷ α ∷ []) "Heb.6.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.6.10"
∷ word (δ ∷ ι ∷ α ∷ κ ∷ ο ∷ ν ∷ ή ∷ σ ∷ α ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.6.10"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.6.10"
∷ word (ἁ ∷ γ ∷ ί ∷ ο ∷ ι ∷ ς ∷ []) "Heb.6.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.10"
∷ word (δ ∷ ι ∷ α ∷ κ ∷ ο ∷ ν ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.6.10"
∷ word (ἐ ∷ π ∷ ι ∷ θ ∷ υ ∷ μ ∷ ο ∷ ῦ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.6.11"
∷ word (δ ∷ ὲ ∷ []) "Heb.6.11"
∷ word (ἕ ∷ κ ∷ α ∷ σ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.6.11"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.6.11"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.6.11"
∷ word (α ∷ ὐ ∷ τ ∷ ὴ ∷ ν ∷ []) "Heb.6.11"
∷ word (ἐ ∷ ν ∷ δ ∷ ε ∷ ί ∷ κ ∷ ν ∷ υ ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.6.11"
∷ word (σ ∷ π ∷ ο ∷ υ ∷ δ ∷ ὴ ∷ ν ∷ []) "Heb.6.11"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.6.11"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.6.11"
∷ word (π ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ φ ∷ ο ∷ ρ ∷ ί ∷ α ∷ ν ∷ []) "Heb.6.11"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.11"
∷ word (ἐ ∷ ∙λ ∷ π ∷ ί ∷ δ ∷ ο ∷ ς ∷ []) "Heb.6.11"
∷ word (ἄ ∷ χ ∷ ρ ∷ ι ∷ []) "Heb.6.11"
∷ word (τ ∷ έ ∷ ∙λ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.6.11"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.6.12"
∷ word (μ ∷ ὴ ∷ []) "Heb.6.12"
∷ word (ν ∷ ω ∷ θ ∷ ρ ∷ ο ∷ ὶ ∷ []) "Heb.6.12"
∷ word (γ ∷ έ ∷ ν ∷ η ∷ σ ∷ θ ∷ ε ∷ []) "Heb.6.12"
∷ word (μ ∷ ι ∷ μ ∷ η ∷ τ ∷ α ∷ ὶ ∷ []) "Heb.6.12"
∷ word (δ ∷ ὲ ∷ []) "Heb.6.12"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.6.12"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.6.12"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.6.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.12"
∷ word (μ ∷ α ∷ κ ∷ ρ ∷ ο ∷ θ ∷ υ ∷ μ ∷ ί ∷ α ∷ ς ∷ []) "Heb.6.12"
∷ word (κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ο ∷ μ ∷ ο ∷ ύ ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.6.12"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.6.12"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.6.12"
∷ word (Τ ∷ ῷ ∷ []) "Heb.6.13"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.6.13"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ὰ ∷ μ ∷ []) "Heb.6.13"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ι ∷ ∙λ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.6.13"
∷ word (ὁ ∷ []) "Heb.6.13"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.6.13"
∷ word (ἐ ∷ π ∷ ε ∷ ὶ ∷ []) "Heb.6.13"
∷ word (κ ∷ α ∷ τ ∷ []) "Heb.6.13"
∷ word (ο ∷ ὐ ∷ δ ∷ ε ∷ ν ∷ ὸ ∷ ς ∷ []) "Heb.6.13"
∷ word (ε ∷ ἶ ∷ χ ∷ ε ∷ ν ∷ []) "Heb.6.13"
∷ word (μ ∷ ε ∷ ί ∷ ζ ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.6.13"
∷ word (ὀ ∷ μ ∷ ό ∷ σ ∷ α ∷ ι ∷ []) "Heb.6.13"
∷ word (ὤ ∷ μ ∷ ο ∷ σ ∷ ε ∷ ν ∷ []) "Heb.6.13"
∷ word (κ ∷ α ∷ θ ∷ []) "Heb.6.13"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.6.13"
∷ word (∙λ ∷ έ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.6.14"
∷ word (Ε ∷ ἰ ∷ []) "Heb.6.14"
∷ word (μ ∷ ὴ ∷ ν ∷ []) "Heb.6.14"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ ο ∷ γ ∷ ῶ ∷ ν ∷ []) "Heb.6.14"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ ο ∷ γ ∷ ή ∷ σ ∷ ω ∷ []) "Heb.6.14"
∷ word (σ ∷ ε ∷ []) "Heb.6.14"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.14"
∷ word (π ∷ ∙λ ∷ η ∷ θ ∷ ύ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.6.14"
∷ word (π ∷ ∙λ ∷ η ∷ θ ∷ υ ∷ ν ∷ ῶ ∷ []) "Heb.6.14"
∷ word (σ ∷ ε ∷ []) "Heb.6.14"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.15"
∷ word (ο ∷ ὕ ∷ τ ∷ ω ∷ ς ∷ []) "Heb.6.15"
∷ word (μ ∷ α ∷ κ ∷ ρ ∷ ο ∷ θ ∷ υ ∷ μ ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.6.15"
∷ word (ἐ ∷ π ∷ έ ∷ τ ∷ υ ∷ χ ∷ ε ∷ ν ∷ []) "Heb.6.15"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.15"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.6.15"
∷ word (ἄ ∷ ν ∷ θ ∷ ρ ∷ ω ∷ π ∷ ο ∷ ι ∷ []) "Heb.6.16"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.6.16"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.6.16"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.6.16"
∷ word (μ ∷ ε ∷ ί ∷ ζ ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.6.16"
∷ word (ὀ ∷ μ ∷ ν ∷ ύ ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.6.16"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.16"
∷ word (π ∷ ά ∷ σ ∷ η ∷ ς ∷ []) "Heb.6.16"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.6.16"
∷ word (ἀ ∷ ν ∷ τ ∷ ι ∷ ∙λ ∷ ο ∷ γ ∷ ί ∷ α ∷ ς ∷ []) "Heb.6.16"
∷ word (π ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.6.16"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.6.16"
∷ word (β ∷ ε ∷ β ∷ α ∷ ί ∷ ω ∷ σ ∷ ι ∷ ν ∷ []) "Heb.6.16"
∷ word (ὁ ∷ []) "Heb.6.16"
∷ word (ὅ ∷ ρ ∷ κ ∷ ο ∷ ς ∷ []) "Heb.6.16"
∷ word (ἐ ∷ ν ∷ []) "Heb.6.17"
∷ word (ᾧ ∷ []) "Heb.6.17"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ σ ∷ σ ∷ ό ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.6.17"
∷ word (β ∷ ο ∷ υ ∷ ∙λ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.6.17"
∷ word (ὁ ∷ []) "Heb.6.17"
∷ word (θ ∷ ε ∷ ὸ ∷ ς ∷ []) "Heb.6.17"
∷ word (ἐ ∷ π ∷ ι ∷ δ ∷ ε ∷ ῖ ∷ ξ ∷ α ∷ ι ∷ []) "Heb.6.17"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.6.17"
∷ word (κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ό ∷ μ ∷ ο ∷ ι ∷ ς ∷ []) "Heb.6.17"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.17"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.6.17"
∷ word (τ ∷ ὸ ∷ []) "Heb.6.17"
∷ word (ἀ ∷ μ ∷ ε ∷ τ ∷ ά ∷ θ ∷ ε ∷ τ ∷ ο ∷ ν ∷ []) "Heb.6.17"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.17"
∷ word (β ∷ ο ∷ υ ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.6.17"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.6.17"
∷ word (ἐ ∷ μ ∷ ε ∷ σ ∷ ί ∷ τ ∷ ε ∷ υ ∷ σ ∷ ε ∷ ν ∷ []) "Heb.6.17"
∷ word (ὅ ∷ ρ ∷ κ ∷ ῳ ∷ []) "Heb.6.17"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.6.18"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.6.18"
∷ word (δ ∷ ύ ∷ ο ∷ []) "Heb.6.18"
∷ word (π ∷ ρ ∷ α ∷ γ ∷ μ ∷ ά ∷ τ ∷ ω ∷ ν ∷ []) "Heb.6.18"
∷ word (ἀ ∷ μ ∷ ε ∷ τ ∷ α ∷ θ ∷ έ ∷ τ ∷ ω ∷ ν ∷ []) "Heb.6.18"
∷ word (ἐ ∷ ν ∷ []) "Heb.6.18"
∷ word (ο ∷ ἷ ∷ ς ∷ []) "Heb.6.18"
∷ word (ἀ ∷ δ ∷ ύ ∷ ν ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.6.18"
∷ word (ψ ∷ ε ∷ ύ ∷ σ ∷ α ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.6.18"
∷ word (θ ∷ ε ∷ ό ∷ ν ∷ []) "Heb.6.18"
∷ word (ἰ ∷ σ ∷ χ ∷ υ ∷ ρ ∷ ὰ ∷ ν ∷ []) "Heb.6.18"
∷ word (π ∷ α ∷ ρ ∷ ά ∷ κ ∷ ∙λ ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.6.18"
∷ word (ἔ ∷ χ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.6.18"
∷ word (ο ∷ ἱ ∷ []) "Heb.6.18"
∷ word (κ ∷ α ∷ τ ∷ α ∷ φ ∷ υ ∷ γ ∷ ό ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.6.18"
∷ word (κ ∷ ρ ∷ α ∷ τ ∷ ῆ ∷ σ ∷ α ∷ ι ∷ []) "Heb.6.18"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.18"
∷ word (π ∷ ρ ∷ ο ∷ κ ∷ ε ∷ ι ∷ μ ∷ έ ∷ ν ∷ η ∷ ς ∷ []) "Heb.6.18"
∷ word (ἐ ∷ ∙λ ∷ π ∷ ί ∷ δ ∷ ο ∷ ς ∷ []) "Heb.6.18"
∷ word (ἣ ∷ ν ∷ []) "Heb.6.19"
∷ word (ὡ ∷ ς ∷ []) "Heb.6.19"
∷ word (ἄ ∷ γ ∷ κ ∷ υ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.6.19"
∷ word (ἔ ∷ χ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.6.19"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.6.19"
∷ word (ψ ∷ υ ∷ χ ∷ ῆ ∷ ς ∷ []) "Heb.6.19"
∷ word (ἀ ∷ σ ∷ φ ∷ α ∷ ∙λ ∷ ῆ ∷ []) "Heb.6.19"
∷ word (τ ∷ ε ∷ []) "Heb.6.19"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.19"
∷ word (β ∷ ε ∷ β ∷ α ∷ ί ∷ α ∷ ν ∷ []) "Heb.6.19"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.6.19"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ρ ∷ χ ∷ ο ∷ μ ∷ έ ∷ ν ∷ η ∷ ν ∷ []) "Heb.6.19"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.6.19"
∷ word (τ ∷ ὸ ∷ []) "Heb.6.19"
∷ word (ἐ ∷ σ ∷ ώ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.6.19"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.6.19"
∷ word (κ ∷ α ∷ τ ∷ α ∷ π ∷ ε ∷ τ ∷ ά ∷ σ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.6.19"
∷ word (ὅ ∷ π ∷ ο ∷ υ ∷ []) "Heb.6.20"
∷ word (π ∷ ρ ∷ ό ∷ δ ∷ ρ ∷ ο ∷ μ ∷ ο ∷ ς ∷ []) "Heb.6.20"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.6.20"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.6.20"
∷ word (ε ∷ ἰ ∷ σ ∷ ῆ ∷ ∙λ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.6.20"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ς ∷ []) "Heb.6.20"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.6.20"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.6.20"
∷ word (τ ∷ ά ∷ ξ ∷ ι ∷ ν ∷ []) "Heb.6.20"
∷ word (Μ ∷ ε ∷ ∙λ ∷ χ ∷ ι ∷ σ ∷ έ ∷ δ ∷ ε ∷ κ ∷ []) "Heb.6.20"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.6.20"
∷ word (γ ∷ ε ∷ ν ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.6.20"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.6.20"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.6.20"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ []) "Heb.6.20"
∷ word (Ο ∷ ὗ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.7.1"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.1"
∷ word (ὁ ∷ []) "Heb.7.1"
∷ word (Μ ∷ ε ∷ ∙λ ∷ χ ∷ ι ∷ σ ∷ έ ∷ δ ∷ ε ∷ κ ∷ []) "Heb.7.1"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.7.1"
∷ word (Σ ∷ α ∷ ∙λ ∷ ή ∷ μ ∷ []) "Heb.7.1"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.7.1"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.7.1"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.7.1"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.7.1"
∷ word (ὑ ∷ ψ ∷ ί ∷ σ ∷ τ ∷ ο ∷ υ ∷ []) "Heb.7.1"
∷ word (ὁ ∷ []) "Heb.7.1"
∷ word (σ ∷ υ ∷ ν ∷ α ∷ ν ∷ τ ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.7.1"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ὰ ∷ μ ∷ []) "Heb.7.1"
∷ word (ὑ ∷ π ∷ ο ∷ σ ∷ τ ∷ ρ ∷ έ ∷ φ ∷ ο ∷ ν ∷ τ ∷ ι ∷ []) "Heb.7.1"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.7.1"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.7.1"
∷ word (κ ∷ ο ∷ π ∷ ῆ ∷ ς ∷ []) "Heb.7.1"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.7.1"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ έ ∷ ω ∷ ν ∷ []) "Heb.7.1"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.1"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ ο ∷ γ ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.7.1"
∷ word (α ∷ ὐ ∷ τ ∷ ό ∷ ν ∷ []) "Heb.7.1"
∷ word (ᾧ ∷ []) "Heb.7.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.2"
∷ word (δ ∷ ε ∷ κ ∷ ά ∷ τ ∷ η ∷ ν ∷ []) "Heb.7.2"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.7.2"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.7.2"
∷ word (ἐ ∷ μ ∷ έ ∷ ρ ∷ ι ∷ σ ∷ ε ∷ ν ∷ []) "Heb.7.2"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ά ∷ μ ∷ []) "Heb.7.2"
∷ word (π ∷ ρ ∷ ῶ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.7.2"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.7.2"
∷ word (ἑ ∷ ρ ∷ μ ∷ η ∷ ν ∷ ε ∷ υ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.7.2"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.7.2"
∷ word (δ ∷ ι ∷ κ ∷ α ∷ ι ∷ ο ∷ σ ∷ ύ ∷ ν ∷ η ∷ ς ∷ []) "Heb.7.2"
∷ word (ἔ ∷ π ∷ ε ∷ ι ∷ τ ∷ α ∷ []) "Heb.7.2"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.2"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.7.2"
∷ word (Σ ∷ α ∷ ∙λ ∷ ή ∷ μ ∷ []) "Heb.7.2"
∷ word (ὅ ∷ []) "Heb.7.2"
∷ word (ἐ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.7.2"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.7.2"
∷ word (ε ∷ ἰ ∷ ρ ∷ ή ∷ ν ∷ η ∷ ς ∷ []) "Heb.7.2"
∷ word (ἀ ∷ π ∷ ά ∷ τ ∷ ω ∷ ρ ∷ []) "Heb.7.3"
∷ word (ἀ ∷ μ ∷ ή ∷ τ ∷ ω ∷ ρ ∷ []) "Heb.7.3"
∷ word (ἀ ∷ γ ∷ ε ∷ ν ∷ ε ∷ α ∷ ∙λ ∷ ό ∷ γ ∷ η ∷ τ ∷ ο ∷ ς ∷ []) "Heb.7.3"
∷ word (μ ∷ ή ∷ τ ∷ ε ∷ []) "Heb.7.3"
∷ word (ἀ ∷ ρ ∷ χ ∷ ὴ ∷ ν ∷ []) "Heb.7.3"
∷ word (ἡ ∷ μ ∷ ε ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.7.3"
∷ word (μ ∷ ή ∷ τ ∷ ε ∷ []) "Heb.7.3"
∷ word (ζ ∷ ω ∷ ῆ ∷ ς ∷ []) "Heb.7.3"
∷ word (τ ∷ έ ∷ ∙λ ∷ ο ∷ ς ∷ []) "Heb.7.3"
∷ word (ἔ ∷ χ ∷ ω ∷ ν ∷ []) "Heb.7.3"
∷ word (ἀ ∷ φ ∷ ω ∷ μ ∷ ο ∷ ι ∷ ω ∷ μ ∷ έ ∷ ν ∷ ο ∷ ς ∷ []) "Heb.7.3"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.3"
∷ word (τ ∷ ῷ ∷ []) "Heb.7.3"
∷ word (υ ∷ ἱ ∷ ῷ ∷ []) "Heb.7.3"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.7.3"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.7.3"
∷ word (μ ∷ έ ∷ ν ∷ ε ∷ ι ∷ []) "Heb.7.3"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.7.3"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.7.3"
∷ word (τ ∷ ὸ ∷ []) "Heb.7.3"
∷ word (δ ∷ ι ∷ η ∷ ν ∷ ε ∷ κ ∷ έ ∷ ς ∷ []) "Heb.7.3"
∷ word (Θ ∷ ε ∷ ω ∷ ρ ∷ ε ∷ ῖ ∷ τ ∷ ε ∷ []) "Heb.7.4"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.4"
∷ word (π ∷ η ∷ ∙λ ∷ ί ∷ κ ∷ ο ∷ ς ∷ []) "Heb.7.4"
∷ word (ο ∷ ὗ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.7.4"
∷ word (ᾧ ∷ []) "Heb.7.4"
∷ word (δ ∷ ε ∷ κ ∷ ά ∷ τ ∷ η ∷ ν ∷ []) "Heb.7.4"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ὰ ∷ μ ∷ []) "Heb.7.4"
∷ word (ἔ ∷ δ ∷ ω ∷ κ ∷ ε ∷ ν ∷ []) "Heb.7.4"
∷ word (ἐ ∷ κ ∷ []) "Heb.7.4"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.7.4"
∷ word (ἀ ∷ κ ∷ ρ ∷ ο ∷ θ ∷ ι ∷ ν ∷ ί ∷ ω ∷ ν ∷ []) "Heb.7.4"
∷ word (ὁ ∷ []) "Heb.7.4"
∷ word (π ∷ α ∷ τ ∷ ρ ∷ ι ∷ ά ∷ ρ ∷ χ ∷ η ∷ ς ∷ []) "Heb.7.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.5"
∷ word (ο ∷ ἱ ∷ []) "Heb.7.5"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.7.5"
∷ word (ἐ ∷ κ ∷ []) "Heb.7.5"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.7.5"
∷ word (υ ∷ ἱ ∷ ῶ ∷ ν ∷ []) "Heb.7.5"
∷ word (Λ ∷ ε ∷ υ ∷ ὶ ∷ []) "Heb.7.5"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.7.5"
∷ word (ἱ ∷ ε ∷ ρ ∷ α ∷ τ ∷ ε ∷ ί ∷ α ∷ ν ∷ []) "Heb.7.5"
∷ word (∙λ ∷ α ∷ μ ∷ β ∷ ά ∷ ν ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.7.5"
∷ word (ἐ ∷ ν ∷ τ ∷ ο ∷ ∙λ ∷ ὴ ∷ ν ∷ []) "Heb.7.5"
∷ word (ἔ ∷ χ ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.7.5"
∷ word (ἀ ∷ π ∷ ο ∷ δ ∷ ε ∷ κ ∷ α ∷ τ ∷ ο ∷ ῦ ∷ ν ∷ []) "Heb.7.5"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.7.5"
∷ word (∙λ ∷ α ∷ ὸ ∷ ν ∷ []) "Heb.7.5"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.7.5"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.7.5"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ν ∷ []) "Heb.7.5"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ []) "Heb.7.5"
∷ word (ἔ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.7.5"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.7.5"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.7.5"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.7.5"
∷ word (κ ∷ α ∷ ί ∷ π ∷ ε ∷ ρ ∷ []) "Heb.7.5"
∷ word (ἐ ∷ ξ ∷ ε ∷ ∙λ ∷ η ∷ ∙λ ∷ υ ∷ θ ∷ ό ∷ τ ∷ α ∷ ς ∷ []) "Heb.7.5"
∷ word (ἐ ∷ κ ∷ []) "Heb.7.5"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.7.5"
∷ word (ὀ ∷ σ ∷ φ ∷ ύ ∷ ο ∷ ς ∷ []) "Heb.7.5"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ά ∷ μ ∷ []) "Heb.7.5"
∷ word (ὁ ∷ []) "Heb.7.6"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.6"
∷ word (μ ∷ ὴ ∷ []) "Heb.7.6"
∷ word (γ ∷ ε ∷ ν ∷ ε ∷ α ∷ ∙λ ∷ ο ∷ γ ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.7.6"
∷ word (ἐ ∷ ξ ∷ []) "Heb.7.6"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.7.6"
∷ word (δ ∷ ε ∷ δ ∷ ε ∷ κ ∷ ά ∷ τ ∷ ω ∷ κ ∷ ε ∷ ν ∷ []) "Heb.7.6"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ά ∷ μ ∷ []) "Heb.7.6"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.6"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.7.6"
∷ word (ἔ ∷ χ ∷ ο ∷ ν ∷ τ ∷ α ∷ []) "Heb.7.6"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.7.6"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.7.6"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ ό ∷ γ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.7.6"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.7.7"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.7"
∷ word (π ∷ ά ∷ σ ∷ η ∷ ς ∷ []) "Heb.7.7"
∷ word (ἀ ∷ ν ∷ τ ∷ ι ∷ ∙λ ∷ ο ∷ γ ∷ ί ∷ α ∷ ς ∷ []) "Heb.7.7"
∷ word (τ ∷ ὸ ∷ []) "Heb.7.7"
∷ word (ἔ ∷ ∙λ ∷ α ∷ τ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.7.7"
∷ word (ὑ ∷ π ∷ ὸ ∷ []) "Heb.7.7"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.7.7"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.7.7"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ ο ∷ γ ∷ ε ∷ ῖ ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.8"
∷ word (ὧ ∷ δ ∷ ε ∷ []) "Heb.7.8"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.7.8"
∷ word (δ ∷ ε ∷ κ ∷ ά ∷ τ ∷ α ∷ ς ∷ []) "Heb.7.8"
∷ word (ἀ ∷ π ∷ ο ∷ θ ∷ ν ∷ ῄ ∷ σ ∷ κ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.7.8"
∷ word (ἄ ∷ ν ∷ θ ∷ ρ ∷ ω ∷ π ∷ ο ∷ ι ∷ []) "Heb.7.8"
∷ word (∙λ ∷ α ∷ μ ∷ β ∷ ά ∷ ν ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.7.8"
∷ word (ἐ ∷ κ ∷ ε ∷ ῖ ∷ []) "Heb.7.8"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.8"
∷ word (μ ∷ α ∷ ρ ∷ τ ∷ υ ∷ ρ ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.7.8"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.7.8"
∷ word (ζ ∷ ῇ ∷ []) "Heb.7.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.9"
∷ word (ὡ ∷ ς ∷ []) "Heb.7.9"
∷ word (ἔ ∷ π ∷ ο ∷ ς ∷ []) "Heb.7.9"
∷ word (ε ∷ ἰ ∷ π ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.7.9"
∷ word (δ ∷ ι ∷ []) "Heb.7.9"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ὰ ∷ μ ∷ []) "Heb.7.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.9"
∷ word (Λ ∷ ε ∷ υ ∷ ὶ ∷ []) "Heb.7.9"
∷ word (ὁ ∷ []) "Heb.7.9"
∷ word (δ ∷ ε ∷ κ ∷ ά ∷ τ ∷ α ∷ ς ∷ []) "Heb.7.9"
∷ word (∙λ ∷ α ∷ μ ∷ β ∷ ά ∷ ν ∷ ω ∷ ν ∷ []) "Heb.7.9"
∷ word (δ ∷ ε ∷ δ ∷ ε ∷ κ ∷ ά ∷ τ ∷ ω ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.9"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.7.10"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.10"
∷ word (ἐ ∷ ν ∷ []) "Heb.7.10"
∷ word (τ ∷ ῇ ∷ []) "Heb.7.10"
∷ word (ὀ ∷ σ ∷ φ ∷ ύ ∷ ϊ ∷ []) "Heb.7.10"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.7.10"
∷ word (π ∷ α ∷ τ ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.7.10"
∷ word (ἦ ∷ ν ∷ []) "Heb.7.10"
∷ word (ὅ ∷ τ ∷ ε ∷ []) "Heb.7.10"
∷ word (σ ∷ υ ∷ ν ∷ ή ∷ ν ∷ τ ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.7.10"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.7.10"
∷ word (Μ ∷ ε ∷ ∙λ ∷ χ ∷ ι ∷ σ ∷ έ ∷ δ ∷ ε ∷ κ ∷ []) "Heb.7.10"
∷ word (Ε ∷ ἰ ∷ []) "Heb.7.11"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.7.11"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.7.11"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ί ∷ ω ∷ σ ∷ ι ∷ ς ∷ []) "Heb.7.11"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.7.11"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.7.11"
∷ word (Λ ∷ ε ∷ υ ∷ ι ∷ τ ∷ ι ∷ κ ∷ ῆ ∷ ς ∷ []) "Heb.7.11"
∷ word (ἱ ∷ ε ∷ ρ ∷ ω ∷ σ ∷ ύ ∷ ν ∷ η ∷ ς ∷ []) "Heb.7.11"
∷ word (ἦ ∷ ν ∷ []) "Heb.7.11"
∷ word (ὁ ∷ []) "Heb.7.11"
∷ word (∙λ ∷ α ∷ ὸ ∷ ς ∷ []) "Heb.7.11"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.11"
∷ word (ἐ ∷ π ∷ []) "Heb.7.11"
∷ word (α ∷ ὐ ∷ τ ∷ ῆ ∷ ς ∷ []) "Heb.7.11"
∷ word (ν ∷ ε ∷ ν ∷ ο ∷ μ ∷ ο ∷ θ ∷ έ ∷ τ ∷ η ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.11"
∷ word (τ ∷ ί ∷ ς ∷ []) "Heb.7.11"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.7.11"
∷ word (χ ∷ ρ ∷ ε ∷ ί ∷ α ∷ []) "Heb.7.11"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.7.11"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.7.11"
∷ word (τ ∷ ά ∷ ξ ∷ ι ∷ ν ∷ []) "Heb.7.11"
∷ word (Μ ∷ ε ∷ ∙λ ∷ χ ∷ ι ∷ σ ∷ έ ∷ δ ∷ ε ∷ κ ∷ []) "Heb.7.11"
∷ word (ἕ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.7.11"
∷ word (ἀ ∷ ν ∷ ί ∷ σ ∷ τ ∷ α ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.7.11"
∷ word (ἱ ∷ ε ∷ ρ ∷ έ ∷ α ∷ []) "Heb.7.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.11"
∷ word (ο ∷ ὐ ∷ []) "Heb.7.11"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.7.11"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.7.11"
∷ word (τ ∷ ά ∷ ξ ∷ ι ∷ ν ∷ []) "Heb.7.11"
∷ word (Ἀ ∷ α ∷ ρ ∷ ὼ ∷ ν ∷ []) "Heb.7.11"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.7.11"
∷ word (μ ∷ ε ∷ τ ∷ α ∷ τ ∷ ι ∷ θ ∷ ε ∷ μ ∷ έ ∷ ν ∷ η ∷ ς ∷ []) "Heb.7.12"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.12"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.7.12"
∷ word (ἱ ∷ ε ∷ ρ ∷ ω ∷ σ ∷ ύ ∷ ν ∷ η ∷ ς ∷ []) "Heb.7.12"
∷ word (ἐ ∷ ξ ∷ []) "Heb.7.12"
∷ word (ἀ ∷ ν ∷ ά ∷ γ ∷ κ ∷ η ∷ ς ∷ []) "Heb.7.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.12"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ υ ∷ []) "Heb.7.12"
∷ word (μ ∷ ε ∷ τ ∷ ά ∷ θ ∷ ε ∷ σ ∷ ι ∷ ς ∷ []) "Heb.7.12"
∷ word (γ ∷ ί ∷ ν ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.12"
∷ word (ἐ ∷ φ ∷ []) "Heb.7.13"
∷ word (ὃ ∷ ν ∷ []) "Heb.7.13"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.13"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.13"
∷ word (τ ∷ α ∷ ῦ ∷ τ ∷ α ∷ []) "Heb.7.13"
∷ word (φ ∷ υ ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.7.13"
∷ word (ἑ ∷ τ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.7.13"
∷ word (μ ∷ ε ∷ τ ∷ έ ∷ σ ∷ χ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.7.13"
∷ word (ἀ ∷ φ ∷ []) "Heb.7.13"
∷ word (ἧ ∷ ς ∷ []) "Heb.7.13"
∷ word (ο ∷ ὐ ∷ δ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.7.13"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ έ ∷ σ ∷ χ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.7.13"
∷ word (τ ∷ ῷ ∷ []) "Heb.7.13"
∷ word (θ ∷ υ ∷ σ ∷ ι ∷ α ∷ σ ∷ τ ∷ η ∷ ρ ∷ ί ∷ ῳ ∷ []) "Heb.7.13"
∷ word (π ∷ ρ ∷ ό ∷ δ ∷ η ∷ ∙λ ∷ ο ∷ ν ∷ []) "Heb.7.14"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.14"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.7.14"
∷ word (ἐ ∷ ξ ∷ []) "Heb.7.14"
∷ word (Ἰ ∷ ο ∷ ύ ∷ δ ∷ α ∷ []) "Heb.7.14"
∷ word (ἀ ∷ ν ∷ α ∷ τ ∷ έ ∷ τ ∷ α ∷ ∙λ ∷ κ ∷ ε ∷ ν ∷ []) "Heb.7.14"
∷ word (ὁ ∷ []) "Heb.7.14"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.7.14"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.7.14"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.7.14"
∷ word (ἣ ∷ ν ∷ []) "Heb.7.14"
∷ word (φ ∷ υ ∷ ∙λ ∷ ὴ ∷ ν ∷ []) "Heb.7.14"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.7.14"
∷ word (ἱ ∷ ε ∷ ρ ∷ έ ∷ ω ∷ ν ∷ []) "Heb.7.14"
∷ word (ο ∷ ὐ ∷ δ ∷ ὲ ∷ ν ∷ []) "Heb.7.14"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ ῆ ∷ ς ∷ []) "Heb.7.14"
∷ word (ἐ ∷ ∙λ ∷ ά ∷ ∙λ ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.7.14"
∷ word (Κ ∷ α ∷ ὶ ∷ []) "Heb.7.15"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ σ ∷ σ ∷ ό ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.7.15"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.7.15"
∷ word (κ ∷ α ∷ τ ∷ ά ∷ δ ∷ η ∷ ∙λ ∷ ό ∷ ν ∷ []) "Heb.7.15"
∷ word (ἐ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.7.15"
∷ word (ε ∷ ἰ ∷ []) "Heb.7.15"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.7.15"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.7.15"
∷ word (ὁ ∷ μ ∷ ο ∷ ι ∷ ό ∷ τ ∷ η ∷ τ ∷ α ∷ []) "Heb.7.15"
∷ word (Μ ∷ ε ∷ ∙λ ∷ χ ∷ ι ∷ σ ∷ έ ∷ δ ∷ ε ∷ κ ∷ []) "Heb.7.15"
∷ word (ἀ ∷ ν ∷ ί ∷ σ ∷ τ ∷ α ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.15"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.7.15"
∷ word (ἕ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ς ∷ []) "Heb.7.15"
∷ word (ὃ ∷ ς ∷ []) "Heb.7.16"
∷ word (ο ∷ ὐ ∷ []) "Heb.7.16"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.7.16"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ν ∷ []) "Heb.7.16"
∷ word (ἐ ∷ ν ∷ τ ∷ ο ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.7.16"
∷ word (σ ∷ α ∷ ρ ∷ κ ∷ ί ∷ ν ∷ η ∷ ς ∷ []) "Heb.7.16"
∷ word (γ ∷ έ ∷ γ ∷ ο ∷ ν ∷ ε ∷ ν ∷ []) "Heb.7.16"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.7.16"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.7.16"
∷ word (δ ∷ ύ ∷ ν ∷ α ∷ μ ∷ ι ∷ ν ∷ []) "Heb.7.16"
∷ word (ζ ∷ ω ∷ ῆ ∷ ς ∷ []) "Heb.7.16"
∷ word (ἀ ∷ κ ∷ α ∷ τ ∷ α ∷ ∙λ ∷ ύ ∷ τ ∷ ο ∷ υ ∷ []) "Heb.7.16"
∷ word (μ ∷ α ∷ ρ ∷ τ ∷ υ ∷ ρ ∷ ε ∷ ῖ ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.17"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.17"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.7.17"
∷ word (Σ ∷ ὺ ∷ []) "Heb.7.17"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.7.17"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.7.17"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.7.17"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ []) "Heb.7.17"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.7.17"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.7.17"
∷ word (τ ∷ ά ∷ ξ ∷ ι ∷ ν ∷ []) "Heb.7.17"
∷ word (Μ ∷ ε ∷ ∙λ ∷ χ ∷ ι ∷ σ ∷ έ ∷ δ ∷ ε ∷ κ ∷ []) "Heb.7.17"
∷ word (ἀ ∷ θ ∷ έ ∷ τ ∷ η ∷ σ ∷ ι ∷ ς ∷ []) "Heb.7.18"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.7.18"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.18"
∷ word (γ ∷ ί ∷ ν ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.18"
∷ word (π ∷ ρ ∷ ο ∷ α ∷ γ ∷ ο ∷ ύ ∷ σ ∷ η ∷ ς ∷ []) "Heb.7.18"
∷ word (ἐ ∷ ν ∷ τ ∷ ο ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.7.18"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.7.18"
∷ word (τ ∷ ὸ ∷ []) "Heb.7.18"
∷ word (α ∷ ὐ ∷ τ ∷ ῆ ∷ ς ∷ []) "Heb.7.18"
∷ word (ἀ ∷ σ ∷ θ ∷ ε ∷ ν ∷ ὲ ∷ ς ∷ []) "Heb.7.18"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.18"
∷ word (ἀ ∷ ν ∷ ω ∷ φ ∷ ε ∷ ∙λ ∷ έ ∷ ς ∷ []) "Heb.7.18"
∷ word (ο ∷ ὐ ∷ δ ∷ ὲ ∷ ν ∷ []) "Heb.7.19"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.19"
∷ word (ἐ ∷ τ ∷ ε ∷ ∙λ ∷ ε ∷ ί ∷ ω ∷ σ ∷ ε ∷ ν ∷ []) "Heb.7.19"
∷ word (ὁ ∷ []) "Heb.7.19"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ς ∷ []) "Heb.7.19"
∷ word (ἐ ∷ π ∷ ε ∷ ι ∷ σ ∷ α ∷ γ ∷ ω ∷ γ ∷ ὴ ∷ []) "Heb.7.19"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.19"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.7.19"
∷ word (ἐ ∷ ∙λ ∷ π ∷ ί ∷ δ ∷ ο ∷ ς ∷ []) "Heb.7.19"
∷ word (δ ∷ ι ∷ []) "Heb.7.19"
∷ word (ἧ ∷ ς ∷ []) "Heb.7.19"
∷ word (ἐ ∷ γ ∷ γ ∷ ί ∷ ζ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.7.19"
∷ word (τ ∷ ῷ ∷ []) "Heb.7.19"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.7.19"
∷ word (Κ ∷ α ∷ ὶ ∷ []) "Heb.7.20"
∷ word (κ ∷ α ∷ θ ∷ []) "Heb.7.20"
∷ word (ὅ ∷ σ ∷ ο ∷ ν ∷ []) "Heb.7.20"
∷ word (ο ∷ ὐ ∷ []) "Heb.7.20"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.7.20"
∷ word (ὁ ∷ ρ ∷ κ ∷ ω ∷ μ ∷ ο ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.7.20"
∷ word (ο ∷ ἱ ∷ []) "Heb.7.20"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.7.20"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.20"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.7.20"
∷ word (ὁ ∷ ρ ∷ κ ∷ ω ∷ μ ∷ ο ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.7.20"
∷ word (ε ∷ ἰ ∷ σ ∷ ὶ ∷ ν ∷ []) "Heb.7.20"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.7.20"
∷ word (γ ∷ ε ∷ γ ∷ ο ∷ ν ∷ ό ∷ τ ∷ ε ∷ ς ∷ []) "Heb.7.20"
∷ word (ὁ ∷ []) "Heb.7.21"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.21"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.7.21"
∷ word (ὁ ∷ ρ ∷ κ ∷ ω ∷ μ ∷ ο ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.7.21"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.7.21"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.7.21"
∷ word (∙λ ∷ έ ∷ γ ∷ ο ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.7.21"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.7.21"
∷ word (α ∷ ὐ ∷ τ ∷ ό ∷ ν ∷ []) "Heb.7.21"
∷ word (Ὤ ∷ μ ∷ ο ∷ σ ∷ ε ∷ ν ∷ []) "Heb.7.21"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.7.21"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.21"
∷ word (ο ∷ ὐ ∷ []) "Heb.7.21"
∷ word (μ ∷ ε ∷ τ ∷ α ∷ μ ∷ ε ∷ ∙λ ∷ η ∷ θ ∷ ή ∷ σ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.21"
∷ word (Σ ∷ ὺ ∷ []) "Heb.7.21"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.7.21"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.7.21"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.7.21"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ []) "Heb.7.21"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.7.22"
∷ word (τ ∷ ο ∷ σ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.7.22"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.7.22"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ς ∷ []) "Heb.7.22"
∷ word (γ ∷ έ ∷ γ ∷ ο ∷ ν ∷ ε ∷ ν ∷ []) "Heb.7.22"
∷ word (ἔ ∷ γ ∷ γ ∷ υ ∷ ο ∷ ς ∷ []) "Heb.7.22"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ς ∷ []) "Heb.7.22"
∷ word (Κ ∷ α ∷ ὶ ∷ []) "Heb.7.23"
∷ word (ο ∷ ἱ ∷ []) "Heb.7.23"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.7.23"
∷ word (π ∷ ∙λ ∷ ε ∷ ί ∷ ο ∷ ν ∷ έ ∷ ς ∷ []) "Heb.7.23"
∷ word (ε ∷ ἰ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.7.23"
∷ word (γ ∷ ε ∷ γ ∷ ο ∷ ν ∷ ό ∷ τ ∷ ε ∷ ς ∷ []) "Heb.7.23"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.7.23"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.7.23"
∷ word (τ ∷ ὸ ∷ []) "Heb.7.23"
∷ word (θ ∷ α ∷ ν ∷ ά ∷ τ ∷ ῳ ∷ []) "Heb.7.23"
∷ word (κ ∷ ω ∷ ∙λ ∷ ύ ∷ ε ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.7.23"
∷ word (π ∷ α ∷ ρ ∷ α ∷ μ ∷ έ ∷ ν ∷ ε ∷ ι ∷ ν ∷ []) "Heb.7.23"
∷ word (ὁ ∷ []) "Heb.7.24"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.24"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.7.24"
∷ word (τ ∷ ὸ ∷ []) "Heb.7.24"
∷ word (μ ∷ έ ∷ ν ∷ ε ∷ ι ∷ ν ∷ []) "Heb.7.24"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.7.24"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.7.24"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.7.24"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ []) "Heb.7.24"
∷ word (ἀ ∷ π ∷ α ∷ ρ ∷ ά ∷ β ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.7.24"
∷ word (ἔ ∷ χ ∷ ε ∷ ι ∷ []) "Heb.7.24"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.7.24"
∷ word (ἱ ∷ ε ∷ ρ ∷ ω ∷ σ ∷ ύ ∷ ν ∷ η ∷ ν ∷ []) "Heb.7.24"
∷ word (ὅ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.7.25"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.25"
∷ word (σ ∷ ῴ ∷ ζ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.7.25"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.7.25"
∷ word (τ ∷ ὸ ∷ []) "Heb.7.25"
∷ word (π ∷ α ∷ ν ∷ τ ∷ ε ∷ ∙λ ∷ ὲ ∷ ς ∷ []) "Heb.7.25"
∷ word (δ ∷ ύ ∷ ν ∷ α ∷ τ ∷ α ∷ ι ∷ []) "Heb.7.25"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.7.25"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ρ ∷ χ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.7.25"
∷ word (δ ∷ ι ∷ []) "Heb.7.25"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.7.25"
∷ word (τ ∷ ῷ ∷ []) "Heb.7.25"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.7.25"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ο ∷ τ ∷ ε ∷ []) "Heb.7.25"
∷ word (ζ ∷ ῶ ∷ ν ∷ []) "Heb.7.25"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.7.25"
∷ word (τ ∷ ὸ ∷ []) "Heb.7.25"
∷ word (ἐ ∷ ν ∷ τ ∷ υ ∷ γ ∷ χ ∷ ά ∷ ν ∷ ε ∷ ι ∷ ν ∷ []) "Heb.7.25"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.7.25"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.7.25"
∷ word (Τ ∷ ο ∷ ι ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.7.26"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.26"
∷ word (ἡ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.7.26"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.26"
∷ word (ἔ ∷ π ∷ ρ ∷ ε ∷ π ∷ ε ∷ ν ∷ []) "Heb.7.26"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ύ ∷ ς ∷ []) "Heb.7.26"
∷ word (ὅ ∷ σ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.7.26"
∷ word (ἄ ∷ κ ∷ α ∷ κ ∷ ο ∷ ς ∷ []) "Heb.7.26"
∷ word (ἀ ∷ μ ∷ ί ∷ α ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.7.26"
∷ word (κ ∷ ε ∷ χ ∷ ω ∷ ρ ∷ ι ∷ σ ∷ μ ∷ έ ∷ ν ∷ ο ∷ ς ∷ []) "Heb.7.26"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.7.26"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.7.26"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ω ∷ ∙λ ∷ ῶ ∷ ν ∷ []) "Heb.7.26"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.7.26"
∷ word (ὑ ∷ ψ ∷ η ∷ ∙λ ∷ ό ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ς ∷ []) "Heb.7.26"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.7.26"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ῶ ∷ ν ∷ []) "Heb.7.26"
∷ word (γ ∷ ε ∷ ν ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.7.26"
∷ word (ὃ ∷ ς ∷ []) "Heb.7.27"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.7.27"
∷ word (ἔ ∷ χ ∷ ε ∷ ι ∷ []) "Heb.7.27"
∷ word (κ ∷ α ∷ θ ∷ []) "Heb.7.27"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.7.27"
∷ word (ἀ ∷ ν ∷ ά ∷ γ ∷ κ ∷ η ∷ ν ∷ []) "Heb.7.27"
∷ word (ὥ ∷ σ ∷ π ∷ ε ∷ ρ ∷ []) "Heb.7.27"
∷ word (ο ∷ ἱ ∷ []) "Heb.7.27"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.7.27"
∷ word (π ∷ ρ ∷ ό ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.7.27"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.7.27"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.7.27"
∷ word (ἰ ∷ δ ∷ ί ∷ ω ∷ ν ∷ []) "Heb.7.27"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.7.27"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.7.27"
∷ word (ἀ ∷ ν ∷ α ∷ φ ∷ έ ∷ ρ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.7.27"
∷ word (ἔ ∷ π ∷ ε ∷ ι ∷ τ ∷ α ∷ []) "Heb.7.27"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.7.27"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.7.27"
∷ word (∙λ ∷ α ∷ ο ∷ ῦ ∷ []) "Heb.7.27"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.7.27"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.27"
∷ word (ἐ ∷ π ∷ ο ∷ ί ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.7.27"
∷ word (ἐ ∷ φ ∷ ά ∷ π ∷ α ∷ ξ ∷ []) "Heb.7.27"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.7.27"
∷ word (ἀ ∷ ν ∷ ε ∷ ν ∷ έ ∷ γ ∷ κ ∷ α ∷ ς ∷ []) "Heb.7.27"
∷ word (ὁ ∷ []) "Heb.7.28"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ς ∷ []) "Heb.7.28"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.7.28"
∷ word (ἀ ∷ ν ∷ θ ∷ ρ ∷ ώ ∷ π ∷ ο ∷ υ ∷ ς ∷ []) "Heb.7.28"
∷ word (κ ∷ α ∷ θ ∷ ί ∷ σ ∷ τ ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.7.28"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.7.28"
∷ word (ἔ ∷ χ ∷ ο ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.7.28"
∷ word (ἀ ∷ σ ∷ θ ∷ έ ∷ ν ∷ ε ∷ ι ∷ α ∷ ν ∷ []) "Heb.7.28"
∷ word (ὁ ∷ []) "Heb.7.28"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ς ∷ []) "Heb.7.28"
∷ word (δ ∷ ὲ ∷ []) "Heb.7.28"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.7.28"
∷ word (ὁ ∷ ρ ∷ κ ∷ ω ∷ μ ∷ ο ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.7.28"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.7.28"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.7.28"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.7.28"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ν ∷ []) "Heb.7.28"
∷ word (υ ∷ ἱ ∷ ό ∷ ν ∷ []) "Heb.7.28"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.7.28"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.7.28"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ []) "Heb.7.28"
∷ word (τ ∷ ε ∷ τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ω ∷ μ ∷ έ ∷ ν ∷ ο ∷ ν ∷ []) "Heb.7.28"
∷ word (Κ ∷ ε ∷ φ ∷ ά ∷ ∙λ ∷ α ∷ ι ∷ ο ∷ ν ∷ []) "Heb.8.1"
∷ word (δ ∷ ὲ ∷ []) "Heb.8.1"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.8.1"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.8.1"
∷ word (∙λ ∷ ε ∷ γ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ ς ∷ []) "Heb.8.1"
∷ word (τ ∷ ο ∷ ι ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.8.1"
∷ word (ἔ ∷ χ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.8.1"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ έ ∷ α ∷ []) "Heb.8.1"
∷ word (ὃ ∷ ς ∷ []) "Heb.8.1"
∷ word (ἐ ∷ κ ∷ ά ∷ θ ∷ ι ∷ σ ∷ ε ∷ ν ∷ []) "Heb.8.1"
∷ word (ἐ ∷ ν ∷ []) "Heb.8.1"
∷ word (δ ∷ ε ∷ ξ ∷ ι ∷ ᾷ ∷ []) "Heb.8.1"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.8.1"
∷ word (θ ∷ ρ ∷ ό ∷ ν ∷ ο ∷ υ ∷ []) "Heb.8.1"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.8.1"
∷ word (μ ∷ ε ∷ γ ∷ α ∷ ∙λ ∷ ω ∷ σ ∷ ύ ∷ ν ∷ η ∷ ς ∷ []) "Heb.8.1"
∷ word (ἐ ∷ ν ∷ []) "Heb.8.1"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.8.1"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.8.1"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.8.2"
∷ word (ἁ ∷ γ ∷ ί ∷ ω ∷ ν ∷ []) "Heb.8.2"
∷ word (∙λ ∷ ε ∷ ι ∷ τ ∷ ο ∷ υ ∷ ρ ∷ γ ∷ ὸ ∷ ς ∷ []) "Heb.8.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.2"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.8.2"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.8.2"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.8.2"
∷ word (ἀ ∷ ∙λ ∷ η ∷ θ ∷ ι ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.8.2"
∷ word (ἣ ∷ ν ∷ []) "Heb.8.2"
∷ word (ἔ ∷ π ∷ η ∷ ξ ∷ ε ∷ ν ∷ []) "Heb.8.2"
∷ word (ὁ ∷ []) "Heb.8.2"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.8.2"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.8.2"
∷ word (ἄ ∷ ν ∷ θ ∷ ρ ∷ ω ∷ π ∷ ο ∷ ς ∷ []) "Heb.8.2"
∷ word (π ∷ ᾶ ∷ ς ∷ []) "Heb.8.3"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.8.3"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.8.3"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.8.3"
∷ word (τ ∷ ὸ ∷ []) "Heb.8.3"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.8.3"
∷ word (δ ∷ ῶ ∷ ρ ∷ ά ∷ []) "Heb.8.3"
∷ word (τ ∷ ε ∷ []) "Heb.8.3"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.3"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.8.3"
∷ word (κ ∷ α ∷ θ ∷ ί ∷ σ ∷ τ ∷ α ∷ τ ∷ α ∷ ι ∷ []) "Heb.8.3"
∷ word (ὅ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.8.3"
∷ word (ἀ ∷ ν ∷ α ∷ γ ∷ κ ∷ α ∷ ῖ ∷ ο ∷ ν ∷ []) "Heb.8.3"
∷ word (ἔ ∷ χ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.8.3"
∷ word (τ ∷ ι ∷ []) "Heb.8.3"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.3"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.8.3"
∷ word (ὃ ∷ []) "Heb.8.3"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ν ∷ έ ∷ γ ∷ κ ∷ ῃ ∷ []) "Heb.8.3"
∷ word (ε ∷ ἰ ∷ []) "Heb.8.4"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.8.4"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.8.4"
∷ word (ἦ ∷ ν ∷ []) "Heb.8.4"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.8.4"
∷ word (γ ∷ ῆ ∷ ς ∷ []) "Heb.8.4"
∷ word (ο ∷ ὐ ∷ δ ∷ []) "Heb.8.4"
∷ word (ἂ ∷ ν ∷ []) "Heb.8.4"
∷ word (ἦ ∷ ν ∷ []) "Heb.8.4"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ύ ∷ ς ∷ []) "Heb.8.4"
∷ word (ὄ ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.8.4"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.8.4"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ ε ∷ ρ ∷ ό ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.8.4"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.8.4"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ν ∷ []) "Heb.8.4"
∷ word (τ ∷ ὰ ∷ []) "Heb.8.4"
∷ word (δ ∷ ῶ ∷ ρ ∷ α ∷ []) "Heb.8.4"
∷ word (ο ∷ ἵ ∷ τ ∷ ι ∷ ν ∷ ε ∷ ς ∷ []) "Heb.8.5"
∷ word (ὑ ∷ π ∷ ο ∷ δ ∷ ε ∷ ί ∷ γ ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.8.5"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.5"
∷ word (σ ∷ κ ∷ ι ∷ ᾷ ∷ []) "Heb.8.5"
∷ word (∙λ ∷ α ∷ τ ∷ ρ ∷ ε ∷ ύ ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.8.5"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.8.5"
∷ word (ἐ ∷ π ∷ ο ∷ υ ∷ ρ ∷ α ∷ ν ∷ ί ∷ ω ∷ ν ∷ []) "Heb.8.5"
∷ word (κ ∷ α ∷ θ ∷ ὼ ∷ ς ∷ []) "Heb.8.5"
∷ word (κ ∷ ε ∷ χ ∷ ρ ∷ η ∷ μ ∷ ά ∷ τ ∷ ι ∷ σ ∷ τ ∷ α ∷ ι ∷ []) "Heb.8.5"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ ῆ ∷ ς ∷ []) "Heb.8.5"
∷ word (μ ∷ έ ∷ ∙λ ∷ ∙λ ∷ ω ∷ ν ∷ []) "Heb.8.5"
∷ word (ἐ ∷ π ∷ ι ∷ τ ∷ ε ∷ ∙λ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.8.5"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.8.5"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ ή ∷ ν ∷ []) "Heb.8.5"
∷ word (Ὅ ∷ ρ ∷ α ∷ []) "Heb.8.5"
∷ word (γ ∷ ά ∷ ρ ∷ []) "Heb.8.5"
∷ word (φ ∷ η ∷ σ ∷ ί ∷ ν ∷ []) "Heb.8.5"
∷ word (π ∷ ο ∷ ι ∷ ή ∷ σ ∷ ε ∷ ι ∷ ς ∷ []) "Heb.8.5"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.8.5"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.8.5"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.8.5"
∷ word (τ ∷ ύ ∷ π ∷ ο ∷ ν ∷ []) "Heb.8.5"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.8.5"
∷ word (δ ∷ ε ∷ ι ∷ χ ∷ θ ∷ έ ∷ ν ∷ τ ∷ α ∷ []) "Heb.8.5"
∷ word (σ ∷ ο ∷ ι ∷ []) "Heb.8.5"
∷ word (ἐ ∷ ν ∷ []) "Heb.8.5"
∷ word (τ ∷ ῷ ∷ []) "Heb.8.5"
∷ word (ὄ ∷ ρ ∷ ε ∷ ι ∷ []) "Heb.8.5"
∷ word (ν ∷ υ ∷ ν ∷ ὶ ∷ []) "Heb.8.6"
∷ word (δ ∷ ὲ ∷ []) "Heb.8.6"
∷ word (δ ∷ ι ∷ α ∷ φ ∷ ο ∷ ρ ∷ ω ∷ τ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.8.6"
∷ word (τ ∷ έ ∷ τ ∷ υ ∷ χ ∷ ε ∷ ν ∷ []) "Heb.8.6"
∷ word (∙λ ∷ ε ∷ ι ∷ τ ∷ ο ∷ υ ∷ ρ ∷ γ ∷ ί ∷ α ∷ ς ∷ []) "Heb.8.6"
∷ word (ὅ ∷ σ ∷ ῳ ∷ []) "Heb.8.6"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.6"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ο ∷ ν ∷ ό ∷ ς ∷ []) "Heb.8.6"
∷ word (ἐ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.8.6"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ς ∷ []) "Heb.8.6"
∷ word (μ ∷ ε ∷ σ ∷ ί ∷ τ ∷ η ∷ ς ∷ []) "Heb.8.6"
∷ word (ἥ ∷ τ ∷ ι ∷ ς ∷ []) "Heb.8.6"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.8.6"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ο ∷ σ ∷ ι ∷ ν ∷ []) "Heb.8.6"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ι ∷ ς ∷ []) "Heb.8.6"
∷ word (ν ∷ ε ∷ ν ∷ ο ∷ μ ∷ ο ∷ θ ∷ έ ∷ τ ∷ η ∷ τ ∷ α ∷ ι ∷ []) "Heb.8.6"
∷ word (Ε ∷ ἰ ∷ []) "Heb.8.7"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.8.7"
∷ word (ἡ ∷ []) "Heb.8.7"
∷ word (π ∷ ρ ∷ ώ ∷ τ ∷ η ∷ []) "Heb.8.7"
∷ word (ἐ ∷ κ ∷ ε ∷ ί ∷ ν ∷ η ∷ []) "Heb.8.7"
∷ word (ἦ ∷ ν ∷ []) "Heb.8.7"
∷ word (ἄ ∷ μ ∷ ε ∷ μ ∷ π ∷ τ ∷ ο ∷ ς ∷ []) "Heb.8.7"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.8.7"
∷ word (ἂ ∷ ν ∷ []) "Heb.8.7"
∷ word (δ ∷ ε ∷ υ ∷ τ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.8.7"
∷ word (ἐ ∷ ζ ∷ η ∷ τ ∷ ε ∷ ῖ ∷ τ ∷ ο ∷ []) "Heb.8.7"
∷ word (τ ∷ ό ∷ π ∷ ο ∷ ς ∷ []) "Heb.8.7"
∷ word (μ ∷ ε ∷ μ ∷ φ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.8.8"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.8.8"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.8.8"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.8.8"
∷ word (Ἰ ∷ δ ∷ ο ∷ ὺ ∷ []) "Heb.8.8"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ι ∷ []) "Heb.8.8"
∷ word (ἔ ∷ ρ ∷ χ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.8.8"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.8.8"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.8.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.8"
∷ word (σ ∷ υ ∷ ν ∷ τ ∷ ε ∷ ∙λ ∷ έ ∷ σ ∷ ω ∷ []) "Heb.8.8"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.8.8"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.8.8"
∷ word (ο ∷ ἶ ∷ κ ∷ ο ∷ ν ∷ []) "Heb.8.8"
∷ word (Ἰ ∷ σ ∷ ρ ∷ α ∷ ὴ ∷ ∙λ ∷ []) "Heb.8.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.8"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.8.8"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.8.8"
∷ word (ο ∷ ἶ ∷ κ ∷ ο ∷ ν ∷ []) "Heb.8.8"
∷ word (Ἰ ∷ ο ∷ ύ ∷ δ ∷ α ∷ []) "Heb.8.8"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ν ∷ []) "Heb.8.8"
∷ word (κ ∷ α ∷ ι ∷ ν ∷ ή ∷ ν ∷ []) "Heb.8.8"
∷ word (ο ∷ ὐ ∷ []) "Heb.8.9"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.8.9"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.8.9"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ν ∷ []) "Heb.8.9"
∷ word (ἣ ∷ ν ∷ []) "Heb.8.9"
∷ word (ἐ ∷ π ∷ ο ∷ ί ∷ η ∷ σ ∷ α ∷ []) "Heb.8.9"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.8.9"
∷ word (π ∷ α ∷ τ ∷ ρ ∷ ά ∷ σ ∷ ι ∷ ν ∷ []) "Heb.8.9"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.8.9"
∷ word (ἐ ∷ ν ∷ []) "Heb.8.9"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ ᾳ ∷ []) "Heb.8.9"
∷ word (ἐ ∷ π ∷ ι ∷ ∙λ ∷ α ∷ β ∷ ο ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ []) "Heb.8.9"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.8.9"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.8.9"
∷ word (χ ∷ ε ∷ ι ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.8.9"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.8.9"
∷ word (ἐ ∷ ξ ∷ α ∷ γ ∷ α ∷ γ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.8.9"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.8.9"
∷ word (ἐ ∷ κ ∷ []) "Heb.8.9"
∷ word (γ ∷ ῆ ∷ ς ∷ []) "Heb.8.9"
∷ word (Α ∷ ἰ ∷ γ ∷ ύ ∷ π ∷ τ ∷ ο ∷ υ ∷ []) "Heb.8.9"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.8.9"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὶ ∷ []) "Heb.8.9"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.8.9"
∷ word (ἐ ∷ ν ∷ έ ∷ μ ∷ ε ∷ ι ∷ ν ∷ α ∷ ν ∷ []) "Heb.8.9"
∷ word (ἐ ∷ ν ∷ []) "Heb.8.9"
∷ word (τ ∷ ῇ ∷ []) "Heb.8.9"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ ῃ ∷ []) "Heb.8.9"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.8.9"
∷ word (κ ∷ ἀ ∷ γ ∷ ὼ ∷ []) "Heb.8.9"
∷ word (ἠ ∷ μ ∷ έ ∷ ∙λ ∷ η ∷ σ ∷ α ∷ []) "Heb.8.9"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.8.9"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.8.9"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.8.9"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.8.10"
∷ word (α ∷ ὕ ∷ τ ∷ η ∷ []) "Heb.8.10"
∷ word (ἡ ∷ []) "Heb.8.10"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ []) "Heb.8.10"
∷ word (ἣ ∷ ν ∷ []) "Heb.8.10"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ σ ∷ ο ∷ μ ∷ α ∷ ι ∷ []) "Heb.8.10"
∷ word (τ ∷ ῷ ∷ []) "Heb.8.10"
∷ word (ο ∷ ἴ ∷ κ ∷ ῳ ∷ []) "Heb.8.10"
∷ word (Ἰ ∷ σ ∷ ρ ∷ α ∷ ὴ ∷ ∙λ ∷ []) "Heb.8.10"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.8.10"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.8.10"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.8.10"
∷ word (ἐ ∷ κ ∷ ε ∷ ί ∷ ν ∷ α ∷ ς ∷ []) "Heb.8.10"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.8.10"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.8.10"
∷ word (δ ∷ ι ∷ δ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.8.10"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.8.10"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.8.10"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.8.10"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.8.10"
∷ word (δ ∷ ι ∷ ά ∷ ν ∷ ο ∷ ι ∷ α ∷ ν ∷ []) "Heb.8.10"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.8.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.10"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.8.10"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ ς ∷ []) "Heb.8.10"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.8.10"
∷ word (ἐ ∷ π ∷ ι ∷ γ ∷ ρ ∷ ά ∷ ψ ∷ ω ∷ []) "Heb.8.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ύ ∷ ς ∷ []) "Heb.8.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.10"
∷ word (ἔ ∷ σ ∷ ο ∷ μ ∷ α ∷ ι ∷ []) "Heb.8.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.8.10"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.8.10"
∷ word (θ ∷ ε ∷ ό ∷ ν ∷ []) "Heb.8.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὶ ∷ []) "Heb.8.10"
∷ word (ἔ ∷ σ ∷ ο ∷ ν ∷ τ ∷ α ∷ ί ∷ []) "Heb.8.10"
∷ word (μ ∷ ο ∷ ι ∷ []) "Heb.8.10"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.8.10"
∷ word (∙λ ∷ α ∷ ό ∷ ν ∷ []) "Heb.8.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.11"
∷ word (ο ∷ ὐ ∷ []) "Heb.8.11"
∷ word (μ ∷ ὴ ∷ []) "Heb.8.11"
∷ word (δ ∷ ι ∷ δ ∷ ά ∷ ξ ∷ ω ∷ σ ∷ ι ∷ ν ∷ []) "Heb.8.11"
∷ word (ἕ ∷ κ ∷ α ∷ σ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.8.11"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.8.11"
∷ word (π ∷ ο ∷ ∙λ ∷ ί ∷ τ ∷ η ∷ ν ∷ []) "Heb.8.11"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.8.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.11"
∷ word (ἕ ∷ κ ∷ α ∷ σ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.8.11"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.8.11"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ὸ ∷ ν ∷ []) "Heb.8.11"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.8.11"
∷ word (∙λ ∷ έ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.8.11"
∷ word (Γ ∷ ν ∷ ῶ ∷ θ ∷ ι ∷ []) "Heb.8.11"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.8.11"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.8.11"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.8.11"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.8.11"
∷ word (ε ∷ ἰ ∷ δ ∷ ή ∷ σ ∷ ο ∷ υ ∷ σ ∷ ί ∷ ν ∷ []) "Heb.8.11"
∷ word (μ ∷ ε ∷ []) "Heb.8.11"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.8.11"
∷ word (μ ∷ ι ∷ κ ∷ ρ ∷ ο ∷ ῦ ∷ []) "Heb.8.11"
∷ word (ἕ ∷ ω ∷ ς ∷ []) "Heb.8.11"
∷ word (μ ∷ ε ∷ γ ∷ ά ∷ ∙λ ∷ ο ∷ υ ∷ []) "Heb.8.11"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.8.11"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.8.12"
∷ word (ἵ ∷ ∙λ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.8.12"
∷ word (ἔ ∷ σ ∷ ο ∷ μ ∷ α ∷ ι ∷ []) "Heb.8.12"
∷ word (τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.8.12"
∷ word (ἀ ∷ δ ∷ ι ∷ κ ∷ ί ∷ α ∷ ι ∷ ς ∷ []) "Heb.8.12"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.8.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.12"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.8.12"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.8.12"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.8.12"
∷ word (ο ∷ ὐ ∷ []) "Heb.8.12"
∷ word (μ ∷ ὴ ∷ []) "Heb.8.12"
∷ word (μ ∷ ν ∷ η ∷ σ ∷ θ ∷ ῶ ∷ []) "Heb.8.12"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.8.12"
∷ word (ἐ ∷ ν ∷ []) "Heb.8.13"
∷ word (τ ∷ ῷ ∷ []) "Heb.8.13"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.8.13"
∷ word (Κ ∷ α ∷ ι ∷ ν ∷ ὴ ∷ ν ∷ []) "Heb.8.13"
∷ word (π ∷ ε ∷ π ∷ α ∷ ∙λ ∷ α ∷ ί ∷ ω ∷ κ ∷ ε ∷ ν ∷ []) "Heb.8.13"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.8.13"
∷ word (π ∷ ρ ∷ ώ ∷ τ ∷ η ∷ ν ∷ []) "Heb.8.13"
∷ word (τ ∷ ὸ ∷ []) "Heb.8.13"
∷ word (δ ∷ ὲ ∷ []) "Heb.8.13"
∷ word (π ∷ α ∷ ∙λ ∷ α ∷ ι ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.8.13"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.8.13"
∷ word (γ ∷ η ∷ ρ ∷ ά ∷ σ ∷ κ ∷ ο ∷ ν ∷ []) "Heb.8.13"
∷ word (ἐ ∷ γ ∷ γ ∷ ὺ ∷ ς ∷ []) "Heb.8.13"
∷ word (ἀ ∷ φ ∷ α ∷ ν ∷ ι ∷ σ ∷ μ ∷ ο ∷ ῦ ∷ []) "Heb.8.13"
∷ word (Ε ∷ ἶ ∷ χ ∷ ε ∷ []) "Heb.9.1"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.9.1"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.9.1"
∷ word (ἡ ∷ []) "Heb.9.1"
∷ word (π ∷ ρ ∷ ώ ∷ τ ∷ η ∷ []) "Heb.9.1"
∷ word (δ ∷ ι ∷ κ ∷ α ∷ ι ∷ ώ ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.9.1"
∷ word (∙λ ∷ α ∷ τ ∷ ρ ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.9.1"
∷ word (τ ∷ ό ∷ []) "Heb.9.1"
∷ word (τ ∷ ε ∷ []) "Heb.9.1"
∷ word (ἅ ∷ γ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.9.1"
∷ word (κ ∷ ο ∷ σ ∷ μ ∷ ι ∷ κ ∷ ό ∷ ν ∷ []) "Heb.9.1"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ ὴ ∷ []) "Heb.9.2"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.9.2"
∷ word (κ ∷ α ∷ τ ∷ ε ∷ σ ∷ κ ∷ ε ∷ υ ∷ ά ∷ σ ∷ θ ∷ η ∷ []) "Heb.9.2"
∷ word (ἡ ∷ []) "Heb.9.2"
∷ word (π ∷ ρ ∷ ώ ∷ τ ∷ η ∷ []) "Heb.9.2"
∷ word (ἐ ∷ ν ∷ []) "Heb.9.2"
∷ word (ᾗ ∷ []) "Heb.9.2"
∷ word (ἥ ∷ []) "Heb.9.2"
∷ word (τ ∷ ε ∷ []) "Heb.9.2"
∷ word (∙λ ∷ υ ∷ χ ∷ ν ∷ ί ∷ α ∷ []) "Heb.9.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.2"
∷ word (ἡ ∷ []) "Heb.9.2"
∷ word (τ ∷ ρ ∷ ά ∷ π ∷ ε ∷ ζ ∷ α ∷ []) "Heb.9.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.2"
∷ word (ἡ ∷ []) "Heb.9.2"
∷ word (π ∷ ρ ∷ ό ∷ θ ∷ ε ∷ σ ∷ ι ∷ ς ∷ []) "Heb.9.2"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.9.2"
∷ word (ἄ ∷ ρ ∷ τ ∷ ω ∷ ν ∷ []) "Heb.9.2"
∷ word (ἥ ∷ τ ∷ ι ∷ ς ∷ []) "Heb.9.2"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.9.2"
∷ word (Ἅ ∷ γ ∷ ι ∷ α ∷ []) "Heb.9.2"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.9.3"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.3"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.3"
∷ word (δ ∷ ε ∷ ύ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.9.3"
∷ word (κ ∷ α ∷ τ ∷ α ∷ π ∷ έ ∷ τ ∷ α ∷ σ ∷ μ ∷ α ∷ []) "Heb.9.3"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ ὴ ∷ []) "Heb.9.3"
∷ word (ἡ ∷ []) "Heb.9.3"
∷ word (∙λ ∷ ε ∷ γ ∷ ο ∷ μ ∷ έ ∷ ν ∷ η ∷ []) "Heb.9.3"
∷ word (Ἅ ∷ γ ∷ ι ∷ α ∷ []) "Heb.9.3"
∷ word (Ἁ ∷ γ ∷ ί ∷ ω ∷ ν ∷ []) "Heb.9.3"
∷ word (χ ∷ ρ ∷ υ ∷ σ ∷ ο ∷ ῦ ∷ ν ∷ []) "Heb.9.4"
∷ word (ἔ ∷ χ ∷ ο ∷ υ ∷ σ ∷ α ∷ []) "Heb.9.4"
∷ word (θ ∷ υ ∷ μ ∷ ι ∷ α ∷ τ ∷ ή ∷ ρ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.9.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.4"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.9.4"
∷ word (κ ∷ ι ∷ β ∷ ω ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.9.4"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.4"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ς ∷ []) "Heb.9.4"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ κ ∷ ε ∷ κ ∷ α ∷ ∙λ ∷ υ ∷ μ ∷ μ ∷ έ ∷ ν ∷ η ∷ ν ∷ []) "Heb.9.4"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ο ∷ θ ∷ ε ∷ ν ∷ []) "Heb.9.4"
∷ word (χ ∷ ρ ∷ υ ∷ σ ∷ ί ∷ ῳ ∷ []) "Heb.9.4"
∷ word (ἐ ∷ ν ∷ []) "Heb.9.4"
∷ word (ᾗ ∷ []) "Heb.9.4"
∷ word (σ ∷ τ ∷ ά ∷ μ ∷ ν ∷ ο ∷ ς ∷ []) "Heb.9.4"
∷ word (χ ∷ ρ ∷ υ ∷ σ ∷ ῆ ∷ []) "Heb.9.4"
∷ word (ἔ ∷ χ ∷ ο ∷ υ ∷ σ ∷ α ∷ []) "Heb.9.4"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.4"
∷ word (μ ∷ ά ∷ ν ∷ ν ∷ α ∷ []) "Heb.9.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.4"
∷ word (ἡ ∷ []) "Heb.9.4"
∷ word (ῥ ∷ ά ∷ β ∷ δ ∷ ο ∷ ς ∷ []) "Heb.9.4"
∷ word (Ἀ ∷ α ∷ ρ ∷ ὼ ∷ ν ∷ []) "Heb.9.4"
∷ word (ἡ ∷ []) "Heb.9.4"
∷ word (β ∷ ∙λ ∷ α ∷ σ ∷ τ ∷ ή ∷ σ ∷ α ∷ σ ∷ α ∷ []) "Heb.9.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.4"
∷ word (α ∷ ἱ ∷ []) "Heb.9.4"
∷ word (π ∷ ∙λ ∷ ά ∷ κ ∷ ε ∷ ς ∷ []) "Heb.9.4"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.4"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ς ∷ []) "Heb.9.4"
∷ word (ὑ ∷ π ∷ ε ∷ ρ ∷ ά ∷ ν ∷ ω ∷ []) "Heb.9.5"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.5"
∷ word (α ∷ ὐ ∷ τ ∷ ῆ ∷ ς ∷ []) "Heb.9.5"
∷ word (Χ ∷ ε ∷ ρ ∷ ο ∷ υ ∷ β ∷ ὶ ∷ ν ∷ []) "Heb.9.5"
∷ word (δ ∷ ό ∷ ξ ∷ η ∷ ς ∷ []) "Heb.9.5"
∷ word (κ ∷ α ∷ τ ∷ α ∷ σ ∷ κ ∷ ι ∷ ά ∷ ζ ∷ ο ∷ ν ∷ τ ∷ α ∷ []) "Heb.9.5"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.5"
∷ word (ἱ ∷ ∙λ ∷ α ∷ σ ∷ τ ∷ ή ∷ ρ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.9.5"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.9.5"
∷ word (ὧ ∷ ν ∷ []) "Heb.9.5"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.9.5"
∷ word (ἔ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.9.5"
∷ word (ν ∷ ῦ ∷ ν ∷ []) "Heb.9.5"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.9.5"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.9.5"
∷ word (μ ∷ έ ∷ ρ ∷ ο ∷ ς ∷ []) "Heb.9.5"
∷ word (Τ ∷ ο ∷ ύ ∷ τ ∷ ω ∷ ν ∷ []) "Heb.9.6"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.6"
∷ word (ο ∷ ὕ ∷ τ ∷ ω ∷ ς ∷ []) "Heb.9.6"
∷ word (κ ∷ α ∷ τ ∷ ε ∷ σ ∷ κ ∷ ε ∷ υ ∷ α ∷ σ ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.9.6"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.6"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.9.6"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.9.6"
∷ word (π ∷ ρ ∷ ώ ∷ τ ∷ η ∷ ν ∷ []) "Heb.9.6"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ ὴ ∷ ν ∷ []) "Heb.9.6"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.9.6"
∷ word (π ∷ α ∷ ν ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.9.6"
∷ word (ε ∷ ἰ ∷ σ ∷ ί ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.6"
∷ word (ο ∷ ἱ ∷ []) "Heb.9.6"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.9.6"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.9.6"
∷ word (∙λ ∷ α ∷ τ ∷ ρ ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.9.6"
∷ word (ἐ ∷ π ∷ ι ∷ τ ∷ ε ∷ ∙λ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.9.6"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.7"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.7"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.9.7"
∷ word (δ ∷ ε ∷ υ ∷ τ ∷ έ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.9.7"
∷ word (ἅ ∷ π ∷ α ∷ ξ ∷ []) "Heb.9.7"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.9.7"
∷ word (ἐ ∷ ν ∷ ι ∷ α ∷ υ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.9.7"
∷ word (μ ∷ ό ∷ ν ∷ ο ∷ ς ∷ []) "Heb.9.7"
∷ word (ὁ ∷ []) "Heb.9.7"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ύ ∷ ς ∷ []) "Heb.9.7"
∷ word (ο ∷ ὐ ∷ []) "Heb.9.7"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.9.7"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.9.7"
∷ word (ὃ ∷ []) "Heb.9.7"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ε ∷ ι ∷ []) "Heb.9.7"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.9.7"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.9.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.7"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.9.7"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.9.7"
∷ word (∙λ ∷ α ∷ ο ∷ ῦ ∷ []) "Heb.9.7"
∷ word (ἀ ∷ γ ∷ ν ∷ ο ∷ η ∷ μ ∷ ά ∷ τ ∷ ω ∷ ν ∷ []) "Heb.9.7"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.9.8"
∷ word (δ ∷ η ∷ ∙λ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.9.8"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.9.8"
∷ word (π ∷ ν ∷ ε ∷ ύ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.9.8"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.9.8"
∷ word (ἁ ∷ γ ∷ ί ∷ ο ∷ υ ∷ []) "Heb.9.8"
∷ word (μ ∷ ή ∷ π ∷ ω ∷ []) "Heb.9.8"
∷ word (π ∷ ε ∷ φ ∷ α ∷ ν ∷ ε ∷ ρ ∷ ῶ ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.9.8"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.9.8"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.9.8"
∷ word (ἁ ∷ γ ∷ ί ∷ ω ∷ ν ∷ []) "Heb.9.8"
∷ word (ὁ ∷ δ ∷ ὸ ∷ ν ∷ []) "Heb.9.8"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.9.8"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.8"
∷ word (π ∷ ρ ∷ ώ ∷ τ ∷ η ∷ ς ∷ []) "Heb.9.8"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.9.8"
∷ word (ἐ ∷ χ ∷ ο ∷ ύ ∷ σ ∷ η ∷ ς ∷ []) "Heb.9.8"
∷ word (σ ∷ τ ∷ ά ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.8"
∷ word (ἥ ∷ τ ∷ ι ∷ ς ∷ []) "Heb.9.9"
∷ word (π ∷ α ∷ ρ ∷ α ∷ β ∷ ο ∷ ∙λ ∷ ὴ ∷ []) "Heb.9.9"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.9"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.9.9"
∷ word (κ ∷ α ∷ ι ∷ ρ ∷ ὸ ∷ ν ∷ []) "Heb.9.9"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.9.9"
∷ word (ἐ ∷ ν ∷ ε ∷ σ ∷ τ ∷ η ∷ κ ∷ ό ∷ τ ∷ α ∷ []) "Heb.9.9"
∷ word (κ ∷ α ∷ θ ∷ []) "Heb.9.9"
∷ word (ἣ ∷ ν ∷ []) "Heb.9.9"
∷ word (δ ∷ ῶ ∷ ρ ∷ ά ∷ []) "Heb.9.9"
∷ word (τ ∷ ε ∷ []) "Heb.9.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.9"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ι ∷ []) "Heb.9.9"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.9.9"
∷ word (μ ∷ ὴ ∷ []) "Heb.9.9"
∷ word (δ ∷ υ ∷ ν ∷ ά ∷ μ ∷ ε ∷ ν ∷ α ∷ ι ∷ []) "Heb.9.9"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.9.9"
∷ word (σ ∷ υ ∷ ν ∷ ε ∷ ί ∷ δ ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.9"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ῶ ∷ σ ∷ α ∷ ι ∷ []) "Heb.9.9"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.9.9"
∷ word (∙λ ∷ α ∷ τ ∷ ρ ∷ ε ∷ ύ ∷ ο ∷ ν ∷ τ ∷ α ∷ []) "Heb.9.9"
∷ word (μ ∷ ό ∷ ν ∷ ο ∷ ν ∷ []) "Heb.9.10"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.9.10"
∷ word (β ∷ ρ ∷ ώ ∷ μ ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.10"
∷ word (π ∷ ό ∷ μ ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.10"
∷ word (δ ∷ ι ∷ α ∷ φ ∷ ό ∷ ρ ∷ ο ∷ ι ∷ ς ∷ []) "Heb.9.10"
∷ word (β ∷ α ∷ π ∷ τ ∷ ι ∷ σ ∷ μ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.9.10"
∷ word (δ ∷ ι ∷ κ ∷ α ∷ ι ∷ ώ ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.9.10"
∷ word (σ ∷ α ∷ ρ ∷ κ ∷ ὸ ∷ ς ∷ []) "Heb.9.10"
∷ word (μ ∷ έ ∷ χ ∷ ρ ∷ ι ∷ []) "Heb.9.10"
∷ word (κ ∷ α ∷ ι ∷ ρ ∷ ο ∷ ῦ ∷ []) "Heb.9.10"
∷ word (δ ∷ ι ∷ ο ∷ ρ ∷ θ ∷ ώ ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.9.10"
∷ word (ἐ ∷ π ∷ ι ∷ κ ∷ ε ∷ ί ∷ μ ∷ ε ∷ ν ∷ α ∷ []) "Heb.9.10"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.9.11"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.11"
∷ word (π ∷ α ∷ ρ ∷ α ∷ γ ∷ ε ∷ ν ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.9.11"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.9.11"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.9.11"
∷ word (γ ∷ ε ∷ ν ∷ ο ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.9.11"
∷ word (ἀ ∷ γ ∷ α ∷ θ ∷ ῶ ∷ ν ∷ []) "Heb.9.11"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.9.11"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.11"
∷ word (μ ∷ ε ∷ ί ∷ ζ ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.9.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.11"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ο ∷ τ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.9.11"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.9.11"
∷ word (ο ∷ ὐ ∷ []) "Heb.9.11"
∷ word (χ ∷ ε ∷ ι ∷ ρ ∷ ο ∷ π ∷ ο ∷ ι ∷ ή ∷ τ ∷ ο ∷ υ ∷ []) "Heb.9.11"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ []) "Heb.9.11"
∷ word (ἔ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.9.11"
∷ word (ο ∷ ὐ ∷ []) "Heb.9.11"
∷ word (τ ∷ α ∷ ύ ∷ τ ∷ η ∷ ς ∷ []) "Heb.9.11"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.11"
∷ word (κ ∷ τ ∷ ί ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.9.11"
∷ word (ο ∷ ὐ ∷ δ ∷ ὲ ∷ []) "Heb.9.12"
∷ word (δ ∷ ι ∷ []) "Heb.9.12"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.9.12"
∷ word (τ ∷ ρ ∷ ά ∷ γ ∷ ω ∷ ν ∷ []) "Heb.9.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.12"
∷ word (μ ∷ ό ∷ σ ∷ χ ∷ ω ∷ ν ∷ []) "Heb.9.12"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.9.12"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.12"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.9.12"
∷ word (ἰ ∷ δ ∷ ί ∷ ο ∷ υ ∷ []) "Heb.9.12"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.9.12"
∷ word (ε ∷ ἰ ∷ σ ∷ ῆ ∷ ∙λ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.9.12"
∷ word (ἐ ∷ φ ∷ ά ∷ π ∷ α ∷ ξ ∷ []) "Heb.9.12"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.12"
∷ word (τ ∷ ὰ ∷ []) "Heb.9.12"
∷ word (ἅ ∷ γ ∷ ι ∷ α ∷ []) "Heb.9.12"
∷ word (α ∷ ἰ ∷ ω ∷ ν ∷ ί ∷ α ∷ ν ∷ []) "Heb.9.12"
∷ word (∙λ ∷ ύ ∷ τ ∷ ρ ∷ ω ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.12"
∷ word (ε ∷ ὑ ∷ ρ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.9.12"
∷ word (ε ∷ ἰ ∷ []) "Heb.9.13"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.9.13"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.13"
∷ word (α ∷ ἷ ∷ μ ∷ α ∷ []) "Heb.9.13"
∷ word (τ ∷ ρ ∷ ά ∷ γ ∷ ω ∷ ν ∷ []) "Heb.9.13"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.13"
∷ word (τ ∷ α ∷ ύ ∷ ρ ∷ ω ∷ ν ∷ []) "Heb.9.13"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.13"
∷ word (σ ∷ π ∷ ο ∷ δ ∷ ὸ ∷ ς ∷ []) "Heb.9.13"
∷ word (δ ∷ α ∷ μ ∷ ά ∷ ∙λ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.9.13"
∷ word (ῥ ∷ α ∷ ν ∷ τ ∷ ί ∷ ζ ∷ ο ∷ υ ∷ σ ∷ α ∷ []) "Heb.9.13"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.9.13"
∷ word (κ ∷ ε ∷ κ ∷ ο ∷ ι ∷ ν ∷ ω ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.9.13"
∷ word (ἁ ∷ γ ∷ ι ∷ ά ∷ ζ ∷ ε ∷ ι ∷ []) "Heb.9.13"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.9.13"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.9.13"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.13"
∷ word (σ ∷ α ∷ ρ ∷ κ ∷ ὸ ∷ ς ∷ []) "Heb.9.13"
∷ word (κ ∷ α ∷ θ ∷ α ∷ ρ ∷ ό ∷ τ ∷ η ∷ τ ∷ α ∷ []) "Heb.9.13"
∷ word (π ∷ ό ∷ σ ∷ ῳ ∷ []) "Heb.9.14"
∷ word (μ ∷ ᾶ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ν ∷ []) "Heb.9.14"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.14"
∷ word (α ∷ ἷ ∷ μ ∷ α ∷ []) "Heb.9.14"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.9.14"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.9.14"
∷ word (ὃ ∷ ς ∷ []) "Heb.9.14"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.9.14"
∷ word (π ∷ ν ∷ ε ∷ ύ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.9.14"
∷ word (α ∷ ἰ ∷ ω ∷ ν ∷ ί ∷ ο ∷ υ ∷ []) "Heb.9.14"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.9.14"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ή ∷ ν ∷ ε ∷ γ ∷ κ ∷ ε ∷ ν ∷ []) "Heb.9.14"
∷ word (ἄ ∷ μ ∷ ω ∷ μ ∷ ο ∷ ν ∷ []) "Heb.9.14"
∷ word (τ ∷ ῷ ∷ []) "Heb.9.14"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.9.14"
∷ word (κ ∷ α ∷ θ ∷ α ∷ ρ ∷ ι ∷ ε ∷ ῖ ∷ []) "Heb.9.14"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.9.14"
∷ word (σ ∷ υ ∷ ν ∷ ε ∷ ί ∷ δ ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.14"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.9.14"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.9.14"
∷ word (ν ∷ ε ∷ κ ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.9.14"
∷ word (ἔ ∷ ρ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.9.14"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.14"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.14"
∷ word (∙λ ∷ α ∷ τ ∷ ρ ∷ ε ∷ ύ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.9.14"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.9.14"
∷ word (ζ ∷ ῶ ∷ ν ∷ τ ∷ ι ∷ []) "Heb.9.14"
∷ word (Κ ∷ α ∷ ὶ ∷ []) "Heb.9.15"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.9.15"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.9.15"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ς ∷ []) "Heb.9.15"
∷ word (κ ∷ α ∷ ι ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.9.15"
∷ word (μ ∷ ε ∷ σ ∷ ί ∷ τ ∷ η ∷ ς ∷ []) "Heb.9.15"
∷ word (ἐ ∷ σ ∷ τ ∷ ί ∷ ν ∷ []) "Heb.9.15"
∷ word (ὅ ∷ π ∷ ω ∷ ς ∷ []) "Heb.9.15"
∷ word (θ ∷ α ∷ ν ∷ ά ∷ τ ∷ ο ∷ υ ∷ []) "Heb.9.15"
∷ word (γ ∷ ε ∷ ν ∷ ο ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ []) "Heb.9.15"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.15"
∷ word (ἀ ∷ π ∷ ο ∷ ∙λ ∷ ύ ∷ τ ∷ ρ ∷ ω ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.15"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.9.15"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.9.15"
∷ word (τ ∷ ῇ ∷ []) "Heb.9.15"
∷ word (π ∷ ρ ∷ ώ ∷ τ ∷ ῃ ∷ []) "Heb.9.15"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ ῃ ∷ []) "Heb.9.15"
∷ word (π ∷ α ∷ ρ ∷ α ∷ β ∷ ά ∷ σ ∷ ε ∷ ω ∷ ν ∷ []) "Heb.9.15"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.9.15"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ν ∷ []) "Heb.9.15"
∷ word (∙λ ∷ ά ∷ β ∷ ω ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.15"
∷ word (ο ∷ ἱ ∷ []) "Heb.9.15"
∷ word (κ ∷ ε ∷ κ ∷ ∙λ ∷ η ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ []) "Heb.9.15"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.15"
∷ word (α ∷ ἰ ∷ ω ∷ ν ∷ ί ∷ ο ∷ υ ∷ []) "Heb.9.15"
∷ word (κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ο ∷ μ ∷ ί ∷ α ∷ ς ∷ []) "Heb.9.15"
∷ word (ὅ ∷ π ∷ ο ∷ υ ∷ []) "Heb.9.16"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.9.16"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ []) "Heb.9.16"
∷ word (θ ∷ ά ∷ ν ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.9.16"
∷ word (ἀ ∷ ν ∷ ά ∷ γ ∷ κ ∷ η ∷ []) "Heb.9.16"
∷ word (φ ∷ έ ∷ ρ ∷ ε ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.9.16"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.9.16"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ε ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ []) "Heb.9.16"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ []) "Heb.9.17"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.9.17"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.9.17"
∷ word (ν ∷ ε ∷ κ ∷ ρ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.9.17"
∷ word (β ∷ ε ∷ β ∷ α ∷ ί ∷ α ∷ []) "Heb.9.17"
∷ word (ἐ ∷ π ∷ ε ∷ ὶ ∷ []) "Heb.9.17"
∷ word (μ ∷ ή ∷ π ∷ ο ∷ τ ∷ ε ∷ []) "Heb.9.17"
∷ word (ἰ ∷ σ ∷ χ ∷ ύ ∷ ε ∷ ι ∷ []) "Heb.9.17"
∷ word (ὅ ∷ τ ∷ ε ∷ []) "Heb.9.17"
∷ word (ζ ∷ ῇ ∷ []) "Heb.9.17"
∷ word (ὁ ∷ []) "Heb.9.17"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ έ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.9.17"
∷ word (ὅ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.9.18"
∷ word (ο ∷ ὐ ∷ δ ∷ ὲ ∷ []) "Heb.9.18"
∷ word (ἡ ∷ []) "Heb.9.18"
∷ word (π ∷ ρ ∷ ώ ∷ τ ∷ η ∷ []) "Heb.9.18"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.9.18"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.9.18"
∷ word (ἐ ∷ γ ∷ κ ∷ ε ∷ κ ∷ α ∷ ί ∷ ν ∷ ι ∷ σ ∷ τ ∷ α ∷ ι ∷ []) "Heb.9.18"
∷ word (∙λ ∷ α ∷ ∙λ ∷ η ∷ θ ∷ ε ∷ ί ∷ σ ∷ η ∷ ς ∷ []) "Heb.9.19"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.9.19"
∷ word (π ∷ ά ∷ σ ∷ η ∷ ς ∷ []) "Heb.9.19"
∷ word (ἐ ∷ ν ∷ τ ∷ ο ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.9.19"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.9.19"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.9.19"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ν ∷ []) "Heb.9.19"
∷ word (ὑ ∷ π ∷ ὸ ∷ []) "Heb.9.19"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ έ ∷ ω ∷ ς ∷ []) "Heb.9.19"
∷ word (π ∷ α ∷ ν ∷ τ ∷ ὶ ∷ []) "Heb.9.19"
∷ word (τ ∷ ῷ ∷ []) "Heb.9.19"
∷ word (∙λ ∷ α ∷ ῷ ∷ []) "Heb.9.19"
∷ word (∙λ ∷ α ∷ β ∷ ὼ ∷ ν ∷ []) "Heb.9.19"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.19"
∷ word (α ∷ ἷ ∷ μ ∷ α ∷ []) "Heb.9.19"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.9.19"
∷ word (μ ∷ ό ∷ σ ∷ χ ∷ ω ∷ ν ∷ []) "Heb.9.19"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.9.19"
∷ word (ὕ ∷ δ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.9.19"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.19"
∷ word (ἐ ∷ ρ ∷ ί ∷ ο ∷ υ ∷ []) "Heb.9.19"
∷ word (κ ∷ ο ∷ κ ∷ κ ∷ ί ∷ ν ∷ ο ∷ υ ∷ []) "Heb.9.19"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.19"
∷ word (ὑ ∷ σ ∷ σ ∷ ώ ∷ π ∷ ο ∷ υ ∷ []) "Heb.9.19"
∷ word (α ∷ ὐ ∷ τ ∷ ό ∷ []) "Heb.9.19"
∷ word (τ ∷ ε ∷ []) "Heb.9.19"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.19"
∷ word (β ∷ ι ∷ β ∷ ∙λ ∷ ί ∷ ο ∷ ν ∷ []) "Heb.9.19"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.19"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.9.19"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.9.19"
∷ word (∙λ ∷ α ∷ ὸ ∷ ν ∷ []) "Heb.9.19"
∷ word (ἐ ∷ ρ ∷ ά ∷ ν ∷ τ ∷ ι ∷ σ ∷ ε ∷ ν ∷ []) "Heb.9.19"
∷ word (∙λ ∷ έ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.9.20"
∷ word (Τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.9.20"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.20"
∷ word (α ∷ ἷ ∷ μ ∷ α ∷ []) "Heb.9.20"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.20"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ς ∷ []) "Heb.9.20"
∷ word (ἧ ∷ ς ∷ []) "Heb.9.20"
∷ word (ἐ ∷ ν ∷ ε ∷ τ ∷ ε ∷ ί ∷ ∙λ ∷ α ∷ τ ∷ ο ∷ []) "Heb.9.20"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.9.20"
∷ word (ὑ ∷ μ ∷ ᾶ ∷ ς ∷ []) "Heb.9.20"
∷ word (ὁ ∷ []) "Heb.9.20"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.9.20"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.21"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.9.21"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ ὴ ∷ ν ∷ []) "Heb.9.21"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.21"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.21"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.9.21"
∷ word (τ ∷ ὰ ∷ []) "Heb.9.21"
∷ word (σ ∷ κ ∷ ε ∷ ύ ∷ η ∷ []) "Heb.9.21"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.21"
∷ word (∙λ ∷ ε ∷ ι ∷ τ ∷ ο ∷ υ ∷ ρ ∷ γ ∷ ί ∷ α ∷ ς ∷ []) "Heb.9.21"
∷ word (τ ∷ ῷ ∷ []) "Heb.9.21"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.9.21"
∷ word (ὁ ∷ μ ∷ ο ∷ ί ∷ ω ∷ ς ∷ []) "Heb.9.21"
∷ word (ἐ ∷ ρ ∷ ά ∷ ν ∷ τ ∷ ι ∷ σ ∷ ε ∷ ν ∷ []) "Heb.9.21"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.22"
∷ word (σ ∷ χ ∷ ε ∷ δ ∷ ὸ ∷ ν ∷ []) "Heb.9.22"
∷ word (ἐ ∷ ν ∷ []) "Heb.9.22"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.9.22"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.9.22"
∷ word (κ ∷ α ∷ θ ∷ α ∷ ρ ∷ ί ∷ ζ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.9.22"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.9.22"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.9.22"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ν ∷ []) "Heb.9.22"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.22"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.9.22"
∷ word (α ∷ ἱ ∷ μ ∷ α ∷ τ ∷ ε ∷ κ ∷ χ ∷ υ ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.9.22"
∷ word (ο ∷ ὐ ∷ []) "Heb.9.22"
∷ word (γ ∷ ί ∷ ν ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.9.22"
∷ word (ἄ ∷ φ ∷ ε ∷ σ ∷ ι ∷ ς ∷ []) "Heb.9.22"
∷ word (Ἀ ∷ ν ∷ ά ∷ γ ∷ κ ∷ η ∷ []) "Heb.9.23"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.9.23"
∷ word (τ ∷ ὰ ∷ []) "Heb.9.23"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.9.23"
∷ word (ὑ ∷ π ∷ ο ∷ δ ∷ ε ∷ ί ∷ γ ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.9.23"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.9.23"
∷ word (ἐ ∷ ν ∷ []) "Heb.9.23"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.9.23"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.9.23"
∷ word (τ ∷ ο ∷ ύ ∷ τ ∷ ο ∷ ι ∷ ς ∷ []) "Heb.9.23"
∷ word (κ ∷ α ∷ θ ∷ α ∷ ρ ∷ ί ∷ ζ ∷ ε ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.9.23"
∷ word (α ∷ ὐ ∷ τ ∷ ὰ ∷ []) "Heb.9.23"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.23"
∷ word (τ ∷ ὰ ∷ []) "Heb.9.23"
∷ word (ἐ ∷ π ∷ ο ∷ υ ∷ ρ ∷ ά ∷ ν ∷ ι ∷ α ∷ []) "Heb.9.23"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ο ∷ σ ∷ ι ∷ []) "Heb.9.23"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ι ∷ ς ∷ []) "Heb.9.23"
∷ word (π ∷ α ∷ ρ ∷ ὰ ∷ []) "Heb.9.23"
∷ word (τ ∷ α ∷ ύ ∷ τ ∷ α ∷ ς ∷ []) "Heb.9.23"
∷ word (ο ∷ ὐ ∷ []) "Heb.9.24"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.9.24"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.24"
∷ word (χ ∷ ε ∷ ι ∷ ρ ∷ ο ∷ π ∷ ο ∷ ί ∷ η ∷ τ ∷ α ∷ []) "Heb.9.24"
∷ word (ε ∷ ἰ ∷ σ ∷ ῆ ∷ ∙λ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.9.24"
∷ word (ἅ ∷ γ ∷ ι ∷ α ∷ []) "Heb.9.24"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ό ∷ ς ∷ []) "Heb.9.24"
∷ word (ἀ ∷ ν ∷ τ ∷ ί ∷ τ ∷ υ ∷ π ∷ α ∷ []) "Heb.9.24"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.9.24"
∷ word (ἀ ∷ ∙λ ∷ η ∷ θ ∷ ι ∷ ν ∷ ῶ ∷ ν ∷ []) "Heb.9.24"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ []) "Heb.9.24"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.24"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.9.24"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.9.24"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ό ∷ ν ∷ []) "Heb.9.24"
∷ word (ν ∷ ῦ ∷ ν ∷ []) "Heb.9.24"
∷ word (ἐ ∷ μ ∷ φ ∷ α ∷ ν ∷ ι ∷ σ ∷ θ ∷ ῆ ∷ ν ∷ α ∷ ι ∷ []) "Heb.9.24"
∷ word (τ ∷ ῷ ∷ []) "Heb.9.24"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ώ ∷ π ∷ ῳ ∷ []) "Heb.9.24"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.9.24"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.9.24"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.9.24"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.9.24"
∷ word (ο ∷ ὐ ∷ δ ∷ []) "Heb.9.25"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.9.25"
∷ word (π ∷ ο ∷ ∙λ ∷ ∙λ ∷ ά ∷ κ ∷ ι ∷ ς ∷ []) "Heb.9.25"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ῃ ∷ []) "Heb.9.25"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ό ∷ ν ∷ []) "Heb.9.25"
∷ word (ὥ ∷ σ ∷ π ∷ ε ∷ ρ ∷ []) "Heb.9.25"
∷ word (ὁ ∷ []) "Heb.9.25"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.9.25"
∷ word (ε ∷ ἰ ∷ σ ∷ έ ∷ ρ ∷ χ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.9.25"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.25"
∷ word (τ ∷ ὰ ∷ []) "Heb.9.25"
∷ word (ἅ ∷ γ ∷ ι ∷ α ∷ []) "Heb.9.25"
∷ word (κ ∷ α ∷ τ ∷ []) "Heb.9.25"
∷ word (ἐ ∷ ν ∷ ι ∷ α ∷ υ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.9.25"
∷ word (ἐ ∷ ν ∷ []) "Heb.9.25"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.9.25"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ο ∷ τ ∷ ρ ∷ ί ∷ ῳ ∷ []) "Heb.9.25"
∷ word (ἐ ∷ π ∷ ε ∷ ὶ ∷ []) "Heb.9.26"
∷ word (ἔ ∷ δ ∷ ε ∷ ι ∷ []) "Heb.9.26"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.9.26"
∷ word (π ∷ ο ∷ ∙λ ∷ ∙λ ∷ ά ∷ κ ∷ ι ∷ ς ∷ []) "Heb.9.26"
∷ word (π ∷ α ∷ θ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.9.26"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.9.26"
∷ word (κ ∷ α ∷ τ ∷ α ∷ β ∷ ο ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.9.26"
∷ word (κ ∷ ό ∷ σ ∷ μ ∷ ο ∷ υ ∷ []) "Heb.9.26"
∷ word (ν ∷ υ ∷ ν ∷ ὶ ∷ []) "Heb.9.26"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.26"
∷ word (ἅ ∷ π ∷ α ∷ ξ ∷ []) "Heb.9.26"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.9.26"
∷ word (σ ∷ υ ∷ ν ∷ τ ∷ ε ∷ ∙λ ∷ ε ∷ ί ∷ ᾳ ∷ []) "Heb.9.26"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.9.26"
∷ word (α ∷ ἰ ∷ ώ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.9.26"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.26"
∷ word (ἀ ∷ θ ∷ έ ∷ τ ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.9.26"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.9.26"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.9.26"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.9.26"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.9.26"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.9.26"
∷ word (π ∷ ε ∷ φ ∷ α ∷ ν ∷ έ ∷ ρ ∷ ω ∷ τ ∷ α ∷ ι ∷ []) "Heb.9.26"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.27"
∷ word (κ ∷ α ∷ θ ∷ []) "Heb.9.27"
∷ word (ὅ ∷ σ ∷ ο ∷ ν ∷ []) "Heb.9.27"
∷ word (ἀ ∷ π ∷ ό ∷ κ ∷ ε ∷ ι ∷ τ ∷ α ∷ ι ∷ []) "Heb.9.27"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.9.27"
∷ word (ἀ ∷ ν ∷ θ ∷ ρ ∷ ώ ∷ π ∷ ο ∷ ι ∷ ς ∷ []) "Heb.9.27"
∷ word (ἅ ∷ π ∷ α ∷ ξ ∷ []) "Heb.9.27"
∷ word (ἀ ∷ π ∷ ο ∷ θ ∷ α ∷ ν ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.9.27"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.9.27"
∷ word (δ ∷ ὲ ∷ []) "Heb.9.27"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.9.27"
∷ word (κ ∷ ρ ∷ ί ∷ σ ∷ ι ∷ ς ∷ []) "Heb.9.27"
∷ word (ο ∷ ὕ ∷ τ ∷ ω ∷ ς ∷ []) "Heb.9.28"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.9.28"
∷ word (ὁ ∷ []) "Heb.9.28"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ό ∷ ς ∷ []) "Heb.9.28"
∷ word (ἅ ∷ π ∷ α ∷ ξ ∷ []) "Heb.9.28"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ν ∷ ε ∷ χ ∷ θ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.9.28"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.28"
∷ word (τ ∷ ὸ ∷ []) "Heb.9.28"
∷ word (π ∷ ο ∷ ∙λ ∷ ∙λ ∷ ῶ ∷ ν ∷ []) "Heb.9.28"
∷ word (ἀ ∷ ν ∷ ε ∷ ν ∷ ε ∷ γ ∷ κ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.9.28"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.9.28"
∷ word (ἐ ∷ κ ∷ []) "Heb.9.28"
∷ word (δ ∷ ε ∷ υ ∷ τ ∷ έ ∷ ρ ∷ ο ∷ υ ∷ []) "Heb.9.28"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.9.28"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.9.28"
∷ word (ὀ ∷ φ ∷ θ ∷ ή ∷ σ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.9.28"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.9.28"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.9.28"
∷ word (ἀ ∷ π ∷ ε ∷ κ ∷ δ ∷ ε ∷ χ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ ς ∷ []) "Heb.9.28"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.9.28"
∷ word (σ ∷ ω ∷ τ ∷ η ∷ ρ ∷ ί ∷ α ∷ ν ∷ []) "Heb.9.28"
∷ word (Σ ∷ κ ∷ ι ∷ ὰ ∷ ν ∷ []) "Heb.10.1"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.1"
∷ word (ἔ ∷ χ ∷ ω ∷ ν ∷ []) "Heb.10.1"
∷ word (ὁ ∷ []) "Heb.10.1"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ς ∷ []) "Heb.10.1"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.10.1"
∷ word (μ ∷ ε ∷ ∙λ ∷ ∙λ ∷ ό ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.10.1"
∷ word (ἀ ∷ γ ∷ α ∷ θ ∷ ῶ ∷ ν ∷ []) "Heb.10.1"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.10.1"
∷ word (α ∷ ὐ ∷ τ ∷ ὴ ∷ ν ∷ []) "Heb.10.1"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.1"
∷ word (ε ∷ ἰ ∷ κ ∷ ό ∷ ν ∷ α ∷ []) "Heb.10.1"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.10.1"
∷ word (π ∷ ρ ∷ α ∷ γ ∷ μ ∷ ά ∷ τ ∷ ω ∷ ν ∷ []) "Heb.10.1"
∷ word (κ ∷ α ∷ τ ∷ []) "Heb.10.1"
∷ word (ἐ ∷ ν ∷ ι ∷ α ∷ υ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.10.1"
∷ word (τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.10.1"
∷ word (α ∷ ὐ ∷ τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.10.1"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ι ∷ ς ∷ []) "Heb.10.1"
∷ word (ἃ ∷ ς ∷ []) "Heb.10.1"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.10.1"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.10.1"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.1"
∷ word (δ ∷ ι ∷ η ∷ ν ∷ ε ∷ κ ∷ ὲ ∷ ς ∷ []) "Heb.10.1"
∷ word (ο ∷ ὐ ∷ δ ∷ έ ∷ π ∷ ο ∷ τ ∷ ε ∷ []) "Heb.10.1"
∷ word (δ ∷ ύ ∷ ν ∷ α ∷ τ ∷ α ∷ ι ∷ []) "Heb.10.1"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.10.1"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ρ ∷ χ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.10.1"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ῶ ∷ σ ∷ α ∷ ι ∷ []) "Heb.10.1"
∷ word (ἐ ∷ π ∷ ε ∷ ὶ ∷ []) "Heb.10.2"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.10.2"
∷ word (ἂ ∷ ν ∷ []) "Heb.10.2"
∷ word (ἐ ∷ π ∷ α ∷ ύ ∷ σ ∷ α ∷ ν ∷ τ ∷ ο ∷ []) "Heb.10.2"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ ε ∷ ρ ∷ ό ∷ μ ∷ ε ∷ ν ∷ α ∷ ι ∷ []) "Heb.10.2"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.10.2"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.2"
∷ word (μ ∷ η ∷ δ ∷ ε ∷ μ ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.2"
∷ word (ἔ ∷ χ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.10.2"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.10.2"
∷ word (σ ∷ υ ∷ ν ∷ ε ∷ ί ∷ δ ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.10.2"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.10.2"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.10.2"
∷ word (∙λ ∷ α ∷ τ ∷ ρ ∷ ε ∷ ύ ∷ ο ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.10.2"
∷ word (ἅ ∷ π ∷ α ∷ ξ ∷ []) "Heb.10.2"
∷ word (κ ∷ ε ∷ κ ∷ α ∷ θ ∷ α ∷ ρ ∷ ι ∷ σ ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.10.2"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ []) "Heb.10.3"
∷ word (ἐ ∷ ν ∷ []) "Heb.10.3"
∷ word (α ∷ ὐ ∷ τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.10.3"
∷ word (ἀ ∷ ν ∷ ά ∷ μ ∷ ν ∷ η ∷ σ ∷ ι ∷ ς ∷ []) "Heb.10.3"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.10.3"
∷ word (κ ∷ α ∷ τ ∷ []) "Heb.10.3"
∷ word (ἐ ∷ ν ∷ ι ∷ α ∷ υ ∷ τ ∷ ό ∷ ν ∷ []) "Heb.10.3"
∷ word (ἀ ∷ δ ∷ ύ ∷ ν ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.10.4"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.4"
∷ word (α ∷ ἷ ∷ μ ∷ α ∷ []) "Heb.10.4"
∷ word (τ ∷ α ∷ ύ ∷ ρ ∷ ω ∷ ν ∷ []) "Heb.10.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.4"
∷ word (τ ∷ ρ ∷ ά ∷ γ ∷ ω ∷ ν ∷ []) "Heb.10.4"
∷ word (ἀ ∷ φ ∷ α ∷ ι ∷ ρ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.10.4"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.4"
∷ word (δ ∷ ι ∷ ὸ ∷ []) "Heb.10.5"
∷ word (ε ∷ ἰ ∷ σ ∷ ε ∷ ρ ∷ χ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.10.5"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.10.5"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.10.5"
∷ word (κ ∷ ό ∷ σ ∷ μ ∷ ο ∷ ν ∷ []) "Heb.10.5"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.10.5"
∷ word (Θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.5"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.5"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ ο ∷ ρ ∷ ὰ ∷ ν ∷ []) "Heb.10.5"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.10.5"
∷ word (ἠ ∷ θ ∷ έ ∷ ∙λ ∷ η ∷ σ ∷ α ∷ ς ∷ []) "Heb.10.5"
∷ word (σ ∷ ῶ ∷ μ ∷ α ∷ []) "Heb.10.5"
∷ word (δ ∷ ὲ ∷ []) "Heb.10.5"
∷ word (κ ∷ α ∷ τ ∷ η ∷ ρ ∷ τ ∷ ί ∷ σ ∷ ω ∷ []) "Heb.10.5"
∷ word (μ ∷ ο ∷ ι ∷ []) "Heb.10.5"
∷ word (ὁ ∷ ∙λ ∷ ο ∷ κ ∷ α ∷ υ ∷ τ ∷ ώ ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.10.6"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.6"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.10.6"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.6"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.10.6"
∷ word (ε ∷ ὐ ∷ δ ∷ ό ∷ κ ∷ η ∷ σ ∷ α ∷ ς ∷ []) "Heb.10.6"
∷ word (τ ∷ ό ∷ τ ∷ ε ∷ []) "Heb.10.7"
∷ word (ε ∷ ἶ ∷ π ∷ ο ∷ ν ∷ []) "Heb.10.7"
∷ word (Ἰ ∷ δ ∷ ο ∷ ὺ ∷ []) "Heb.10.7"
∷ word (ἥ ∷ κ ∷ ω ∷ []) "Heb.10.7"
∷ word (ἐ ∷ ν ∷ []) "Heb.10.7"
∷ word (κ ∷ ε ∷ φ ∷ α ∷ ∙λ ∷ ί ∷ δ ∷ ι ∷ []) "Heb.10.7"
∷ word (β ∷ ι ∷ β ∷ ∙λ ∷ ί ∷ ο ∷ υ ∷ []) "Heb.10.7"
∷ word (γ ∷ έ ∷ γ ∷ ρ ∷ α ∷ π ∷ τ ∷ α ∷ ι ∷ []) "Heb.10.7"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.10.7"
∷ word (ἐ ∷ μ ∷ ο ∷ ῦ ∷ []) "Heb.10.7"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.10.7"
∷ word (π ∷ ο ∷ ι ∷ ῆ ∷ σ ∷ α ∷ ι ∷ []) "Heb.10.7"
∷ word (ὁ ∷ []) "Heb.10.7"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.10.7"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.7"
∷ word (θ ∷ έ ∷ ∙λ ∷ η ∷ μ ∷ ά ∷ []) "Heb.10.7"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.10.7"
∷ word (ἀ ∷ ν ∷ ώ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.10.8"
∷ word (∙λ ∷ έ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.10.8"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.10.8"
∷ word (Θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.8"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ ο ∷ ρ ∷ ὰ ∷ ς ∷ []) "Heb.10.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.8"
∷ word (ὁ ∷ ∙λ ∷ ο ∷ κ ∷ α ∷ υ ∷ τ ∷ ώ ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.10.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.8"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.10.8"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.8"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.10.8"
∷ word (ἠ ∷ θ ∷ έ ∷ ∙λ ∷ η ∷ σ ∷ α ∷ ς ∷ []) "Heb.10.8"
∷ word (ο ∷ ὐ ∷ δ ∷ ὲ ∷ []) "Heb.10.8"
∷ word (ε ∷ ὐ ∷ δ ∷ ό ∷ κ ∷ η ∷ σ ∷ α ∷ ς ∷ []) "Heb.10.8"
∷ word (α ∷ ἵ ∷ τ ∷ ι ∷ ν ∷ ε ∷ ς ∷ []) "Heb.10.8"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.10.8"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ν ∷ []) "Heb.10.8"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.10.8"
∷ word (τ ∷ ό ∷ τ ∷ ε ∷ []) "Heb.10.9"
∷ word (ε ∷ ἴ ∷ ρ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.10.9"
∷ word (Ἰ ∷ δ ∷ ο ∷ ὺ ∷ []) "Heb.10.9"
∷ word (ἥ ∷ κ ∷ ω ∷ []) "Heb.10.9"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.10.9"
∷ word (π ∷ ο ∷ ι ∷ ῆ ∷ σ ∷ α ∷ ι ∷ []) "Heb.10.9"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.9"
∷ word (θ ∷ έ ∷ ∙λ ∷ η ∷ μ ∷ ά ∷ []) "Heb.10.9"
∷ word (σ ∷ ο ∷ υ ∷ []) "Heb.10.9"
∷ word (ἀ ∷ ν ∷ α ∷ ι ∷ ρ ∷ ε ∷ ῖ ∷ []) "Heb.10.9"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.9"
∷ word (π ∷ ρ ∷ ῶ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.10.9"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.10.9"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.9"
∷ word (δ ∷ ε ∷ ύ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.10.9"
∷ word (σ ∷ τ ∷ ή ∷ σ ∷ ῃ ∷ []) "Heb.10.9"
∷ word (ἐ ∷ ν ∷ []) "Heb.10.10"
∷ word (ᾧ ∷ []) "Heb.10.10"
∷ word (θ ∷ ε ∷ ∙λ ∷ ή ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.10.10"
∷ word (ἡ ∷ γ ∷ ι ∷ α ∷ σ ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ []) "Heb.10.10"
∷ word (ἐ ∷ σ ∷ μ ∷ ὲ ∷ ν ∷ []) "Heb.10.10"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.10.10"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.10.10"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ ο ∷ ρ ∷ ᾶ ∷ ς ∷ []) "Heb.10.10"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.10.10"
∷ word (σ ∷ ώ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.10.10"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ []) "Heb.10.10"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.10.10"
∷ word (ἐ ∷ φ ∷ ά ∷ π ∷ α ∷ ξ ∷ []) "Heb.10.10"
∷ word (Κ ∷ α ∷ ὶ ∷ []) "Heb.10.11"
∷ word (π ∷ ᾶ ∷ ς ∷ []) "Heb.10.11"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.10.11"
∷ word (ἱ ∷ ε ∷ ρ ∷ ε ∷ ὺ ∷ ς ∷ []) "Heb.10.11"
∷ word (ἕ ∷ σ ∷ τ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.10.11"
∷ word (κ ∷ α ∷ θ ∷ []) "Heb.10.11"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.10.11"
∷ word (∙λ ∷ ε ∷ ι ∷ τ ∷ ο ∷ υ ∷ ρ ∷ γ ∷ ῶ ∷ ν ∷ []) "Heb.10.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.11"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.10.11"
∷ word (α ∷ ὐ ∷ τ ∷ ὰ ∷ ς ∷ []) "Heb.10.11"
∷ word (π ∷ ο ∷ ∙λ ∷ ∙λ ∷ ά ∷ κ ∷ ι ∷ ς ∷ []) "Heb.10.11"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ω ∷ ν ∷ []) "Heb.10.11"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.11"
∷ word (α ∷ ἵ ∷ τ ∷ ι ∷ ν ∷ ε ∷ ς ∷ []) "Heb.10.11"
∷ word (ο ∷ ὐ ∷ δ ∷ έ ∷ π ∷ ο ∷ τ ∷ ε ∷ []) "Heb.10.11"
∷ word (δ ∷ ύ ∷ ν ∷ α ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.10.11"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ ε ∷ ∙λ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.10.11"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.11"
∷ word (ο ∷ ὗ ∷ τ ∷ ο ∷ ς ∷ []) "Heb.10.12"
∷ word (δ ∷ ὲ ∷ []) "Heb.10.12"
∷ word (μ ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.12"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.10.12"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.10.12"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ν ∷ έ ∷ γ ∷ κ ∷ α ∷ ς ∷ []) "Heb.10.12"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.12"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.10.12"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.12"
∷ word (δ ∷ ι ∷ η ∷ ν ∷ ε ∷ κ ∷ ὲ ∷ ς ∷ []) "Heb.10.12"
∷ word (ἐ ∷ κ ∷ ά ∷ θ ∷ ι ∷ σ ∷ ε ∷ ν ∷ []) "Heb.10.12"
∷ word (ἐ ∷ ν ∷ []) "Heb.10.12"
∷ word (δ ∷ ε ∷ ξ ∷ ι ∷ ᾷ ∷ []) "Heb.10.12"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.10.12"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.10.12"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.13"
∷ word (∙λ ∷ ο ∷ ι ∷ π ∷ ὸ ∷ ν ∷ []) "Heb.10.13"
∷ word (ἐ ∷ κ ∷ δ ∷ ε ∷ χ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.10.13"
∷ word (ἕ ∷ ω ∷ ς ∷ []) "Heb.10.13"
∷ word (τ ∷ ε ∷ θ ∷ ῶ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.10.13"
∷ word (ο ∷ ἱ ∷ []) "Heb.10.13"
∷ word (ἐ ∷ χ ∷ θ ∷ ρ ∷ ο ∷ ὶ ∷ []) "Heb.10.13"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.10.13"
∷ word (ὑ ∷ π ∷ ο ∷ π ∷ ό ∷ δ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.10.13"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.10.13"
∷ word (π ∷ ο ∷ δ ∷ ῶ ∷ ν ∷ []) "Heb.10.13"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.10.13"
∷ word (μ ∷ ι ∷ ᾷ ∷ []) "Heb.10.14"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.14"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ ο ∷ ρ ∷ ᾷ ∷ []) "Heb.10.14"
∷ word (τ ∷ ε ∷ τ ∷ ε ∷ ∙λ ∷ ε ∷ ί ∷ ω ∷ κ ∷ ε ∷ ν ∷ []) "Heb.10.14"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.10.14"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.14"
∷ word (δ ∷ ι ∷ η ∷ ν ∷ ε ∷ κ ∷ ὲ ∷ ς ∷ []) "Heb.10.14"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.10.14"
∷ word (ἁ ∷ γ ∷ ι ∷ α ∷ ζ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.10.14"
∷ word (μ ∷ α ∷ ρ ∷ τ ∷ υ ∷ ρ ∷ ε ∷ ῖ ∷ []) "Heb.10.15"
∷ word (δ ∷ ὲ ∷ []) "Heb.10.15"
∷ word (ἡ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.10.15"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.15"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.15"
∷ word (π ∷ ν ∷ ε ∷ ῦ ∷ μ ∷ α ∷ []) "Heb.10.15"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.15"
∷ word (ἅ ∷ γ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.10.15"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.10.15"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.15"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.15"
∷ word (ε ∷ ἰ ∷ ρ ∷ η ∷ κ ∷ έ ∷ ν ∷ α ∷ ι ∷ []) "Heb.10.15"
∷ word (Α ∷ ὕ ∷ τ ∷ η ∷ []) "Heb.10.16"
∷ word (ἡ ∷ []) "Heb.10.16"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ []) "Heb.10.16"
∷ word (ἣ ∷ ν ∷ []) "Heb.10.16"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ σ ∷ ο ∷ μ ∷ α ∷ ι ∷ []) "Heb.10.16"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.10.16"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.10.16"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.10.16"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.10.16"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.10.16"
∷ word (ἐ ∷ κ ∷ ε ∷ ί ∷ ν ∷ α ∷ ς ∷ []) "Heb.10.16"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ []) "Heb.10.16"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.10.16"
∷ word (δ ∷ ι ∷ δ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.10.16"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.10.16"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.10.16"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.10.16"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.16"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.10.16"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.16"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.10.16"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.16"
∷ word (δ ∷ ι ∷ ά ∷ ν ∷ ο ∷ ι ∷ α ∷ ν ∷ []) "Heb.10.16"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.10.16"
∷ word (ἐ ∷ π ∷ ι ∷ γ ∷ ρ ∷ ά ∷ ψ ∷ ω ∷ []) "Heb.10.16"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ύ ∷ ς ∷ []) "Heb.10.16"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.17"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.10.17"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.10.17"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.10.17"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.17"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.10.17"
∷ word (ἀ ∷ ν ∷ ο ∷ μ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.10.17"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.10.17"
∷ word (ο ∷ ὐ ∷ []) "Heb.10.17"
∷ word (μ ∷ ὴ ∷ []) "Heb.10.17"
∷ word (μ ∷ ν ∷ η ∷ σ ∷ θ ∷ ή ∷ σ ∷ ο ∷ μ ∷ α ∷ ι ∷ []) "Heb.10.17"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.10.17"
∷ word (ὅ ∷ π ∷ ο ∷ υ ∷ []) "Heb.10.18"
∷ word (δ ∷ ὲ ∷ []) "Heb.10.18"
∷ word (ἄ ∷ φ ∷ ε ∷ σ ∷ ι ∷ ς ∷ []) "Heb.10.18"
∷ word (τ ∷ ο ∷ ύ ∷ τ ∷ ω ∷ ν ∷ []) "Heb.10.18"
∷ word (ο ∷ ὐ ∷ κ ∷ έ ∷ τ ∷ ι ∷ []) "Heb.10.18"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ ο ∷ ρ ∷ ὰ ∷ []) "Heb.10.18"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.10.18"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.18"
∷ word (Ἔ ∷ χ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.10.19"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.10.19"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ο ∷ ί ∷ []) "Heb.10.19"
∷ word (π ∷ α ∷ ρ ∷ ρ ∷ η ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.19"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.10.19"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.19"
∷ word (ε ∷ ἴ ∷ σ ∷ ο ∷ δ ∷ ο ∷ ν ∷ []) "Heb.10.19"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.10.19"
∷ word (ἁ ∷ γ ∷ ί ∷ ω ∷ ν ∷ []) "Heb.10.19"
∷ word (ἐ ∷ ν ∷ []) "Heb.10.19"
∷ word (τ ∷ ῷ ∷ []) "Heb.10.19"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.10.19"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ []) "Heb.10.19"
∷ word (ἣ ∷ ν ∷ []) "Heb.10.20"
∷ word (ἐ ∷ ν ∷ ε ∷ κ ∷ α ∷ ί ∷ ν ∷ ι ∷ σ ∷ ε ∷ ν ∷ []) "Heb.10.20"
∷ word (ἡ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.10.20"
∷ word (ὁ ∷ δ ∷ ὸ ∷ ν ∷ []) "Heb.10.20"
∷ word (π ∷ ρ ∷ ό ∷ σ ∷ φ ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.10.20"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.20"
∷ word (ζ ∷ ῶ ∷ σ ∷ α ∷ ν ∷ []) "Heb.10.20"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.10.20"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.10.20"
∷ word (κ ∷ α ∷ τ ∷ α ∷ π ∷ ε ∷ τ ∷ ά ∷ σ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.10.20"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ []) "Heb.10.20"
∷ word (ἔ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.10.20"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.10.20"
∷ word (σ ∷ α ∷ ρ ∷ κ ∷ ὸ ∷ ς ∷ []) "Heb.10.20"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.10.20"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.21"
∷ word (ἱ ∷ ε ∷ ρ ∷ έ ∷ α ∷ []) "Heb.10.21"
∷ word (μ ∷ έ ∷ γ ∷ α ∷ ν ∷ []) "Heb.10.21"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.10.21"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.10.21"
∷ word (ο ∷ ἶ ∷ κ ∷ ο ∷ ν ∷ []) "Heb.10.21"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.10.21"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.10.21"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ρ ∷ χ ∷ ώ ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.10.22"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.10.22"
∷ word (ἀ ∷ ∙λ ∷ η ∷ θ ∷ ι ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.10.22"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.22"
∷ word (ἐ ∷ ν ∷ []) "Heb.10.22"
∷ word (π ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ φ ∷ ο ∷ ρ ∷ ί ∷ ᾳ ∷ []) "Heb.10.22"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.10.22"
∷ word (ῥ ∷ ε ∷ ρ ∷ α ∷ ν ∷ τ ∷ ι ∷ σ ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ []) "Heb.10.22"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.10.22"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.22"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.10.22"
∷ word (σ ∷ υ ∷ ν ∷ ε ∷ ι ∷ δ ∷ ή ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.10.22"
∷ word (π ∷ ο ∷ ν ∷ η ∷ ρ ∷ ᾶ ∷ ς ∷ []) "Heb.10.22"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.22"
∷ word (∙λ ∷ ε ∷ ∙λ ∷ ο ∷ υ ∷ σ ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ []) "Heb.10.22"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.22"
∷ word (σ ∷ ῶ ∷ μ ∷ α ∷ []) "Heb.10.22"
∷ word (ὕ ∷ δ ∷ α ∷ τ ∷ ι ∷ []) "Heb.10.22"
∷ word (κ ∷ α ∷ θ ∷ α ∷ ρ ∷ ῷ ∷ []) "Heb.10.22"
∷ word (κ ∷ α ∷ τ ∷ έ ∷ χ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.10.23"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.23"
∷ word (ὁ ∷ μ ∷ ο ∷ ∙λ ∷ ο ∷ γ ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.23"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.10.23"
∷ word (ἐ ∷ ∙λ ∷ π ∷ ί ∷ δ ∷ ο ∷ ς ∷ []) "Heb.10.23"
∷ word (ἀ ∷ κ ∷ ∙λ ∷ ι ∷ ν ∷ ῆ ∷ []) "Heb.10.23"
∷ word (π ∷ ι ∷ σ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.10.23"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.23"
∷ word (ὁ ∷ []) "Heb.10.23"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ι ∷ ∙λ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.10.23"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.24"
∷ word (κ ∷ α ∷ τ ∷ α ∷ ν ∷ ο ∷ ῶ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.10.24"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ή ∷ ∙λ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.10.24"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.10.24"
∷ word (π ∷ α ∷ ρ ∷ ο ∷ ξ ∷ υ ∷ σ ∷ μ ∷ ὸ ∷ ν ∷ []) "Heb.10.24"
∷ word (ἀ ∷ γ ∷ ά ∷ π ∷ η ∷ ς ∷ []) "Heb.10.24"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.24"
∷ word (κ ∷ α ∷ ∙λ ∷ ῶ ∷ ν ∷ []) "Heb.10.24"
∷ word (ἔ ∷ ρ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.10.24"
∷ word (μ ∷ ὴ ∷ []) "Heb.10.25"
∷ word (ἐ ∷ γ ∷ κ ∷ α ∷ τ ∷ α ∷ ∙λ ∷ ε ∷ ί ∷ π ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.10.25"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.25"
∷ word (ἐ ∷ π ∷ ι ∷ σ ∷ υ ∷ ν ∷ α ∷ γ ∷ ω ∷ γ ∷ ὴ ∷ ν ∷ []) "Heb.10.25"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.10.25"
∷ word (κ ∷ α ∷ θ ∷ ὼ ∷ ς ∷ []) "Heb.10.25"
∷ word (ἔ ∷ θ ∷ ο ∷ ς ∷ []) "Heb.10.25"
∷ word (τ ∷ ι ∷ σ ∷ ί ∷ ν ∷ []) "Heb.10.25"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.10.25"
∷ word (π ∷ α ∷ ρ ∷ α ∷ κ ∷ α ∷ ∙λ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.10.25"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.25"
∷ word (τ ∷ ο ∷ σ ∷ ο ∷ ύ ∷ τ ∷ ῳ ∷ []) "Heb.10.25"
∷ word (μ ∷ ᾶ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ν ∷ []) "Heb.10.25"
∷ word (ὅ ∷ σ ∷ ῳ ∷ []) "Heb.10.25"
∷ word (β ∷ ∙λ ∷ έ ∷ π ∷ ε ∷ τ ∷ ε ∷ []) "Heb.10.25"
∷ word (ἐ ∷ γ ∷ γ ∷ ί ∷ ζ ∷ ο ∷ υ ∷ σ ∷ α ∷ ν ∷ []) "Heb.10.25"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.25"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.10.25"
∷ word (Ἑ ∷ κ ∷ ο ∷ υ ∷ σ ∷ ί ∷ ω ∷ ς ∷ []) "Heb.10.26"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.26"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ α ∷ ν ∷ ό ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.10.26"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.10.26"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.10.26"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.26"
∷ word (∙λ ∷ α ∷ β ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.10.26"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.26"
∷ word (ἐ ∷ π ∷ ί ∷ γ ∷ ν ∷ ω ∷ σ ∷ ι ∷ ν ∷ []) "Heb.10.26"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.10.26"
∷ word (ἀ ∷ ∙λ ∷ η ∷ θ ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.26"
∷ word (ο ∷ ὐ ∷ κ ∷ έ ∷ τ ∷ ι ∷ []) "Heb.10.26"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.10.26"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.10.26"
∷ word (ἀ ∷ π ∷ ο ∷ ∙λ ∷ ε ∷ ί ∷ π ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.10.26"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ []) "Heb.10.26"
∷ word (φ ∷ ο ∷ β ∷ ε ∷ ρ ∷ ὰ ∷ []) "Heb.10.27"
∷ word (δ ∷ έ ∷ []) "Heb.10.27"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.10.27"
∷ word (ἐ ∷ κ ∷ δ ∷ ο ∷ χ ∷ ὴ ∷ []) "Heb.10.27"
∷ word (κ ∷ ρ ∷ ί ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.10.27"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.27"
∷ word (π ∷ υ ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.10.27"
∷ word (ζ ∷ ῆ ∷ ∙λ ∷ ο ∷ ς ∷ []) "Heb.10.27"
∷ word (ἐ ∷ σ ∷ θ ∷ ί ∷ ε ∷ ι ∷ ν ∷ []) "Heb.10.27"
∷ word (μ ∷ έ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.10.27"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.10.27"
∷ word (ὑ ∷ π ∷ ε ∷ ν ∷ α ∷ ν ∷ τ ∷ ί ∷ ο ∷ υ ∷ ς ∷ []) "Heb.10.27"
∷ word (ἀ ∷ θ ∷ ε ∷ τ ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.10.28"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.10.28"
∷ word (ν ∷ ό ∷ μ ∷ ο ∷ ν ∷ []) "Heb.10.28"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ έ ∷ ω ∷ ς ∷ []) "Heb.10.28"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.10.28"
∷ word (ο ∷ ἰ ∷ κ ∷ τ ∷ ι ∷ ρ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.10.28"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.10.28"
∷ word (δ ∷ υ ∷ σ ∷ ὶ ∷ ν ∷ []) "Heb.10.28"
∷ word (ἢ ∷ []) "Heb.10.28"
∷ word (τ ∷ ρ ∷ ι ∷ σ ∷ ὶ ∷ ν ∷ []) "Heb.10.28"
∷ word (μ ∷ ά ∷ ρ ∷ τ ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.10.28"
∷ word (ἀ ∷ π ∷ ο ∷ θ ∷ ν ∷ ῄ ∷ σ ∷ κ ∷ ε ∷ ι ∷ []) "Heb.10.28"
∷ word (π ∷ ό ∷ σ ∷ ῳ ∷ []) "Heb.10.29"
∷ word (δ ∷ ο ∷ κ ∷ ε ∷ ῖ ∷ τ ∷ ε ∷ []) "Heb.10.29"
∷ word (χ ∷ ε ∷ ί ∷ ρ ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.10.29"
∷ word (ἀ ∷ ξ ∷ ι ∷ ω ∷ θ ∷ ή ∷ σ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.10.29"
∷ word (τ ∷ ι ∷ μ ∷ ω ∷ ρ ∷ ί ∷ α ∷ ς ∷ []) "Heb.10.29"
∷ word (ὁ ∷ []) "Heb.10.29"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.10.29"
∷ word (υ ∷ ἱ ∷ ὸ ∷ ν ∷ []) "Heb.10.29"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.10.29"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.10.29"
∷ word (κ ∷ α ∷ τ ∷ α ∷ π ∷ α ∷ τ ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.10.29"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.29"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.29"
∷ word (α ∷ ἷ ∷ μ ∷ α ∷ []) "Heb.10.29"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.10.29"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ς ∷ []) "Heb.10.29"
∷ word (κ ∷ ο ∷ ι ∷ ν ∷ ὸ ∷ ν ∷ []) "Heb.10.29"
∷ word (ἡ ∷ γ ∷ η ∷ σ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.10.29"
∷ word (ἐ ∷ ν ∷ []) "Heb.10.29"
∷ word (ᾧ ∷ []) "Heb.10.29"
∷ word (ἡ ∷ γ ∷ ι ∷ ά ∷ σ ∷ θ ∷ η ∷ []) "Heb.10.29"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.29"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.29"
∷ word (π ∷ ν ∷ ε ∷ ῦ ∷ μ ∷ α ∷ []) "Heb.10.29"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.10.29"
∷ word (χ ∷ ά ∷ ρ ∷ ι ∷ τ ∷ ο ∷ ς ∷ []) "Heb.10.29"
∷ word (ἐ ∷ ν ∷ υ ∷ β ∷ ρ ∷ ί ∷ σ ∷ α ∷ ς ∷ []) "Heb.10.29"
∷ word (ο ∷ ἴ ∷ δ ∷ α ∷ μ ∷ ε ∷ ν ∷ []) "Heb.10.30"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.30"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.10.30"
∷ word (ε ∷ ἰ ∷ π ∷ ό ∷ ν ∷ τ ∷ α ∷ []) "Heb.10.30"
∷ word (Ἐ ∷ μ ∷ ο ∷ ὶ ∷ []) "Heb.10.30"
∷ word (ἐ ∷ κ ∷ δ ∷ ί ∷ κ ∷ η ∷ σ ∷ ι ∷ ς ∷ []) "Heb.10.30"
∷ word (ἐ ∷ γ ∷ ὼ ∷ []) "Heb.10.30"
∷ word (ἀ ∷ ν ∷ τ ∷ α ∷ π ∷ ο ∷ δ ∷ ώ ∷ σ ∷ ω ∷ []) "Heb.10.30"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.30"
∷ word (π ∷ ά ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.10.30"
∷ word (Κ ∷ ρ ∷ ι ∷ ν ∷ ε ∷ ῖ ∷ []) "Heb.10.30"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.10.30"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.10.30"
∷ word (∙λ ∷ α ∷ ὸ ∷ ν ∷ []) "Heb.10.30"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.10.30"
∷ word (φ ∷ ο ∷ β ∷ ε ∷ ρ ∷ ὸ ∷ ν ∷ []) "Heb.10.31"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.31"
∷ word (ἐ ∷ μ ∷ π ∷ ε ∷ σ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.10.31"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.10.31"
∷ word (χ ∷ ε ∷ ῖ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.10.31"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.10.31"
∷ word (ζ ∷ ῶ ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.10.31"
∷ word (Ἀ ∷ ν ∷ α ∷ μ ∷ ι ∷ μ ∷ ν ∷ ῄ ∷ σ ∷ κ ∷ ε ∷ σ ∷ θ ∷ ε ∷ []) "Heb.10.32"
∷ word (δ ∷ ὲ ∷ []) "Heb.10.32"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.10.32"
∷ word (π ∷ ρ ∷ ό ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.10.32"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.10.32"
∷ word (ἐ ∷ ν ∷ []) "Heb.10.32"
∷ word (α ∷ ἷ ∷ ς ∷ []) "Heb.10.32"
∷ word (φ ∷ ω ∷ τ ∷ ι ∷ σ ∷ θ ∷ έ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.10.32"
∷ word (π ∷ ο ∷ ∙λ ∷ ∙λ ∷ ὴ ∷ ν ∷ []) "Heb.10.32"
∷ word (ἄ ∷ θ ∷ ∙λ ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.10.32"
∷ word (ὑ ∷ π ∷ ε ∷ μ ∷ ε ∷ ί ∷ ν ∷ α ∷ τ ∷ ε ∷ []) "Heb.10.32"
∷ word (π ∷ α ∷ θ ∷ η ∷ μ ∷ ά ∷ τ ∷ ω ∷ ν ∷ []) "Heb.10.32"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.10.33"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.10.33"
∷ word (ὀ ∷ ν ∷ ε ∷ ι ∷ δ ∷ ι ∷ σ ∷ μ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.10.33"
∷ word (τ ∷ ε ∷ []) "Heb.10.33"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.33"
∷ word (θ ∷ ∙λ ∷ ί ∷ ψ ∷ ε ∷ σ ∷ ι ∷ ν ∷ []) "Heb.10.33"
∷ word (θ ∷ ε ∷ α ∷ τ ∷ ρ ∷ ι ∷ ζ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.10.33"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.10.33"
∷ word (δ ∷ ὲ ∷ []) "Heb.10.33"
∷ word (κ ∷ ο ∷ ι ∷ ν ∷ ω ∷ ν ∷ ο ∷ ὶ ∷ []) "Heb.10.33"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.10.33"
∷ word (ο ∷ ὕ ∷ τ ∷ ω ∷ ς ∷ []) "Heb.10.33"
∷ word (ἀ ∷ ν ∷ α ∷ σ ∷ τ ∷ ρ ∷ ε ∷ φ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.10.33"
∷ word (γ ∷ ε ∷ ν ∷ η ∷ θ ∷ έ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.10.33"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.34"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.34"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.10.34"
∷ word (δ ∷ ε ∷ σ ∷ μ ∷ ί ∷ ο ∷ ι ∷ ς ∷ []) "Heb.10.34"
∷ word (σ ∷ υ ∷ ν ∷ ε ∷ π ∷ α ∷ θ ∷ ή ∷ σ ∷ α ∷ τ ∷ ε ∷ []) "Heb.10.34"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.34"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.34"
∷ word (ἁ ∷ ρ ∷ π ∷ α ∷ γ ∷ ὴ ∷ ν ∷ []) "Heb.10.34"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.10.34"
∷ word (ὑ ∷ π ∷ α ∷ ρ ∷ χ ∷ ό ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.10.34"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.10.34"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.10.34"
∷ word (χ ∷ α ∷ ρ ∷ ᾶ ∷ ς ∷ []) "Heb.10.34"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ δ ∷ έ ∷ ξ ∷ α ∷ σ ∷ θ ∷ ε ∷ []) "Heb.10.34"
∷ word (γ ∷ ι ∷ ν ∷ ώ ∷ σ ∷ κ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.10.34"
∷ word (ἔ ∷ χ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.10.34"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.10.34"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ο ∷ ν ∷ α ∷ []) "Heb.10.34"
∷ word (ὕ ∷ π ∷ α ∷ ρ ∷ ξ ∷ ι ∷ ν ∷ []) "Heb.10.34"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.34"
∷ word (μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ σ ∷ α ∷ ν ∷ []) "Heb.10.34"
∷ word (μ ∷ ὴ ∷ []) "Heb.10.35"
∷ word (ἀ ∷ π ∷ ο ∷ β ∷ ά ∷ ∙λ ∷ η ∷ τ ∷ ε ∷ []) "Heb.10.35"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.10.35"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.35"
∷ word (π ∷ α ∷ ρ ∷ ρ ∷ η ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.35"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.10.35"
∷ word (ἥ ∷ τ ∷ ι ∷ ς ∷ []) "Heb.10.35"
∷ word (ἔ ∷ χ ∷ ε ∷ ι ∷ []) "Heb.10.35"
∷ word (μ ∷ ε ∷ γ ∷ ά ∷ ∙λ ∷ η ∷ ν ∷ []) "Heb.10.35"
∷ word (μ ∷ ι ∷ σ ∷ θ ∷ α ∷ π ∷ ο ∷ δ ∷ ο ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.35"
∷ word (ὑ ∷ π ∷ ο ∷ μ ∷ ο ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.10.36"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.36"
∷ word (ἔ ∷ χ ∷ ε ∷ τ ∷ ε ∷ []) "Heb.10.36"
∷ word (χ ∷ ρ ∷ ε ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.36"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.10.36"
∷ word (τ ∷ ὸ ∷ []) "Heb.10.36"
∷ word (θ ∷ έ ∷ ∙λ ∷ η ∷ μ ∷ α ∷ []) "Heb.10.36"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.10.36"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.10.36"
∷ word (π ∷ ο ∷ ι ∷ ή ∷ σ ∷ α ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.10.36"
∷ word (κ ∷ ο ∷ μ ∷ ί ∷ σ ∷ η ∷ σ ∷ θ ∷ ε ∷ []) "Heb.10.36"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.10.36"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ν ∷ []) "Heb.10.36"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.10.37"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.10.37"
∷ word (μ ∷ ι ∷ κ ∷ ρ ∷ ὸ ∷ ν ∷ []) "Heb.10.37"
∷ word (ὅ ∷ σ ∷ ο ∷ ν ∷ []) "Heb.10.37"
∷ word (ὅ ∷ σ ∷ ο ∷ ν ∷ []) "Heb.10.37"
∷ word (ὁ ∷ []) "Heb.10.37"
∷ word (ἐ ∷ ρ ∷ χ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.10.37"
∷ word (ἥ ∷ ξ ∷ ε ∷ ι ∷ []) "Heb.10.37"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.37"
∷ word (ο ∷ ὐ ∷ []) "Heb.10.37"
∷ word (χ ∷ ρ ∷ ο ∷ ν ∷ ί ∷ σ ∷ ε ∷ ι ∷ []) "Heb.10.37"
∷ word (ὁ ∷ []) "Heb.10.38"
∷ word (δ ∷ ὲ ∷ []) "Heb.10.38"
∷ word (δ ∷ ί ∷ κ ∷ α ∷ ι ∷ ό ∷ ς ∷ []) "Heb.10.38"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.10.38"
∷ word (ἐ ∷ κ ∷ []) "Heb.10.38"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.10.38"
∷ word (ζ ∷ ή ∷ σ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.10.38"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.10.38"
∷ word (ἐ ∷ ὰ ∷ ν ∷ []) "Heb.10.38"
∷ word (ὑ ∷ π ∷ ο ∷ σ ∷ τ ∷ ε ∷ ί ∷ ∙λ ∷ η ∷ τ ∷ α ∷ ι ∷ []) "Heb.10.38"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.10.38"
∷ word (ε ∷ ὐ ∷ δ ∷ ο ∷ κ ∷ ε ∷ ῖ ∷ []) "Heb.10.38"
∷ word (ἡ ∷ []) "Heb.10.38"
∷ word (ψ ∷ υ ∷ χ ∷ ή ∷ []) "Heb.10.38"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.10.38"
∷ word (ἐ ∷ ν ∷ []) "Heb.10.38"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.10.38"
∷ word (ἡ ∷ μ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.10.39"
∷ word (δ ∷ ὲ ∷ []) "Heb.10.39"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.10.39"
∷ word (ἐ ∷ σ ∷ μ ∷ ὲ ∷ ν ∷ []) "Heb.10.39"
∷ word (ὑ ∷ π ∷ ο ∷ σ ∷ τ ∷ ο ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.10.39"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.10.39"
∷ word (ἀ ∷ π ∷ ώ ∷ ∙λ ∷ ε ∷ ι ∷ α ∷ ν ∷ []) "Heb.10.39"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.10.39"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.10.39"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.10.39"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ π ∷ ο ∷ ί ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.10.39"
∷ word (ψ ∷ υ ∷ χ ∷ ῆ ∷ ς ∷ []) "Heb.10.39"
∷ word (Ἔ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.11.1"
∷ word (δ ∷ ὲ ∷ []) "Heb.11.1"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ι ∷ ς ∷ []) "Heb.11.1"
∷ word (ἐ ∷ ∙λ ∷ π ∷ ι ∷ ζ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.11.1"
∷ word (ὑ ∷ π ∷ ό ∷ σ ∷ τ ∷ α ∷ σ ∷ ι ∷ ς ∷ []) "Heb.11.1"
∷ word (π ∷ ρ ∷ α ∷ γ ∷ μ ∷ ά ∷ τ ∷ ω ∷ ν ∷ []) "Heb.11.1"
∷ word (ἔ ∷ ∙λ ∷ ε ∷ γ ∷ χ ∷ ο ∷ ς ∷ []) "Heb.11.1"
∷ word (ο ∷ ὐ ∷ []) "Heb.11.1"
∷ word (β ∷ ∙λ ∷ ε ∷ π ∷ ο ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.11.1"
∷ word (ἐ ∷ ν ∷ []) "Heb.11.2"
∷ word (τ ∷ α ∷ ύ ∷ τ ∷ ῃ ∷ []) "Heb.11.2"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.11.2"
∷ word (ἐ ∷ μ ∷ α ∷ ρ ∷ τ ∷ υ ∷ ρ ∷ ή ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.2"
∷ word (ο ∷ ἱ ∷ []) "Heb.11.2"
∷ word (π ∷ ρ ∷ ε ∷ σ ∷ β ∷ ύ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ι ∷ []) "Heb.11.2"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.3"
∷ word (ν ∷ ο ∷ ο ∷ ῦ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.11.3"
∷ word (κ ∷ α ∷ τ ∷ η ∷ ρ ∷ τ ∷ ί ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.11.3"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.11.3"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ ς ∷ []) "Heb.11.3"
∷ word (ῥ ∷ ή ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.11.3"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.11.3"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.11.3"
∷ word (τ ∷ ὸ ∷ []) "Heb.11.3"
∷ word (μ ∷ ὴ ∷ []) "Heb.11.3"
∷ word (ἐ ∷ κ ∷ []) "Heb.11.3"
∷ word (φ ∷ α ∷ ι ∷ ν ∷ ο ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.11.3"
∷ word (τ ∷ ὸ ∷ []) "Heb.11.3"
∷ word (β ∷ ∙λ ∷ ε ∷ π ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.11.3"
∷ word (γ ∷ ε ∷ γ ∷ ο ∷ ν ∷ έ ∷ ν ∷ α ∷ ι ∷ []) "Heb.11.3"
∷ word (Π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.4"
∷ word (π ∷ ∙λ ∷ ε ∷ ί ∷ ο ∷ ν ∷ α ∷ []) "Heb.11.4"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.11.4"
∷ word (Ἅ ∷ β ∷ ε ∷ ∙λ ∷ []) "Heb.11.4"
∷ word (π ∷ α ∷ ρ ∷ ὰ ∷ []) "Heb.11.4"
∷ word (Κ ∷ ά ∷ ϊ ∷ ν ∷ []) "Heb.11.4"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ή ∷ ν ∷ ε ∷ γ ∷ κ ∷ ε ∷ ν ∷ []) "Heb.11.4"
∷ word (τ ∷ ῷ ∷ []) "Heb.11.4"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.11.4"
∷ word (δ ∷ ι ∷ []) "Heb.11.4"
∷ word (ἧ ∷ ς ∷ []) "Heb.11.4"
∷ word (ἐ ∷ μ ∷ α ∷ ρ ∷ τ ∷ υ ∷ ρ ∷ ή ∷ θ ∷ η ∷ []) "Heb.11.4"
∷ word (ε ∷ ἶ ∷ ν ∷ α ∷ ι ∷ []) "Heb.11.4"
∷ word (δ ∷ ί ∷ κ ∷ α ∷ ι ∷ ο ∷ ς ∷ []) "Heb.11.4"
∷ word (μ ∷ α ∷ ρ ∷ τ ∷ υ ∷ ρ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.11.4"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.11.4"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.11.4"
∷ word (δ ∷ ώ ∷ ρ ∷ ο ∷ ι ∷ ς ∷ []) "Heb.11.4"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.11.4"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.4"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.11.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.4"
∷ word (δ ∷ ι ∷ []) "Heb.11.4"
∷ word (α ∷ ὐ ∷ τ ∷ ῆ ∷ ς ∷ []) "Heb.11.4"
∷ word (ἀ ∷ π ∷ ο ∷ θ ∷ α ∷ ν ∷ ὼ ∷ ν ∷ []) "Heb.11.4"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.11.4"
∷ word (∙λ ∷ α ∷ ∙λ ∷ ε ∷ ῖ ∷ []) "Heb.11.4"
∷ word (Π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.5"
∷ word (Ἑ ∷ ν ∷ ὼ ∷ χ ∷ []) "Heb.11.5"
∷ word (μ ∷ ε ∷ τ ∷ ε ∷ τ ∷ έ ∷ θ ∷ η ∷ []) "Heb.11.5"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.5"
∷ word (μ ∷ ὴ ∷ []) "Heb.11.5"
∷ word (ἰ ∷ δ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.11.5"
∷ word (θ ∷ ά ∷ ν ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.11.5"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.5"
∷ word (ο ∷ ὐ ∷ χ ∷ []) "Heb.11.5"
∷ word (η ∷ ὑ ∷ ρ ∷ ί ∷ σ ∷ κ ∷ ε ∷ τ ∷ ο ∷ []) "Heb.11.5"
∷ word (δ ∷ ι ∷ ό ∷ τ ∷ ι ∷ []) "Heb.11.5"
∷ word (μ ∷ ε ∷ τ ∷ έ ∷ θ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.11.5"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.11.5"
∷ word (ὁ ∷ []) "Heb.11.5"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.11.5"
∷ word (π ∷ ρ ∷ ὸ ∷ []) "Heb.11.5"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.11.5"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.5"
∷ word (μ ∷ ε ∷ τ ∷ α ∷ θ ∷ έ ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.11.5"
∷ word (μ ∷ ε ∷ μ ∷ α ∷ ρ ∷ τ ∷ ύ ∷ ρ ∷ η ∷ τ ∷ α ∷ ι ∷ []) "Heb.11.5"
∷ word (ε ∷ ὐ ∷ α ∷ ρ ∷ ε ∷ σ ∷ τ ∷ η ∷ κ ∷ έ ∷ ν ∷ α ∷ ι ∷ []) "Heb.11.5"
∷ word (τ ∷ ῷ ∷ []) "Heb.11.5"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.11.5"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.11.6"
∷ word (δ ∷ ὲ ∷ []) "Heb.11.6"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.11.6"
∷ word (ἀ ∷ δ ∷ ύ ∷ ν ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.11.6"
∷ word (ε ∷ ὐ ∷ α ∷ ρ ∷ ε ∷ σ ∷ τ ∷ ῆ ∷ σ ∷ α ∷ ι ∷ []) "Heb.11.6"
∷ word (π ∷ ι ∷ σ ∷ τ ∷ ε ∷ ῦ ∷ σ ∷ α ∷ ι ∷ []) "Heb.11.6"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.11.6"
∷ word (δ ∷ ε ∷ ῖ ∷ []) "Heb.11.6"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.6"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ρ ∷ χ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.11.6"
∷ word (τ ∷ ῷ ∷ []) "Heb.11.6"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.11.6"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.11.6"
∷ word (ἔ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.11.6"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.6"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.11.6"
∷ word (ἐ ∷ κ ∷ ζ ∷ η ∷ τ ∷ ο ∷ ῦ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.6"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.11.6"
∷ word (μ ∷ ι ∷ σ ∷ θ ∷ α ∷ π ∷ ο ∷ δ ∷ ό ∷ τ ∷ η ∷ ς ∷ []) "Heb.11.6"
∷ word (γ ∷ ί ∷ ν ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.11.6"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.7"
∷ word (χ ∷ ρ ∷ η ∷ μ ∷ α ∷ τ ∷ ι ∷ σ ∷ θ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.11.7"
∷ word (Ν ∷ ῶ ∷ ε ∷ []) "Heb.11.7"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.11.7"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.11.7"
∷ word (μ ∷ η ∷ δ ∷ έ ∷ π ∷ ω ∷ []) "Heb.11.7"
∷ word (β ∷ ∙λ ∷ ε ∷ π ∷ ο ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.11.7"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ α ∷ β ∷ η ∷ θ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.11.7"
∷ word (κ ∷ α ∷ τ ∷ ε ∷ σ ∷ κ ∷ ε ∷ ύ ∷ α ∷ σ ∷ ε ∷ ν ∷ []) "Heb.11.7"
∷ word (κ ∷ ι ∷ β ∷ ω ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.11.7"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.11.7"
∷ word (σ ∷ ω ∷ τ ∷ η ∷ ρ ∷ ί ∷ α ∷ ν ∷ []) "Heb.11.7"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.7"
∷ word (ο ∷ ἴ ∷ κ ∷ ο ∷ υ ∷ []) "Heb.11.7"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.11.7"
∷ word (δ ∷ ι ∷ []) "Heb.11.7"
∷ word (ἧ ∷ ς ∷ []) "Heb.11.7"
∷ word (κ ∷ α ∷ τ ∷ έ ∷ κ ∷ ρ ∷ ι ∷ ν ∷ ε ∷ ν ∷ []) "Heb.11.7"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.7"
∷ word (κ ∷ ό ∷ σ ∷ μ ∷ ο ∷ ν ∷ []) "Heb.11.7"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.7"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.7"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.11.7"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.11.7"
∷ word (δ ∷ ι ∷ κ ∷ α ∷ ι ∷ ο ∷ σ ∷ ύ ∷ ν ∷ η ∷ ς ∷ []) "Heb.11.7"
∷ word (ἐ ∷ γ ∷ έ ∷ ν ∷ ε ∷ τ ∷ ο ∷ []) "Heb.11.7"
∷ word (κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ό ∷ μ ∷ ο ∷ ς ∷ []) "Heb.11.7"
∷ word (Π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.8"
∷ word (κ ∷ α ∷ ∙λ ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.8"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ὰ ∷ μ ∷ []) "Heb.11.8"
∷ word (ὑ ∷ π ∷ ή ∷ κ ∷ ο ∷ υ ∷ σ ∷ ε ∷ ν ∷ []) "Heb.11.8"
∷ word (ἐ ∷ ξ ∷ ε ∷ ∙λ ∷ θ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.11.8"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.11.8"
∷ word (τ ∷ ό ∷ π ∷ ο ∷ ν ∷ []) "Heb.11.8"
∷ word (ὃ ∷ ν ∷ []) "Heb.11.8"
∷ word (ἤ ∷ μ ∷ ε ∷ ∙λ ∷ ∙λ ∷ ε ∷ ν ∷ []) "Heb.11.8"
∷ word (∙λ ∷ α ∷ μ ∷ β ∷ ά ∷ ν ∷ ε ∷ ι ∷ ν ∷ []) "Heb.11.8"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.11.8"
∷ word (κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ο ∷ μ ∷ ί ∷ α ∷ ν ∷ []) "Heb.11.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.8"
∷ word (ἐ ∷ ξ ∷ ῆ ∷ ∙λ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.11.8"
∷ word (μ ∷ ὴ ∷ []) "Heb.11.8"
∷ word (ἐ ∷ π ∷ ι ∷ σ ∷ τ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.8"
∷ word (π ∷ ο ∷ ῦ ∷ []) "Heb.11.8"
∷ word (ἔ ∷ ρ ∷ χ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.11.8"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.9"
∷ word (π ∷ α ∷ ρ ∷ ῴ ∷ κ ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.11.9"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.11.9"
∷ word (γ ∷ ῆ ∷ ν ∷ []) "Heb.11.9"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.9"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.11.9"
∷ word (ὡ ∷ ς ∷ []) "Heb.11.9"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ο ∷ τ ∷ ρ ∷ ί ∷ α ∷ ν ∷ []) "Heb.11.9"
∷ word (ἐ ∷ ν ∷ []) "Heb.11.9"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.11.9"
∷ word (κ ∷ α ∷ τ ∷ ο ∷ ι ∷ κ ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.11.9"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.11.9"
∷ word (Ἰ ∷ σ ∷ α ∷ ὰ ∷ κ ∷ []) "Heb.11.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.9"
∷ word (Ἰ ∷ α ∷ κ ∷ ὼ ∷ β ∷ []) "Heb.11.9"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.11.9"
∷ word (σ ∷ υ ∷ γ ∷ κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ό ∷ μ ∷ ω ∷ ν ∷ []) "Heb.11.9"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.9"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.11.9"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.9"
∷ word (α ∷ ὐ ∷ τ ∷ ῆ ∷ ς ∷ []) "Heb.11.9"
∷ word (ἐ ∷ ξ ∷ ε ∷ δ ∷ έ ∷ χ ∷ ε ∷ τ ∷ ο ∷ []) "Heb.11.10"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.11.10"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.11.10"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.11.10"
∷ word (θ ∷ ε ∷ μ ∷ ε ∷ ∙λ ∷ ί ∷ ο ∷ υ ∷ ς ∷ []) "Heb.11.10"
∷ word (ἔ ∷ χ ∷ ο ∷ υ ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.10"
∷ word (π ∷ ό ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.11.10"
∷ word (ἧ ∷ ς ∷ []) "Heb.11.10"
∷ word (τ ∷ ε ∷ χ ∷ ν ∷ ί ∷ τ ∷ η ∷ ς ∷ []) "Heb.11.10"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.10"
∷ word (δ ∷ η ∷ μ ∷ ι ∷ ο ∷ υ ∷ ρ ∷ γ ∷ ὸ ∷ ς ∷ []) "Heb.11.10"
∷ word (ὁ ∷ []) "Heb.11.10"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.11.10"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.11"
∷ word (α ∷ ὐ ∷ τ ∷ ῇ ∷ []) "Heb.11.11"
∷ word (Σ ∷ ά ∷ ρ ∷ ρ ∷ ᾳ ∷ []) "Heb.11.11"
∷ word (δ ∷ ύ ∷ ν ∷ α ∷ μ ∷ ι ∷ ν ∷ []) "Heb.11.11"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.11.11"
∷ word (κ ∷ α ∷ τ ∷ α ∷ β ∷ ο ∷ ∙λ ∷ ὴ ∷ ν ∷ []) "Heb.11.11"
∷ word (σ ∷ π ∷ έ ∷ ρ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.11.11"
∷ word (ἔ ∷ ∙λ ∷ α ∷ β ∷ ε ∷ ν ∷ []) "Heb.11.11"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.11"
∷ word (π ∷ α ∷ ρ ∷ ὰ ∷ []) "Heb.11.11"
∷ word (κ ∷ α ∷ ι ∷ ρ ∷ ὸ ∷ ν ∷ []) "Heb.11.11"
∷ word (ἡ ∷ ∙λ ∷ ι ∷ κ ∷ ί ∷ α ∷ ς ∷ []) "Heb.11.11"
∷ word (ἐ ∷ π ∷ ε ∷ ὶ ∷ []) "Heb.11.11"
∷ word (π ∷ ι ∷ σ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.11.11"
∷ word (ἡ ∷ γ ∷ ή ∷ σ ∷ α ∷ τ ∷ ο ∷ []) "Heb.11.11"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.11"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ι ∷ ∙λ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.11.11"
∷ word (δ ∷ ι ∷ ὸ ∷ []) "Heb.11.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.12"
∷ word (ἀ ∷ φ ∷ []) "Heb.11.12"
∷ word (ἑ ∷ ν ∷ ὸ ∷ ς ∷ []) "Heb.11.12"
∷ word (ἐ ∷ γ ∷ ε ∷ ν ∷ ν ∷ ή ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.12"
∷ word (τ ∷ α ∷ ῦ ∷ τ ∷ α ∷ []) "Heb.11.12"
∷ word (ν ∷ ε ∷ ν ∷ ε ∷ κ ∷ ρ ∷ ω ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ []) "Heb.11.12"
∷ word (κ ∷ α ∷ θ ∷ ὼ ∷ ς ∷ []) "Heb.11.12"
∷ word (τ ∷ ὰ ∷ []) "Heb.11.12"
∷ word (ἄ ∷ σ ∷ τ ∷ ρ ∷ α ∷ []) "Heb.11.12"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.12"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ο ∷ ῦ ∷ []) "Heb.11.12"
∷ word (τ ∷ ῷ ∷ []) "Heb.11.12"
∷ word (π ∷ ∙λ ∷ ή ∷ θ ∷ ε ∷ ι ∷ []) "Heb.11.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.12"
∷ word (ὡ ∷ ς ∷ []) "Heb.11.12"
∷ word (ἡ ∷ []) "Heb.11.12"
∷ word (ἄ ∷ μ ∷ μ ∷ ο ∷ ς ∷ []) "Heb.11.12"
∷ word (ἡ ∷ []) "Heb.11.12"
∷ word (π ∷ α ∷ ρ ∷ ὰ ∷ []) "Heb.11.12"
∷ word (τ ∷ ὸ ∷ []) "Heb.11.12"
∷ word (χ ∷ ε ∷ ῖ ∷ ∙λ ∷ ο ∷ ς ∷ []) "Heb.11.12"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.12"
∷ word (θ ∷ α ∷ ∙λ ∷ ά ∷ σ ∷ σ ∷ η ∷ ς ∷ []) "Heb.11.12"
∷ word (ἡ ∷ []) "Heb.11.12"
∷ word (ἀ ∷ ν ∷ α ∷ ρ ∷ ί ∷ θ ∷ μ ∷ η ∷ τ ∷ ο ∷ ς ∷ []) "Heb.11.12"
∷ word (Κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.11.13"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.11.13"
∷ word (ἀ ∷ π ∷ έ ∷ θ ∷ α ∷ ν ∷ ο ∷ ν ∷ []) "Heb.11.13"
∷ word (ο ∷ ὗ ∷ τ ∷ ο ∷ ι ∷ []) "Heb.11.13"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.11.13"
∷ word (μ ∷ ὴ ∷ []) "Heb.11.13"
∷ word (∙λ ∷ α ∷ β ∷ ό ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.11.13"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.11.13"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.11.13"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.11.13"
∷ word (π ∷ ό ∷ ρ ∷ ρ ∷ ω ∷ θ ∷ ε ∷ ν ∷ []) "Heb.11.13"
∷ word (α ∷ ὐ ∷ τ ∷ ὰ ∷ ς ∷ []) "Heb.11.13"
∷ word (ἰ ∷ δ ∷ ό ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.11.13"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.13"
∷ word (ἀ ∷ σ ∷ π ∷ α ∷ σ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.11.13"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.13"
∷ word (ὁ ∷ μ ∷ ο ∷ ∙λ ∷ ο ∷ γ ∷ ή ∷ σ ∷ α ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.11.13"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.11.13"
∷ word (ξ ∷ έ ∷ ν ∷ ο ∷ ι ∷ []) "Heb.11.13"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.13"
∷ word (π ∷ α ∷ ρ ∷ ε ∷ π ∷ ί ∷ δ ∷ η ∷ μ ∷ ο ∷ ί ∷ []) "Heb.11.13"
∷ word (ε ∷ ἰ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.13"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.11.13"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.13"
∷ word (γ ∷ ῆ ∷ ς ∷ []) "Heb.11.13"
∷ word (ο ∷ ἱ ∷ []) "Heb.11.14"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.11.14"
∷ word (τ ∷ ο ∷ ι ∷ α ∷ ῦ ∷ τ ∷ α ∷ []) "Heb.11.14"
∷ word (∙λ ∷ έ ∷ γ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.11.14"
∷ word (ἐ ∷ μ ∷ φ ∷ α ∷ ν ∷ ί ∷ ζ ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.14"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.11.14"
∷ word (π ∷ α ∷ τ ∷ ρ ∷ ί ∷ δ ∷ α ∷ []) "Heb.11.14"
∷ word (ἐ ∷ π ∷ ι ∷ ζ ∷ η ∷ τ ∷ ο ∷ ῦ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.14"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.15"
∷ word (ε ∷ ἰ ∷ []) "Heb.11.15"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.11.15"
∷ word (ἐ ∷ κ ∷ ε ∷ ί ∷ ν ∷ η ∷ ς ∷ []) "Heb.11.15"
∷ word (μ ∷ ν ∷ η ∷ μ ∷ ο ∷ ν ∷ ε ∷ ύ ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.15"
∷ word (ἀ ∷ φ ∷ []) "Heb.11.15"
∷ word (ἧ ∷ ς ∷ []) "Heb.11.15"
∷ word (ἐ ∷ ξ ∷ έ ∷ β ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.15"
∷ word (ε ∷ ἶ ∷ χ ∷ ο ∷ ν ∷ []) "Heb.11.15"
∷ word (ἂ ∷ ν ∷ []) "Heb.11.15"
∷ word (κ ∷ α ∷ ι ∷ ρ ∷ ὸ ∷ ν ∷ []) "Heb.11.15"
∷ word (ἀ ∷ ν ∷ α ∷ κ ∷ ά ∷ μ ∷ ψ ∷ α ∷ ι ∷ []) "Heb.11.15"
∷ word (ν ∷ ῦ ∷ ν ∷ []) "Heb.11.16"
∷ word (δ ∷ ὲ ∷ []) "Heb.11.16"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.16"
∷ word (ὀ ∷ ρ ∷ έ ∷ γ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.11.16"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ []) "Heb.11.16"
∷ word (ἔ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.11.16"
∷ word (ἐ ∷ π ∷ ο ∷ υ ∷ ρ ∷ α ∷ ν ∷ ί ∷ ο ∷ υ ∷ []) "Heb.11.16"
∷ word (δ ∷ ι ∷ ὸ ∷ []) "Heb.11.16"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.11.16"
∷ word (ἐ ∷ π ∷ α ∷ ι ∷ σ ∷ χ ∷ ύ ∷ ν ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.11.16"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.11.16"
∷ word (ὁ ∷ []) "Heb.11.16"
∷ word (θ ∷ ε ∷ ὸ ∷ ς ∷ []) "Heb.11.16"
∷ word (θ ∷ ε ∷ ὸ ∷ ς ∷ []) "Heb.11.16"
∷ word (ἐ ∷ π ∷ ι ∷ κ ∷ α ∷ ∙λ ∷ ε ∷ ῖ ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.11.16"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.11.16"
∷ word (ἡ ∷ τ ∷ ο ∷ ί ∷ μ ∷ α ∷ σ ∷ ε ∷ ν ∷ []) "Heb.11.16"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.11.16"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.11.16"
∷ word (π ∷ ό ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.11.16"
∷ word (Π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.17"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ν ∷ ή ∷ ν ∷ ο ∷ χ ∷ ε ∷ ν ∷ []) "Heb.11.17"
∷ word (Ἀ ∷ β ∷ ρ ∷ α ∷ ὰ ∷ μ ∷ []) "Heb.11.17"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.17"
∷ word (Ἰ ∷ σ ∷ α ∷ ὰ ∷ κ ∷ []) "Heb.11.17"
∷ word (π ∷ ε ∷ ι ∷ ρ ∷ α ∷ ζ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.17"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.17"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.17"
∷ word (μ ∷ ο ∷ ν ∷ ο ∷ γ ∷ ε ∷ ν ∷ ῆ ∷ []) "Heb.11.17"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ έ ∷ φ ∷ ε ∷ ρ ∷ ε ∷ ν ∷ []) "Heb.11.17"
∷ word (ὁ ∷ []) "Heb.11.17"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.11.17"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.11.17"
∷ word (ἀ ∷ ν ∷ α ∷ δ ∷ ε ∷ ξ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.17"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.11.18"
∷ word (ὃ ∷ ν ∷ []) "Heb.11.18"
∷ word (ἐ ∷ ∙λ ∷ α ∷ ∙λ ∷ ή ∷ θ ∷ η ∷ []) "Heb.11.18"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.11.18"
∷ word (Ἐ ∷ ν ∷ []) "Heb.11.18"
∷ word (Ἰ ∷ σ ∷ α ∷ ὰ ∷ κ ∷ []) "Heb.11.18"
∷ word (κ ∷ ∙λ ∷ η ∷ θ ∷ ή ∷ σ ∷ ε ∷ τ ∷ α ∷ ί ∷ []) "Heb.11.18"
∷ word (σ ∷ ο ∷ ι ∷ []) "Heb.11.18"
∷ word (σ ∷ π ∷ έ ∷ ρ ∷ μ ∷ α ∷ []) "Heb.11.18"
∷ word (∙λ ∷ ο ∷ γ ∷ ι ∷ σ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.19"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.11.19"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.19"
∷ word (ἐ ∷ κ ∷ []) "Heb.11.19"
∷ word (ν ∷ ε ∷ κ ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.11.19"
∷ word (ἐ ∷ γ ∷ ε ∷ ί ∷ ρ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.11.19"
∷ word (δ ∷ υ ∷ ν ∷ α ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.11.19"
∷ word (ὁ ∷ []) "Heb.11.19"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.11.19"
∷ word (ὅ ∷ θ ∷ ε ∷ ν ∷ []) "Heb.11.19"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.11.19"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.19"
∷ word (ἐ ∷ ν ∷ []) "Heb.11.19"
∷ word (π ∷ α ∷ ρ ∷ α ∷ β ∷ ο ∷ ∙λ ∷ ῇ ∷ []) "Heb.11.19"
∷ word (ἐ ∷ κ ∷ ο ∷ μ ∷ ί ∷ σ ∷ α ∷ τ ∷ ο ∷ []) "Heb.11.19"
∷ word (Π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.20"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.20"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.11.20"
∷ word (μ ∷ ε ∷ ∙λ ∷ ∙λ ∷ ό ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.11.20"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ ό ∷ γ ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.11.20"
∷ word (Ἰ ∷ σ ∷ α ∷ ὰ ∷ κ ∷ []) "Heb.11.20"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.20"
∷ word (Ἰ ∷ α ∷ κ ∷ ὼ ∷ β ∷ []) "Heb.11.20"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.20"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.20"
∷ word (Ἠ ∷ σ ∷ α ∷ ῦ ∷ []) "Heb.11.20"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.21"
∷ word (Ἰ ∷ α ∷ κ ∷ ὼ ∷ β ∷ []) "Heb.11.21"
∷ word (ἀ ∷ π ∷ ο ∷ θ ∷ ν ∷ ῄ ∷ σ ∷ κ ∷ ω ∷ ν ∷ []) "Heb.11.21"
∷ word (ἕ ∷ κ ∷ α ∷ σ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.11.21"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.11.21"
∷ word (υ ∷ ἱ ∷ ῶ ∷ ν ∷ []) "Heb.11.21"
∷ word (Ἰ ∷ ω ∷ σ ∷ ὴ ∷ φ ∷ []) "Heb.11.21"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ ό ∷ γ ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.11.21"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.21"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ κ ∷ ύ ∷ ν ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.11.21"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.11.21"
∷ word (τ ∷ ὸ ∷ []) "Heb.11.21"
∷ word (ἄ ∷ κ ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.11.21"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.21"
∷ word (ῥ ∷ ά ∷ β ∷ δ ∷ ο ∷ υ ∷ []) "Heb.11.21"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.11.21"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.22"
∷ word (Ἰ ∷ ω ∷ σ ∷ ὴ ∷ φ ∷ []) "Heb.11.22"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ υ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.11.22"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.11.22"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.22"
∷ word (ἐ ∷ ξ ∷ ό ∷ δ ∷ ο ∷ υ ∷ []) "Heb.11.22"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.11.22"
∷ word (υ ∷ ἱ ∷ ῶ ∷ ν ∷ []) "Heb.11.22"
∷ word (Ἰ ∷ σ ∷ ρ ∷ α ∷ ὴ ∷ ∙λ ∷ []) "Heb.11.22"
∷ word (ἐ ∷ μ ∷ ν ∷ η ∷ μ ∷ ό ∷ ν ∷ ε ∷ υ ∷ σ ∷ ε ∷ ν ∷ []) "Heb.11.22"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.22"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.11.22"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.11.22"
∷ word (ὀ ∷ σ ∷ τ ∷ έ ∷ ω ∷ ν ∷ []) "Heb.11.22"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.11.22"
∷ word (ἐ ∷ ν ∷ ε ∷ τ ∷ ε ∷ ί ∷ ∙λ ∷ α ∷ τ ∷ ο ∷ []) "Heb.11.22"
∷ word (Π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.23"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ ῆ ∷ ς ∷ []) "Heb.11.23"
∷ word (γ ∷ ε ∷ ν ∷ ν ∷ η ∷ θ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.11.23"
∷ word (ἐ ∷ κ ∷ ρ ∷ ύ ∷ β ∷ η ∷ []) "Heb.11.23"
∷ word (τ ∷ ρ ∷ ί ∷ μ ∷ η ∷ ν ∷ ο ∷ ν ∷ []) "Heb.11.23"
∷ word (ὑ ∷ π ∷ ὸ ∷ []) "Heb.11.23"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.11.23"
∷ word (π ∷ α ∷ τ ∷ έ ∷ ρ ∷ ω ∷ ν ∷ []) "Heb.11.23"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.11.23"
∷ word (δ ∷ ι ∷ ό ∷ τ ∷ ι ∷ []) "Heb.11.23"
∷ word (ε ∷ ἶ ∷ δ ∷ ο ∷ ν ∷ []) "Heb.11.23"
∷ word (ἀ ∷ σ ∷ τ ∷ ε ∷ ῖ ∷ ο ∷ ν ∷ []) "Heb.11.23"
∷ word (τ ∷ ὸ ∷ []) "Heb.11.23"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ί ∷ ο ∷ ν ∷ []) "Heb.11.23"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.23"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.11.23"
∷ word (ἐ ∷ φ ∷ ο ∷ β ∷ ή ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.23"
∷ word (τ ∷ ὸ ∷ []) "Heb.11.23"
∷ word (δ ∷ ι ∷ ά ∷ τ ∷ α ∷ γ ∷ μ ∷ α ∷ []) "Heb.11.23"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.23"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ έ ∷ ω ∷ ς ∷ []) "Heb.11.23"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.24"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ ῆ ∷ ς ∷ []) "Heb.11.24"
∷ word (μ ∷ έ ∷ γ ∷ α ∷ ς ∷ []) "Heb.11.24"
∷ word (γ ∷ ε ∷ ν ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.24"
∷ word (ἠ ∷ ρ ∷ ν ∷ ή ∷ σ ∷ α ∷ τ ∷ ο ∷ []) "Heb.11.24"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.11.24"
∷ word (υ ∷ ἱ ∷ ὸ ∷ ς ∷ []) "Heb.11.24"
∷ word (θ ∷ υ ∷ γ ∷ α ∷ τ ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.11.24"
∷ word (Φ ∷ α ∷ ρ ∷ α ∷ ώ ∷ []) "Heb.11.24"
∷ word (μ ∷ ᾶ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ν ∷ []) "Heb.11.25"
∷ word (ἑ ∷ ∙λ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.25"
∷ word (σ ∷ υ ∷ γ ∷ κ ∷ α ∷ κ ∷ ο ∷ υ ∷ χ ∷ ε ∷ ῖ ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.11.25"
∷ word (τ ∷ ῷ ∷ []) "Heb.11.25"
∷ word (∙λ ∷ α ∷ ῷ ∷ []) "Heb.11.25"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.25"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.11.25"
∷ word (ἢ ∷ []) "Heb.11.25"
∷ word (π ∷ ρ ∷ ό ∷ σ ∷ κ ∷ α ∷ ι ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.11.25"
∷ word (ἔ ∷ χ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.11.25"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.11.25"
∷ word (ἀ ∷ π ∷ ό ∷ ∙λ ∷ α ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.25"
∷ word (μ ∷ ε ∷ ί ∷ ζ ∷ ο ∷ ν ∷ α ∷ []) "Heb.11.26"
∷ word (π ∷ ∙λ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.11.26"
∷ word (ἡ ∷ γ ∷ η ∷ σ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.26"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.11.26"
∷ word (Α ∷ ἰ ∷ γ ∷ ύ ∷ π ∷ τ ∷ ο ∷ υ ∷ []) "Heb.11.26"
∷ word (θ ∷ η ∷ σ ∷ α ∷ υ ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.11.26"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.26"
∷ word (ὀ ∷ ν ∷ ε ∷ ι ∷ δ ∷ ι ∷ σ ∷ μ ∷ ὸ ∷ ν ∷ []) "Heb.11.26"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.26"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.11.26"
∷ word (ἀ ∷ π ∷ έ ∷ β ∷ ∙λ ∷ ε ∷ π ∷ ε ∷ ν ∷ []) "Heb.11.26"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.11.26"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.11.26"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.11.26"
∷ word (μ ∷ ι ∷ σ ∷ θ ∷ α ∷ π ∷ ο ∷ δ ∷ ο ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.11.26"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.27"
∷ word (κ ∷ α ∷ τ ∷ έ ∷ ∙λ ∷ ι ∷ π ∷ ε ∷ ν ∷ []) "Heb.11.27"
∷ word (Α ∷ ἴ ∷ γ ∷ υ ∷ π ∷ τ ∷ ο ∷ ν ∷ []) "Heb.11.27"
∷ word (μ ∷ ὴ ∷ []) "Heb.11.27"
∷ word (φ ∷ ο ∷ β ∷ η ∷ θ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.11.27"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.27"
∷ word (θ ∷ υ ∷ μ ∷ ὸ ∷ ν ∷ []) "Heb.11.27"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.27"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ έ ∷ ω ∷ ς ∷ []) "Heb.11.27"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.11.27"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.11.27"
∷ word (ἀ ∷ ό ∷ ρ ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.11.27"
∷ word (ὡ ∷ ς ∷ []) "Heb.11.27"
∷ word (ὁ ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.11.27"
∷ word (ἐ ∷ κ ∷ α ∷ ρ ∷ τ ∷ έ ∷ ρ ∷ η ∷ σ ∷ ε ∷ ν ∷ []) "Heb.11.27"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.28"
∷ word (π ∷ ε ∷ π ∷ ο ∷ ί ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.11.28"
∷ word (τ ∷ ὸ ∷ []) "Heb.11.28"
∷ word (π ∷ ά ∷ σ ∷ χ ∷ α ∷ []) "Heb.11.28"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.28"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.11.28"
∷ word (π ∷ ρ ∷ ό ∷ σ ∷ χ ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.28"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.28"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.11.28"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.11.28"
∷ word (μ ∷ ὴ ∷ []) "Heb.11.28"
∷ word (ὁ ∷ []) "Heb.11.28"
∷ word (ὀ ∷ ∙λ ∷ ο ∷ θ ∷ ρ ∷ ε ∷ ύ ∷ ω ∷ ν ∷ []) "Heb.11.28"
∷ word (τ ∷ ὰ ∷ []) "Heb.11.28"
∷ word (π ∷ ρ ∷ ω ∷ τ ∷ ό ∷ τ ∷ ο ∷ κ ∷ α ∷ []) "Heb.11.28"
∷ word (θ ∷ ί ∷ γ ∷ ῃ ∷ []) "Heb.11.28"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.11.28"
∷ word (Π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.29"
∷ word (δ ∷ ι ∷ έ ∷ β ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.29"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.11.29"
∷ word (Ἐ ∷ ρ ∷ υ ∷ θ ∷ ρ ∷ ὰ ∷ ν ∷ []) "Heb.11.29"
∷ word (Θ ∷ ά ∷ ∙λ ∷ α ∷ σ ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.29"
∷ word (ὡ ∷ ς ∷ []) "Heb.11.29"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.11.29"
∷ word (ξ ∷ η ∷ ρ ∷ ᾶ ∷ ς ∷ []) "Heb.11.29"
∷ word (γ ∷ ῆ ∷ ς ∷ []) "Heb.11.29"
∷ word (ἧ ∷ ς ∷ []) "Heb.11.29"
∷ word (π ∷ ε ∷ ῖ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.11.29"
∷ word (∙λ ∷ α ∷ β ∷ ό ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.11.29"
∷ word (ο ∷ ἱ ∷ []) "Heb.11.29"
∷ word (Α ∷ ἰ ∷ γ ∷ ύ ∷ π ∷ τ ∷ ι ∷ ο ∷ ι ∷ []) "Heb.11.29"
∷ word (κ ∷ α ∷ τ ∷ ε ∷ π ∷ ό ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.29"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.30"
∷ word (τ ∷ ὰ ∷ []) "Heb.11.30"
∷ word (τ ∷ ε ∷ ί ∷ χ ∷ η ∷ []) "Heb.11.30"
∷ word (Ἰ ∷ ε ∷ ρ ∷ ι ∷ χ ∷ ὼ ∷ []) "Heb.11.30"
∷ word (ἔ ∷ π ∷ ε ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.30"
∷ word (κ ∷ υ ∷ κ ∷ ∙λ ∷ ω ∷ θ ∷ έ ∷ ν ∷ τ ∷ α ∷ []) "Heb.11.30"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.11.30"
∷ word (ἑ ∷ π ∷ τ ∷ ὰ ∷ []) "Heb.11.30"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.11.30"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ι ∷ []) "Heb.11.31"
∷ word (Ῥ ∷ α ∷ ὰ ∷ β ∷ []) "Heb.11.31"
∷ word (ἡ ∷ []) "Heb.11.31"
∷ word (π ∷ ό ∷ ρ ∷ ν ∷ η ∷ []) "Heb.11.31"
∷ word (ο ∷ ὐ ∷ []) "Heb.11.31"
∷ word (σ ∷ υ ∷ ν ∷ α ∷ π ∷ ώ ∷ ∙λ ∷ ε ∷ τ ∷ ο ∷ []) "Heb.11.31"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.11.31"
∷ word (ἀ ∷ π ∷ ε ∷ ι ∷ θ ∷ ή ∷ σ ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.31"
∷ word (δ ∷ ε ∷ ξ ∷ α ∷ μ ∷ έ ∷ ν ∷ η ∷ []) "Heb.11.31"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.11.31"
∷ word (κ ∷ α ∷ τ ∷ α ∷ σ ∷ κ ∷ ό ∷ π ∷ ο ∷ υ ∷ ς ∷ []) "Heb.11.31"
∷ word (μ ∷ ε ∷ τ ∷ []) "Heb.11.31"
∷ word (ε ∷ ἰ ∷ ρ ∷ ή ∷ ν ∷ η ∷ ς ∷ []) "Heb.11.31"
∷ word (Κ ∷ α ∷ ὶ ∷ []) "Heb.11.32"
∷ word (τ ∷ ί ∷ []) "Heb.11.32"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.11.32"
∷ word (∙λ ∷ έ ∷ γ ∷ ω ∷ []) "Heb.11.32"
∷ word (ἐ ∷ π ∷ ι ∷ ∙λ ∷ ε ∷ ί ∷ ψ ∷ ε ∷ ι ∷ []) "Heb.11.32"
∷ word (μ ∷ ε ∷ []) "Heb.11.32"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.11.32"
∷ word (δ ∷ ι ∷ η ∷ γ ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.11.32"
∷ word (ὁ ∷ []) "Heb.11.32"
∷ word (χ ∷ ρ ∷ ό ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.32"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.11.32"
∷ word (Γ ∷ ε ∷ δ ∷ ε ∷ ώ ∷ ν ∷ []) "Heb.11.32"
∷ word (Β ∷ α ∷ ρ ∷ ά ∷ κ ∷ []) "Heb.11.32"
∷ word (Σ ∷ α ∷ μ ∷ ψ ∷ ώ ∷ ν ∷ []) "Heb.11.32"
∷ word (Ἰ ∷ ε ∷ φ ∷ θ ∷ ά ∷ ε ∷ []) "Heb.11.32"
∷ word (Δ ∷ α ∷ υ ∷ ί ∷ δ ∷ []) "Heb.11.32"
∷ word (τ ∷ ε ∷ []) "Heb.11.32"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.32"
∷ word (Σ ∷ α ∷ μ ∷ ο ∷ υ ∷ ὴ ∷ ∙λ ∷ []) "Heb.11.32"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.32"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.11.32"
∷ word (π ∷ ρ ∷ ο ∷ φ ∷ η ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.11.32"
∷ word (ο ∷ ἳ ∷ []) "Heb.11.33"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.11.33"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.11.33"
∷ word (κ ∷ α ∷ τ ∷ η ∷ γ ∷ ω ∷ ν ∷ ί ∷ σ ∷ α ∷ ν ∷ τ ∷ ο ∷ []) "Heb.11.33"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.11.33"
∷ word (ε ∷ ἰ ∷ ρ ∷ γ ∷ ά ∷ σ ∷ α ∷ ν ∷ τ ∷ ο ∷ []) "Heb.11.33"
∷ word (δ ∷ ι ∷ κ ∷ α ∷ ι ∷ ο ∷ σ ∷ ύ ∷ ν ∷ η ∷ ν ∷ []) "Heb.11.33"
∷ word (ἐ ∷ π ∷ έ ∷ τ ∷ υ ∷ χ ∷ ο ∷ ν ∷ []) "Heb.11.33"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.11.33"
∷ word (ἔ ∷ φ ∷ ρ ∷ α ∷ ξ ∷ α ∷ ν ∷ []) "Heb.11.33"
∷ word (σ ∷ τ ∷ ό ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.11.33"
∷ word (∙λ ∷ ε ∷ ό ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.11.33"
∷ word (ἔ ∷ σ ∷ β ∷ ε ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.34"
∷ word (δ ∷ ύ ∷ ν ∷ α ∷ μ ∷ ι ∷ ν ∷ []) "Heb.11.34"
∷ word (π ∷ υ ∷ ρ ∷ ό ∷ ς ∷ []) "Heb.11.34"
∷ word (ἔ ∷ φ ∷ υ ∷ γ ∷ ο ∷ ν ∷ []) "Heb.11.34"
∷ word (σ ∷ τ ∷ ό ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.11.34"
∷ word (μ ∷ α ∷ χ ∷ α ∷ ί ∷ ρ ∷ η ∷ ς ∷ []) "Heb.11.34"
∷ word (ἐ ∷ δ ∷ υ ∷ ν ∷ α ∷ μ ∷ ώ ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.34"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.11.34"
∷ word (ἀ ∷ σ ∷ θ ∷ ε ∷ ν ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.11.34"
∷ word (ἐ ∷ γ ∷ ε ∷ ν ∷ ή ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.34"
∷ word (ἰ ∷ σ ∷ χ ∷ υ ∷ ρ ∷ ο ∷ ὶ ∷ []) "Heb.11.34"
∷ word (ἐ ∷ ν ∷ []) "Heb.11.34"
∷ word (π ∷ ο ∷ ∙λ ∷ έ ∷ μ ∷ ῳ ∷ []) "Heb.11.34"
∷ word (π ∷ α ∷ ρ ∷ ε ∷ μ ∷ β ∷ ο ∷ ∙λ ∷ ὰ ∷ ς ∷ []) "Heb.11.34"
∷ word (ἔ ∷ κ ∷ ∙λ ∷ ι ∷ ν ∷ α ∷ ν ∷ []) "Heb.11.34"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ο ∷ τ ∷ ρ ∷ ί ∷ ω ∷ ν ∷ []) "Heb.11.34"
∷ word (ἔ ∷ ∙λ ∷ α ∷ β ∷ ο ∷ ν ∷ []) "Heb.11.35"
∷ word (γ ∷ υ ∷ ν ∷ α ∷ ῖ ∷ κ ∷ ε ∷ ς ∷ []) "Heb.11.35"
∷ word (ἐ ∷ ξ ∷ []) "Heb.11.35"
∷ word (ἀ ∷ ν ∷ α ∷ σ ∷ τ ∷ ά ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.11.35"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.11.35"
∷ word (ν ∷ ε ∷ κ ∷ ρ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.11.35"
∷ word (α ∷ ὐ ∷ τ ∷ ῶ ∷ ν ∷ []) "Heb.11.35"
∷ word (ἄ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ι ∷ []) "Heb.11.35"
∷ word (δ ∷ ὲ ∷ []) "Heb.11.35"
∷ word (ἐ ∷ τ ∷ υ ∷ μ ∷ π ∷ α ∷ ν ∷ ί ∷ σ ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.35"
∷ word (ο ∷ ὐ ∷ []) "Heb.11.35"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ δ ∷ ε ∷ ξ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.11.35"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.11.35"
∷ word (ἀ ∷ π ∷ ο ∷ ∙λ ∷ ύ ∷ τ ∷ ρ ∷ ω ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.35"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.11.35"
∷ word (κ ∷ ρ ∷ ε ∷ ί ∷ τ ∷ τ ∷ ο ∷ ν ∷ ο ∷ ς ∷ []) "Heb.11.35"
∷ word (ἀ ∷ ν ∷ α ∷ σ ∷ τ ∷ ά ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.11.35"
∷ word (τ ∷ ύ ∷ χ ∷ ω ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.35"
∷ word (ἕ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ι ∷ []) "Heb.11.36"
∷ word (δ ∷ ὲ ∷ []) "Heb.11.36"
∷ word (ἐ ∷ μ ∷ π ∷ α ∷ ι ∷ γ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.11.36"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.36"
∷ word (μ ∷ α ∷ σ ∷ τ ∷ ί ∷ γ ∷ ω ∷ ν ∷ []) "Heb.11.36"
∷ word (π ∷ ε ∷ ῖ ∷ ρ ∷ α ∷ ν ∷ []) "Heb.11.36"
∷ word (ἔ ∷ ∙λ ∷ α ∷ β ∷ ο ∷ ν ∷ []) "Heb.11.36"
∷ word (ἔ ∷ τ ∷ ι ∷ []) "Heb.11.36"
∷ word (δ ∷ ὲ ∷ []) "Heb.11.36"
∷ word (δ ∷ ε ∷ σ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.11.36"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.36"
∷ word (φ ∷ υ ∷ ∙λ ∷ α ∷ κ ∷ ῆ ∷ ς ∷ []) "Heb.11.36"
∷ word (ἐ ∷ ∙λ ∷ ι ∷ θ ∷ ά ∷ σ ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.37"
∷ word (ἐ ∷ π ∷ ρ ∷ ί ∷ σ ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.11.37"
∷ word (ἐ ∷ ν ∷ []) "Heb.11.37"
∷ word (φ ∷ ό ∷ ν ∷ ῳ ∷ []) "Heb.11.37"
∷ word (μ ∷ α ∷ χ ∷ α ∷ ί ∷ ρ ∷ η ∷ ς ∷ []) "Heb.11.37"
∷ word (ἀ ∷ π ∷ έ ∷ θ ∷ α ∷ ν ∷ ο ∷ ν ∷ []) "Heb.11.37"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ ῆ ∷ ∙λ ∷ θ ∷ ο ∷ ν ∷ []) "Heb.11.37"
∷ word (ἐ ∷ ν ∷ []) "Heb.11.37"
∷ word (μ ∷ η ∷ ∙λ ∷ ω ∷ τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.11.37"
∷ word (ἐ ∷ ν ∷ []) "Heb.11.37"
∷ word (α ∷ ἰ ∷ γ ∷ ε ∷ ί ∷ ο ∷ ι ∷ ς ∷ []) "Heb.11.37"
∷ word (δ ∷ έ ∷ ρ ∷ μ ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.37"
∷ word (ὑ ∷ σ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.11.37"
∷ word (θ ∷ ∙λ ∷ ι ∷ β ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.11.37"
∷ word (κ ∷ α ∷ κ ∷ ο ∷ υ ∷ χ ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.11.37"
∷ word (ὧ ∷ ν ∷ []) "Heb.11.38"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.11.38"
∷ word (ἦ ∷ ν ∷ []) "Heb.11.38"
∷ word (ἄ ∷ ξ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.11.38"
∷ word (ὁ ∷ []) "Heb.11.38"
∷ word (κ ∷ ό ∷ σ ∷ μ ∷ ο ∷ ς ∷ []) "Heb.11.38"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.11.38"
∷ word (ἐ ∷ ρ ∷ η ∷ μ ∷ ί ∷ α ∷ ι ∷ ς ∷ []) "Heb.11.38"
∷ word (π ∷ ∙λ ∷ α ∷ ν ∷ ώ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.11.38"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.38"
∷ word (ὄ ∷ ρ ∷ ε ∷ σ ∷ ι ∷ []) "Heb.11.38"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.38"
∷ word (σ ∷ π ∷ η ∷ ∙λ ∷ α ∷ ί ∷ ο ∷ ι ∷ ς ∷ []) "Heb.11.38"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.38"
∷ word (τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.11.38"
∷ word (ὀ ∷ π ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.11.38"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.38"
∷ word (γ ∷ ῆ ∷ ς ∷ []) "Heb.11.38"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.11.39"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.11.39"
∷ word (μ ∷ α ∷ ρ ∷ τ ∷ υ ∷ ρ ∷ η ∷ θ ∷ έ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.11.39"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.11.39"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.11.39"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.11.39"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.11.39"
∷ word (ἐ ∷ κ ∷ ο ∷ μ ∷ ί ∷ σ ∷ α ∷ ν ∷ τ ∷ ο ∷ []) "Heb.11.39"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.11.39"
∷ word (ἐ ∷ π ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ α ∷ ν ∷ []) "Heb.11.39"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.11.40"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.11.40"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.11.40"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.11.40"
∷ word (κ ∷ ρ ∷ ε ∷ ῖ ∷ τ ∷ τ ∷ ό ∷ ν ∷ []) "Heb.11.40"
∷ word (τ ∷ ι ∷ []) "Heb.11.40"
∷ word (π ∷ ρ ∷ ο ∷ β ∷ ∙λ ∷ ε ∷ ψ ∷ α ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ []) "Heb.11.40"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.11.40"
∷ word (μ ∷ ὴ ∷ []) "Heb.11.40"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.11.40"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.11.40"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ω ∷ θ ∷ ῶ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.11.40"
∷ word (Τ ∷ ο ∷ ι ∷ γ ∷ α ∷ ρ ∷ ο ∷ ῦ ∷ ν ∷ []) "Heb.12.1"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.1"
∷ word (ἡ ∷ μ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.12.1"
∷ word (τ ∷ ο ∷ σ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.12.1"
∷ word (ἔ ∷ χ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.12.1"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ κ ∷ ε ∷ ί ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.12.1"
∷ word (ἡ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.12.1"
∷ word (ν ∷ έ ∷ φ ∷ ο ∷ ς ∷ []) "Heb.12.1"
∷ word (μ ∷ α ∷ ρ ∷ τ ∷ ύ ∷ ρ ∷ ω ∷ ν ∷ []) "Heb.12.1"
∷ word (ὄ ∷ γ ∷ κ ∷ ο ∷ ν ∷ []) "Heb.12.1"
∷ word (ἀ ∷ π ∷ ο ∷ θ ∷ έ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.12.1"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.12.1"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.1"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.12.1"
∷ word (ε ∷ ὐ ∷ π ∷ ε ∷ ρ ∷ ί ∷ σ ∷ τ ∷ α ∷ τ ∷ ο ∷ ν ∷ []) "Heb.12.1"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ν ∷ []) "Heb.12.1"
∷ word (δ ∷ ι ∷ []) "Heb.12.1"
∷ word (ὑ ∷ π ∷ ο ∷ μ ∷ ο ∷ ν ∷ ῆ ∷ ς ∷ []) "Heb.12.1"
∷ word (τ ∷ ρ ∷ έ ∷ χ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.12.1"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.1"
∷ word (π ∷ ρ ∷ ο ∷ κ ∷ ε ∷ ί ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.12.1"
∷ word (ἡ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.12.1"
∷ word (ἀ ∷ γ ∷ ῶ ∷ ν ∷ α ∷ []) "Heb.12.1"
∷ word (ἀ ∷ φ ∷ ο ∷ ρ ∷ ῶ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.12.2"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.12.2"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.2"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.12.2"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.12.2"
∷ word (ἀ ∷ ρ ∷ χ ∷ η ∷ γ ∷ ὸ ∷ ν ∷ []) "Heb.12.2"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.2"
∷ word (τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ω ∷ τ ∷ ὴ ∷ ν ∷ []) "Heb.12.2"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ν ∷ []) "Heb.12.2"
∷ word (ὃ ∷ ς ∷ []) "Heb.12.2"
∷ word (ἀ ∷ ν ∷ τ ∷ ὶ ∷ []) "Heb.12.2"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.12.2"
∷ word (π ∷ ρ ∷ ο ∷ κ ∷ ε ∷ ι ∷ μ ∷ έ ∷ ν ∷ η ∷ ς ∷ []) "Heb.12.2"
∷ word (α ∷ ὐ ∷ τ ∷ ῷ ∷ []) "Heb.12.2"
∷ word (χ ∷ α ∷ ρ ∷ ᾶ ∷ ς ∷ []) "Heb.12.2"
∷ word (ὑ ∷ π ∷ έ ∷ μ ∷ ε ∷ ι ∷ ν ∷ ε ∷ ν ∷ []) "Heb.12.2"
∷ word (σ ∷ τ ∷ α ∷ υ ∷ ρ ∷ ὸ ∷ ν ∷ []) "Heb.12.2"
∷ word (α ∷ ἰ ∷ σ ∷ χ ∷ ύ ∷ ν ∷ η ∷ ς ∷ []) "Heb.12.2"
∷ word (κ ∷ α ∷ τ ∷ α ∷ φ ∷ ρ ∷ ο ∷ ν ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.12.2"
∷ word (ἐ ∷ ν ∷ []) "Heb.12.2"
∷ word (δ ∷ ε ∷ ξ ∷ ι ∷ ᾷ ∷ []) "Heb.12.2"
∷ word (τ ∷ ε ∷ []) "Heb.12.2"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.12.2"
∷ word (θ ∷ ρ ∷ ό ∷ ν ∷ ο ∷ υ ∷ []) "Heb.12.2"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.12.2"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.12.2"
∷ word (κ ∷ ε ∷ κ ∷ ά ∷ θ ∷ ι ∷ κ ∷ ε ∷ ν ∷ []) "Heb.12.2"
∷ word (Ἀ ∷ ν ∷ α ∷ ∙λ ∷ ο ∷ γ ∷ ί ∷ σ ∷ α ∷ σ ∷ θ ∷ ε ∷ []) "Heb.12.3"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.3"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.3"
∷ word (τ ∷ ο ∷ ι ∷ α ∷ ύ ∷ τ ∷ η ∷ ν ∷ []) "Heb.12.3"
∷ word (ὑ ∷ π ∷ ο ∷ μ ∷ ε ∷ μ ∷ ε ∷ ν ∷ η ∷ κ ∷ ό ∷ τ ∷ α ∷ []) "Heb.12.3"
∷ word (ὑ ∷ π ∷ ὸ ∷ []) "Heb.12.3"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.12.3"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ω ∷ ∙λ ∷ ῶ ∷ ν ∷ []) "Heb.12.3"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.12.3"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.12.3"
∷ word (ἀ ∷ ν ∷ τ ∷ ι ∷ ∙λ ∷ ο ∷ γ ∷ ί ∷ α ∷ ν ∷ []) "Heb.12.3"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.12.3"
∷ word (μ ∷ ὴ ∷ []) "Heb.12.3"
∷ word (κ ∷ ά ∷ μ ∷ η ∷ τ ∷ ε ∷ []) "Heb.12.3"
∷ word (τ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.12.3"
∷ word (ψ ∷ υ ∷ χ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.12.3"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.12.3"
∷ word (ἐ ∷ κ ∷ ∙λ ∷ υ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.12.3"
∷ word (ο ∷ ὔ ∷ π ∷ ω ∷ []) "Heb.12.4"
∷ word (μ ∷ έ ∷ χ ∷ ρ ∷ ι ∷ ς ∷ []) "Heb.12.4"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.12.4"
∷ word (ἀ ∷ ν ∷ τ ∷ ι ∷ κ ∷ α ∷ τ ∷ έ ∷ σ ∷ τ ∷ η ∷ τ ∷ ε ∷ []) "Heb.12.4"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.12.4"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.12.4"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ν ∷ []) "Heb.12.4"
∷ word (ἀ ∷ ν ∷ τ ∷ α ∷ γ ∷ ω ∷ ν ∷ ι ∷ ζ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.12.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.5"
∷ word (ἐ ∷ κ ∷ ∙λ ∷ έ ∷ ∙λ ∷ η ∷ σ ∷ θ ∷ ε ∷ []) "Heb.12.5"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.12.5"
∷ word (π ∷ α ∷ ρ ∷ α ∷ κ ∷ ∙λ ∷ ή ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.12.5"
∷ word (ἥ ∷ τ ∷ ι ∷ ς ∷ []) "Heb.12.5"
∷ word (ὑ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.12.5"
∷ word (ὡ ∷ ς ∷ []) "Heb.12.5"
∷ word (υ ∷ ἱ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.12.5"
∷ word (δ ∷ ι ∷ α ∷ ∙λ ∷ έ ∷ γ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.12.5"
∷ word (Υ ∷ ἱ ∷ έ ∷ []) "Heb.12.5"
∷ word (μ ∷ ο ∷ υ ∷ []) "Heb.12.5"
∷ word (μ ∷ ὴ ∷ []) "Heb.12.5"
∷ word (ὀ ∷ ∙λ ∷ ι ∷ γ ∷ ώ ∷ ρ ∷ ε ∷ ι ∷ []) "Heb.12.5"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.12.5"
∷ word (κ ∷ υ ∷ ρ ∷ ί ∷ ο ∷ υ ∷ []) "Heb.12.5"
∷ word (μ ∷ η ∷ δ ∷ ὲ ∷ []) "Heb.12.5"
∷ word (ἐ ∷ κ ∷ ∙λ ∷ ύ ∷ ο ∷ υ ∷ []) "Heb.12.5"
∷ word (ὑ ∷ π ∷ []) "Heb.12.5"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.12.5"
∷ word (ἐ ∷ ∙λ ∷ ε ∷ γ ∷ χ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ς ∷ []) "Heb.12.5"
∷ word (ὃ ∷ ν ∷ []) "Heb.12.6"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.6"
∷ word (ἀ ∷ γ ∷ α ∷ π ∷ ᾷ ∷ []) "Heb.12.6"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.12.6"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ε ∷ ύ ∷ ε ∷ ι ∷ []) "Heb.12.6"
∷ word (μ ∷ α ∷ σ ∷ τ ∷ ι ∷ γ ∷ ο ∷ ῖ ∷ []) "Heb.12.6"
∷ word (δ ∷ ὲ ∷ []) "Heb.12.6"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ []) "Heb.12.6"
∷ word (υ ∷ ἱ ∷ ὸ ∷ ν ∷ []) "Heb.12.6"
∷ word (ὃ ∷ ν ∷ []) "Heb.12.6"
∷ word (π ∷ α ∷ ρ ∷ α ∷ δ ∷ έ ∷ χ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.12.6"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.12.7"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ε ∷ ί ∷ α ∷ ν ∷ []) "Heb.12.7"
∷ word (ὑ ∷ π ∷ ο ∷ μ ∷ έ ∷ ν ∷ ε ∷ τ ∷ ε ∷ []) "Heb.12.7"
∷ word (ὡ ∷ ς ∷ []) "Heb.12.7"
∷ word (υ ∷ ἱ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.12.7"
∷ word (ὑ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.12.7"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.12.7"
∷ word (ὁ ∷ []) "Heb.12.7"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.12.7"
∷ word (τ ∷ ί ∷ ς ∷ []) "Heb.12.7"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.7"
∷ word (υ ∷ ἱ ∷ ὸ ∷ ς ∷ []) "Heb.12.7"
∷ word (ὃ ∷ ν ∷ []) "Heb.12.7"
∷ word (ο ∷ ὐ ∷ []) "Heb.12.7"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ε ∷ ύ ∷ ε ∷ ι ∷ []) "Heb.12.7"
∷ word (π ∷ α ∷ τ ∷ ή ∷ ρ ∷ []) "Heb.12.7"
∷ word (ε ∷ ἰ ∷ []) "Heb.12.8"
∷ word (δ ∷ ὲ ∷ []) "Heb.12.8"
∷ word (χ ∷ ω ∷ ρ ∷ ί ∷ ς ∷ []) "Heb.12.8"
∷ word (ἐ ∷ σ ∷ τ ∷ ε ∷ []) "Heb.12.8"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.12.8"
∷ word (ἧ ∷ ς ∷ []) "Heb.12.8"
∷ word (μ ∷ έ ∷ τ ∷ ο ∷ χ ∷ ο ∷ ι ∷ []) "Heb.12.8"
∷ word (γ ∷ ε ∷ γ ∷ ό ∷ ν ∷ α ∷ σ ∷ ι ∷ []) "Heb.12.8"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.12.8"
∷ word (ἄ ∷ ρ ∷ α ∷ []) "Heb.12.8"
∷ word (ν ∷ ό ∷ θ ∷ ο ∷ ι ∷ []) "Heb.12.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.8"
∷ word (ο ∷ ὐ ∷ χ ∷ []) "Heb.12.8"
∷ word (υ ∷ ἱ ∷ ο ∷ ί ∷ []) "Heb.12.8"
∷ word (ἐ ∷ σ ∷ τ ∷ ε ∷ []) "Heb.12.8"
∷ word (ε ∷ ἶ ∷ τ ∷ α ∷ []) "Heb.12.9"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.12.9"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.12.9"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.12.9"
∷ word (σ ∷ α ∷ ρ ∷ κ ∷ ὸ ∷ ς ∷ []) "Heb.12.9"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.12.9"
∷ word (π ∷ α ∷ τ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.12.9"
∷ word (ε ∷ ἴ ∷ χ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.12.9"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ε ∷ υ ∷ τ ∷ ὰ ∷ ς ∷ []) "Heb.12.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.9"
∷ word (ἐ ∷ ν ∷ ε ∷ τ ∷ ρ ∷ ε ∷ π ∷ ό ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.12.9"
∷ word (ο ∷ ὐ ∷ []) "Heb.12.9"
∷ word (π ∷ ο ∷ ∙λ ∷ ὺ ∷ []) "Heb.12.9"
∷ word (μ ∷ ᾶ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ν ∷ []) "Heb.12.9"
∷ word (ὑ ∷ π ∷ ο ∷ τ ∷ α ∷ γ ∷ η ∷ σ ∷ ό ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.12.9"
∷ word (τ ∷ ῷ ∷ []) "Heb.12.9"
∷ word (π ∷ α ∷ τ ∷ ρ ∷ ὶ ∷ []) "Heb.12.9"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.12.9"
∷ word (π ∷ ν ∷ ε ∷ υ ∷ μ ∷ ά ∷ τ ∷ ω ∷ ν ∷ []) "Heb.12.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.9"
∷ word (ζ ∷ ή ∷ σ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.12.9"
∷ word (ο ∷ ἱ ∷ []) "Heb.12.10"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.12.10"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.10"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.12.10"
∷ word (ὀ ∷ ∙λ ∷ ί ∷ γ ∷ α ∷ ς ∷ []) "Heb.12.10"
∷ word (ἡ ∷ μ ∷ έ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.12.10"
∷ word (κ ∷ α ∷ τ ∷ ὰ ∷ []) "Heb.12.10"
∷ word (τ ∷ ὸ ∷ []) "Heb.12.10"
∷ word (δ ∷ ο ∷ κ ∷ ο ∷ ῦ ∷ ν ∷ []) "Heb.12.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.12.10"
∷ word (ἐ ∷ π ∷ α ∷ ί ∷ δ ∷ ε ∷ υ ∷ ο ∷ ν ∷ []) "Heb.12.10"
∷ word (ὁ ∷ []) "Heb.12.10"
∷ word (δ ∷ ὲ ∷ []) "Heb.12.10"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.12.10"
∷ word (τ ∷ ὸ ∷ []) "Heb.12.10"
∷ word (σ ∷ υ ∷ μ ∷ φ ∷ έ ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.12.10"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.12.10"
∷ word (τ ∷ ὸ ∷ []) "Heb.12.10"
∷ word (μ ∷ ε ∷ τ ∷ α ∷ ∙λ ∷ α ∷ β ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.12.10"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.12.10"
∷ word (ἁ ∷ γ ∷ ι ∷ ό ∷ τ ∷ η ∷ τ ∷ ο ∷ ς ∷ []) "Heb.12.10"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.12.10"
∷ word (π ∷ ᾶ ∷ σ ∷ α ∷ []) "Heb.12.11"
∷ word (δ ∷ ὲ ∷ []) "Heb.12.11"
∷ word (π ∷ α ∷ ι ∷ δ ∷ ε ∷ ί ∷ α ∷ []) "Heb.12.11"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.12.11"
∷ word (μ ∷ ὲ ∷ ν ∷ []) "Heb.12.11"
∷ word (τ ∷ ὸ ∷ []) "Heb.12.11"
∷ word (π ∷ α ∷ ρ ∷ ὸ ∷ ν ∷ []) "Heb.12.11"
∷ word (ο ∷ ὐ ∷ []) "Heb.12.11"
∷ word (δ ∷ ο ∷ κ ∷ ε ∷ ῖ ∷ []) "Heb.12.11"
∷ word (χ ∷ α ∷ ρ ∷ ᾶ ∷ ς ∷ []) "Heb.12.11"
∷ word (ε ∷ ἶ ∷ ν ∷ α ∷ ι ∷ []) "Heb.12.11"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.12.11"
∷ word (∙λ ∷ ύ ∷ π ∷ η ∷ ς ∷ []) "Heb.12.11"
∷ word (ὕ ∷ σ ∷ τ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.12.11"
∷ word (δ ∷ ὲ ∷ []) "Heb.12.11"
∷ word (κ ∷ α ∷ ρ ∷ π ∷ ὸ ∷ ν ∷ []) "Heb.12.11"
∷ word (ε ∷ ἰ ∷ ρ ∷ η ∷ ν ∷ ι ∷ κ ∷ ὸ ∷ ν ∷ []) "Heb.12.11"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.12.11"
∷ word (δ ∷ ι ∷ []) "Heb.12.11"
∷ word (α ∷ ὐ ∷ τ ∷ ῆ ∷ ς ∷ []) "Heb.12.11"
∷ word (γ ∷ ε ∷ γ ∷ υ ∷ μ ∷ ν ∷ α ∷ σ ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ ς ∷ []) "Heb.12.11"
∷ word (ἀ ∷ π ∷ ο ∷ δ ∷ ί ∷ δ ∷ ω ∷ σ ∷ ι ∷ ν ∷ []) "Heb.12.11"
∷ word (δ ∷ ι ∷ κ ∷ α ∷ ι ∷ ο ∷ σ ∷ ύ ∷ ν ∷ η ∷ ς ∷ []) "Heb.12.11"
∷ word (Δ ∷ ι ∷ ὸ ∷ []) "Heb.12.12"
∷ word (τ ∷ ὰ ∷ ς ∷ []) "Heb.12.12"
∷ word (π ∷ α ∷ ρ ∷ ε ∷ ι ∷ μ ∷ έ ∷ ν ∷ α ∷ ς ∷ []) "Heb.12.12"
∷ word (χ ∷ ε ∷ ῖ ∷ ρ ∷ α ∷ ς ∷ []) "Heb.12.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.12"
∷ word (τ ∷ ὰ ∷ []) "Heb.12.12"
∷ word (π ∷ α ∷ ρ ∷ α ∷ ∙λ ∷ ε ∷ ∙λ ∷ υ ∷ μ ∷ έ ∷ ν ∷ α ∷ []) "Heb.12.12"
∷ word (γ ∷ ό ∷ ν ∷ α ∷ τ ∷ α ∷ []) "Heb.12.12"
∷ word (ἀ ∷ ν ∷ ο ∷ ρ ∷ θ ∷ ώ ∷ σ ∷ α ∷ τ ∷ ε ∷ []) "Heb.12.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.13"
∷ word (τ ∷ ρ ∷ ο ∷ χ ∷ ι ∷ ὰ ∷ ς ∷ []) "Heb.12.13"
∷ word (ὀ ∷ ρ ∷ θ ∷ ὰ ∷ ς ∷ []) "Heb.12.13"
∷ word (π ∷ ο ∷ ι ∷ ε ∷ ῖ ∷ τ ∷ ε ∷ []) "Heb.12.13"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.12.13"
∷ word (π ∷ ο ∷ σ ∷ ὶ ∷ ν ∷ []) "Heb.12.13"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.12.13"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.12.13"
∷ word (μ ∷ ὴ ∷ []) "Heb.12.13"
∷ word (τ ∷ ὸ ∷ []) "Heb.12.13"
∷ word (χ ∷ ω ∷ ∙λ ∷ ὸ ∷ ν ∷ []) "Heb.12.13"
∷ word (ἐ ∷ κ ∷ τ ∷ ρ ∷ α ∷ π ∷ ῇ ∷ []) "Heb.12.13"
∷ word (ἰ ∷ α ∷ θ ∷ ῇ ∷ []) "Heb.12.13"
∷ word (δ ∷ ὲ ∷ []) "Heb.12.13"
∷ word (μ ∷ ᾶ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ν ∷ []) "Heb.12.13"
∷ word (Ε ∷ ἰ ∷ ρ ∷ ή ∷ ν ∷ η ∷ ν ∷ []) "Heb.12.14"
∷ word (δ ∷ ι ∷ ώ ∷ κ ∷ ε ∷ τ ∷ ε ∷ []) "Heb.12.14"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.12.14"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.12.14"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.14"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.14"
∷ word (ἁ ∷ γ ∷ ι ∷ α ∷ σ ∷ μ ∷ ό ∷ ν ∷ []) "Heb.12.14"
∷ word (ο ∷ ὗ ∷ []) "Heb.12.14"
∷ word (χ ∷ ω ∷ ρ ∷ ὶ ∷ ς ∷ []) "Heb.12.14"
∷ word (ο ∷ ὐ ∷ δ ∷ ε ∷ ὶ ∷ ς ∷ []) "Heb.12.14"
∷ word (ὄ ∷ ψ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.12.14"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.14"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.12.14"
∷ word (ἐ ∷ π ∷ ι ∷ σ ∷ κ ∷ ο ∷ π ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.12.15"
∷ word (μ ∷ ή ∷ []) "Heb.12.15"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.12.15"
∷ word (ὑ ∷ σ ∷ τ ∷ ε ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.12.15"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.12.15"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.12.15"
∷ word (χ ∷ ά ∷ ρ ∷ ι ∷ τ ∷ ο ∷ ς ∷ []) "Heb.12.15"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.12.15"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.12.15"
∷ word (μ ∷ ή ∷ []) "Heb.12.15"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.12.15"
∷ word (ῥ ∷ ί ∷ ζ ∷ α ∷ []) "Heb.12.15"
∷ word (π ∷ ι ∷ κ ∷ ρ ∷ ί ∷ α ∷ ς ∷ []) "Heb.12.15"
∷ word (ἄ ∷ ν ∷ ω ∷ []) "Heb.12.15"
∷ word (φ ∷ ύ ∷ ο ∷ υ ∷ σ ∷ α ∷ []) "Heb.12.15"
∷ word (ἐ ∷ ν ∷ ο ∷ χ ∷ ∙λ ∷ ῇ ∷ []) "Heb.12.15"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.15"
∷ word (δ ∷ ι ∷ []) "Heb.12.15"
∷ word (α ∷ ὐ ∷ τ ∷ ῆ ∷ ς ∷ []) "Heb.12.15"
∷ word (μ ∷ ι ∷ α ∷ ν ∷ θ ∷ ῶ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.12.15"
∷ word (π ∷ ο ∷ ∙λ ∷ ∙λ ∷ ο ∷ ί ∷ []) "Heb.12.15"
∷ word (μ ∷ ή ∷ []) "Heb.12.16"
∷ word (τ ∷ ι ∷ ς ∷ []) "Heb.12.16"
∷ word (π ∷ ό ∷ ρ ∷ ν ∷ ο ∷ ς ∷ []) "Heb.12.16"
∷ word (ἢ ∷ []) "Heb.12.16"
∷ word (β ∷ έ ∷ β ∷ η ∷ ∙λ ∷ ο ∷ ς ∷ []) "Heb.12.16"
∷ word (ὡ ∷ ς ∷ []) "Heb.12.16"
∷ word (Ἠ ∷ σ ∷ α ∷ ῦ ∷ []) "Heb.12.16"
∷ word (ὃ ∷ ς ∷ []) "Heb.12.16"
∷ word (ἀ ∷ ν ∷ τ ∷ ὶ ∷ []) "Heb.12.16"
∷ word (β ∷ ρ ∷ ώ ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.12.16"
∷ word (μ ∷ ι ∷ ᾶ ∷ ς ∷ []) "Heb.12.16"
∷ word (ἀ ∷ π ∷ έ ∷ δ ∷ ε ∷ τ ∷ ο ∷ []) "Heb.12.16"
∷ word (τ ∷ ὰ ∷ []) "Heb.12.16"
∷ word (π ∷ ρ ∷ ω ∷ τ ∷ ο ∷ τ ∷ ό ∷ κ ∷ ι ∷ α ∷ []) "Heb.12.16"
∷ word (ἑ ∷ α ∷ υ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.12.16"
∷ word (ἴ ∷ σ ∷ τ ∷ ε ∷ []) "Heb.12.17"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.17"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.12.17"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.17"
∷ word (μ ∷ ε ∷ τ ∷ έ ∷ π ∷ ε ∷ ι ∷ τ ∷ α ∷ []) "Heb.12.17"
∷ word (θ ∷ έ ∷ ∙λ ∷ ω ∷ ν ∷ []) "Heb.12.17"
∷ word (κ ∷ ∙λ ∷ η ∷ ρ ∷ ο ∷ ν ∷ ο ∷ μ ∷ ῆ ∷ σ ∷ α ∷ ι ∷ []) "Heb.12.17"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.12.17"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ ο ∷ γ ∷ ί ∷ α ∷ ν ∷ []) "Heb.12.17"
∷ word (ἀ ∷ π ∷ ε ∷ δ ∷ ο ∷ κ ∷ ι ∷ μ ∷ ά ∷ σ ∷ θ ∷ η ∷ []) "Heb.12.17"
∷ word (μ ∷ ε ∷ τ ∷ α ∷ ν ∷ ο ∷ ί ∷ α ∷ ς ∷ []) "Heb.12.17"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.17"
∷ word (τ ∷ ό ∷ π ∷ ο ∷ ν ∷ []) "Heb.12.17"
∷ word (ο ∷ ὐ ∷ χ ∷ []) "Heb.12.17"
∷ word (ε ∷ ὗ ∷ ρ ∷ ε ∷ ν ∷ []) "Heb.12.17"
∷ word (κ ∷ α ∷ ί ∷ π ∷ ε ∷ ρ ∷ []) "Heb.12.17"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.12.17"
∷ word (δ ∷ α ∷ κ ∷ ρ ∷ ύ ∷ ω ∷ ν ∷ []) "Heb.12.17"
∷ word (ἐ ∷ κ ∷ ζ ∷ η ∷ τ ∷ ή ∷ σ ∷ α ∷ ς ∷ []) "Heb.12.17"
∷ word (α ∷ ὐ ∷ τ ∷ ή ∷ ν ∷ []) "Heb.12.17"
∷ word (Ο ∷ ὐ ∷ []) "Heb.12.18"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.18"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ∙λ ∷ η ∷ ∙λ ∷ ύ ∷ θ ∷ α ∷ τ ∷ ε ∷ []) "Heb.12.18"
∷ word (ψ ∷ η ∷ ∙λ ∷ α ∷ φ ∷ ω ∷ μ ∷ έ ∷ ν ∷ ῳ ∷ []) "Heb.12.18"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.18"
∷ word (κ ∷ ε ∷ κ ∷ α ∷ υ ∷ μ ∷ έ ∷ ν ∷ ῳ ∷ []) "Heb.12.18"
∷ word (π ∷ υ ∷ ρ ∷ ὶ ∷ []) "Heb.12.18"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.18"
∷ word (γ ∷ ν ∷ ό ∷ φ ∷ ῳ ∷ []) "Heb.12.18"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.18"
∷ word (ζ ∷ ό ∷ φ ∷ ῳ ∷ []) "Heb.12.18"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.18"
∷ word (θ ∷ υ ∷ έ ∷ ∙λ ∷ ∙λ ∷ ῃ ∷ []) "Heb.12.18"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.19"
∷ word (σ ∷ ά ∷ ∙λ ∷ π ∷ ι ∷ γ ∷ γ ∷ ο ∷ ς ∷ []) "Heb.12.19"
∷ word (ἤ ∷ χ ∷ ῳ ∷ []) "Heb.12.19"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.19"
∷ word (φ ∷ ω ∷ ν ∷ ῇ ∷ []) "Heb.12.19"
∷ word (ῥ ∷ η ∷ μ ∷ ά ∷ τ ∷ ω ∷ ν ∷ []) "Heb.12.19"
∷ word (ἧ ∷ ς ∷ []) "Heb.12.19"
∷ word (ο ∷ ἱ ∷ []) "Heb.12.19"
∷ word (ἀ ∷ κ ∷ ο ∷ ύ ∷ σ ∷ α ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.12.19"
∷ word (π ∷ α ∷ ρ ∷ ῃ ∷ τ ∷ ή ∷ σ ∷ α ∷ ν ∷ τ ∷ ο ∷ []) "Heb.12.19"
∷ word (μ ∷ ὴ ∷ []) "Heb.12.19"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ τ ∷ ε ∷ θ ∷ ῆ ∷ ν ∷ α ∷ ι ∷ []) "Heb.12.19"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.12.19"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ν ∷ []) "Heb.12.19"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.12.20"
∷ word (ἔ ∷ φ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.12.20"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.20"
∷ word (τ ∷ ὸ ∷ []) "Heb.12.20"
∷ word (δ ∷ ι ∷ α ∷ σ ∷ τ ∷ ε ∷ ∙λ ∷ ∙λ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.12.20"
∷ word (Κ ∷ ἂ ∷ ν ∷ []) "Heb.12.20"
∷ word (θ ∷ η ∷ ρ ∷ ί ∷ ο ∷ ν ∷ []) "Heb.12.20"
∷ word (θ ∷ ί ∷ γ ∷ ῃ ∷ []) "Heb.12.20"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.12.20"
∷ word (ὄ ∷ ρ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.12.20"
∷ word (∙λ ∷ ι ∷ θ ∷ ο ∷ β ∷ ο ∷ ∙λ ∷ η ∷ θ ∷ ή ∷ σ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.12.20"
∷ word (κ ∷ α ∷ ί ∷ []) "Heb.12.21"
∷ word (ο ∷ ὕ ∷ τ ∷ ω ∷ []) "Heb.12.21"
∷ word (φ ∷ ο ∷ β ∷ ε ∷ ρ ∷ ὸ ∷ ν ∷ []) "Heb.12.21"
∷ word (ἦ ∷ ν ∷ []) "Heb.12.21"
∷ word (τ ∷ ὸ ∷ []) "Heb.12.21"
∷ word (φ ∷ α ∷ ν ∷ τ ∷ α ∷ ζ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ν ∷ []) "Heb.12.21"
∷ word (Μ ∷ ω ∷ ϋ ∷ σ ∷ ῆ ∷ ς ∷ []) "Heb.12.21"
∷ word (ε ∷ ἶ ∷ π ∷ ε ∷ ν ∷ []) "Heb.12.21"
∷ word (Ἔ ∷ κ ∷ φ ∷ ο ∷ β ∷ ό ∷ ς ∷ []) "Heb.12.21"
∷ word (ε ∷ ἰ ∷ μ ∷ ι ∷ []) "Heb.12.21"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.21"
∷ word (ἔ ∷ ν ∷ τ ∷ ρ ∷ ο ∷ μ ∷ ο ∷ ς ∷ []) "Heb.12.21"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.12.22"
∷ word (π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ∙λ ∷ η ∷ ∙λ ∷ ύ ∷ θ ∷ α ∷ τ ∷ ε ∷ []) "Heb.12.22"
∷ word (Σ ∷ ι ∷ ὼ ∷ ν ∷ []) "Heb.12.22"
∷ word (ὄ ∷ ρ ∷ ε ∷ ι ∷ []) "Heb.12.22"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.22"
∷ word (π ∷ ό ∷ ∙λ ∷ ε ∷ ι ∷ []) "Heb.12.22"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.12.22"
∷ word (ζ ∷ ῶ ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.12.22"
∷ word (Ἰ ∷ ε ∷ ρ ∷ ο ∷ υ ∷ σ ∷ α ∷ ∙λ ∷ ὴ ∷ μ ∷ []) "Heb.12.22"
∷ word (ἐ ∷ π ∷ ο ∷ υ ∷ ρ ∷ α ∷ ν ∷ ί ∷ ῳ ∷ []) "Heb.12.22"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.22"
∷ word (μ ∷ υ ∷ ρ ∷ ι ∷ ά ∷ σ ∷ ι ∷ ν ∷ []) "Heb.12.22"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ω ∷ ν ∷ []) "Heb.12.22"
∷ word (π ∷ α ∷ ν ∷ η ∷ γ ∷ ύ ∷ ρ ∷ ε ∷ ι ∷ []) "Heb.12.22"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.23"
∷ word (ἐ ∷ κ ∷ κ ∷ ∙λ ∷ η ∷ σ ∷ ί ∷ ᾳ ∷ []) "Heb.12.23"
∷ word (π ∷ ρ ∷ ω ∷ τ ∷ ο ∷ τ ∷ ό ∷ κ ∷ ω ∷ ν ∷ []) "Heb.12.23"
∷ word (ἀ ∷ π ∷ ο ∷ γ ∷ ε ∷ γ ∷ ρ ∷ α ∷ μ ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.12.23"
∷ word (ἐ ∷ ν ∷ []) "Heb.12.23"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.12.23"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.23"
∷ word (κ ∷ ρ ∷ ι ∷ τ ∷ ῇ ∷ []) "Heb.12.23"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.12.23"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.12.23"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.23"
∷ word (π ∷ ν ∷ ε ∷ ύ ∷ μ ∷ α ∷ σ ∷ ι ∷ []) "Heb.12.23"
∷ word (δ ∷ ι ∷ κ ∷ α ∷ ί ∷ ω ∷ ν ∷ []) "Heb.12.23"
∷ word (τ ∷ ε ∷ τ ∷ ε ∷ ∙λ ∷ ε ∷ ι ∷ ω ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.12.23"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.24"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ς ∷ []) "Heb.12.24"
∷ word (ν ∷ έ ∷ α ∷ ς ∷ []) "Heb.12.24"
∷ word (μ ∷ ε ∷ σ ∷ ί ∷ τ ∷ ῃ ∷ []) "Heb.12.24"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ []) "Heb.12.24"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.24"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.12.24"
∷ word (ῥ ∷ α ∷ ν ∷ τ ∷ ι ∷ σ ∷ μ ∷ ο ∷ ῦ ∷ []) "Heb.12.24"
∷ word (κ ∷ ρ ∷ ε ∷ ῖ ∷ τ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.12.24"
∷ word (∙λ ∷ α ∷ ∙λ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ι ∷ []) "Heb.12.24"
∷ word (π ∷ α ∷ ρ ∷ ὰ ∷ []) "Heb.12.24"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.24"
∷ word (Ἅ ∷ β ∷ ε ∷ ∙λ ∷ []) "Heb.12.24"
∷ word (Β ∷ ∙λ ∷ έ ∷ π ∷ ε ∷ τ ∷ ε ∷ []) "Heb.12.25"
∷ word (μ ∷ ὴ ∷ []) "Heb.12.25"
∷ word (π ∷ α ∷ ρ ∷ α ∷ ι ∷ τ ∷ ή ∷ σ ∷ η ∷ σ ∷ θ ∷ ε ∷ []) "Heb.12.25"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.25"
∷ word (∙λ ∷ α ∷ ∙λ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ α ∷ []) "Heb.12.25"
∷ word (ε ∷ ἰ ∷ []) "Heb.12.25"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.25"
∷ word (ἐ ∷ κ ∷ ε ∷ ῖ ∷ ν ∷ ο ∷ ι ∷ []) "Heb.12.25"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.12.25"
∷ word (ἐ ∷ ξ ∷ έ ∷ φ ∷ υ ∷ γ ∷ ο ∷ ν ∷ []) "Heb.12.25"
∷ word (ἐ ∷ π ∷ ὶ ∷ []) "Heb.12.25"
∷ word (γ ∷ ῆ ∷ ς ∷ []) "Heb.12.25"
∷ word (π ∷ α ∷ ρ ∷ α ∷ ι ∷ τ ∷ η ∷ σ ∷ ά ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.12.25"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.25"
∷ word (χ ∷ ρ ∷ η ∷ μ ∷ α ∷ τ ∷ ί ∷ ζ ∷ ο ∷ ν ∷ τ ∷ α ∷ []) "Heb.12.25"
∷ word (π ∷ ο ∷ ∙λ ∷ ὺ ∷ []) "Heb.12.25"
∷ word (μ ∷ ᾶ ∷ ∙λ ∷ ∙λ ∷ ο ∷ ν ∷ []) "Heb.12.25"
∷ word (ἡ ∷ μ ∷ ε ∷ ῖ ∷ ς ∷ []) "Heb.12.25"
∷ word (ο ∷ ἱ ∷ []) "Heb.12.25"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.25"
∷ word (ἀ ∷ π ∷ []) "Heb.12.25"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ῶ ∷ ν ∷ []) "Heb.12.25"
∷ word (ἀ ∷ π ∷ ο ∷ σ ∷ τ ∷ ρ ∷ ε ∷ φ ∷ ό ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.12.25"
∷ word (ο ∷ ὗ ∷ []) "Heb.12.26"
∷ word (ἡ ∷ []) "Heb.12.26"
∷ word (φ ∷ ω ∷ ν ∷ ὴ ∷ []) "Heb.12.26"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.12.26"
∷ word (γ ∷ ῆ ∷ ν ∷ []) "Heb.12.26"
∷ word (ἐ ∷ σ ∷ ά ∷ ∙λ ∷ ε ∷ υ ∷ σ ∷ ε ∷ ν ∷ []) "Heb.12.26"
∷ word (τ ∷ ό ∷ τ ∷ ε ∷ []) "Heb.12.26"
∷ word (ν ∷ ῦ ∷ ν ∷ []) "Heb.12.26"
∷ word (δ ∷ ὲ ∷ []) "Heb.12.26"
∷ word (ἐ ∷ π ∷ ή ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ τ ∷ α ∷ ι ∷ []) "Heb.12.26"
∷ word (∙λ ∷ έ ∷ γ ∷ ω ∷ ν ∷ []) "Heb.12.26"
∷ word (Ἔ ∷ τ ∷ ι ∷ []) "Heb.12.26"
∷ word (ἅ ∷ π ∷ α ∷ ξ ∷ []) "Heb.12.26"
∷ word (ἐ ∷ γ ∷ ὼ ∷ []) "Heb.12.26"
∷ word (σ ∷ ε ∷ ί ∷ σ ∷ ω ∷ []) "Heb.12.26"
∷ word (ο ∷ ὐ ∷ []) "Heb.12.26"
∷ word (μ ∷ ό ∷ ν ∷ ο ∷ ν ∷ []) "Heb.12.26"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.12.26"
∷ word (γ ∷ ῆ ∷ ν ∷ []) "Heb.12.26"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.12.26"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.26"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.12.26"
∷ word (ο ∷ ὐ ∷ ρ ∷ α ∷ ν ∷ ό ∷ ν ∷ []) "Heb.12.26"
∷ word (τ ∷ ὸ ∷ []) "Heb.12.27"
∷ word (δ ∷ ὲ ∷ []) "Heb.12.27"
∷ word (Ἔ ∷ τ ∷ ι ∷ []) "Heb.12.27"
∷ word (ἅ ∷ π ∷ α ∷ ξ ∷ []) "Heb.12.27"
∷ word (δ ∷ η ∷ ∙λ ∷ ο ∷ ῖ ∷ []) "Heb.12.27"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.12.27"
∷ word (σ ∷ α ∷ ∙λ ∷ ε ∷ υ ∷ ο ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.12.27"
∷ word (μ ∷ ε ∷ τ ∷ ά ∷ θ ∷ ε ∷ σ ∷ ι ∷ ν ∷ []) "Heb.12.27"
∷ word (ὡ ∷ ς ∷ []) "Heb.12.27"
∷ word (π ∷ ε ∷ π ∷ ο ∷ ι ∷ η ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.12.27"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.12.27"
∷ word (μ ∷ ε ∷ ί ∷ ν ∷ ῃ ∷ []) "Heb.12.27"
∷ word (τ ∷ ὰ ∷ []) "Heb.12.27"
∷ word (μ ∷ ὴ ∷ []) "Heb.12.27"
∷ word (σ ∷ α ∷ ∙λ ∷ ε ∷ υ ∷ ό ∷ μ ∷ ε ∷ ν ∷ α ∷ []) "Heb.12.27"
∷ word (δ ∷ ι ∷ ὸ ∷ []) "Heb.12.28"
∷ word (β ∷ α ∷ σ ∷ ι ∷ ∙λ ∷ ε ∷ ί ∷ α ∷ ν ∷ []) "Heb.12.28"
∷ word (ἀ ∷ σ ∷ ά ∷ ∙λ ∷ ε ∷ υ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.12.28"
∷ word (π ∷ α ∷ ρ ∷ α ∷ ∙λ ∷ α ∷ μ ∷ β ∷ ά ∷ ν ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.12.28"
∷ word (ἔ ∷ χ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.12.28"
∷ word (χ ∷ ά ∷ ρ ∷ ι ∷ ν ∷ []) "Heb.12.28"
∷ word (δ ∷ ι ∷ []) "Heb.12.28"
∷ word (ἧ ∷ ς ∷ []) "Heb.12.28"
∷ word (∙λ ∷ α ∷ τ ∷ ρ ∷ ε ∷ ύ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.12.28"
∷ word (ε ∷ ὐ ∷ α ∷ ρ ∷ έ ∷ σ ∷ τ ∷ ω ∷ ς ∷ []) "Heb.12.28"
∷ word (τ ∷ ῷ ∷ []) "Heb.12.28"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.12.28"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.12.28"
∷ word (ε ∷ ὐ ∷ ∙λ ∷ α ∷ β ∷ ε ∷ ί ∷ α ∷ ς ∷ []) "Heb.12.28"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.28"
∷ word (δ ∷ έ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.12.28"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.12.29"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.12.29"
∷ word (ὁ ∷ []) "Heb.12.29"
∷ word (θ ∷ ε ∷ ὸ ∷ ς ∷ []) "Heb.12.29"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.12.29"
∷ word (π ∷ ῦ ∷ ρ ∷ []) "Heb.12.29"
∷ word (κ ∷ α ∷ τ ∷ α ∷ ν ∷ α ∷ ∙λ ∷ ί ∷ σ ∷ κ ∷ ο ∷ ν ∷ []) "Heb.12.29"
∷ word (Ἡ ∷ []) "Heb.13.1"
∷ word (φ ∷ ι ∷ ∙λ ∷ α ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ί ∷ α ∷ []) "Heb.13.1"
∷ word (μ ∷ ε ∷ ν ∷ έ ∷ τ ∷ ω ∷ []) "Heb.13.1"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.13.2"
∷ word (φ ∷ ι ∷ ∙λ ∷ ο ∷ ξ ∷ ε ∷ ν ∷ ί ∷ α ∷ ς ∷ []) "Heb.13.2"
∷ word (μ ∷ ὴ ∷ []) "Heb.13.2"
∷ word (ἐ ∷ π ∷ ι ∷ ∙λ ∷ α ∷ ν ∷ θ ∷ ά ∷ ν ∷ ε ∷ σ ∷ θ ∷ ε ∷ []) "Heb.13.2"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.13.2"
∷ word (τ ∷ α ∷ ύ ∷ τ ∷ η ∷ ς ∷ []) "Heb.13.2"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.2"
∷ word (ἔ ∷ ∙λ ∷ α ∷ θ ∷ ό ∷ ν ∷ []) "Heb.13.2"
∷ word (τ ∷ ι ∷ ν ∷ ε ∷ ς ∷ []) "Heb.13.2"
∷ word (ξ ∷ ε ∷ ν ∷ ί ∷ σ ∷ α ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.13.2"
∷ word (ἀ ∷ γ ∷ γ ∷ έ ∷ ∙λ ∷ ο ∷ υ ∷ ς ∷ []) "Heb.13.2"
∷ word (μ ∷ ι ∷ μ ∷ ν ∷ ῄ ∷ σ ∷ κ ∷ ε ∷ σ ∷ θ ∷ ε ∷ []) "Heb.13.3"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.13.3"
∷ word (δ ∷ ε ∷ σ ∷ μ ∷ ί ∷ ω ∷ ν ∷ []) "Heb.13.3"
∷ word (ὡ ∷ ς ∷ []) "Heb.13.3"
∷ word (σ ∷ υ ∷ ν ∷ δ ∷ ε ∷ δ ∷ ε ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ []) "Heb.13.3"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.13.3"
∷ word (κ ∷ α ∷ κ ∷ ο ∷ υ ∷ χ ∷ ο ∷ υ ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.13.3"
∷ word (ὡ ∷ ς ∷ []) "Heb.13.3"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.3"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὶ ∷ []) "Heb.13.3"
∷ word (ὄ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.13.3"
∷ word (ἐ ∷ ν ∷ []) "Heb.13.3"
∷ word (σ ∷ ώ ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.13.3"
∷ word (τ ∷ ί ∷ μ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.13.4"
∷ word (ὁ ∷ []) "Heb.13.4"
∷ word (γ ∷ ά ∷ μ ∷ ο ∷ ς ∷ []) "Heb.13.4"
∷ word (ἐ ∷ ν ∷ []) "Heb.13.4"
∷ word (π ∷ ᾶ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.13.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.4"
∷ word (ἡ ∷ []) "Heb.13.4"
∷ word (κ ∷ ο ∷ ί ∷ τ ∷ η ∷ []) "Heb.13.4"
∷ word (ἀ ∷ μ ∷ ί ∷ α ∷ ν ∷ τ ∷ ο ∷ ς ∷ []) "Heb.13.4"
∷ word (π ∷ ό ∷ ρ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.13.4"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.4"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.4"
∷ word (μ ∷ ο ∷ ι ∷ χ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.13.4"
∷ word (κ ∷ ρ ∷ ι ∷ ν ∷ ε ∷ ῖ ∷ []) "Heb.13.4"
∷ word (ὁ ∷ []) "Heb.13.4"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.13.4"
∷ word (ἀ ∷ φ ∷ ι ∷ ∙λ ∷ ά ∷ ρ ∷ γ ∷ υ ∷ ρ ∷ ο ∷ ς ∷ []) "Heb.13.5"
∷ word (ὁ ∷ []) "Heb.13.5"
∷ word (τ ∷ ρ ∷ ό ∷ π ∷ ο ∷ ς ∷ []) "Heb.13.5"
∷ word (ἀ ∷ ρ ∷ κ ∷ ο ∷ ύ ∷ μ ∷ ε ∷ ν ∷ ο ∷ ι ∷ []) "Heb.13.5"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.13.5"
∷ word (π ∷ α ∷ ρ ∷ ο ∷ ῦ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.13.5"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.13.5"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.5"
∷ word (ε ∷ ἴ ∷ ρ ∷ η ∷ κ ∷ ε ∷ ν ∷ []) "Heb.13.5"
∷ word (Ο ∷ ὐ ∷ []) "Heb.13.5"
∷ word (μ ∷ ή ∷ []) "Heb.13.5"
∷ word (σ ∷ ε ∷ []) "Heb.13.5"
∷ word (ἀ ∷ ν ∷ ῶ ∷ []) "Heb.13.5"
∷ word (ο ∷ ὐ ∷ δ ∷ []) "Heb.13.5"
∷ word (ο ∷ ὐ ∷ []) "Heb.13.5"
∷ word (μ ∷ ή ∷ []) "Heb.13.5"
∷ word (σ ∷ ε ∷ []) "Heb.13.5"
∷ word (ἐ ∷ γ ∷ κ ∷ α ∷ τ ∷ α ∷ ∙λ ∷ ί ∷ π ∷ ω ∷ []) "Heb.13.5"
∷ word (ὥ ∷ σ ∷ τ ∷ ε ∷ []) "Heb.13.6"
∷ word (θ ∷ α ∷ ρ ∷ ρ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.13.6"
∷ word (ἡ ∷ μ ∷ ᾶ ∷ ς ∷ []) "Heb.13.6"
∷ word (∙λ ∷ έ ∷ γ ∷ ε ∷ ι ∷ ν ∷ []) "Heb.13.6"
∷ word (Κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ς ∷ []) "Heb.13.6"
∷ word (ἐ ∷ μ ∷ ο ∷ ὶ ∷ []) "Heb.13.6"
∷ word (β ∷ ο ∷ η ∷ θ ∷ ό ∷ ς ∷ []) "Heb.13.6"
∷ word (ο ∷ ὐ ∷ []) "Heb.13.6"
∷ word (φ ∷ ο ∷ β ∷ η ∷ θ ∷ ή ∷ σ ∷ ο ∷ μ ∷ α ∷ ι ∷ []) "Heb.13.6"
∷ word (τ ∷ ί ∷ []) "Heb.13.6"
∷ word (π ∷ ο ∷ ι ∷ ή ∷ σ ∷ ε ∷ ι ∷ []) "Heb.13.6"
∷ word (μ ∷ ο ∷ ι ∷ []) "Heb.13.6"
∷ word (ἄ ∷ ν ∷ θ ∷ ρ ∷ ω ∷ π ∷ ο ∷ ς ∷ []) "Heb.13.6"
∷ word (Μ ∷ ν ∷ η ∷ μ ∷ ο ∷ ν ∷ ε ∷ ύ ∷ ε ∷ τ ∷ ε ∷ []) "Heb.13.7"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.13.7"
∷ word (ἡ ∷ γ ∷ ο ∷ υ ∷ μ ∷ έ ∷ ν ∷ ω ∷ ν ∷ []) "Heb.13.7"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.13.7"
∷ word (ο ∷ ἵ ∷ τ ∷ ι ∷ ν ∷ ε ∷ ς ∷ []) "Heb.13.7"
∷ word (ἐ ∷ ∙λ ∷ ά ∷ ∙λ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.13.7"
∷ word (ὑ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.13.7"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.13.7"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ν ∷ []) "Heb.13.7"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.13.7"
∷ word (θ ∷ ε ∷ ο ∷ ῦ ∷ []) "Heb.13.7"
∷ word (ὧ ∷ ν ∷ []) "Heb.13.7"
∷ word (ἀ ∷ ν ∷ α ∷ θ ∷ ε ∷ ω ∷ ρ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.13.7"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.13.7"
∷ word (ἔ ∷ κ ∷ β ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.13.7"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.13.7"
∷ word (ἀ ∷ ν ∷ α ∷ σ ∷ τ ∷ ρ ∷ ο ∷ φ ∷ ῆ ∷ ς ∷ []) "Heb.13.7"
∷ word (μ ∷ ι ∷ μ ∷ ε ∷ ῖ ∷ σ ∷ θ ∷ ε ∷ []) "Heb.13.7"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.13.7"
∷ word (π ∷ ί ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.13.7"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ς ∷ []) "Heb.13.8"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.13.8"
∷ word (ἐ ∷ χ ∷ θ ∷ ὲ ∷ ς ∷ []) "Heb.13.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.8"
∷ word (σ ∷ ή ∷ μ ∷ ε ∷ ρ ∷ ο ∷ ν ∷ []) "Heb.13.8"
∷ word (ὁ ∷ []) "Heb.13.8"
∷ word (α ∷ ὐ ∷ τ ∷ ό ∷ ς ∷ []) "Heb.13.8"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.8"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.13.8"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.13.8"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ ς ∷ []) "Heb.13.8"
∷ word (δ ∷ ι ∷ δ ∷ α ∷ χ ∷ α ∷ ῖ ∷ ς ∷ []) "Heb.13.9"
∷ word (π ∷ ο ∷ ι ∷ κ ∷ ί ∷ ∙λ ∷ α ∷ ι ∷ ς ∷ []) "Heb.13.9"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.9"
∷ word (ξ ∷ έ ∷ ν ∷ α ∷ ι ∷ ς ∷ []) "Heb.13.9"
∷ word (μ ∷ ὴ ∷ []) "Heb.13.9"
∷ word (π ∷ α ∷ ρ ∷ α ∷ φ ∷ έ ∷ ρ ∷ ε ∷ σ ∷ θ ∷ ε ∷ []) "Heb.13.9"
∷ word (κ ∷ α ∷ ∙λ ∷ ὸ ∷ ν ∷ []) "Heb.13.9"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.9"
∷ word (χ ∷ ά ∷ ρ ∷ ι ∷ τ ∷ ι ∷ []) "Heb.13.9"
∷ word (β ∷ ε ∷ β ∷ α ∷ ι ∷ ο ∷ ῦ ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.13.9"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.13.9"
∷ word (κ ∷ α ∷ ρ ∷ δ ∷ ί ∷ α ∷ ν ∷ []) "Heb.13.9"
∷ word (ο ∷ ὐ ∷ []) "Heb.13.9"
∷ word (β ∷ ρ ∷ ώ ∷ μ ∷ α ∷ σ ∷ ι ∷ ν ∷ []) "Heb.13.9"
∷ word (ἐ ∷ ν ∷ []) "Heb.13.9"
∷ word (ο ∷ ἷ ∷ ς ∷ []) "Heb.13.9"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.13.9"
∷ word (ὠ ∷ φ ∷ ε ∷ ∙λ ∷ ή ∷ θ ∷ η ∷ σ ∷ α ∷ ν ∷ []) "Heb.13.9"
∷ word (ο ∷ ἱ ∷ []) "Heb.13.9"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ π ∷ α ∷ τ ∷ ο ∷ ῦ ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.13.9"
∷ word (ἔ ∷ χ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.13.10"
∷ word (θ ∷ υ ∷ σ ∷ ι ∷ α ∷ σ ∷ τ ∷ ή ∷ ρ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.13.10"
∷ word (ἐ ∷ ξ ∷ []) "Heb.13.10"
∷ word (ο ∷ ὗ ∷ []) "Heb.13.10"
∷ word (φ ∷ α ∷ γ ∷ ε ∷ ῖ ∷ ν ∷ []) "Heb.13.10"
∷ word (ο ∷ ὐ ∷ κ ∷ []) "Heb.13.10"
∷ word (ἔ ∷ χ ∷ ο ∷ υ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.13.10"
∷ word (ἐ ∷ ξ ∷ ο ∷ υ ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.13.10"
∷ word (ο ∷ ἱ ∷ []) "Heb.13.10"
∷ word (τ ∷ ῇ ∷ []) "Heb.13.10"
∷ word (σ ∷ κ ∷ η ∷ ν ∷ ῇ ∷ []) "Heb.13.10"
∷ word (∙λ ∷ α ∷ τ ∷ ρ ∷ ε ∷ ύ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.13.10"
∷ word (ὧ ∷ ν ∷ []) "Heb.13.11"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.11"
∷ word (ε ∷ ἰ ∷ σ ∷ φ ∷ έ ∷ ρ ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.13.11"
∷ word (ζ ∷ ῴ ∷ ω ∷ ν ∷ []) "Heb.13.11"
∷ word (τ ∷ ὸ ∷ []) "Heb.13.11"
∷ word (α ∷ ἷ ∷ μ ∷ α ∷ []) "Heb.13.11"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.13.11"
∷ word (ἁ ∷ μ ∷ α ∷ ρ ∷ τ ∷ ί ∷ α ∷ ς ∷ []) "Heb.13.11"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.13.11"
∷ word (τ ∷ ὰ ∷ []) "Heb.13.11"
∷ word (ἅ ∷ γ ∷ ι ∷ α ∷ []) "Heb.13.11"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.13.11"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.13.11"
∷ word (ἀ ∷ ρ ∷ χ ∷ ι ∷ ε ∷ ρ ∷ έ ∷ ω ∷ ς ∷ []) "Heb.13.11"
∷ word (τ ∷ ο ∷ ύ ∷ τ ∷ ω ∷ ν ∷ []) "Heb.13.11"
∷ word (τ ∷ ὰ ∷ []) "Heb.13.11"
∷ word (σ ∷ ώ ∷ μ ∷ α ∷ τ ∷ α ∷ []) "Heb.13.11"
∷ word (κ ∷ α ∷ τ ∷ α ∷ κ ∷ α ∷ ί ∷ ε ∷ τ ∷ α ∷ ι ∷ []) "Heb.13.11"
∷ word (ἔ ∷ ξ ∷ ω ∷ []) "Heb.13.11"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.13.11"
∷ word (π ∷ α ∷ ρ ∷ ε ∷ μ ∷ β ∷ ο ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.13.11"
∷ word (δ ∷ ι ∷ ὸ ∷ []) "Heb.13.12"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.12"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ς ∷ []) "Heb.13.12"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.13.12"
∷ word (ἁ ∷ γ ∷ ι ∷ ά ∷ σ ∷ ῃ ∷ []) "Heb.13.12"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.13.12"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.13.12"
∷ word (ἰ ∷ δ ∷ ί ∷ ο ∷ υ ∷ []) "Heb.13.12"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ο ∷ ς ∷ []) "Heb.13.12"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.13.12"
∷ word (∙λ ∷ α ∷ ό ∷ ν ∷ []) "Heb.13.12"
∷ word (ἔ ∷ ξ ∷ ω ∷ []) "Heb.13.12"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.13.12"
∷ word (π ∷ ύ ∷ ∙λ ∷ η ∷ ς ∷ []) "Heb.13.12"
∷ word (ἔ ∷ π ∷ α ∷ θ ∷ ε ∷ ν ∷ []) "Heb.13.12"
∷ word (τ ∷ ο ∷ ί ∷ ν ∷ υ ∷ ν ∷ []) "Heb.13.13"
∷ word (ἐ ∷ ξ ∷ ε ∷ ρ ∷ χ ∷ ώ ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.13.13"
∷ word (π ∷ ρ ∷ ὸ ∷ ς ∷ []) "Heb.13.13"
∷ word (α ∷ ὐ ∷ τ ∷ ὸ ∷ ν ∷ []) "Heb.13.13"
∷ word (ἔ ∷ ξ ∷ ω ∷ []) "Heb.13.13"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.13.13"
∷ word (π ∷ α ∷ ρ ∷ ε ∷ μ ∷ β ∷ ο ∷ ∙λ ∷ ῆ ∷ ς ∷ []) "Heb.13.13"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.13.13"
∷ word (ὀ ∷ ν ∷ ε ∷ ι ∷ δ ∷ ι ∷ σ ∷ μ ∷ ὸ ∷ ν ∷ []) "Heb.13.13"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.13.13"
∷ word (φ ∷ έ ∷ ρ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.13.13"
∷ word (ο ∷ ὐ ∷ []) "Heb.13.14"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.14"
∷ word (ἔ ∷ χ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.13.14"
∷ word (ὧ ∷ δ ∷ ε ∷ []) "Heb.13.14"
∷ word (μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ σ ∷ α ∷ ν ∷ []) "Heb.13.14"
∷ word (π ∷ ό ∷ ∙λ ∷ ι ∷ ν ∷ []) "Heb.13.14"
∷ word (ἀ ∷ ∙λ ∷ ∙λ ∷ ὰ ∷ []) "Heb.13.14"
∷ word (τ ∷ ὴ ∷ ν ∷ []) "Heb.13.14"
∷ word (μ ∷ έ ∷ ∙λ ∷ ∙λ ∷ ο ∷ υ ∷ σ ∷ α ∷ ν ∷ []) "Heb.13.14"
∷ word (ἐ ∷ π ∷ ι ∷ ζ ∷ η ∷ τ ∷ ο ∷ ῦ ∷ μ ∷ ε ∷ ν ∷ []) "Heb.13.14"
∷ word (δ ∷ ι ∷ []) "Heb.13.15"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.13.15"
∷ word (ο ∷ ὖ ∷ ν ∷ []) "Heb.13.15"
∷ word (ἀ ∷ ν ∷ α ∷ φ ∷ έ ∷ ρ ∷ ω ∷ μ ∷ ε ∷ ν ∷ []) "Heb.13.15"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ν ∷ []) "Heb.13.15"
∷ word (α ∷ ἰ ∷ ν ∷ έ ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.13.15"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.13.15"
∷ word (π ∷ α ∷ ν ∷ τ ∷ ὸ ∷ ς ∷ []) "Heb.13.15"
∷ word (τ ∷ ῷ ∷ []) "Heb.13.15"
∷ word (θ ∷ ε ∷ ῷ ∷ []) "Heb.13.15"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ []) "Heb.13.15"
∷ word (ἔ ∷ σ ∷ τ ∷ ι ∷ ν ∷ []) "Heb.13.15"
∷ word (κ ∷ α ∷ ρ ∷ π ∷ ὸ ∷ ν ∷ []) "Heb.13.15"
∷ word (χ ∷ ε ∷ ι ∷ ∙λ ∷ έ ∷ ω ∷ ν ∷ []) "Heb.13.15"
∷ word (ὁ ∷ μ ∷ ο ∷ ∙λ ∷ ο ∷ γ ∷ ο ∷ ύ ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.13.15"
∷ word (τ ∷ ῷ ∷ []) "Heb.13.15"
∷ word (ὀ ∷ ν ∷ ό ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.13.15"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.13.15"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.13.16"
∷ word (δ ∷ ὲ ∷ []) "Heb.13.16"
∷ word (ε ∷ ὐ ∷ π ∷ ο ∷ ι ∷ ΐ ∷ α ∷ ς ∷ []) "Heb.13.16"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.16"
∷ word (κ ∷ ο ∷ ι ∷ ν ∷ ω ∷ ν ∷ ί ∷ α ∷ ς ∷ []) "Heb.13.16"
∷ word (μ ∷ ὴ ∷ []) "Heb.13.16"
∷ word (ἐ ∷ π ∷ ι ∷ ∙λ ∷ α ∷ ν ∷ θ ∷ ά ∷ ν ∷ ε ∷ σ ∷ θ ∷ ε ∷ []) "Heb.13.16"
∷ word (τ ∷ ο ∷ ι ∷ α ∷ ύ ∷ τ ∷ α ∷ ι ∷ ς ∷ []) "Heb.13.16"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.16"
∷ word (θ ∷ υ ∷ σ ∷ ί ∷ α ∷ ι ∷ ς ∷ []) "Heb.13.16"
∷ word (ε ∷ ὐ ∷ α ∷ ρ ∷ ε ∷ σ ∷ τ ∷ ε ∷ ῖ ∷ τ ∷ α ∷ ι ∷ []) "Heb.13.16"
∷ word (ὁ ∷ []) "Heb.13.16"
∷ word (θ ∷ ε ∷ ό ∷ ς ∷ []) "Heb.13.16"
∷ word (Π ∷ ε ∷ ί ∷ θ ∷ ε ∷ σ ∷ θ ∷ ε ∷ []) "Heb.13.17"
∷ word (τ ∷ ο ∷ ῖ ∷ ς ∷ []) "Heb.13.17"
∷ word (ἡ ∷ γ ∷ ο ∷ υ ∷ μ ∷ έ ∷ ν ∷ ο ∷ ι ∷ ς ∷ []) "Heb.13.17"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.13.17"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.17"
∷ word (ὑ ∷ π ∷ ε ∷ ί ∷ κ ∷ ε ∷ τ ∷ ε ∷ []) "Heb.13.17"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ὶ ∷ []) "Heb.13.17"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.17"
∷ word (ἀ ∷ γ ∷ ρ ∷ υ ∷ π ∷ ν ∷ ο ∷ ῦ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.13.17"
∷ word (ὑ ∷ π ∷ ὲ ∷ ρ ∷ []) "Heb.13.17"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.13.17"
∷ word (ψ ∷ υ ∷ χ ∷ ῶ ∷ ν ∷ []) "Heb.13.17"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.13.17"
∷ word (ὡ ∷ ς ∷ []) "Heb.13.17"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ ν ∷ []) "Heb.13.17"
∷ word (ἀ ∷ π ∷ ο ∷ δ ∷ ώ ∷ σ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.13.17"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.13.17"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.13.17"
∷ word (χ ∷ α ∷ ρ ∷ ᾶ ∷ ς ∷ []) "Heb.13.17"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.13.17"
∷ word (π ∷ ο ∷ ι ∷ ῶ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.13.17"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.17"
∷ word (μ ∷ ὴ ∷ []) "Heb.13.17"
∷ word (σ ∷ τ ∷ ε ∷ ν ∷ ά ∷ ζ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.13.17"
∷ word (ἀ ∷ ∙λ ∷ υ ∷ σ ∷ ι ∷ τ ∷ ε ∷ ∙λ ∷ ὲ ∷ ς ∷ []) "Heb.13.17"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.17"
∷ word (ὑ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.13.17"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.13.17"
∷ word (Π ∷ ρ ∷ ο ∷ σ ∷ ε ∷ ύ ∷ χ ∷ ε ∷ σ ∷ θ ∷ ε ∷ []) "Heb.13.18"
∷ word (π ∷ ε ∷ ρ ∷ ὶ ∷ []) "Heb.13.18"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.13.18"
∷ word (π ∷ ε ∷ ι ∷ θ ∷ ό ∷ μ ∷ ε ∷ θ ∷ α ∷ []) "Heb.13.18"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.18"
∷ word (ὅ ∷ τ ∷ ι ∷ []) "Heb.13.18"
∷ word (κ ∷ α ∷ ∙λ ∷ ὴ ∷ ν ∷ []) "Heb.13.18"
∷ word (σ ∷ υ ∷ ν ∷ ε ∷ ί ∷ δ ∷ η ∷ σ ∷ ι ∷ ν ∷ []) "Heb.13.18"
∷ word (ἔ ∷ χ ∷ ο ∷ μ ∷ ε ∷ ν ∷ []) "Heb.13.18"
∷ word (ἐ ∷ ν ∷ []) "Heb.13.18"
∷ word (π ∷ ᾶ ∷ σ ∷ ι ∷ ν ∷ []) "Heb.13.18"
∷ word (κ ∷ α ∷ ∙λ ∷ ῶ ∷ ς ∷ []) "Heb.13.18"
∷ word (θ ∷ έ ∷ ∙λ ∷ ο ∷ ν ∷ τ ∷ ε ∷ ς ∷ []) "Heb.13.18"
∷ word (ἀ ∷ ν ∷ α ∷ σ ∷ τ ∷ ρ ∷ έ ∷ φ ∷ ε ∷ σ ∷ θ ∷ α ∷ ι ∷ []) "Heb.13.18"
∷ word (π ∷ ε ∷ ρ ∷ ι ∷ σ ∷ σ ∷ ο ∷ τ ∷ έ ∷ ρ ∷ ω ∷ ς ∷ []) "Heb.13.19"
∷ word (δ ∷ ὲ ∷ []) "Heb.13.19"
∷ word (π ∷ α ∷ ρ ∷ α ∷ κ ∷ α ∷ ∙λ ∷ ῶ ∷ []) "Heb.13.19"
∷ word (τ ∷ ο ∷ ῦ ∷ τ ∷ ο ∷ []) "Heb.13.19"
∷ word (π ∷ ο ∷ ι ∷ ῆ ∷ σ ∷ α ∷ ι ∷ []) "Heb.13.19"
∷ word (ἵ ∷ ν ∷ α ∷ []) "Heb.13.19"
∷ word (τ ∷ ά ∷ χ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.13.19"
∷ word (ἀ ∷ π ∷ ο ∷ κ ∷ α ∷ τ ∷ α ∷ σ ∷ τ ∷ α ∷ θ ∷ ῶ ∷ []) "Heb.13.19"
∷ word (ὑ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.13.19"
∷ word (Ὁ ∷ []) "Heb.13.20"
∷ word (δ ∷ ὲ ∷ []) "Heb.13.20"
∷ word (θ ∷ ε ∷ ὸ ∷ ς ∷ []) "Heb.13.20"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.13.20"
∷ word (ε ∷ ἰ ∷ ρ ∷ ή ∷ ν ∷ η ∷ ς ∷ []) "Heb.13.20"
∷ word (ὁ ∷ []) "Heb.13.20"
∷ word (ἀ ∷ ν ∷ α ∷ γ ∷ α ∷ γ ∷ ὼ ∷ ν ∷ []) "Heb.13.20"
∷ word (ἐ ∷ κ ∷ []) "Heb.13.20"
∷ word (ν ∷ ε ∷ κ ∷ ρ ∷ ῶ ∷ ν ∷ []) "Heb.13.20"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.13.20"
∷ word (π ∷ ο ∷ ι ∷ μ ∷ έ ∷ ν ∷ α ∷ []) "Heb.13.20"
∷ word (τ ∷ ῶ ∷ ν ∷ []) "Heb.13.20"
∷ word (π ∷ ρ ∷ ο ∷ β ∷ ά ∷ τ ∷ ω ∷ ν ∷ []) "Heb.13.20"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.13.20"
∷ word (μ ∷ έ ∷ γ ∷ α ∷ ν ∷ []) "Heb.13.20"
∷ word (ἐ ∷ ν ∷ []) "Heb.13.20"
∷ word (α ∷ ἵ ∷ μ ∷ α ∷ τ ∷ ι ∷ []) "Heb.13.20"
∷ word (δ ∷ ι ∷ α ∷ θ ∷ ή ∷ κ ∷ η ∷ ς ∷ []) "Heb.13.20"
∷ word (α ∷ ἰ ∷ ω ∷ ν ∷ ί ∷ ο ∷ υ ∷ []) "Heb.13.20"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.13.20"
∷ word (κ ∷ ύ ∷ ρ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.13.20"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.13.20"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ ν ∷ []) "Heb.13.20"
∷ word (κ ∷ α ∷ τ ∷ α ∷ ρ ∷ τ ∷ ί ∷ σ ∷ α ∷ ι ∷ []) "Heb.13.21"
∷ word (ὑ ∷ μ ∷ ᾶ ∷ ς ∷ []) "Heb.13.21"
∷ word (ἐ ∷ ν ∷ []) "Heb.13.21"
∷ word (π ∷ α ∷ ν ∷ τ ∷ ὶ ∷ []) "Heb.13.21"
∷ word (ἀ ∷ γ ∷ α ∷ θ ∷ ῷ ∷ []) "Heb.13.21"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.13.21"
∷ word (τ ∷ ὸ ∷ []) "Heb.13.21"
∷ word (π ∷ ο ∷ ι ∷ ῆ ∷ σ ∷ α ∷ ι ∷ []) "Heb.13.21"
∷ word (τ ∷ ὸ ∷ []) "Heb.13.21"
∷ word (θ ∷ έ ∷ ∙λ ∷ η ∷ μ ∷ α ∷ []) "Heb.13.21"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.13.21"
∷ word (π ∷ ο ∷ ι ∷ ῶ ∷ ν ∷ []) "Heb.13.21"
∷ word (ἐ ∷ ν ∷ []) "Heb.13.21"
∷ word (ἡ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.13.21"
∷ word (τ ∷ ὸ ∷ []) "Heb.13.21"
∷ word (ε ∷ ὐ ∷ ά ∷ ρ ∷ ε ∷ σ ∷ τ ∷ ο ∷ ν ∷ []) "Heb.13.21"
∷ word (ἐ ∷ ν ∷ ώ ∷ π ∷ ι ∷ ο ∷ ν ∷ []) "Heb.13.21"
∷ word (α ∷ ὐ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.13.21"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.13.21"
∷ word (Ἰ ∷ η ∷ σ ∷ ο ∷ ῦ ∷ []) "Heb.13.21"
∷ word (Χ ∷ ρ ∷ ι ∷ σ ∷ τ ∷ ο ∷ ῦ ∷ []) "Heb.13.21"
∷ word (ᾧ ∷ []) "Heb.13.21"
∷ word (ἡ ∷ []) "Heb.13.21"
∷ word (δ ∷ ό ∷ ξ ∷ α ∷ []) "Heb.13.21"
∷ word (ε ∷ ἰ ∷ ς ∷ []) "Heb.13.21"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.13.21"
∷ word (α ∷ ἰ ∷ ῶ ∷ ν ∷ α ∷ ς ∷ []) "Heb.13.21"
∷ word (ἀ ∷ μ ∷ ή ∷ ν ∷ []) "Heb.13.21"
∷ word (Π ∷ α ∷ ρ ∷ α ∷ κ ∷ α ∷ ∙λ ∷ ῶ ∷ []) "Heb.13.22"
∷ word (δ ∷ ὲ ∷ []) "Heb.13.22"
∷ word (ὑ ∷ μ ∷ ᾶ ∷ ς ∷ []) "Heb.13.22"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ο ∷ ί ∷ []) "Heb.13.22"
∷ word (ἀ ∷ ν ∷ έ ∷ χ ∷ ε ∷ σ ∷ θ ∷ ε ∷ []) "Heb.13.22"
∷ word (τ ∷ ο ∷ ῦ ∷ []) "Heb.13.22"
∷ word (∙λ ∷ ό ∷ γ ∷ ο ∷ υ ∷ []) "Heb.13.22"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.13.22"
∷ word (π ∷ α ∷ ρ ∷ α ∷ κ ∷ ∙λ ∷ ή ∷ σ ∷ ε ∷ ω ∷ ς ∷ []) "Heb.13.22"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.22"
∷ word (γ ∷ ὰ ∷ ρ ∷ []) "Heb.13.22"
∷ word (δ ∷ ι ∷ ὰ ∷ []) "Heb.13.22"
∷ word (β ∷ ρ ∷ α ∷ χ ∷ έ ∷ ω ∷ ν ∷ []) "Heb.13.22"
∷ word (ἐ ∷ π ∷ έ ∷ σ ∷ τ ∷ ε ∷ ι ∷ ∙λ ∷ α ∷ []) "Heb.13.22"
∷ word (ὑ ∷ μ ∷ ῖ ∷ ν ∷ []) "Heb.13.22"
∷ word (γ ∷ ι ∷ ν ∷ ώ ∷ σ ∷ κ ∷ ε ∷ τ ∷ ε ∷ []) "Heb.13.23"
∷ word (τ ∷ ὸ ∷ ν ∷ []) "Heb.13.23"
∷ word (ἀ ∷ δ ∷ ε ∷ ∙λ ∷ φ ∷ ὸ ∷ ν ∷ []) "Heb.13.23"
∷ word (ἡ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.13.23"
∷ word (Τ ∷ ι ∷ μ ∷ ό ∷ θ ∷ ε ∷ ο ∷ ν ∷ []) "Heb.13.23"
∷ word (ἀ ∷ π ∷ ο ∷ ∙λ ∷ ε ∷ ∙λ ∷ υ ∷ μ ∷ έ ∷ ν ∷ ο ∷ ν ∷ []) "Heb.13.23"
∷ word (μ ∷ ε ∷ θ ∷ []) "Heb.13.23"
∷ word (ο ∷ ὗ ∷ []) "Heb.13.23"
∷ word (ἐ ∷ ὰ ∷ ν ∷ []) "Heb.13.23"
∷ word (τ ∷ ά ∷ χ ∷ ι ∷ ο ∷ ν ∷ []) "Heb.13.23"
∷ word (ἔ ∷ ρ ∷ χ ∷ η ∷ τ ∷ α ∷ ι ∷ []) "Heb.13.23"
∷ word (ὄ ∷ ψ ∷ ο ∷ μ ∷ α ∷ ι ∷ []) "Heb.13.23"
∷ word (ὑ ∷ μ ∷ ᾶ ∷ ς ∷ []) "Heb.13.23"
∷ word (ἀ ∷ σ ∷ π ∷ ά ∷ σ ∷ α ∷ σ ∷ θ ∷ ε ∷ []) "Heb.13.24"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.13.24"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.13.24"
∷ word (ἡ ∷ γ ∷ ο ∷ υ ∷ μ ∷ έ ∷ ν ∷ ο ∷ υ ∷ ς ∷ []) "Heb.13.24"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.13.24"
∷ word (κ ∷ α ∷ ὶ ∷ []) "Heb.13.24"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ α ∷ ς ∷ []) "Heb.13.24"
∷ word (τ ∷ ο ∷ ὺ ∷ ς ∷ []) "Heb.13.24"
∷ word (ἁ ∷ γ ∷ ί ∷ ο ∷ υ ∷ ς ∷ []) "Heb.13.24"
∷ word (ἀ ∷ σ ∷ π ∷ ά ∷ ζ ∷ ο ∷ ν ∷ τ ∷ α ∷ ι ∷ []) "Heb.13.24"
∷ word (ὑ ∷ μ ∷ ᾶ ∷ ς ∷ []) "Heb.13.24"
∷ word (ο ∷ ἱ ∷ []) "Heb.13.24"
∷ word (ἀ ∷ π ∷ ὸ ∷ []) "Heb.13.24"
∷ word (τ ∷ ῆ ∷ ς ∷ []) "Heb.13.24"
∷ word (Ἰ ∷ τ ∷ α ∷ ∙λ ∷ ί ∷ α ∷ ς ∷ []) "Heb.13.24"
∷ word (ἡ ∷ []) "Heb.13.25"
∷ word (χ ∷ ά ∷ ρ ∷ ι ∷ ς ∷ []) "Heb.13.25"
∷ word (μ ∷ ε ∷ τ ∷ ὰ ∷ []) "Heb.13.25"
∷ word (π ∷ ά ∷ ν ∷ τ ∷ ω ∷ ν ∷ []) "Heb.13.25"
∷ word (ὑ ∷ μ ∷ ῶ ∷ ν ∷ []) "Heb.13.25"
∷ []
|
{
"alphanum_fraction": 0.3305637491,
"avg_line_length": 46.404569349,
"ext": "agda",
"hexsha": "5a6608e2e9d2c1dda535e4bedf0318484333ca3b",
"lang": "Agda",
"max_forks_count": 5,
"max_forks_repo_forks_event_max_datetime": "2017-06-11T11:25:09.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-02-27T22:34:13.000Z",
"max_forks_repo_head_hexsha": "915c46c27c7f8aad5907474d8484f2685a4cd6a7",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "scott-fleischman/GreekGrammar",
"max_forks_repo_path": "agda/Text/Greek/SBLGNT/Heb.agda",
"max_issues_count": 13,
"max_issues_repo_head_hexsha": "915c46c27c7f8aad5907474d8484f2685a4cd6a7",
"max_issues_repo_issues_event_max_datetime": "2020-09-07T11:58:38.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-05-28T20:04:08.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "scott-fleischman/GreekGrammar",
"max_issues_repo_path": "agda/Text/Greek/SBLGNT/Heb.agda",
"max_line_length": 95,
"max_stars_count": 44,
"max_stars_repo_head_hexsha": "915c46c27c7f8aad5907474d8484f2685a4cd6a7",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "scott-fleischman/GreekGrammar",
"max_stars_repo_path": "agda/Text/Greek/SBLGNT/Heb.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-06T15:41:57.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-05-29T14:48:51.000Z",
"num_tokens": 166434,
"size": 229517
}
|
------------------------------------------------------------------------------
-- Totality of predecessor function
------------------------------------------------------------------------------
{-# OPTIONS --allow-unsolved-metas #-}
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module FOT.FOTC.Data.Nat.PredTotality where
open import FOTC.Base
data N : D → Set where
nzero : N zero
nsucc : ∀ {n} → N n → N (succ₁ n)
-- Induction principle generated by Coq 8.4pl4 when we define the data
-- type N in Prop.
N-ind₁ : (A : D → Set) →
A zero →
(∀ {n} → N n → A n → A (succ₁ n)) →
∀ {n} → N n → A n
N-ind₁ A A0 h nzero = A0
N-ind₁ A A0 h (nsucc Nn) = h Nn (N-ind₁ A A0 h Nn)
-- The induction principle removing the hypothesis N n from the
-- inductive step.
N-ind₂ : (A : D → Set) →
A zero →
(∀ {n} → A n → A (succ₁ n)) →
∀ {n} → N n → A n
N-ind₂ A A0 h nzero = A0
N-ind₂ A A0 h (nsucc Nn) = h (N-ind₂ A A0 h Nn)
-- Proof by pattern matching.
pred-N : ∀ {n} → N n → N (pred₁ n)
pred-N nzero = subst N (sym pred-0) nzero
pred-N (nsucc {n} Nn) = subst N (sym (pred-S n)) Nn
-- Proof using N-ind₁.
pred-N₁ : ∀ {n} → N n → N (pred₁ n)
pred-N₁ = N-ind₁ A A0 is
where
A : D → Set
A i = N (pred₁ i)
A0 : A zero
A0 = subst N (sym pred-0) nzero
is : ∀ {i} → N i → A i → A (succ₁ i)
is {i} Ni Ai = subst N (sym (pred-S i)) Ni
-- Proof using N-ind₂.
-- pred-N₂ : ∀ {n} → N n → N (pred₁ n)
-- pred-N₂ = N-ind₂ A A0 is
-- where
-- A : D → Set
-- A i = N (pred₁ i)
-- A0 : A zero
-- A0 = subst N (sym pred-0) nzero
-- is : ∀ {i} → A i → A (succ₁ i)
-- is {i} Ai = {!!}
|
{
"alphanum_fraction": 0.4724847137,
"avg_line_length": 26.8507462687,
"ext": "agda",
"hexsha": "b0b87d768ef23605cd081dd3b537f768dcecfd9d",
"lang": "Agda",
"max_forks_count": 3,
"max_forks_repo_forks_event_max_datetime": "2018-03-14T08:50:00.000Z",
"max_forks_repo_forks_event_min_datetime": "2016-09-19T14:18:30.000Z",
"max_forks_repo_head_hexsha": "2fc9f2b81052a2e0822669f02036c5750371b72d",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "asr/fotc",
"max_forks_repo_path": "notes/FOT/FOTC/Data/Nat/PredTotality.agda",
"max_issues_count": 2,
"max_issues_repo_head_hexsha": "2fc9f2b81052a2e0822669f02036c5750371b72d",
"max_issues_repo_issues_event_max_datetime": "2017-01-01T14:34:26.000Z",
"max_issues_repo_issues_event_min_datetime": "2016-10-12T17:28:16.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "asr/fotc",
"max_issues_repo_path": "notes/FOT/FOTC/Data/Nat/PredTotality.agda",
"max_line_length": 78,
"max_stars_count": 11,
"max_stars_repo_head_hexsha": "2fc9f2b81052a2e0822669f02036c5750371b72d",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "asr/fotc",
"max_stars_repo_path": "notes/FOT/FOTC/Data/Nat/PredTotality.agda",
"max_stars_repo_stars_event_max_datetime": "2021-09-12T16:09:54.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-09-03T20:53:42.000Z",
"num_tokens": 629,
"size": 1799
}
|
postulate
F : Set → Set
_ : {@0 A : Set} → F λ { → A }
|
{
"alphanum_fraction": 0.4237288136,
"avg_line_length": 14.75,
"ext": "agda",
"hexsha": "a3031ee04816d6761d14a2b8cd2562337bf5eaf4",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "cc026a6a97a3e517bb94bafa9d49233b067c7559",
"max_forks_repo_licenses": [
"BSD-2-Clause"
],
"max_forks_repo_name": "cagix/agda",
"max_forks_repo_path": "test/Fail/Issue5341.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "cc026a6a97a3e517bb94bafa9d49233b067c7559",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"BSD-2-Clause"
],
"max_issues_repo_name": "cagix/agda",
"max_issues_repo_path": "test/Fail/Issue5341.agda",
"max_line_length": 32,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "cc026a6a97a3e517bb94bafa9d49233b067c7559",
"max_stars_repo_licenses": [
"BSD-2-Clause"
],
"max_stars_repo_name": "cagix/agda",
"max_stars_repo_path": "test/Fail/Issue5341.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 26,
"size": 59
}
|
-- Andreas 2019-11-06, issue #4172, examples by nad.
-- Single constructor matches for non-indexed types should be ok
-- even when argument is erased, as long as pattern variables
-- are only used in erased context on the rhs.
-- https://github.com/agda/agda/issues/4172#issue-517690102
record Erased (A : Set) : Set where
constructor [_]
field
@0 erased : A
open Erased
data W (A : Set) (B : A → Set) : Set where
sup : (x : A) → (B x → W A B) → W A B
lemma :
{A : Set} {B : A → Set} →
Erased (W A B) → W (Erased A) (λ x → Erased (B (erased x)))
lemma [ sup x f ] = sup [ x ] λ ([ y ]) → lemma [ f y ]
-- https://github.com/agda/agda/issues/4172#issuecomment-549768270
data ⊥ : Set where
data E : Set where
c : E → E
magic : @0 E → ⊥
magic (c e) = magic e
|
{
"alphanum_fraction": 0.6163682864,
"avg_line_length": 23.696969697,
"ext": "agda",
"hexsha": "47e8a014900085f51305dd91ea6403a07f484d99",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "c8a3cfa002e77acc5ae1993bae413fde42d4f93b",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "strake/agda",
"max_forks_repo_path": "test/Succeed/Issue4172.agda",
"max_issues_count": 1,
"max_issues_repo_head_hexsha": "c8a3cfa002e77acc5ae1993bae413fde42d4f93b",
"max_issues_repo_issues_event_max_datetime": "2020-01-26T18:22:08.000Z",
"max_issues_repo_issues_event_min_datetime": "2020-01-26T18:22:08.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "strake/agda",
"max_issues_repo_path": "test/Succeed/Issue4172.agda",
"max_line_length": 66,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "c8a3cfa002e77acc5ae1993bae413fde42d4f93b",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "strake/agda",
"max_stars_repo_path": "test/Succeed/Issue4172.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 271,
"size": 782
}
|
S : Set; S = S
|
{
"alphanum_fraction": 0.4,
"avg_line_length": 7.5,
"ext": "agda",
"hexsha": "055e5cc99e910754c936568cce651d4419355ece",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cruhland/agda",
"max_forks_repo_path": "test/interaction/Issue5268.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cruhland/agda",
"max_issues_repo_path": "test/interaction/Issue5268.agda",
"max_line_length": 14,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cruhland/agda",
"max_stars_repo_path": "test/interaction/Issue5268.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 8,
"size": 15
}
|
------------------------------------------------------------------------
-- A formalization of the polymorphic lambda calculus extended with
-- iso-recursive types
------------------------------------------------------------------------
-- Author: Sandro Stucki
-- Copyright (c) 2015 EPFL
-- The code in this directory contains an Agda formalization of the
-- Girard-Reynolds polymorphic lambda calculus (System F) extended
-- with iso-recursive types.
--
-- The code makes heavy use of the Agda standard library, which is
-- freely available from
--
-- https://github.com/agda/agda-stdlib/
--
-- The code has been tested using Agda 2.6.0.1 and version 1.0.1 of the
-- Agda standard library.
module README where
------------------------------------------------------------------------
-- Module overview
-- The formalization is organized in the following modules.
-- Syntax for terms and types along with support for term/type
-- substitutions. These modules also contain church/CPS encodings for
-- some other forms, such as existential types or tuples.
open import SystemF.Term
open import SystemF.Type
-- Typing derivations along with substitution/weakening lemmas.
open import SystemF.WtTerm
-- A (functional) call-by-value small-step semantics. This module
-- also contains a type soundness proof with respect to to said
-- semantics as well as a proof of its equivalence (strong
-- bisimilarity) to the big-step semantics mentioned below. The type
-- soundness proof uses the common progress & preservation
-- (i.e. subject reduction) structure.
open import SystemF.Reduction
-- Two equivalent versions of a (functional) call-by-value big-step
-- semantics along with corresponding type soundness proofs. The
-- second version is formulated without the use of productivity
-- checker workarounds. The latter module also contains an
-- equivalence proof of the two semantics.
open import SystemF.Eval
open import SystemF.Eval.NoWorkarounds
-- Decision procedures for type checking and a uniqueness proof for
-- typing derivations.
open import SystemF.TypeCheck
-- Danielsson's partiality-and-failure monad. This monad provides the
-- domain in which functional operational semantics are formulated.
open import PartialityAndFailure
|
{
"alphanum_fraction": 0.7018165707,
"avg_line_length": 37,
"ext": "agda",
"hexsha": "8ca169541028064cdab6edec75c69721c65fed51",
"lang": "Agda",
"max_forks_count": 8,
"max_forks_repo_forks_event_max_datetime": "2021-07-06T23:12:48.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-05-29T12:24:46.000Z",
"max_forks_repo_head_hexsha": "ea262cf7714cdb762643f10275c568596f57cd1d",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "sstucki/system-f-agda",
"max_forks_repo_path": "src/README.agda",
"max_issues_count": 2,
"max_issues_repo_head_hexsha": "ea262cf7714cdb762643f10275c568596f57cd1d",
"max_issues_repo_issues_event_max_datetime": "2019-05-11T19:23:26.000Z",
"max_issues_repo_issues_event_min_datetime": "2017-05-30T06:43:04.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "sstucki/system-f-agda",
"max_issues_repo_path": "src/README.agda",
"max_line_length": 72,
"max_stars_count": 68,
"max_stars_repo_head_hexsha": "ea262cf7714cdb762643f10275c568596f57cd1d",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "sstucki/system-f-agda",
"max_stars_repo_path": "src/README.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-01T01:25:16.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-05-26T13:12:56.000Z",
"num_tokens": 473,
"size": 2257
}
|
-- Andreas, 2016-09-28
-- Level constraints X <= a and a <= X should solve X = a.
-- {-# OPTIONS -v tc.constr.add:40 #-}
open import Common.Level
module _ (a : Level) where
mutual
X : Level
X = _
data C : Set (lsuc X) where
c : Set a → C -- constrains X by a <= X
data D : Set (lsuc a) where
c : Set X → D -- constrains X by X <= a
-- should succeed
|
{
"alphanum_fraction": 0.576,
"avg_line_length": 18.75,
"ext": "agda",
"hexsha": "4d3b7e8f78cbc5464053a30d33b5283c11cc343c",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cruhland/agda",
"max_forks_repo_path": "test/Succeed/LevelLeqGeq.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cruhland/agda",
"max_issues_repo_path": "test/Succeed/LevelLeqGeq.agda",
"max_line_length": 58,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cruhland/agda",
"max_stars_repo_path": "test/Succeed/LevelLeqGeq.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 127,
"size": 375
}
|
{-# OPTIONS --allow-unsolved-metas #-}
{-# OPTIONS --show-implicit #-}
module HeapProperties where
open import HeapPropertiesDefs public
open import HeapLemmasForSplitting public
|
{
"alphanum_fraction": 0.7663043478,
"avg_line_length": 26.2857142857,
"ext": "agda",
"hexsha": "2ad02190926d1f136ee37f2fefff10bb309548e3",
"lang": "Agda",
"max_forks_count": 11,
"max_forks_repo_forks_event_max_datetime": "2021-06-09T18:40:19.000Z",
"max_forks_repo_forks_event_min_datetime": "2018-05-24T08:20:52.000Z",
"max_forks_repo_head_hexsha": "bda0fac3aadfbce2eacdb89095d100125fa4fdd6",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "ivoysey/Obsidian",
"max_forks_repo_path": "formalization/heapProperties.agda",
"max_issues_count": 259,
"max_issues_repo_head_hexsha": "bda0fac3aadfbce2eacdb89095d100125fa4fdd6",
"max_issues_repo_issues_event_max_datetime": "2022-03-29T18:20:05.000Z",
"max_issues_repo_issues_event_min_datetime": "2017-08-18T19:50:41.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "ivoysey/Obsidian",
"max_issues_repo_path": "formalization/heapProperties.agda",
"max_line_length": 43,
"max_stars_count": 79,
"max_stars_repo_head_hexsha": "bda0fac3aadfbce2eacdb89095d100125fa4fdd6",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "ivoysey/Obsidian",
"max_stars_repo_path": "formalization/heapProperties.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-27T10:34:28.000Z",
"max_stars_repo_stars_event_min_datetime": "2017-08-19T16:24:10.000Z",
"num_tokens": 42,
"size": 184
}
|
{-# OPTIONS --without-K #-}
open import HoTT
{- A proof that (A * B) * C ≃ (C * B) * A, which combined with commutativity
- proves associativity.
-
- Agda has a hard time compiling this but sometimes it succeeds.
-
- Favonia (2016 May): I have consistent success in compiling this file.
-
-}
open import homotopy.JoinComm
module homotopy.JoinAssocCubical where
{- Square and cube lemmas. Some of these are probably generally useful -}
private
app=cst-square : ∀ {i j} {A : Type i} {B : Type j}
{b : B} {f : A → B} (p : ∀ a → f a == b)
{a₁ a₂ : A} (q : a₁ == a₂)
→ Square (p a₁) (ap f q) idp (p a₂)
app=cst-square p idp = hid-square
app=cst-square= : ∀ {i j} {A : Type i} {B : Type j}
{b : B} {f : A → B} {p₁ p₂ : ∀ a → f a == b}
(α : ∀ a → p₁ a == p₂ a) {a₁ a₂ : A} (q : a₁ == a₂)
→ Cube (app=cst-square p₁ q)
(app=cst-square p₂ q)
(horiz-degen-square $ α a₁)
hid-square
hid-square
(horiz-degen-square $ α a₂)
app=cst-square= α idp = y-degen-cube idp
app=cst-square-β : ∀ {i j} {A : Type i} {B : Type j} {b : B} {f : A → B}
(g : (a : A) → f a == b) {x y : A} (p : x == y)
{sq : Square (g x) (ap f p) idp (g y)}
→ apd g p == ↓-app=cst-from-square sq
→ app=cst-square g p == sq
app=cst-square-β g idp α =
! horiz-degen-square-idp ∙ ap horiz-degen-square α ∙ horiz-degen-square-β _
ap-∘-app=cst-square : ∀ {i j k} {A : Type i} {B : Type j} {C : Type k}
{b : B} {f : A → B} (h : B → C) (g : (a : A) → f a == b)
{x y : A} (p : x == y)
→ Cube (app=cst-square (ap h ∘ g) p)
(ap-square h (app=cst-square g p))
hid-square
(horiz-degen-square $ ap-∘ h f p)
ids
hid-square
ap-∘-app=cst-square h g idp =
cube-shift-right (! ap-square-hid) $
cube-shift-top (! horiz-degen-square-idp) $
x-degen-cube idp
cube-to-↓-rtriangle : ∀ {i j} {A : Type i} {B : Type j}
{b₀ b₁ : A → B} {b : B} {p₀₁ : (a : A) → b₀ a == b₁ a}
{p₀ : (a : A) → b₀ a == b} {p₁ : (a : A) → b₁ a == b}
{x y : A} {q : x == y}
{sqx : Square (p₀₁ x) (p₀ x) (p₁ x) idp}
{sqy : Square (p₀₁ y) (p₀ y) (p₁ y) idp}
→ Cube sqx sqy (natural-square p₀₁ q) (app=cst-square p₀ q)
(app=cst-square p₁ q) ids
→ sqx == sqy [ (λ z → Square (p₀₁ z) (p₀ z) (p₁ z) idp) ↓ q ]
cube-to-↓-rtriangle {q = idp} cu = x-degen-cube-out cu
{- approximately, [massage] describes the action of
- [switch : (A * B) * C → (C * B) * A] on the level of squares -}
private
massage : ∀ {i} {A : Type i} {a₀₀ a₀₁ a₁₀ a₁₁ : A}
{p₀₋ : a₀₀ == a₀₁} {p₋₀ : a₀₀ == a₁₀}
{p₋₁ : a₀₁ == a₁₁} {p₁₋ : a₁₀ == a₁₁}
→ Square p₀₋ p₋₀ p₋₁ p₁₋
→ Square (! p₀₋) (p₋₁ ∙ ! p₁₋) idp (! p₋₀)
massage ids = ids
massage-massage : ∀ {i} {A : Type i} {a₀₀ a₀₁ a₁₀ : A}
{p₀₋ : a₀₀ == a₀₁} {p₋₀ : a₀₀ == a₁₀} {p₁₋ : a₁₀ == a₀₁}
(sq : Square p₀₋ p₋₀ idp p₁₋)
→ Cube (massage (massage sq)) sq
(horiz-degen-square (!-! p₀₋)) (horiz-degen-square (!-! p₋₀))
ids (horiz-degen-square (!-! p₁₋))
massage-massage = square-bot-J
(λ sq → Cube (massage (massage sq)) sq
(horiz-degen-square (!-! _)) (horiz-degen-square (!-! _))
ids (horiz-degen-square (!-! _)))
idc
ap-square-massage : ∀ {i j} {A : Type i} {B : Type j} (f : A → B)
{a₀₀ a₀₁ a₁₀ : A} {p₀₋ : a₀₀ == a₀₁} {p₋₀ : a₀₀ == a₁₀} {p₁₋ : a₁₀ == a₀₁}
(sq : Square p₀₋ p₋₀ idp p₁₋)
→ Cube (ap-square f (massage sq)) (massage (ap-square f sq))
(horiz-degen-square (ap-! f p₀₋))
(horiz-degen-square (ap-! f p₁₋))
ids
(horiz-degen-square (ap-! f p₋₀))
ap-square-massage f = square-bot-J
(λ sq → Cube (ap-square f (massage sq)) (massage (ap-square f sq))
(horiz-degen-square (ap-! f _))
(horiz-degen-square (ap-! f _))
ids
(horiz-degen-square (ap-! f _)))
idc
massage-cube : ∀ {i} {A : Type i}
{a₀₀₀ a₀₁₀ a₁₀₀ a₁₁₀ a₀₀₁ a₀₁₁ a₁₀₁ a₁₁₁ : A}
{p₀₋₀ : a₀₀₀ == a₀₁₀} {p₋₀₀ : a₀₀₀ == a₁₀₀}
{p₋₁₀ : a₀₁₀ == a₁₁₀} {p₁₋₀ : a₁₀₀ == a₁₁₀}
{sq₋₋₀ : Square p₀₋₀ p₋₀₀ p₋₁₀ p₁₋₀} -- left
{p₀₋₁ : a₀₀₁ == a₀₁₁} {p₋₀₁ : a₀₀₁ == a₁₀₁}
{p₋₁₁ : a₀₁₁ == a₁₁₁} {p₁₋₁ : a₁₀₁ == a₁₁₁}
{sq₋₋₁ : Square p₀₋₁ p₋₀₁ p₋₁₁ p₁₋₁} -- right
{p₀₀₋ : a₀₀₀ == a₀₀₁} {p₀₁₋ : a₀₁₀ == a₀₁₁}
{p₁₀₋ : a₁₀₀ == a₁₀₁} {p₁₁₋ : a₁₁₀ == a₁₁₁}
{sq₀₋₋ : Square p₀₋₀ p₀₀₋ p₀₁₋ p₀₋₁} -- back
{sq₋₀₋ : Square p₋₀₀ p₀₀₋ p₁₀₋ p₋₀₁} -- top
{sq₋₁₋ : Square p₋₁₀ p₀₁₋ p₁₁₋ p₋₁₁} -- bottom
{sq₁₋₋ : Square p₁₋₀ p₁₀₋ p₁₁₋ p₁₋₁} -- front
→ Cube sq₋₋₀ sq₋₋₁ sq₀₋₋ sq₋₀₋ sq₋₁₋ sq₁₋₋
→ Cube (massage sq₋₋₀) (massage sq₋₋₁)
(!□v sq₀₋₋) (sq₋₁₋ ⊡v !□v sq₁₋₋) vid-square (!□v sq₋₀₋)
massage-cube idc = idc
private
module _ {i j k} {A : Type i} {B : Type j} {C : Type k} where
{- Define an involutive map [switch] -}
module SwitchLeft = PushoutRec {d = *-span A B} {D = (C * B) * A}
(λ a → right a)
(λ b → left (right b))
(λ {(a , b) → ! (glue (right b , a))})
switch-coh-fill : (a : A) (b : B) (c : C) → Σ
(Square (! (glue (left c , a))) (ap SwitchLeft.f (glue (a , b)))
idp (! (ap left (glue (c , b)))))
(λ sq → Cube
sq (massage $ app=cst-square (λ j → glue (j , a)) (glue (c , b)))
hid-square (horiz-degen-square (SwitchLeft.glue-β (a , b)))
ids hid-square)
switch-coh-fill a b c = fill-cube-left _ _ _ _ _
module SwitchCoh (c : C) = PushoutElim {d = *-span A B}
{P = λ k → SwitchLeft.f k == left (left c)}
(λ a → ! (glue (left c , a)))
(λ b → ! (ap left (glue (c , b))))
(↓-app=cst-from-square ∘ λ {(a , b) → fst (switch-coh-fill a b c)})
module Switch = PushoutRec {d = *-span (A * B) C} {D = (C * B) * A}
SwitchLeft.f
(λ c → left (left c))
(λ {(k , c) → SwitchCoh.f c k})
switch = Switch.f
module _ {i j k} {A : Type i} {B : Type j} {C : Type k} where
{- Proof that [switch] is involutive. There are three squares involved:
- one indexed by A × B, one indexed by A × C, and one by B × C.
- These are related by a cube indexed by A × B × C.
- We get the squares for free by defining the cube, as long as
- we make sure the right faces are dependent on the right types. -}
{- Three big square terms follow; unfortunately Agda can't figure out
- what these have to be on its own. Don't worry about the defns. -}
switch-inv-left-square : (a : A) (b : B)
→ Square idp (ap (switch {A = C} ∘ SwitchLeft.f) (glue (a , b)))
(ap left (glue (a , b))) idp
switch-inv-left-square a b = square-symmetry $
(horiz-degen-square (ap-∘ switch SwitchLeft.f (glue (a , b))))
⊡h ap-square switch (horiz-degen-square (SwitchLeft.glue-β (a , b)))
⊡h horiz-degen-square (ap-! switch (glue (right b , a)))
⊡h !□v (!□h hid-square)
⊡h !□v (horiz-degen-square (Switch.glue-β (right b , a)))
⊡h !□v hid-square
⊡h horiz-degen-square (!-! _)
switch-inv-coh-left : (c : C) (a : A)
→ Square idp (ap (switch {B = B}) (SwitchCoh.f c (left a)))
(glue (left a , c)) idp
switch-inv-coh-left c a = square-symmetry $
hid-square
⊡h ap-square switch hid-square
⊡h horiz-degen-square (ap-! switch (glue (left c , a)))
⊡h !□v (!□h hid-square)
⊡h !□v (horiz-degen-square (Switch.glue-β (left c , a)))
⊡h !□v hid-square
⊡h horiz-degen-square (!-! _)
switch-inv-coh-right : (c : C) (b : B)
→ Square idp (ap (switch {C = A}) (SwitchCoh.f c (right b)))
(glue (right b , c)) idp
switch-inv-coh-right c b = square-symmetry $
hid-square
⊡h ap-square switch hid-square
⊡h horiz-degen-square (ap-! switch (ap left (glue (c , b))))
⊡h !□v (!□h (horiz-degen-square (ap-∘ switch left (glue (c , b)))))
⊡h !□v hid-square
⊡h !□v (horiz-degen-square (SwitchLeft.glue-β (c , b)))
⊡h horiz-degen-square (!-! _)
module SwitchInvLeft = PushoutElim {d = *-span A B}
{P = λ k → switch {A = C} (switch (left k)) == left k}
(λ a → idp)
(λ b → idp)
(↓-='-from-square ∘ uncurry switch-inv-left-square)
{- In very small steps, build up the cube -}
module Coh (a : A) (b : B) (c : C) where
step₁ : Cube
(app=cst-square (ap switch ∘ SwitchCoh.f c) (glue (a , b)))
(ap-square switch (app=cst-square (SwitchCoh.f c) (glue (a , b))))
_ _ _ _
step₁ = ap-∘-app=cst-square switch (SwitchCoh.f c) (glue (a , b))
step₂ : Cube
(ap-square switch (app=cst-square (SwitchCoh.f c) (glue (a , b))))
(ap-square switch $ massage $
app=cst-square (λ j → glue (j , a)) (glue (c , b)))
_ _ _ _
step₂ =
cube-shift-left
(! (ap (ap-square switch)
(app=cst-square-β (SwitchCoh.f c) (glue (a , b))
(SwitchCoh.glue-β c (a , b)))))
(ap-cube switch (snd (switch-coh-fill a b c)))
step₃ : Cube
(ap-square switch $ massage $
app=cst-square (λ j → glue (j , a)) (glue (c , b)))
(massage $ ap-square switch $
app=cst-square (λ j → glue (j , a)) (glue (c , b)))
_ _ _ _
step₃ = ap-square-massage switch
(app=cst-square (λ j → glue (j , a)) (glue (c , b)))
step₄ : Cube
(massage $ ap-square switch $
app=cst-square (λ j → glue (j , a)) (glue (c , b)))
(massage $
app=cst-square (λ j → ap switch (glue (j , a))) (glue (c , b)))
_ _ _ _
step₄ = massage-cube $ cube-!-x $
ap-∘-app=cst-square switch (λ j → glue (j , a)) (glue (c , b))
step₅ : Cube
(massage $
app=cst-square (λ j → ap switch (glue (j , a))) (glue (c , b)))
(massage $ app=cst-square (SwitchCoh.f a) (glue (c , b)))
_ _ _ _
step₅ = massage-cube $
app=cst-square= (λ j → Switch.glue-β (j , a)) (glue (c , b))
step₆ : Cube
(massage $ app=cst-square (SwitchCoh.f a) (glue (c , b)))
(massage $ massage $
app=cst-square (λ k → glue (k , c)) (glue (a , b)))
_ _ _ _
step₆ = massage-cube $
cube-shift-left
(! (app=cst-square-β (SwitchCoh.f a) (glue (c , b))
(SwitchCoh.glue-β a (c , b))))
(snd (switch-coh-fill c b a))
step₇ : Cube
(massage $ massage $
app=cst-square (λ k → glue {d = *-span (A * B) C} (k , c))
(glue (a , b)))
(app=cst-square (λ k → glue (k , c)) (glue (a , b)))
_ _ _ _
step₇ = massage-massage _
switch-inv-cube : Cube
(switch-inv-coh-left c a) (switch-inv-coh-right c b)
(switch-inv-left-square a b)
(app=cst-square (ap switch ∘ SwitchCoh.f c) (glue (a , b)))
(app=cst-square (λ k → glue (k , c)) (glue (a , b)))
ids
switch-inv-cube = cube-rotate-x→z $
step₁ ∙³x step₂ ∙³x step₃ ∙³x step₄ ∙³x step₅ ∙³x step₆ ∙³x step₇
module SwitchInvCoh (c : C) = PushoutElim {d = *-span A B}
{P = λ k → Square (SwitchInvLeft.f k) (ap switch (SwitchCoh.f c k))
(glue (k , c)) idp}
(switch-inv-coh-left c)
(switch-inv-coh-right c)
(cube-to-↓-rtriangle ∘ λ {(a , b) →
cube-shift-back
(! (natural-square-β SwitchInvLeft.f (glue (a , b))
(SwitchInvLeft.glue-β (a , b))))
(Coh.switch-inv-cube a b c)})
abstract
switch-inv : (l : (A * B) * C) → switch (switch l) == l
switch-inv = Pushout-elim
SwitchInvLeft.f
(λ c → idp)
(↓-∘=idf-from-square switch switch ∘ λ {(k , c) →
ap (ap switch) (Switch.glue-β (k , c)) ∙v⊡ SwitchInvCoh.f c k})
module _ {i j k} {A : Type i} {B : Type j} {C : Type k} where
join-rearrange-equiv : (A * B) * C ≃ (C * B) * A
join-rearrange-equiv = equiv switch switch switch-inv switch-inv
join-rearrange-path : (A * B) * C == (C * B) * A
join-rearrange-path = ua join-rearrange-equiv
join-assoc-path : (A * B) * C == A * (B * C)
join-assoc-path = join-rearrange-path ∙ swap-path ∙ ap (A *_) swap-path
*-assoc = join-assoc-path
module _ {i j k} (X : Ptd i) (Y : Ptd j) (Z : Ptd k) where
join-rearrange-⊙path : (X ⊙* Y) ⊙* Z == (Z ⊙* Y) ⊙* X
join-rearrange-⊙path =
⊙ua (⊙≃-in join-rearrange-equiv (! (glue (left (snd Z), snd X))))
|
{
"alphanum_fraction": 0.506292815,
"avg_line_length": 38.1580547112,
"ext": "agda",
"hexsha": "c8ca03dc25e822b5bff671b02e223f1162aad094",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "bc849346a17b33e2679a5b3f2b8efbe7835dc4b6",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cmknapp/HoTT-Agda",
"max_forks_repo_path": "theorems/homotopy/JoinAssocCubical.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "bc849346a17b33e2679a5b3f2b8efbe7835dc4b6",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cmknapp/HoTT-Agda",
"max_issues_repo_path": "theorems/homotopy/JoinAssocCubical.agda",
"max_line_length": 79,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "bc849346a17b33e2679a5b3f2b8efbe7835dc4b6",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cmknapp/HoTT-Agda",
"max_stars_repo_path": "theorems/homotopy/JoinAssocCubical.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 4897,
"size": 12554
}
|
-- {-# OPTIONS -v tc.meta:25 #-}
-- Andreas, 2013-05-23
module DontPruneBlocked where
open import Common.Equality
open import Common.Product
data Bool : Set where
true false : Bool
if : {A : Set} → Bool → A → A → A
if true a b = a
if false a b = b
test1 :
let Fst : Bool → Bool → Bool
Fst = _
I : Bool → Bool
I = _
in (a b : Bool) →
(if (Fst true false) (Fst a b) (Fst b a) ≡ I a) × -- don't prune b from Fst!
(a ≡ I a) ×
(Fst a b ≡ a)
test1 a b = refl , refl , refl
test : (A : Set) →
let X : Bool
X = _
Fst : A → A → A
Fst = _
Snd : A → A → A
Snd = _
I : A → A
I = _
in (a b : A) →
(if X (Fst a b) (Snd a b) ≡ I a) × -- don't prune a from Fst and Snd!
(if X (Snd a b) (Fst a b) ≡ I b) × -- don't prune b from Fst and Snd!
(a ≡ I a) ×
(X ≡ true)
test A a b = refl , refl , refl , refl
-- Expected result: unsolved metas
--
-- (unless someone implemented unification that produces definitions by case).
--
-- The test case should prevent overzealous pruning:
-- If the first equation pruned away the b, then the second
-- would have an unbound rhs.
|
{
"alphanum_fraction": 0.5398305085,
"avg_line_length": 24.0816326531,
"ext": "agda",
"hexsha": "b544e8c514e23399eae23257db2703925e6019a8",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "231d6ad8e77b67ff8c4b1cb35a6c31ccd988c3e9",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "Agda-zh/agda",
"max_forks_repo_path": "test/Succeed/DontPruneBlocked.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "shlevy/agda",
"max_issues_repo_path": "test/Succeed/DontPruneBlocked.agda",
"max_line_length": 84,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "shlevy/agda",
"max_stars_repo_path": "test/Succeed/DontPruneBlocked.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 421,
"size": 1180
}
|
-- The following file contains various examples of highlighting.
-- It does not necessarily typecheck (but it should parse)
a : A → Set
a b : A → Set
postulate a : A → Set
abstract a b : A → Set
abstracta : A → Set
postulate abstract a : A → Set
private
a b : A → Set
abstract a : A → Set
pattern-a : A → Set
abstractSet : Set
x-rewrite : abstractSet
|
{
"alphanum_fraction": 0.6825842697,
"avg_line_length": 22.25,
"ext": "agda",
"hexsha": "d94b4e76100290cdc65ff6dc6763ae723cc2be8e",
"lang": "Agda",
"max_forks_count": 11,
"max_forks_repo_forks_event_max_datetime": "2022-03-12T11:41:10.000Z",
"max_forks_repo_forks_event_min_datetime": "2022-02-20T00:51:47.000Z",
"max_forks_repo_head_hexsha": "ba7aef428c0b900675696de17e1ee6bc9d7e684e",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "Seanpm2001-GitHub/agda-github-syntax-highlighting",
"max_forks_repo_path": "examples.agda",
"max_issues_count": 4,
"max_issues_repo_head_hexsha": "ba7aef428c0b900675696de17e1ee6bc9d7e684e",
"max_issues_repo_issues_event_max_datetime": "2021-03-15T07:30:04.000Z",
"max_issues_repo_issues_event_min_datetime": "2020-04-11T06:15:39.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "Seanpm2001-GitHub/agda-github-syntax-highlighting",
"max_issues_repo_path": "examples.agda",
"max_line_length": 64,
"max_stars_count": 3,
"max_stars_repo_head_hexsha": "ba7aef428c0b900675696de17e1ee6bc9d7e684e",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "agda/agda-github-syntax-highlighting",
"max_stars_repo_path": "examples.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-20T00:51:43.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-04-15T20:13:02.000Z",
"num_tokens": 105,
"size": 356
}
|
-- Andreas, 2014-02-11 issue raised by Niccolo Veltri
-- {-# OPTIONS -v term.matrices:40 #-}
open import Common.Equality
data _=⟨_⟩⇒*_ {X : Set}(x : X)(f : X → X) : X → Set where
done : x =⟨ f ⟩⇒* x
next : ∀{y z} → f y ≡ z → x =⟨ f ⟩⇒* y → x =⟨ f ⟩⇒* z
trans* : ∀{X}{x y z}{f : X → X} → x =⟨ f ⟩⇒* y → y =⟨ f ⟩⇒* z → x =⟨ f ⟩⇒* z
trans* p done = p
trans* p (next r q) = next r (trans* p q)
const* : ∀{X}{x y}{f : X → X} → x =⟨ f ⟩⇒* y → f x ≡ x → x ≡ y
const* done q = refl
const* (next r p) q with const* p q
const* (next r p) q | refl = trans (sym q) r
bad : ∀{X}{x y z}{f : X → X} → x =⟨ f ⟩⇒* z → f z ≡ x → x =⟨ f ⟩⇒* y →
y =⟨ f ⟩⇒* x
bad done p q rewrite const* q p = done
bad (next p q) r s =
next r (bad (trans* (next r done) q) p (trans* (next r done) s))
{- PROBLEM WAS:
Interesting part of original call matrix (argss 2-7 of 0-8)
A
? ? = ? ? ?
? = ? ? ? ?
? ? ? ? < ?
? ? ? = ? ?
? ? ? ? ? ?
? ? ? ? < ?
A2 = A*A
? ? ? ? < ?
? = ? ? ? ?
? ? ? ? ? ?
? ? ? = ? ?
? ? ? ? ? ?
? ? ? ? ? ?
Funny, A4 would be worse than A2 why is ist not continuing to iterate?
==> BUG IN 'notWorse' for call graphs.
======================================================================
======================= Initial call matrices ========================
======================================================================
Source: 0
Target: 0
Matrix: = ? ? ? ? ? ? ? ?
? = ? ? ? ? ? ? ?
? ? ? ? = ? ? ? ?
? ? ? = ? ? ? ? ?
? ? ? ? ? ? < ? ?
? ? ? ? ? = ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? < ? ?
? ? ? ? ? ? ? ? ?
======================================================================
========================= New call matrices ==========================
======================================================================
Source: 0
Target: 0
Matrix: = ? ? ? ? ? ? ? ?
? = ? ? ? ? ? ? ?
? ? ? ? ? ? < ? ?
? ? ? = ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? = ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
Idempotent call matrices (no dot patterns):
Other call matrices (no dot patterns):
[the two matrices above]
-}
data Top : Set where
tt : Top
id : Top → Top
id x = x
loop : tt =⟨ id ⟩⇒* tt
loop = bad (next refl done) refl done
|
{
"alphanum_fraction": 0.315969257,
"avg_line_length": 24.914893617,
"ext": "agda",
"hexsha": "8fd50ab4c3ab1c0e11ff8d266629e14dedef056f",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "70c8a575c46f6a568c7518150a1a64fcd03aa437",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "masondesu/agda",
"max_forks_repo_path": "test/fail/Issue1052.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "70c8a575c46f6a568c7518150a1a64fcd03aa437",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "masondesu/agda",
"max_issues_repo_path": "test/fail/Issue1052.agda",
"max_line_length": 76,
"max_stars_count": 1,
"max_stars_repo_head_hexsha": "70c8a575c46f6a568c7518150a1a64fcd03aa437",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "masondesu/agda",
"max_stars_repo_path": "test/fail/Issue1052.agda",
"max_stars_repo_stars_event_max_datetime": "2018-10-10T17:08:44.000Z",
"max_stars_repo_stars_event_min_datetime": "2018-10-10T17:08:44.000Z",
"num_tokens": 837,
"size": 2342
}
|
-- This file comes from the agda class taught by Peter Selinger at
-- Dalhousie University. It contains a bonus question that
-- propostional logic is complete. We will show this in
-- Kalmar.agda.
-- The course link:
-- https://www.mathstat.dal.ca/~selinger/agda-lectures/
{-# OPTIONS --without-K --safe #-}
module PropLogic where
-- We replace the library (lib-3.0) used in class by the stdlib v2.
-- open import Equality
open import Relation.Binary.PropositionalEquality using (_≡_ ; refl ; inspect ; [_] ; trans ; sym)
-- open import Nat
open import Data.Nat using (ℕ)
-- open import Bool
-- renaming and defining new connectives.
open import Data.Bool renaming(_∧_ to _and_ ; _∨_ to _or_) using (Bool ; not ; true ; false)
_implies_ : Bool → Bool → Bool
_implies_ a b = not a or b
-- ----------------------------------------------------------------------
-- * Introduction
-- In this project, we will formalize boolean (i.e., classical)
-- propositional logic, define a notion of derivation for the logic,
-- give a semantics for the logic in terms of truth tables (also known
-- as boolean assignments), and prove the soundness of the derivation
-- rules.
-- ----------------------------------------------------------------------
-- * The set of boolean formulas
-- We start by defining the set of boolean formulas. Informally, the
-- formulas are given by the following grammar:
--
-- Formula A, B ::= P n | A ∧ B | A ⇒ B | ⊥ | ⊤
--
-- Here, n is a natural number, and P n is the nth propositional
-- symbol. A ∧ B is conjunction, A ⇒ B is implication, ⊥ is "false"
-- (also known as a contradiction), and ⊤ is "true". You can type
-- these symbols in Emacs Agda mode using \and, \=>, \bot, and \top.
-- Note that the symbol "⊤" is not the same as the capital letter "T".
-- The set of propositional formulas as an Agda datatype:
data Formula : Set where
P : ℕ -> Formula
_∧_ : Formula -> Formula -> Formula
_⇒_ : Formula -> Formula -> Formula
⊥ : Formula
⊤ : Formula
¬_ : Formula -> Formula
_∨_ : Formula -> Formula -> Formula
infixl 9 _∧_
infixr 8 _⇒_
infix 20 ¬_
-- ----------------------------------------------------------------------
-- * Derivations
-- The most important concept in logic is that of derivability.
-- "Derivation" is another word for "proof". If A₁, ..., Aₙ, B are
-- formulas, we write
--
-- A₁, ..., Aₙ ⊢
--
-- for the statement "the conclusion B can be derived from hypotheses
-- A₁, ..., Aₙ". The symbol "⊢" is pronounced "entails", and we also
-- say "A₁, ..., Aₙ entails B". You can type this symbol as \|- or
-- \entails or \vdash.
--
-- Although entailment "⊢" is somewhat similar to implication "⇒",
-- there is an important difference: an implication A ⇒ B is a
-- formula, so it could be used, for example, as a hypothesis or as a
-- conclusion in a proof. Entailment is a statement about formulas,
-- i.e., entailment means: there exists a proof of B from hypotheses
-- A₁, ..., Aₙ. Entailment is not itself a formula; it is a statement
-- about provability. Thus, entailment is a relation between a list of
-- formulas (the hypotheses) and a formula (the conclusion).
-- ----------------------------------------------------------------------
-- ** Contexts
-- Before we can formalize entailment, we must formalize lists of
-- formulas. A list of formulas is also called a "context". We
-- write Γ for an arbitrary context.
--
-- Because a context can also be empty (a list of zero formulas), it
-- is convenient to use the empty context as the base case. Then we
-- can give the following recursive definition of contexts: a context
-- is either the empty context, or it is obtained from another context
-- by adding one more formula on the right. In other words, we have
-- the following grammar for contexts:
--
-- Context Γ ::= Empty | Γ, A
--
-- We formalize this as the following Agda datatype:
{-
data Context : Set where
Empty : Context
_,_ : Context -> Formula -> Context
-}
-- Modification: We use List Formula as Context instead of defining a
-- new data type. This will ease the proof using list with distinct
-- elements.
open import Data.List using (List ; _∷_ ; [])
Context = List Formula
infixl 7 _,_
-- _,_ : Context -> Formula -> Context
-- _,_ Γ F = F ∷ Γ
pattern _,_ Γ F = F ∷ Γ
pattern Empty = []
-- We also need the membership relation for contexts. We define the
-- relation A ∈ Γ to mean "the formula A is in the context Γ". The
-- symbol ∈ is typed as \in. The membership relation can be
-- recursively defined as follows: the empty context has no members,
-- and the members of the context Γ, A are A and the members of
-- Γ. More formally, we have the following inference rules for
-- membership:
--
-- ───────────── (∈-base)
-- A ∈ Γ, A
--
--
-- A ∈ Γ
-- ───────────── (∈-step)
-- A ∈ Γ, B
--
-- An inference rule, written with a horizontal line, has the
-- following meaning: if the (zero or more) statements above the line
-- are true, then the statement below the line is true. The statements
-- above the line are called the hypotheses of the inference rule, and
-- the statement below the line is called the conclusion. The name of
-- each inference rule (e.g., ∈-base, ∈-step) is written next to the
-- rule. We use inference rules to define a relation, in this case the
-- relation "∈". By definition, "∈" is the smallest relation
-- satisfying (∈-base) and (∈-step).
--
-- We can directly translate these inference rules into Agda as
-- follows:
data _∈_ : Formula -> Context -> Set where
∈-base : ∀ {A : Formula} {Γ : Context} -> A ∈ (Γ , A)
∈-step : ∀ {A B : Formula} {Γ : Context} -> A ∈ Γ -> A ∈ (Γ , B)
infixl 6 _∈_
-- ----------------------------------------------------------------------
-- ** Entailment
-- We now define the entailment relation. Recall that the entailment
-- relation Γ ⊢ A is supposed to mean "the conclusion A can be derived
-- from the hypotheses Γ". Defining entailment therefore requires us
-- to formalize what we mean by "derived". In other words, we have to
-- give a set of proof rules for propositional logic. Let me first
-- write these proof rules in the style of inference rules. These
-- rules define the relation "⊢":
--
-- A ∈ Γ
-- ───────────── (assump)
-- Γ ⊢ A
--
--
-- Γ ⊢ A Γ ⊢ B
-- ───────────────── (∧-intro)
-- Γ ⊢ A ∧ B
--
--
-- Γ ⊢ A ∧ B
-- ───────────────── (∧-elim1)
-- Γ ⊢ A
--
--
-- Γ ⊢ A ∧ B
-- ───────────────── (∧-elim2)
-- Γ ⊢ B
--
--
-- Γ, A ⊢ B
-- ───────────────── (⇒-intro)
-- Γ ⊢ A ⇒ B
--
--
-- Γ ⊢ A ⇒ B Γ ⊢ A
-- ────────────────────────── (⇒-elim)
-- Γ ⊢ B
--
--
-- Γ ⊢ (A ⇒ ⊥) ⇒ ⊥
-- ────────────────────── (double-negation)
-- Γ ⊢ A
--
--
-- ───────────────── (⊤-intro)
-- Γ ⊢ ⊤
--
--
-- The rule (assump) states that if A is one of the hypotheses, then A
-- can be derived from the hypothesis. Basically A is true "by assumption".
--
-- Several of the connectives, such as ∧ and ⇒, have an "introduction"
-- rule, which shows how to prove such a formula, and an "elimination"
-- rule, which shows how such a formula can be used to prove other
-- things. The rule (∧-intro) states that to prove A ∧ B from the
-- given hypotheses Γ, we must separately derive A and B. Conversely,
-- the rules (∧-elim1) and (∧-elim2) state that if we have already
-- derived A ∧ B, then we may separately conclude A and B. The rule
-- (⇒-intro) states that to prove an implication A ⇒ B, we must assume
-- A and prove B. In other words, to derive A ⇒ B from some hypotheses
-- Γ, we must prove B from the hypotheses Γ, A. The rule (⇒-elim) is
-- also known by its Latin name "modus ponens". It states that if we
-- can prove A ⇒ B and we can also prove A, then we may conclude
-- B. The rule (double-negation) is required to make the logic
-- classical. Informally, it states that we can prove A by assuming
-- "not A" and deriving a contradiction. Remember that "not A" is an
-- abbreviation for (A ⇒ ⊥). The rule (⊤-intro) states that ⊤ can be
-- derived from any set of hypotheses.
-- We can directly translate the above rules into Agda:
data _⊢_ : Context -> Formula -> Set where
assump : ∀ {Γ A} -> A ∈ Γ -> Γ ⊢ A
∧-intro : ∀ {Γ A B} -> Γ ⊢ A -> Γ ⊢ B -> Γ ⊢ A ∧ B
∧-elim1 : ∀ {Γ A B} -> Γ ⊢ A ∧ B -> Γ ⊢ A
∧-elim2 : ∀ {Γ A B} -> Γ ⊢ A ∧ B -> Γ ⊢ B
⇒-intro : ∀ {Γ A B} -> Γ , A ⊢ B -> Γ ⊢ A ⇒ B
⇒-elim : ∀ {Γ A B} -> Γ ⊢ A ⇒ B -> Γ ⊢ A -> Γ ⊢ B
double-negation : ∀ {Γ A} -> Γ ⊢ (A ⇒ ⊥) ⇒ ⊥ -> Γ ⊢ A
⊤-intro : ∀ {Γ} -> Γ ⊢ ⊤
¬-intro : ∀ {Γ A} -> Γ , A ⊢ ⊥ -> Γ ⊢ ¬ A
¬-elim : ∀ {Γ A} -> Γ ⊢ ¬ A -> Γ ⊢ A -> Γ ⊢ ⊥
∨-intro1 : ∀ {Γ A B} -> Γ ⊢ A -> Γ ⊢ A ∨ B
∨-intro2 : ∀ {Γ A B} -> Γ ⊢ B -> Γ ⊢ A ∨ B
∨-elim : ∀ {Γ A B C} -> Γ ⊢ A ∨ B -> Γ , A ⊢ C -> Γ , B ⊢ C -> Γ ⊢ C
infixl 4 _⊢_
-- ----------------------------------------------------------------------
-- ** Weakening
-- "Weakening" is the property that if we add additional hypotheses to
-- an entailment (or change their order), the entailment remains valid.
-- More formally, weakening states that Γ ⊢ A and Γ ⊆ Γ' implies Γ' ⊢ A.
--
-- To state weakening, we must first define ⊆. The symbol ⊆ can be
-- typed as \subseteq or \seq.
_⊆_ : Context -> Context -> Set
Γ ⊆ Γ' = ∀ {A} -> A ∈ Γ -> A ∈ Γ'
infix 4 _⊆_
-- We need a lemma about ⊆:
lemma-⊆ : ∀ {Γ Γ' A} -> Γ ⊆ Γ' -> Γ , A ⊆ Γ' , A
lemma-⊆ hyp ∈-base = ∈-base
lemma-⊆ hyp (∈-step hyp2) = ∈-step (hyp hyp2)
lemma-⊆-ext : ∀ {Γ Γ' A} -> Γ ⊆ Γ' -> Γ ⊆ Γ' , A
lemma-⊆-ext hyp = \ x -> ∈-step (hyp x)
lemma-⊆-ext' : ∀ {Γ A} -> Γ ⊆ Γ , A
lemma-⊆-ext' = lemma-⊆-ext \ x -> x
lemma-⊆-empty : ∀ {Γ} -> Empty ⊆ Γ
lemma-⊆-empty {Γ} {A} ()
-- Prove the weakening lemma:
weakening : ∀ {Γ Γ' A} -> Γ ⊢ A -> Γ ⊆ Γ' -> Γ' ⊢ A
weakening (assump x) w = assump (w x)
weakening (∧-intro d d₁) w = ∧-intro (weakening d w) (weakening d₁ w)
weakening (∧-elim1 d) w = ∧-elim1 (weakening d w )
weakening (∧-elim2 d) w = ∧-elim2 (weakening d w)
weakening (⇒-intro d) w = ⇒-intro (weakening d (lemma-⊆ w) )
weakening (⇒-elim d d₁) w = ⇒-elim (weakening d w ) (weakening d₁ w )
weakening (double-negation d) w = double-negation (weakening d w )
weakening ⊤-intro w = ⊤-intro
weakening (¬-intro d) w = ¬-intro (weakening d (lemma-⊆ w ) )
weakening (¬-elim d e) w = ( ¬-elim (weakening d w) (weakening e w))
weakening (∨-intro1 d) w = ∨-intro1 (weakening d w)
weakening (∨-intro2 d) w = ∨-intro2 (weakening d w)
weakening (∨-elim d e f) w = ∨-elim (weakening d w) (weakening e (lemma-⊆ w)) (weakening f (lemma-⊆ w) )
-- ----------------------------------------------------------------------
-- ** A derived rule
-- Classical logic also has the following rule, called "ex falsum
-- quodlibet" or "⊥-elim".
--
-- Γ ⊢ ⊥
-- ───────────────── (⊥-elim)
-- Γ ⊢ A
--
-- The reason we did not include it in the proof rules in the above
-- definition of entailment it that it follows from the other rules.
-- Prove it:
⊥-elim : ∀ {Γ A} -> Γ ⊢ ⊥ -> Γ ⊢ A
⊥-elim {Γ} {A} a = double-negation a-⊥-⊥ where
a-⊥ : Γ ⊢ A ⇒ ⊥
a-⊥ = ⇒-intro (weakening a (lemma-⊆-ext \ x -> x ) )
a-⊥-⊥ : Γ ⊢ (A ⇒ ⊥) ⇒ ⊥
a-⊥-⊥ = ⇒-intro (weakening a (lemma-⊆-ext \ x -> x ) )
-- ----------------------------------------------------------------------
-- * Truth table semantics
-- ----------------------------------------------------------------------
-- ** Truth assignments and interpretation
-- Remember that the atomic formulas of our logic are P 0, P 1, P 2,
-- and so on. The fundamental concept of truth tables is that of a
-- "truth assignment", namely a map from atomic formulas to {T, F}.
-- We usually denote a truth assignment by the letter ρ = \rho.
--
-- We formalize truth assignments as maps from ℕ to Bool.
Assign : Set
Assign = ℕ -> Bool
-- Given a truth assignment ρ, we can compute the truth value (true or
-- false) of any given formula. This is called the "interpretation" of
-- formulas.
interp : Assign -> Formula -> Bool
interp ρ (P x) = ρ x
interp ρ (A ∧ B) = (interp ρ A) and (interp ρ B)
interp ρ (A ⇒ B) = (interp ρ A) implies (interp ρ B)
interp ρ ⊥ = false
interp ρ ⊤ = true
interp ρ (¬ A) = not (interp ρ A)
interp ρ (A ∨ B) = (interp ρ A) or (interp ρ B)
-- Lift the interp function to a list of formulas. We interpret a list
-- of formulas basically as the conjunction of the formulas, i.e., the
-- interpretation of Γ is true if and only if the interpretation of
-- all A ∈ Γ is true.
interps : Assign -> Context -> Bool
interps ρ Empty = true
interps ρ (c , x) = interps ρ c and interp ρ x
-- ----------------------------------------------------------------------
-- ** Semantic entailment
-- We write Γ ⊧ A if under all assignments ρ, if Γ is true, then A is true.
-- A special case is when the context Γ is empty. In that case, ⊧ A means
-- that A is true under all assignments, i.e., A is a tautology.
--
-- The symbol ⊧ is pronounced "models", and you can type it as
-- \models. Please note that this is a different symbol from ⊨ = \|=.
-- We use the symbol "⊧" here.
--
-- The relation ⊧ is also called "semantic entailment" or "truth table
-- entailment", to distinguish it from ⊢, which is "syntactic
-- entailment" or "derivability".
-- We define semantic entailment.
-- _⊧_ : Context -> Formula -> Set
-- Γ ⊧ A = ∀ ρ -> interps ρ Γ ≡ true -> interp ρ A ≡ true
_⊧_ : Context -> Formula -> Set
Γ ⊧ f = (ρ : Assign) -> interps ρ Γ ≡ true -> interp ρ f ≡ true
infix 4 _⊧_
-- ----------------------------------------------------------------------
-- * Soundness
-- ----------------------------------------------------------------------
-- ** Lemmas about the boolean connectives
-- The boolean functions 'and' and 'implies' are defined in Bool.agda.
-- We need to know certain ones of their properties.
boolCases : {p : Set} -> (a : Bool) -> (a ≡ true -> p) -> (a ≡ false -> p) -> p
boolCases true t f = t refl
boolCases false t f = f refl
lemma-and-1 : {a b : Bool} -> a ≡ true -> b ≡ true -> a and b ≡ true
lemma-and-1 refl refl = refl
lemma-and-2 : {a b : Bool} -> a and b ≡ true -> a ≡ true
lemma-and-2 {true} {true} abt = refl
lemma-and-3 : {a b : Bool} -> a and b ≡ true -> b ≡ true
lemma-and-3 {true} {true} abt = refl
lemma-imp-1 : {a b : Bool} -> a implies b ≡ true -> a ≡ true -> b ≡ true
lemma-imp-1 {true} {true} aibt at = refl
lemma-imp-2 : {a b : Bool} -> a ≡ false -> a implies b ≡ true
lemma-imp-2 {false} {true} af = refl
lemma-imp-2 {false} {false} af = refl
lemma-imp-3 : {a b : Bool} -> b ≡ true -> a implies b ≡ true
lemma-imp-3 {true} {true} bt = refl
lemma-imp-3 {false} {b} bt = refl
lemma-doubleNeg : {a : Bool} -> (a implies false) implies false ≡ true -> a ≡ true
lemma-doubleNeg {true} a-f-ft = refl
lemma-not-true : {a : Bool} -> a ≡ true -> not a ≡ false
lemma-not-true {.true} refl = refl
lemma-not-false : {a : Bool} -> a ≡ false -> not a ≡ true
lemma-not-false {.false} refl = refl
lemma-or-1 : {a b : Bool} -> a ≡ true -> a or b ≡ true
lemma-or-1 refl = refl
lemma-or-2 : {a b : Bool} -> b ≡ true -> a or b ≡ true
lemma-or-2 {true} {.true} refl = refl
lemma-or-2 {false} {.true} refl = refl
-- like boolCases
lemma-or-3 : {C : Set} -> {a b : Bool} -> a or b ≡ true -> (a ≡ true -> C) -> (b ≡ true -> C) -> C
lemma-or-3 {a = true} {true} aob ca cb = ca aob
lemma-or-3 {a = false} {true} aob ca cb = cb aob
lemma-or-3 {a = true} {false} aob ca cb = ca refl
-- ----------------------------------------------------------------------
-- ** Lemmas about the soundness of individual rules
-- Each of the proof rules of logic has a semantic counterpart.
lemma-assump : ∀ Γ A -> A ∈ Γ -> Γ ⊧ A
lemma-assump (._ , A) A ∈-base = \ ρ ct -> lemma-and-3 ct
lemma-assump (Γ' , B) A (∈-step hyp) = \ ρ ct -> (lemma-assump Γ' A hyp) ρ (lemma-and-2 ct )
lemma-∧-intro : ∀ Γ A B -> Γ ⊧ A -> Γ ⊧ B -> Γ ⊧ A ∧ B
lemma-∧-intro Γ A B as bs = \ ρ ct -> lemma-and-1 (as ρ ct ) (bs ρ ct )
lemma-∧-elim1 : ∀ Γ A B -> Γ ⊧ A ∧ B -> Γ ⊧ A
lemma-∧-elim1 Γ A B abs = \ ρ ct -> lemma-and-2 (abs ρ ct)
lemma-∧-elim2 : ∀ Γ A B -> Γ ⊧ A ∧ B -> Γ ⊧ B
lemma-∧-elim2 Γ A B abs = \ ρ ct -> lemma-and-3 (abs ρ ct)
lemma-⇒-intro' : ∀ Γ A B -> Γ , A ⊧ B -> Γ ⊧ A ⇒ B
lemma-⇒-intro' Γ A B a-bs ρ ct = boolCases (interp ρ A) (\ x -> lemma-imp-3 (a-bs ρ (lemma-and-1 ct x ) ) ) \ x -> lemma-imp-2 x
lemma-⇒-intro : ∀ Γ A B -> Γ , A ⊧ B -> Γ ⊧ A ⇒ B
lemma-⇒-intro Γ A B a-bs ρ ct with (interp ρ) A | inspect (interp ρ) A
lemma-⇒-intro Γ A B a-bs ρ ct | true | [ eq ] = lemma-imp-3 (a-bs ρ (lemma-and-1 ct eq ) )
lemma-⇒-intro Γ A B a-bs ρ ct | false | [ eq ] = refl
lemma-⇒-elim : ∀ Γ A B -> Γ ⊧ A ⇒ B -> Γ ⊧ A -> Γ ⊧ B
lemma-⇒-elim Γ A B a-bs as = \ ρ ct -> lemma-imp-1 (a-bs ρ ct ) (as ρ ct )
lemma-double-negation : ∀ Γ A -> Γ ⊧ (A ⇒ ⊥) ⇒ ⊥ -> Γ ⊧ A
lemma-double-negation Γ A anns = \ ρ ct -> lemma-doubleNeg (anns ρ ct )
lemma-⊤-intro : ∀ Γ -> Γ ⊧ ⊤
lemma-⊤-intro Γ = \ ρ ct -> refl
lemma-¬-intro : ∀ Γ A -> Γ , A ⊧ ⊥ -> Γ ⊧ ¬ A
lemma-¬-intro Γ A a ρ ct with (interp ρ) A | inspect (interp ρ) A
lemma-¬-intro Γ A a ρ ct | true | [ eq ] = a ρ (lemma-and-1 ct eq)
lemma-¬-intro Γ A a ρ ct | false | [ eq ] = refl
lemma-¬-intro' : ∀ Γ A -> Γ , A ⊧ ⊥ -> Γ ⊧ ¬ A
lemma-¬-intro' Γ A a ρ ct = boolCases (interp ρ A) (\x -> trans (lemma-not-true x ) (a ρ (lemma-and-1 ct x ) ) ) \ x -> lemma-not-false x
lemma-¬-elim : ∀ Γ A -> Γ ⊧ ¬ A -> Γ ⊧ A -> Γ ⊧ ⊥
lemma-¬-elim Γ A a b ρ ct = boolCases (interp ρ A) (\ x -> trans (sym (lemma-not-true x)) (a ρ ct ) ) \ x -> trans (sym x ) (b ρ ct)
lemma-∨-intro1 : ∀ Γ A B -> Γ ⊧ A -> Γ ⊧ A ∨ B
lemma-∨-intro1 Γ A B a ρ ct = lemma-or-1 (a ρ ct )
lemma-∨-intro2 : ∀ Γ A B -> Γ ⊧ B -> Γ ⊧ A ∨ B
lemma-∨-intro2 Γ A B a ρ ct = lemma-or-2 (a ρ ct )
lemma-∨-elim : ∀ Γ A B C -> Γ ⊧ A ∨ B -> Γ , A ⊧ C -> Γ , B ⊧ C -> Γ ⊧ C
lemma-∨-elim Γ A B C aob ac bc ρ ct = lemma-or-3 (aob ρ ct) (\ x -> ac ρ (lemma-and-1 ct x ) ) \ x -> bc ρ (lemma-and-1 ct x )
-- ----------------------------------------------------------------------
-- * The soundness theorem of boolean logic.
-- Soundness states that Γ ⊢ A implies Γ ⊧ A, or equivalently:
-- everything that is provable is valid.
-- 4. Prove the soundness of boolean logic.
sound : ∀ Γ A -> Γ ⊢ A -> Γ ⊧ A
sound Γ A (assump x) = lemma-assump Γ A x
sound Γ (A ∧ B) (∧-intro hyp hyp₁) = lemma-∧-intro Γ A B (sound Γ A hyp) (sound Γ B hyp₁)
sound Γ A (∧-elim1 {B = B} hyp) = lemma-∧-elim1 Γ A B (sound Γ (A ∧ B) hyp )
sound Γ A (∧-elim2 {A = A₁} hyp) = lemma-∧-elim2 Γ A₁ A ((sound Γ (A₁ ∧ A) hyp ) )
sound Γ (A ⇒ B) (⇒-intro hyp) = lemma-⇒-intro Γ A B (sound (Γ , A) B hyp )
sound Γ A (⇒-elim {A = A₁} hyp hyp₁) = lemma-⇒-elim Γ A₁ A (sound Γ (A₁ ⇒ A) hyp ) (sound Γ A₁ hyp₁)
sound Γ A (double-negation hyp) = lemma-double-negation Γ A (sound Γ ((A ⇒ ⊥) ⇒ ⊥) hyp)
sound Γ .⊤ ⊤-intro = λ ρ _ → refl
sound Γ (¬ A) (¬-intro x) = lemma-¬-intro' Γ A ((sound (Γ , A) ⊥ x ) )
sound Γ .⊥ (¬-elim {A = A} x y) = lemma-¬-elim Γ A (sound Γ (¬ A) x) (sound Γ A y)
sound Γ (A ∨ B) (∨-intro1 x) = lemma-∨-intro1 Γ A B (sound Γ A x )
sound Γ (A ∨ B) (∨-intro2 x) = lemma-∨-intro2 Γ A B (sound Γ B x )
sound Γ C (∨-elim {A = A} {B} x y z) = lemma-∨-elim Γ A B C (sound Γ (A ∨ B) x ) (sound (Γ , A) C y ) (sound (Γ , B) C z)
-- ----------------------------------------------------------------------
-- * Bonus questions and beyond
-- If you feel adventurous, add more connectives, such as ¬A or A ∨ B,
-- to the boolean logic.
--
-- The proof rules are:
--
-- Γ, A ⊢ ⊥
-- ────────────── (¬-intro)
-- Γ ⊢ ¬A
--
--
-- Γ ⊢ ¬A Γ ⊢ A
-- ───────────────────── (¬-elim)
-- Γ ⊢ ⊥
--
--
-- Γ ⊢ A
-- ───────────── (∨-intro1)
-- Γ ⊢ A ∨ B
--
--
-- Γ ⊢ B
-- ───────────── (∨-intro2)
-- Γ ⊢ A ∨ B
--
--
-- Γ ⊢ A ∨ B Γ, A ⊢ C Γ, B ⊢ C
-- ─────────────────────────────────────── (∨-elim)
-- Γ ⊢ C
-- If you feel extremely ambitious, try to prove completeness, the
-- converse of soundness. Completeness is the statement that Γ ⊧ A
-- implies Γ ⊢ A.
--
-- Warning: this is extremely difficult and far more work than
-- soundness. Neither Frank nor I have been able to finish a proof of
-- completeness.
-- Actually, Peter had finished the proof a couple of days later using
-- conjunction normal form.
completeness-property : Set
completeness-property = ∀ Γ A -> Γ ⊧ A -> Γ ⊢ A
-- Now, I (Bian) will prove this property in Kalmar.agda using
-- Kalmar's lemma.
|
{
"alphanum_fraction": 0.5587645995,
"avg_line_length": 35.587826087,
"ext": "agda",
"hexsha": "686c48d935057178c8bab54c46e5b63bc4a11864",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "646ccb162cf01fa0d1edafcc830db6750099ed21",
"max_forks_repo_licenses": [
"CC0-1.0"
],
"max_forks_repo_name": "onestruggler/Kalmar",
"max_forks_repo_path": "PropLogic.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "646ccb162cf01fa0d1edafcc830db6750099ed21",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"CC0-1.0"
],
"max_issues_repo_name": "onestruggler/Kalmar",
"max_issues_repo_path": "PropLogic.agda",
"max_line_length": 141,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "646ccb162cf01fa0d1edafcc830db6750099ed21",
"max_stars_repo_licenses": [
"CC0-1.0"
],
"max_stars_repo_name": "onestruggler/Kalmar",
"max_stars_repo_path": "PropLogic.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 6923,
"size": 20463
}
|
{-# OPTIONS --safe #-}
module Cubical.Data.Queue where
open import Cubical.Data.Queue.Base public
open import Cubical.Data.Queue.Finite public
|
{
"alphanum_fraction": 0.7671232877,
"avg_line_length": 18.25,
"ext": "agda",
"hexsha": "4959fcbf3fdfa8571165d658dedb6933b439a8b3",
"lang": "Agda",
"max_forks_count": 134,
"max_forks_repo_forks_event_max_datetime": "2022-03-23T16:22:13.000Z",
"max_forks_repo_forks_event_min_datetime": "2018-11-16T06:11:03.000Z",
"max_forks_repo_head_hexsha": "53e159ec2e43d981b8fcb199e9db788e006af237",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "marcinjangrzybowski/cubical",
"max_forks_repo_path": "Cubical/Data/Queue.agda",
"max_issues_count": 584,
"max_issues_repo_head_hexsha": "53e159ec2e43d981b8fcb199e9db788e006af237",
"max_issues_repo_issues_event_max_datetime": "2022-03-30T12:09:17.000Z",
"max_issues_repo_issues_event_min_datetime": "2018-10-15T09:49:02.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "marcinjangrzybowski/cubical",
"max_issues_repo_path": "Cubical/Data/Queue.agda",
"max_line_length": 44,
"max_stars_count": 301,
"max_stars_repo_head_hexsha": "53e159ec2e43d981b8fcb199e9db788e006af237",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "marcinjangrzybowski/cubical",
"max_stars_repo_path": "Cubical/Data/Queue.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-24T02:10:47.000Z",
"max_stars_repo_stars_event_min_datetime": "2018-10-17T18:00:24.000Z",
"num_tokens": 32,
"size": 146
}
|
--------------------------------------------------------------------------------
-- This is part of Agda Inference Systems
{-# OPTIONS --sized-types #-}
open import Agda.Builtin.Equality
open import Data.Product
open import Data.Sum
open import Size
open import Codata.Thunk
open import Level
open import Relation.Unary using (_⊆_)
module is-lib.InfSys.FlexSCoinduction {𝓁} where
private
variable
U : Set 𝓁
open import is-lib.InfSys.Base {𝓁}
open import is-lib.InfSys.Induction {𝓁}
open import is-lib.InfSys.SCoinduction {𝓁}
open MetaRule
open IS
{- Generalized inference systems -}
SFCoInd⟦_,_⟧ : ∀{𝓁c 𝓁p 𝓁n 𝓁n'} → (I : IS {𝓁c} {𝓁p} {𝓁n} U) → (C : IS {𝓁c} {𝓁p} {𝓁n'} U) → U → Size → Set _
SFCoInd⟦ I , C ⟧ = SCoInd⟦ I ⊓ Ind⟦ I ∪ C ⟧ ⟧
{- Bounded Coinduction Principle -}
bdc-lem : ∀{𝓁c 𝓁p 𝓁n 𝓁' 𝓁''}
→ (I : IS {𝓁c} {𝓁p} {𝓁n} U)
→ (S : U → Set 𝓁')
→ (Q : U → Set 𝓁'')
→ S ⊆ Q
→ S ⊆ ISF[ I ] S
→ S ⊆ ISF[ I ⊓ Q ] S
bdc-lem _ _ _ bd cn Su with cn Su
... | rn , c , refl , pr = rn , (c , bd Su) , refl , pr
bounded-scoind[_,_] : ∀{𝓁c 𝓁p 𝓁n 𝓁n' 𝓁'}
→ (I : IS {𝓁c} {𝓁p} {𝓁n} U)
→ (C : IS {𝓁c} {𝓁p} {𝓁n'} U)
→ (S : U → Set 𝓁')
→ S ⊆ Ind⟦ I ∪ C ⟧ -- S is bounded w.r.t. I ∪ C
→ S ⊆ ISF[ I ] S -- S is consistent w.r.t. I
→ S ⊆ (λ u → ∀{i} → SFCoInd⟦ I , C ⟧ u i)
bounded-scoind[ I , C ] S bd cn Su = scoind[ I ⊓ Ind⟦ I ∪ C ⟧ ] S (bdc-lem I S Ind⟦ I ∪ C ⟧ bd cn) Su
{- Get Ind from SFCoInd -}
sfcoind-to-ind : ∀{𝓁c 𝓁p 𝓁n 𝓁n'}
{is : IS {𝓁c} {𝓁p} {𝓁n} U}{cois : IS {𝓁c} {𝓁p} {𝓁n'} U}
→ (λ u → ∀{i} → SFCoInd⟦ is , cois ⟧ u i) ⊆ Ind⟦ is ∪ cois ⟧
sfcoind-to-ind co with co
sfcoind-to-ind co | sfold (_ , (_ , sd) , refl , _) = sd
{- Apply Rule -}
apply-sfcoind : ∀{𝓁c 𝓁p 𝓁n 𝓁n'}
{is : IS {𝓁c} {𝓁p} {𝓁n} U}{cois : IS {𝓁c} {𝓁p} {𝓁n'} U}
→ (rn : is .Names) → RClosed (is .rules rn) (λ u → ∀{i} → SFCoInd⟦ is , cois ⟧ u i)
apply-sfcoind rn c pr = apply-scoind rn (c , apply-ind (inj₁ rn) c λ i → sfcoind-to-ind (pr i)) pr
{- Postfix - Prefix -}
sfcoind-postfix : ∀{𝓁c 𝓁p 𝓁n 𝓁n'}
{is : IS {𝓁c} {𝓁p} {𝓁n} U}{cois : IS {𝓁c} {𝓁p} {𝓁n'} U}
→ (λ u → ∀{i} → SFCoInd⟦ is , cois ⟧ u i) ⊆ ISF[ is ] (λ u → ∀{i} → SFCoInd⟦ is , cois ⟧ u i)
sfcoind-postfix SFCoInd with SFCoInd
... | sfold (rn , (c , _) , refl , pr) = rn , c , refl , λ i → (pr i) .force
sfcoind-prefix : ∀{𝓁c 𝓁p 𝓁n 𝓁n'}
{is : IS {𝓁c} {𝓁p} {𝓁n} U}{cois : IS {𝓁c} {𝓁p} {𝓁n'} U}
→ ISF[ is ] (λ u → ∀{i} → SFCoInd⟦ is , cois ⟧ u i) ⊆ λ u → ∀{i} → SFCoInd⟦ is , cois ⟧ u i
sfcoind-prefix (rn , c , refl , pr) = apply-sfcoind rn c pr
|
{
"alphanum_fraction": 0.4911504425,
"avg_line_length": 34.7692307692,
"ext": "agda",
"hexsha": "d5512b48a076b65f0309229a2ae1ad057a59385b",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "c4b78e70c3caf68d509f4360b9171d9f80ecb825",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "boystrange/FairSubtypingAgda",
"max_forks_repo_path": "src/is-lib/InfSys/FlexSCoinduction.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "c4b78e70c3caf68d509f4360b9171d9f80ecb825",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "boystrange/FairSubtypingAgda",
"max_issues_repo_path": "src/is-lib/InfSys/FlexSCoinduction.agda",
"max_line_length": 108,
"max_stars_count": 4,
"max_stars_repo_head_hexsha": "c4b78e70c3caf68d509f4360b9171d9f80ecb825",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "boystrange/FairSubtypingAgda",
"max_stars_repo_path": "src/is-lib/InfSys/FlexSCoinduction.agda",
"max_stars_repo_stars_event_max_datetime": "2022-01-24T14:38:47.000Z",
"max_stars_repo_stars_event_min_datetime": "2021-07-29T14:32:30.000Z",
"num_tokens": 1344,
"size": 2712
}
|
module ShadowModule where
module A where
module B where
data D : Set where
open A
module B where
|
{
"alphanum_fraction": 0.7196261682,
"avg_line_length": 9.7272727273,
"ext": "agda",
"hexsha": "e931d945bf7f2cd9b0c0731119f3c0802e4f34e4",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "231d6ad8e77b67ff8c4b1cb35a6c31ccd988c3e9",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "Agda-zh/agda",
"max_forks_repo_path": "test/Fail/ShadowModule.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "shlevy/agda",
"max_issues_repo_path": "test/Fail/ShadowModule.agda",
"max_line_length": 25,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "shlevy/agda",
"max_stars_repo_path": "test/Fail/ShadowModule.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 29,
"size": 107
}
|
module Metalogic.Classical.Propositional.ProofSystem {ℓₚ} (Proposition : Set(ℓₚ)) where
import Lvl
open import Data hiding (empty)
import Data.List
open Data.List using (List ; ∅ ; _⊰_ ; _++_ ; [_ ; _])
open Data.List.Notation
import Data.List.Relation.Membership
import Data.List.Relation.Membership.Proofs
open import Metalogic.Classical.Propositional.Syntax(Proposition)
open import Functional
open Data.List.Relation.Membership{ℓₚ} {Formula}
open Data.List.Relation.Membership.Proofs{ℓₚ} {Formula}
module Meta where
data _⊢_ : List(Formula) → Formula → Set(ℓₚ) where -- TODO: Reduce the number of rules
[⊤]-intro : ∀{Γ} → (Γ ⊢ ⊤)
[⊥]-intro : ∀{Γ}{φ} → (φ ∈ Γ) → ((¬ φ) ∈ Γ) → (Γ ⊢ ⊥)
[⊥]-elim : ∀{Γ}{φ} → (⊥ ∈ Γ) → (Γ ⊢ φ)
[¬]-intro : ∀{Γ}{φ} → ((φ ∈ Γ) → (Γ ⊢ ⊥)) → (Γ ⊢ (¬ φ))
[¬]-elim : ∀{Γ}{φ} → (((¬ φ) ∈ Γ) → (Γ ⊢ ⊥)) → (Γ ⊢ φ)
[∧]-intro : ∀{Γ}{φ₁ φ₂} → (φ₁ ∈ Γ) → (φ₂ ∈ Γ) → (Γ ⊢ (φ₁ ∧ φ₂))
[∧]-elimₗ : ∀{Γ}{φ₁ φ₂} → ((φ₁ ∧ φ₂) ∈ Γ) → (Γ ⊢ φ₁)
[∧]-elimᵣ : ∀{Γ}{φ₁ φ₂} → ((φ₁ ∧ φ₂) ∈ Γ) → (Γ ⊢ φ₂)
[∨]-introₗ : ∀{Γ}{φ₁ φ₂} → (φ₁ ∈ Γ) → (Γ ⊢ (φ₁ ∨ φ₂))
[∨]-introᵣ : ∀{Γ}{φ₁ φ₂} → (φ₂ ∈ Γ) → (Γ ⊢ (φ₁ ∨ φ₂))
[∨]-elim : ∀{Γ}{φ₁ φ₂ φ₃} → ((φ₁ ∈ Γ) → (Γ ⊢ φ₃)) → ((φ₂ ∈ Γ) → (Γ ⊢ φ₃)) → ((φ₁ ∨ φ₂) ∈ Γ) → (Γ ⊢ φ₃)
[⇒]-intro : ∀{Γ}{φ₁ φ₂} → ((φ₁ ∈ Γ) → (Γ ⊢ φ₂)) → (Γ ⊢ (φ₁ ⇒ φ₂))
[⇒]-elim : ∀{Γ}{φ₁ φ₂} → ((φ₁ ⇒ φ₂) ∈ Γ) → (φ₁ ∈ Γ) → (Γ ⊢ φ₂)
[¬¬]-elim : ∀{Γ}{φ} → ((¬ ¬ φ) ∈ Γ) → (Γ ⊢ φ)
[¬¬]-elim{Γ}{φ} ([¬¬φ]-in) =
([¬]-elim{Γ}{φ} ([¬φ]-in ↦
([⊥]-intro{Γ}{¬ φ}
([¬φ]-in)
([¬¬φ]-in)
)
))
_⊬_ : List(Formula) → Formula → Set(ℓₚ)
_⊬_ Γ φ = (_⊢_ Γ φ) → Empty{ℓₚ}
-- Consistency
Inconsistent : List(Formula) → Set(ℓₚ)
Inconsistent Γ = (Γ ⊢ ⊥)
Consistent : List(Formula) → Set(ℓₚ)
Consistent Γ = (Γ ⊬ ⊥)
module TruthTables where
open Meta
-- Natural deduction proof trees.
-- This is a proof system that should reflect the semantic truth of formulas.
module NaturalDeduction where
-- A `Tree` is associated with a formula.
-- [Proposition without assumptions (Axiom)]
-- Represented by the type `Tree(φ)`.
-- It means that a tree with the formula φ at the bottom exists (is constructable).
-- This represents that the formula φ is provable in the natural deduction proof system.
-- [Proposition with an assumption]
-- Represented by the type `Tree(φ₁) → Tree(φ₂)`.
-- It means that a tree with φ₁ as a leaf and φ₂ at the bottom exists (is constructable).
-- This represents that the formula φ₂ is provable if one can assume the formula φ₁.
-- The constructors of `Tree` are all the possible ways to construct a natural deduction proof tree.
-- If a tree with a certain formula cannot be constructed, then it means that the formula is not provable.
{-# NO_POSITIVITY_CHECK #-} -- TODO: Could this be a problem? Maybe not? Classical logic is supposed to be consistent, but maybe that does not have anything to do with this?
data Tree : Formula → Set(ℓₚ) where
[⊤]-intro : Tree(⊤)
[⊥]-intro : ∀{φ} → Tree(φ) → Tree(¬ φ) → Tree(⊥)
[¬]-intro : ∀{φ} → (Tree(φ) → Tree(⊥)) → Tree(¬ φ)
[¬]-elim : ∀{φ} → (Tree(¬ φ) → Tree(⊥)) → Tree(φ)
[∧]-intro : ∀{φ₁ φ₂} → Tree(φ₁) → Tree(φ₂) → Tree(φ₁ ∧ φ₂)
[∧]-elimₗ : ∀{φ₁ φ₂} → Tree(φ₁ ∧ φ₂) → Tree(φ₁)
[∧]-elimᵣ : ∀{φ₁ φ₂} → Tree(φ₁ ∧ φ₂) → Tree(φ₂)
[∨]-introₗ : ∀{φ₁ φ₂} → Tree(φ₁) → Tree(φ₁ ∨ φ₂)
[∨]-introᵣ : ∀{φ₁ φ₂} → Tree(φ₂) → Tree(φ₁ ∨ φ₂)
[∨]-elim : ∀{φ₁ φ₂ φ₃} → (Tree(φ₁) → Tree(φ₃)) → (Tree(φ₂) → Tree(φ₃)) → Tree(φ₁ ∨ φ₂) → Tree(φ₃)
[⇒]-intro : ∀{φ₁ φ₂} → (Tree(φ₁) → Tree(φ₂)) → Tree(φ₁ ⇒ φ₂)
[⇒]-elim : ∀{φ₁ φ₂} → Tree(φ₁ ⇒ φ₂) → Tree(φ₁) → Tree(φ₂)
-- Double negated proposition is positive.
[¬¬]-elim : ∀{φ} → Tree(¬ (¬ φ)) → Tree(φ)
[¬¬]-elim nna = [¬]-elim(na ↦ [⊥]-intro na nna)
-- A contradiction can derive every formula.
[⊥]-elim : ∀{φ} → Tree(⊥) → Tree(φ)
[⊥]-elim bottom = [¬]-elim(_ ↦ bottom)
-- List of natural deduction proof trees.
-- A `Trees` is associated with a list of formulas.
-- If all formulas in the list can be constructed, then all the formulas in the list are provable.
-- This is used to express (⊢) using the usual conventions in formal logic.
-- Trees(Γ) is the statement that all formulas in Γ have proof trees.
Trees : List(Formula) → Set(ℓₚ)
Trees(Γ) = (∀{γ} → (γ ∈ Γ) → Tree(γ))
module Trees where
tree : ∀{Γ}{φ} → Trees(Γ) → (φ ∈ Γ) → Tree(φ)
tree f(x) = f(x)
empty : Trees(∅)
empty ()
singleton : ∀{φ} → Tree(φ) → Trees([ φ ])
singleton (φ-tree) (use) = φ-tree
singleton (φ-tree) (skip ())
-- TODO: This could possibly be generalized to: ∀{Γ₁ Γ₂}{F : T → Set} → (∀{a} → (a ∈ Γ₁) → (a ∈ Γ₂)) → ((∀{γ} → (γ ∈ Γ₂) → F(γ)) → (∀{γ} → (γ ∈ Γ₁) → F(γ)))
from-[∈] : ∀{Γ₁ Γ₂} → (∀{a} → (a ∈ Γ₁) → (a ∈ Γ₂)) → (Trees(Γ₂) → Trees(Γ₁))
from-[∈] (f) (Γ₂-trees) {γ} = liftᵣ (f{γ}) (Γ₂-trees)
push : ∀{Γ}{φ} → Tree(φ) → Trees(Γ) → Trees(φ ⊰ Γ)
push (φ-tree) (Γ-tree) (use) = φ-tree
push (φ-tree) (Γ-tree) (skip membership) = Γ-tree (membership)
pop : ∀{Γ}{φ} → Trees(φ ⊰ Γ) → Trees(Γ)
pop = from-[∈] (skip)
first : ∀{Γ}{φ} → Trees(φ ⊰ Γ) → Tree(φ)
first(f) = f(use)
-- TODO: Could be removed because liftᵣ is easier to use. ALthough a note/tip should be written for these purposes.
-- formula-weaken : ∀{ℓ}{T : Set(ℓ)}{Γ₁ Γ₂} → (Trees(Γ₁) → Trees(Γ₂)) → (Trees(Γ₂) → T) → (Trees(Γ₁) → T)
-- formula-weaken = liftᵣ
[++]-commute : ∀{Γ₁ Γ₂} → Trees(Γ₁ ++ Γ₂) → Trees(Γ₂ ++ Γ₁)
[++]-commute {Γ₁}{Γ₂} (trees) = trees ∘ ([∈][++]-commute{_}{Γ₂}{Γ₁})
[++]-left : ∀{Γ₁ Γ₂} → Trees(Γ₁ ++ Γ₂) → Trees(Γ₁)
[++]-left {Γ₁}{Γ₂} (trees) ([∈]-[Γ₁]) = trees ([∈][++]-expandᵣ {_}{Γ₁}{Γ₂} [∈]-[Γ₁])
[++]-right : ∀{Γ₁ Γ₂} → Trees(Γ₁ ++ Γ₂) → Trees(Γ₂)
[++]-right {Γ₁}{Γ₂} (trees) ([∈]-[Γ₂]) = trees ([∈][++]-expandₗ {_}{Γ₁}{Γ₂} [∈]-[Γ₂])
[++]-deduplicate : ∀{Γ} → Trees(Γ ++ Γ) → Trees(Γ)
[++]-deduplicate {Γ} (trees) {γ} = liftᵣ([∈][++]-expandₗ {γ}{Γ}{Γ})(trees{γ})
[⊰]-reorderₗ : ∀{Γ₁ Γ₂}{φ} → Trees(Γ₁ ++ (φ ⊰ Γ₂)) → Trees(φ ⊰ (Γ₁ ++ Γ₂))
[⊰]-reorderₗ {Γ₁}{Γ₂}{φ} (Γ₁φΓ₂-trees) = push (φ-tree) ([++]-commute{Γ₂}{Γ₁} Γ₂Γ₁-trees) where
φΓ₂Γ₁-trees : Trees(φ ⊰ (Γ₂ ++ Γ₁))
φΓ₂Γ₁-trees = [++]-commute{Γ₁}{φ ⊰ Γ₂} (Γ₁φΓ₂-trees)
φ-tree : Tree(φ)
φ-tree = first{Γ₂ ++ Γ₁}{φ} (φΓ₂Γ₁-trees)
Γ₂Γ₁-trees : Trees(Γ₂ ++ Γ₁)
Γ₂Γ₁-trees = pop{Γ₂ ++ Γ₁}{φ} (φΓ₂Γ₁-trees)
-- Γ₁ ++ (φ ⊰ Γ₂) //assumption
-- (φ ⊰ Γ₂) ++ Γ₁ //Trees.[++]-commute
-- φ ⊰ (Γ₂ ++ Γ₁) //Definition: (++)
-- φ ⊰ (Γ₁ ++ Γ₂) //Trees.[++]-commute
push-many : ∀{Γ₁ Γ₂} → Trees(Γ₁) → Trees(Γ₂) → Trees(Γ₁ ++ Γ₂)
push-many{∅} {Γ₂} ([∅]-trees) ([Γ₂]-trees) = [Γ₂]-trees
push-many{φ ⊰ Γ₁}{Γ₂} ([φ⊰Γ₁]-trees) ([Γ₂]-trees) = [⊰]-reorderₗ{Γ₁}{Γ₂}{φ} (push-many{Γ₁}{φ ⊰ Γ₂} (pop [φ⊰Γ₁]-trees) (push (first [φ⊰Γ₁]-trees) [Γ₂]-trees))
-- Derivability
-- Proof of: If there exists a tree for every formula in Γ, then there exists a tree for the formula φ.
data _⊢_ (Γ : List(Formula)) (φ : Formula) : Set(ℓₚ) where
[⊢]-construct : (Trees(Γ) → Tree(φ)) → (Γ ⊢ φ)
module Theorems where
[⊢]-from-trees : ∀{Γ₁ Γ₂}{φ} → (Trees(Γ₂) → Trees(Γ₁)) → (Γ₁ ⊢ φ) → (Γ₂ ⊢ φ)
[⊢]-from-trees (trees-fn) ([⊢]-construct (Γ₁⊢φ)) = [⊢]-construct ((Γ₁⊢φ) ∘ (trees-fn))
[⊢]-formula-weaken : ∀{Γ}{φ₁ φ₂} → (Γ ⊢ φ₁) → ((φ₂ ⊰ Γ) ⊢ φ₁)
[⊢]-formula-weaken {_}{_}{φ₂} = [⊢]-from-trees (Trees.pop {_}{φ₂})
[⊢]-weakenₗ : ∀{Γ₂}{φ} → (Γ₂ ⊢ φ) → ∀{Γ₁} → ((Γ₁ ++ Γ₂) ⊢ φ)
[⊢]-weakenₗ {_} {_} (Γ₂⊢φ) {∅} = (Γ₂⊢φ)
[⊢]-weakenₗ {Γ₂}{φ} (Γ₂⊢φ) {φ₂ ⊰ Γ₁} = [⊢]-formula-weaken {Γ₁ ++ Γ₂} ([⊢]-weakenₗ (Γ₂⊢φ) {Γ₁})
[⊢]-reorder-[++] : ∀{Γ₁ Γ₂}{φ} → ((Γ₁ ++ Γ₂) ⊢ φ) → ((Γ₂ ++ Γ₁) ⊢ φ)
[⊢]-reorder-[++] {Γ₁}{Γ₂} = [⊢]-from-trees (Trees.[++]-commute {Γ₂}{Γ₁})
[⊢]-apply : ∀{Γ}{φ} → (Γ ⊢ φ) → Trees(Γ) → Tree(φ)
[⊢]-apply ([⊢]-construct [Γ]⊢[φ]) (Γ-trees) = ([Γ]⊢[φ]) (Γ-trees)
[⊢]-apply-first : ∀{Γ}{φ₁ φ₂} → Tree(φ₁) → ((φ₁ ⊰ Γ) ⊢ φ₂) → (Γ ⊢ φ₂)
[⊢]-apply-first ([φ₁]-tree) ([⊢]-construct ([φ₁⊰Γ]⊢[φ₂])) =
[⊢]-construct([Γ]⊢[φ₂] ↦
([φ₁⊰Γ]⊢[φ₂]) (Trees.push ([φ₁]-tree) (\{γ} → [Γ]⊢[φ₂] {γ}))
)
[⊢]-apply-many : ∀{Γ₁ Γ₂}{φ} → Trees(Γ₁) → ((Γ₁ ++ Γ₂) ⊢ φ) → (Γ₂ ⊢ φ)
[⊢]-apply-many ([Γ₁]-trees) ([⊢]-construct ([Γ₁++Γ₂]⊢[φ])) =
[⊢]-construct([Γ₂]⊢[φ] ↦
([Γ₁++Γ₂]⊢[φ]) (Trees.push-many ([Γ₁]-trees) (\{γ} → [Γ₂]⊢[φ] {γ}))
)
[⊢]-reorderᵣ-[⊰] : ∀{Γ₁ Γ₂}{φ₁ φ₂} → ((Γ₁ ++ (φ₁ ⊰ Γ₂)) ⊢ φ₂) ← ((φ₁ ⊰ (Γ₁ ++ Γ₂)) ⊢ φ₂)
[⊢]-reorderᵣ-[⊰] {Γ₁}{Γ₂}{φ₁} = [⊢]-from-trees (Trees.[⊰]-reorderₗ {Γ₁}{Γ₂}{φ₁})
[⊢]-id : ∀{Γ}{φ} → (φ ∈ Γ) → (Γ ⊢ φ)
[⊢]-id (φ-in) = [⊢]-construct ([∈]-proof ↦ [∈]-proof (φ-in))
-- ((A → B) → B) → C
-- f(g ↦ g(x))
-- Almost like that cut rule.
[⊢]-compose : ∀{Γ}{φ₁ φ₂} → (Γ ⊢ φ₁) → ((φ₁ ⊰ Γ) ⊢ φ₂) → (Γ ⊢ φ₂)
[⊢]-compose ([Γ]⊢[φ₁]) ([φ₁Γ]⊢[φ₂]) =
[⊢]-construct ([Γ]-trees ↦
let [φ₁]-tree = [⊢]-apply ([Γ]⊢[φ₁]) (\{γ} → [Γ]-trees {γ})
[Γ]⊢[φ₂] = [⊢]-apply-first ([φ₁]-tree) ([φ₁Γ]⊢[φ₂])
in [⊢]-apply ([Γ]⊢[φ₂]) (\{γ} → [Γ]-trees {γ})
)
-- TODO: ∀{Γ}{φ₁ φ₂} → (Γ ⊢ φ₁) → ((φ₁ ∈ Γ) → (Γ ⊢ φ₂)) → (Γ ⊢ φ₂) Provable?
[⊢]-membership-precedingₗ : ∀{Γ}{φ₁ φ₂} → ((φ₁ ∈ Γ) → (Γ ⊢ φ₂)) ← ((φ₁ ⊰ Γ) ⊢ φ₂)
[⊢]-membership-precedingₗ{Γ}{φ₁}{φ₂} ([φ₁Γ]⊢[φ₂]) ([φ₁]-in) =
[⊢]-construct([Γ]-trees ↦
[⊢]-apply ([φ₁Γ]⊢[φ₂]) (Trees.push ([Γ]-trees [φ₁]-in) (\{γ} → [Γ]-trees {γ}))
)
{- TODO: Maybe this is unprovable? And also false?
postulate a : ∀{b : Set(ℓₚ)} → b
[⊢]-membership-precedingᵣ : ∀{Γ}{φ₁ φ₂} → ((φ₁ ∈ Γ) → (Γ ⊢ φ₂)) → ((φ₁ ⊰ Γ) ⊢ φ₂)
[⊢]-membership-precedingᵣ{Γ}{φ₁}{φ₂} (incl) =
[⊢]-construct ([φ₁Γ]-trees ↦
let [Γ]-trees = Trees.pop (\{γ} → [φ₁Γ]-trees {γ})
[φ₁]-in = a
[Γ]⊢[φ₂] = incl([φ₁]-in)
in [⊢]-apply ([Γ]⊢[φ₂]) ([Γ]-trees)
)
-}
[⊢][⊤]-intro : ∀{Γ} → (Γ ⊢ ⊤)
[⊢][⊤]-intro =
[⊢]-construct(const [⊤]-intro)
[⊢][⊥]-intro : ∀{Γ}{φ} → (φ ∈ Γ) → ((¬ φ) ∈ Γ) → (Γ ⊢ ⊥)
[⊢][⊥]-intro ([φ]-in) ([¬φ]-in) =
[⊢]-construct(assumption-trees ↦
([⊥]-intro
(assumption-trees ([φ]-in))
(assumption-trees ([¬φ]-in))
)
)
[⊢][⊥]-elim : ∀{Γ}{φ} → (⊥ ∈ Γ) → (Γ ⊢ φ)
[⊢][⊥]-elim ([⊥]-in) =
[⊢]-construct(assumption-trees ↦
([⊥]-elim
(assumption-trees ([⊥]-in))
)
)
[⊢][¬]-intro : ∀{Γ}{φ} → ((φ ⊰ Γ) ⊢ ⊥) → (Γ ⊢ (¬ φ))
[⊢][¬]-intro ([⊢]-construct φΓ⊢⊥) =
[⊢]-construct(assumption-trees ↦
([¬]-intro (φ-tree ↦
(φΓ⊢⊥) (Trees.push (φ-tree) (\{γ} → assumption-trees {γ}))
))
)
[⊢][¬]-elim : ∀{Γ}{φ} → (((¬ φ) ⊰ Γ) ⊢ ⊥) → (Γ ⊢ φ)
[⊢][¬]-elim ([⊢]-construct ¬φΓ⊢⊥) =
[⊢]-construct(assumption-trees ↦
([¬]-elim (φ-tree ↦
(¬φΓ⊢⊥) (Trees.push (φ-tree) (\{γ} → assumption-trees {γ}))
))
)
[⊢][∧]-intro : ∀{Γ}{φ₁ φ₂} → (φ₁ ∈ Γ) → (φ₂ ∈ Γ) → (Γ ⊢ (φ₁ ∧ φ₂))
[⊢][∧]-intro ([φ₁]-in) ([φ₂]-in) =
[⊢]-construct(assumption-trees ↦
([∧]-intro
(assumption-trees ([φ₁]-in))
(assumption-trees ([φ₂]-in))
)
)
[⊢][∧]-elimₗ : ∀{Γ}{φ₁ φ₂} → ((φ₁ ∧ φ₂) ∈ Γ) → (Γ ⊢ φ₁)
[⊢][∧]-elimₗ ([φ₁∧φ₂]-in) =
[⊢]-construct(assumption-trees ↦
[∧]-elimₗ (assumption-trees ([φ₁∧φ₂]-in))
)
[⊢][∧]-elimᵣ : ∀{Γ}{φ₁ φ₂} → ((φ₁ ∧ φ₂) ∈ Γ) → (Γ ⊢ φ₂)
[⊢][∧]-elimᵣ ([φ₁∧φ₂]-in) =
[⊢]-construct(assumption-trees ↦
[∧]-elimᵣ (assumption-trees ([φ₁∧φ₂]-in))
)
[⊢][∨]-introₗ : ∀{Γ}{φ₁ φ₂} → (φ₁ ∈ Γ) → (Γ ⊢ (φ₁ ∨ φ₂))
[⊢][∨]-introₗ ([φ₁]-in) =
[⊢]-construct(assumption-trees ↦
[∨]-introₗ (assumption-trees ([φ₁]-in))
)
[⊢][∨]-introᵣ : ∀{Γ}{φ₁ φ₂} → (φ₂ ∈ Γ) → (Γ ⊢ (φ₁ ∨ φ₂))
[⊢][∨]-introᵣ ([φ₂]-in) =
[⊢]-construct(assumption-trees ↦
[∨]-introᵣ (assumption-trees ([φ₂]-in))
)
[⊢][∨]-elim : ∀{Γ₁ Γ₂}{φ₁ φ₂ φ₃} → ((φ₁ ⊰ Γ₁) ⊢ φ₃) → ((φ₂ ⊰ Γ₂) ⊢ φ₃) → (((φ₁ ∨ φ₂) ⊰ (Γ₁ ++ Γ₂)) ⊢ φ₃)
[⊢][∨]-elim {Γ₁}{Γ₂} ([⊢]-construct φ₁Γ⊢φ₃) ([⊢]-construct φ₂Γ⊢φ₃) = [⊢]-construct
(assumption-trees ↦ [∨]-elim
(φ₁-tree ↦ (φ₁Γ⊢φ₃) (Trees.push (φ₁-tree) (Trees.[++]-left {Γ₁}{Γ₂} (Trees.pop (\{γ} → assumption-trees {γ})))))
(φ₂-tree ↦ (φ₂Γ⊢φ₃) (Trees.push (φ₂-tree) (Trees.[++]-right {Γ₁}{Γ₂} (Trees.pop (\{γ} → assumption-trees {γ})))))
(assumption-trees (use))
)
[⊢][⇒]-intro : ∀{Γ}{φ₁ φ₂} → ((φ₁ ⊰ Γ) ⊢ φ₂) → (Γ ⊢ (φ₁ ⇒ φ₂))
[⊢][⇒]-intro ([⊢]-construct φ₁Γ⊢φ₂) = [⊢]-construct
(assumption-trees ↦ [⇒]-intro
(φ-tree ↦ (φ₁Γ⊢φ₂) (Trees.push (φ-tree) (\{γ} → assumption-trees {γ})))
)
[⊢][⇒]-elim : ∀{Γ}{φ₁ φ₂} → ((φ₁ ⇒ φ₂) ∈ Γ) → (φ₁ ∈ Γ) → (Γ ⊢ φ₂)
[⊢][⇒]-elim ([φ₁⇒φ₂]-in) ([φ₁]-in) =
[⊢]-construct(assumption-trees ↦
[⇒]-elim
(assumption-trees ([φ₁⇒φ₂]-in))
(assumption-trees ([φ₁]-in))
)
-- [⊢]-metaᵣ : ∀{a}{b} → _⊢_ a b → Meta._⊢_ a b
-- [⊢]-metaₗ : ∀{a}{b} → _⊢_ a b ← Meta._⊢_ a b
{-[⊢]-rules : Meta.[⊢]-rules (_⊢_)
[⊢]-rules =
record{
[⊤]-intro = \{Γ} → [⊢][⊤]-intro {Γ} ;
[⊥]-intro = \{Γ}{φ} → [⊢][⊥]-intro {Γ}{φ} ;
[⊥]-elim = \{Γ}{φ} → [⊢][⊥]-elim {Γ}{φ} ;
[¬]-intro = \{Γ}{φ} → [⊢][¬]-intro {Γ}{φ} ;
[¬]-elim = \{Γ}{φ} → [⊢][¬]-elim {Γ}{φ} ;
[∧]-intro = \{Γ}{φ₁}{φ₂} → [⊢][∧]-intro {Γ}{φ₁}{φ₂} ;
[∧]-elimₗ = \{Γ}{φ₁}{φ₂} → [⊢][∧]-elimₗ {Γ}{φ₁}{φ₂} ;
[∧]-elimᵣ = \{Γ}{φ₁}{φ₂} → [⊢][∧]-elimᵣ {Γ}{φ₁}{φ₂} ;
[∨]-introₗ = \{Γ}{φ₁}{φ₂} → [⊢][∨]-introₗ {Γ}{φ₁}{φ₂} ;
[∨]-introᵣ = \{Γ}{φ₁}{φ₂} → [⊢][∨]-introᵣ {Γ}{φ₁}{φ₂} ;
[∨]-elim = \{Γ₁}{Γ₂}{φ₁ φ₂ φ₃} → [⊢][∨]-elim {Γ₁}{Γ₂}{φ₁}{φ₂}{φ₃} ;
[⇒]-intro = \{Γ}{φ₁}{φ₂} → [⊢][⇒]-intro {Γ}{φ₁}{φ₂} ;
[⇒]-elim = \{Γ}{φ₁}{φ₂} → [⊢][⇒]-elim {Γ}{φ₁}{φ₂}
}
-}
|
{
"alphanum_fraction": 0.4609954112,
"avg_line_length": 40.2414772727,
"ext": "agda",
"hexsha": "a967a3bc6649efa7fddd0b4b666e0ec8fc09c1e0",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "Lolirofle/stuff-in-agda",
"max_forks_repo_path": "old/Metalogic/Metalogic/Classical/Propositional/ProofSystem.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "Lolirofle/stuff-in-agda",
"max_issues_repo_path": "old/Metalogic/Metalogic/Classical/Propositional/ProofSystem.agda",
"max_line_length": 175,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "Lolirofle/stuff-in-agda",
"max_stars_repo_path": "old/Metalogic/Metalogic/Classical/Propositional/ProofSystem.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-05T06:53:22.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-04-07T17:58:13.000Z",
"num_tokens": 7193,
"size": 14165
}
|
module nodcap.NF.Axiom where
open import Data.Nat as ℕ using (ℕ; suc; zero)
open import Data.Pos as ℕ⁺
open import Data.List as L using (List; []; _∷_; _++_)
open import Function using (_$_)
open import Relation.Binary.PropositionalEquality as P using (_≡_; _≢_)
open import Data.Environment
open import nodcap.Base
open import nodcap.NF.Typing
{-# TERMINATING #-}
-- Theorem:
-- Identity expansion.
--
-- Problematic calls:
-- * in the recursive calls under ⅋n and ⊗n, it is the
-- size of the resource index which is decreasing, not
-- the size of the type itself.
ax : {A : Type} → ⊢ⁿᶠ A ∷ A ^ ∷ []
ax { 𝟏 }
= exch (bbl [])
$ wait halt
ax { ⊥ }
= wait halt
ax { 𝟎 }
= exch (bbl [])
$ loop
ax { ⊤ }
= loop
ax { A ⊗ B }
= exch (bbl [])
$ recv
$ exch (bwd [] (_ ∷ _ ∷ []))
$ send ax ax
ax { A ⅋ B }
= recv
$ exch (bwd [] (_ ∷ _ ∷ []))
$ send
( exch (bbl []) ax )
( exch (bbl []) ax )
ax { A ⊕ B }
= exch (bbl [])
$ case
( exch (bbl [])
$ sel₁ ax
)
( exch (bbl [])
$ sel₂ ax
)
ax { A & B }
= case
( exch (bbl [])
$ sel₁
$ exch (bbl []) ax
)
( exch (bbl [])
$ sel₂
$ exch (bbl []) ax
)
ax { ![ suc zero ] A }
= mk!₁
$ exch (bbl [])
$ mk?₁
$ exch (bbl []) ax
ax { ![ suc (suc n) ] A }
= exch (bbl [])
$ cont {m = 1} {n = suc n}
$ exch (bwd [] (_ ∷ _ ∷ []))
$ pool {m = 1} {n = suc n}
( ax )
( ax )
ax { ?[ suc zero ] A }
= mk?₁
$ exch (bbl [])
$ mk!₁
$ exch (bbl []) ax
ax { ?[ suc (suc n) ] A }
= cont {m = 1} {n = suc n}
$ exch (bwd [] (_ ∷ _ ∷ []))
$ pool {m = 1} {n = suc n}
( exch (bbl []) ax )
( exch (bbl []) ax )
|
{
"alphanum_fraction": 0.493880049,
"avg_line_length": 19.4523809524,
"ext": "agda",
"hexsha": "954fe8f3ebc4c5743d1f1176160ad098c26c5bac",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2018-09-05T08:58:13.000Z",
"max_forks_repo_forks_event_min_datetime": "2018-09-05T08:58:13.000Z",
"max_forks_repo_head_hexsha": "fb5e78d6182276e4d93c4c0e0d563b6b027bc5c2",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "pepijnkokke/nodcap",
"max_forks_repo_path": "src/cpnd1/nodcap/NF/Axiom.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "fb5e78d6182276e4d93c4c0e0d563b6b027bc5c2",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "pepijnkokke/nodcap",
"max_issues_repo_path": "src/cpnd1/nodcap/NF/Axiom.agda",
"max_line_length": 71,
"max_stars_count": 4,
"max_stars_repo_head_hexsha": "fb5e78d6182276e4d93c4c0e0d563b6b027bc5c2",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "wenkokke/nodcap",
"max_stars_repo_path": "src/cpnd1/nodcap/NF/Axiom.agda",
"max_stars_repo_stars_event_max_datetime": "2019-09-24T20:16:35.000Z",
"max_stars_repo_stars_event_min_datetime": "2018-09-05T08:58:11.000Z",
"num_tokens": 677,
"size": 1634
}
|
module Levitation where
open import Data.Product
record ⊤ : Set1 where
constructor tt
data Desc : Set2 where
`1 : Desc
`Σ : (S : Set1)(D : S → Desc) → Desc
`ind× : (D : Desc) → Desc
`hind× : (H : Set)(D : Desc) → Desc
⟦_⟧ : Desc → Set1 → Set1
⟦ `1 ⟧ X = ⊤
⟦ `Σ S D ⟧ X = Σ S (\s → ⟦ D s ⟧ X)
⟦ `ind× D ⟧ X = X × ⟦ D ⟧ X
⟦ `hind× H D ⟧ X = (H → X) × ⟦ D ⟧ X
data Mu (D : Desc) : Set1 where
con : ⟦ D ⟧ (Mu D) → Mu D
data DescDConst : Set1 where
``1 : DescDConst
``Σ : DescDConst
``ind× : DescDConst
``hind× : DescDConst
DescDChoice : DescDConst → Desc
DescDChoice ``1 = `1
DescDChoice ``Σ = `Σ Set (\S → `hind× S `1)
DescDChoice ``ind× = `ind× `1
DescDChoice ``hind× = `Σ Set (\_ → `ind× `1)
DescD : Desc
DescD = `Σ DescDConst DescDChoice
Desc' : Set1
Desc' = Mu DescD
`1' : Desc'
`1' = con (``1 , tt)
`Σ' : (S : Set)(D : S → Desc') → Desc'
`Σ' S D = con (``Σ , (S , (D , tt)))
`ind×' : (D : Desc') → Desc'
`ind×' D = con (``ind× , (D , tt))
`hind×' : (H : Set)(D : Desc') → Desc'
`hind×' H D = con (``hind× , (H , (D , tt)))
|
{
"alphanum_fraction": 0.4990723562,
"avg_line_length": 20.7307692308,
"ext": "agda",
"hexsha": "a52cff80d715ec229c772018df2d630e446401ae",
"lang": "Agda",
"max_forks_count": 12,
"max_forks_repo_forks_event_max_datetime": "2022-02-11T01:57:40.000Z",
"max_forks_repo_forks_event_min_datetime": "2016-08-14T21:36:35.000Z",
"max_forks_repo_head_hexsha": "8c46f766bddcec2218ddcaa79996e087699a75f2",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "mietek/epigram",
"max_forks_repo_path": "papers/icfp-2010-talk/Levitation.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "8c46f766bddcec2218ddcaa79996e087699a75f2",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "mietek/epigram",
"max_issues_repo_path": "papers/icfp-2010-talk/Levitation.agda",
"max_line_length": 44,
"max_stars_count": 48,
"max_stars_repo_head_hexsha": "8c46f766bddcec2218ddcaa79996e087699a75f2",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "mietek/epigram",
"max_stars_repo_path": "papers/icfp-2010-talk/Levitation.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-11T01:55:28.000Z",
"max_stars_repo_stars_event_min_datetime": "2016-01-09T17:36:19.000Z",
"num_tokens": 484,
"size": 1078
}
|
--
-- Created by Dependently-Typed Lambda Calculus on 2020-10-08
-- Connective
-- Author: dplaindoux
--
{-# OPTIONS --without-K #-}
module Connective where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl)
open Eq.≡-Reasoning
open import Data.Nat using (ℕ)
open import Function using (_∘_)
open import Isomorphism using (_≃_; _≲_; extensionality)
open Isomorphism.≃-Reasoning
data _×_ (A B : Set) : Set where
⟨_,_⟩ :
A
→ B
-----
→ A × B
proj₁ : ∀ {A B : Set}
→ A × B
-----
→ A
proj₁ ⟨ x , y ⟩ = x
proj₂ : ∀ {A B : Set}
→ A × B
-----
→ B
proj₂ ⟨ x , y ⟩ = y
|
{
"alphanum_fraction": 0.5888888889,
"avg_line_length": 16.1538461538,
"ext": "agda",
"hexsha": "7b20fc3a7c019c85ee867b8a0b29a938a3b1b9f8",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "a81447af3ab2ba898bb7d57be71369abbba12d81",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "d-plaindoux/colca",
"max_forks_repo_path": "src/exercices/Connective.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "a81447af3ab2ba898bb7d57be71369abbba12d81",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "d-plaindoux/colca",
"max_issues_repo_path": "src/exercices/Connective.agda",
"max_line_length": 61,
"max_stars_count": 2,
"max_stars_repo_head_hexsha": "a81447af3ab2ba898bb7d57be71369abbba12d81",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "d-plaindoux/colca",
"max_stars_repo_path": "src/exercices/Connective.agda",
"max_stars_repo_stars_event_max_datetime": "2021-05-04T09:35:36.000Z",
"max_stars_repo_stars_event_min_datetime": "2021-03-12T18:31:14.000Z",
"num_tokens": 219,
"size": 630
}
|
module Generic.Test.Elim where
open import Generic.Core
open import Generic.Function.Elim
open import Generic.Test.Data.Vec
-- Is it possible to get rid of these `lift`s?
elimVec′ : ∀ {n α π} {A : Set α}
-> (P : ∀ {n} -> Vec A n -> Set π)
-> (∀ {n} {xs : Vec A n} x -> P xs -> P (x ∷ᵥ xs))
-> P []ᵥ
-> (xs : Vec A n)
-> P xs
elimVec′ P f z = elim P (lift z , λ x r -> lift (f x r))
|
{
"alphanum_fraction": 0.5151515152,
"avg_line_length": 28.6,
"ext": "agda",
"hexsha": "e8c70d76f196d5fe743976513c0f1be3306d7182",
"lang": "Agda",
"max_forks_count": 4,
"max_forks_repo_forks_event_max_datetime": "2021-01-27T12:57:09.000Z",
"max_forks_repo_forks_event_min_datetime": "2017-07-17T07:23:39.000Z",
"max_forks_repo_head_hexsha": "e102b0ec232f2796232bd82bf8e3906c1f8a93fe",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "turion/Generic",
"max_forks_repo_path": "src/Generic/Test/Elim.agda",
"max_issues_count": 9,
"max_issues_repo_head_hexsha": "e102b0ec232f2796232bd82bf8e3906c1f8a93fe",
"max_issues_repo_issues_event_max_datetime": "2022-01-04T15:43:14.000Z",
"max_issues_repo_issues_event_min_datetime": "2017-04-06T18:58:09.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "turion/Generic",
"max_issues_repo_path": "src/Generic/Test/Elim.agda",
"max_line_length": 59,
"max_stars_count": 30,
"max_stars_repo_head_hexsha": "e102b0ec232f2796232bd82bf8e3906c1f8a93fe",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "turion/Generic",
"max_stars_repo_path": "src/Generic/Test/Elim.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-05T10:19:38.000Z",
"max_stars_repo_stars_event_min_datetime": "2016-07-19T21:10:54.000Z",
"num_tokens": 147,
"size": 429
}
|
------------------------------------------------------------------------
-- Some corollaries
------------------------------------------------------------------------
module TotalParserCombinators.Derivative.Corollaries where
open import Data.List
open import Function.Base
open import Function.Inverse using (_↔_)
import Function.Related as Related
import Relation.Binary.PropositionalEquality as P
open Related using (SK-sym)
open import TotalParserCombinators.Derivative.Definition
open import TotalParserCombinators.Derivative.LeftInverse
open import TotalParserCombinators.Derivative.RightInverse
open import TotalParserCombinators.Derivative.SoundComplete
open import TotalParserCombinators.Parser
open import TotalParserCombinators.Semantics
-- D is correct.
correct : ∀ {Tok R xs x s} {t} {p : Parser Tok R xs} →
x ∈ D t p · s ↔ x ∈ p · t ∷ s
correct {p = p} = record
{ to = P.→-to-⟶ $ sound p
; from = P.→-to-⟶ complete
; inverse-of = record
{ left-inverse-of = complete∘sound p
; right-inverse-of = sound∘complete
}
}
-- D is monotone.
mono : ∀ {Tok R xs₁ xs₂ t}
{p₁ : Parser Tok R xs₁} {p₂ : Parser Tok R xs₂} →
p₁ ≲ p₂ → D t p₁ ≲ D t p₂
mono p₁≲p₂ = complete ∘ p₁≲p₂ ∘ sound _
-- D preserves parser and language equivalence.
cong : ∀ {k Tok R xs₁ xs₂}
{p₁ : Parser Tok R xs₁} {p₂ : Parser Tok R xs₂} →
p₁ ∼[ k ] p₂ → ∀ {t} → D t p₁ ∼[ k ] D t p₂
cong {p₁ = p₁} {p₂} p₁≈p₂ {t} {x} {s} =
x ∈ D t p₁ · s ↔⟨ correct ⟩
x ∈ p₁ · t ∷ s ∼⟨ p₁≈p₂ ⟩
x ∈ p₂ · t ∷ s ↔⟨ SK-sym correct ⟩
x ∈ D t p₂ · s ∎
where open Related.EquationalReasoning
|
{
"alphanum_fraction": 0.5940353013,
"avg_line_length": 31,
"ext": "agda",
"hexsha": "051a4880be26001ce045374a6ce5b6b93d0002d4",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "76774f54f466cfe943debf2da731074fe0c33644",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "nad/parser-combinators",
"max_forks_repo_path": "TotalParserCombinators/Derivative/Corollaries.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "76774f54f466cfe943debf2da731074fe0c33644",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "nad/parser-combinators",
"max_issues_repo_path": "TotalParserCombinators/Derivative/Corollaries.agda",
"max_line_length": 72,
"max_stars_count": 1,
"max_stars_repo_head_hexsha": "76774f54f466cfe943debf2da731074fe0c33644",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "nad/parser-combinators",
"max_stars_repo_path": "TotalParserCombinators/Derivative/Corollaries.agda",
"max_stars_repo_stars_event_max_datetime": "2020-07-03T08:56:13.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-07-03T08:56:13.000Z",
"num_tokens": 532,
"size": 1643
}
|
{-# OPTIONS --safe --sized-types #-}
module STLC.Operational where
open import STLC.Operational.Base
|
{
"alphanum_fraction": 0.7450980392,
"avg_line_length": 20.4,
"ext": "agda",
"hexsha": "99fce9465cc41c5429afedd022b885a6ac1acddb",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "59bc9648f326b7359801fb31ff6f957a166876fc",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "TrulyNonstrict/STLC",
"max_forks_repo_path": "STLC/Operational.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "59bc9648f326b7359801fb31ff6f957a166876fc",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "TrulyNonstrict/STLC",
"max_issues_repo_path": "STLC/Operational.agda",
"max_line_length": 36,
"max_stars_count": 1,
"max_stars_repo_head_hexsha": "59bc9648f326b7359801fb31ff6f957a166876fc",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "TypesLogicsCats/STLC",
"max_stars_repo_path": "STLC/Operational.agda",
"max_stars_repo_stars_event_max_datetime": "2020-03-16T23:53:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-03-16T23:53:48.000Z",
"num_tokens": 26,
"size": 102
}
|
{-# OPTIONS --cubical-compatible #-}
module WithoutK-PatternSynonyms2 where
-- Equality defined with two indices.
data _≡_ {A : Set} : A → A → Set where
refl : ∀ x → x ≡ x
pattern r x = refl x
-- The --cubical-compatible option works with pattern synonyms.
K : (A : Set) (x : A) (P : x ≡ x → Set) → P (refl x) → (p : x ≡ x ) → P p
K A .x P pr (r x) = pr
|
{
"alphanum_fraction": 0.5900277008,
"avg_line_length": 25.7857142857,
"ext": "agda",
"hexsha": "7e2ef48383a88e6d1f9267c30e8a7ab1d1693db6",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "98c9382a59f707c2c97d75919e389fc2a783ac75",
"max_forks_repo_licenses": [
"BSD-2-Clause"
],
"max_forks_repo_name": "KDr2/agda",
"max_forks_repo_path": "test/Fail/WithoutK-PatternSynonyms2.agda",
"max_issues_count": 6,
"max_issues_repo_head_hexsha": "98c9382a59f707c2c97d75919e389fc2a783ac75",
"max_issues_repo_issues_event_max_datetime": "2021-11-24T08:31:10.000Z",
"max_issues_repo_issues_event_min_datetime": "2021-10-18T08:12:24.000Z",
"max_issues_repo_licenses": [
"BSD-2-Clause"
],
"max_issues_repo_name": "KDr2/agda",
"max_issues_repo_path": "test/Fail/WithoutK-PatternSynonyms2.agda",
"max_line_length": 74,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "98c9382a59f707c2c97d75919e389fc2a783ac75",
"max_stars_repo_licenses": [
"BSD-2-Clause"
],
"max_stars_repo_name": "KDr2/agda",
"max_stars_repo_path": "test/Fail/WithoutK-PatternSynonyms2.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 130,
"size": 361
}
|
open import Relation.Binary.Core
module BBHeap.Insert {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_)
(trans≤ : Transitive _≤_) where
open import BBHeap _≤_
open import BBHeap.Properties _≤_
open import BBHeap.Subtyping.Properties _≤_ trans≤
open import Bound.Lower A
open import Bound.Lower.Order _≤_
open import Bound.Lower.Order.Properties _≤_ trans≤
open import Data.Sum renaming (_⊎_ to _∨_)
open import Order.Total _≤_ tot≤
mutual
insert : {b : Bound}{x : A} → LeB b (val x) → BBHeap b → BBHeap b
insert b≤x leaf = left b≤x lf⋘
insert {x = x} b≤x (left {x = y} b≤y l⋘r)
with tot≤ x y
... | inj₁ x≤y
with lemma-insert⋘ (lexy refl≤) l⋘r
... | inj₁ lᵢ⋘r = left b≤x (subtyping⋘ (lexy x≤y) (lexy x≤y) lᵢ⋘r)
... | inj₂ lᵢ⋗r = right b≤x (subtyping⋙ (lexy x≤y) (lexy x≤y) (lemma⋗ lᵢ⋗r))
insert {x = x} b≤x (left {x = y} b≤y l⋘r) | inj₂ y≤x
with lemma-insert⋘ (lexy y≤x) l⋘r
... | inj₁ lᵢ⋘r = left b≤y lᵢ⋘r
... | inj₂ lᵢ⋗r = right b≤y (lemma⋗ lᵢ⋗r)
insert {x = x} b≤x (right {x = y} b≤y l⋙r)
with tot≤ x y
... | inj₁ x≤y
with lemma-insert⋙ (lexy refl≤) l⋙r
... | inj₁ l⋙rᵢ = right b≤x (subtyping⋙ (lexy x≤y) (lexy x≤y) l⋙rᵢ)
... | inj₂ l≃rᵢ = left b≤x (subtyping⋘ (lexy x≤y) (lexy x≤y) (lemma≃ l≃rᵢ))
insert {x = x} b≤x (right {x = y} b≤y l⋙r) | inj₂ y≤x
with lemma-insert⋙ (lexy y≤x) l⋙r
... | inj₁ l⋙rᵢ = right b≤y l⋙rᵢ
... | inj₂ l≃rᵢ = left b≤y (lemma≃ l≃rᵢ)
lemma-insert⋘ : {b b' : Bound}{x : A}{h : BBHeap b}{h' : BBHeap b'} → (b≤x : LeB b (val x)) → h ⋘ h' → insert b≤x h ⋘ h' ∨ insert b≤x h ⋗ h'
lemma-insert⋘ b≤x lf⋘ = inj₂ (⋗lf b≤x)
lemma-insert⋘ {x = x} b≤x (ll⋘ {x = y} b≤y b'≤y' l⋘r l'⋘r' l'≃r' r≃l')
with tot≤ x y
... | inj₁ x≤y
with lemma-insert⋘ (lexy refl≤) l⋘r
... | inj₁ lᵢ⋘r = inj₁ (ll⋘ b≤x b'≤y' (subtyping⋘ (lexy x≤y) (lexy x≤y) lᵢ⋘r) l'⋘r' l'≃r' (subtyping≃l (lexy x≤y) r≃l'))
... | inj₂ lᵢ⋗r = inj₁ (lr⋘ b≤x b'≤y' (subtyping⋙ (lexy x≤y) (lexy x≤y) (lemma⋗ lᵢ⋗r)) l'⋘r' l'≃r' (subtyping⋗l (lexy x≤y) (lemma⋗≃ lᵢ⋗r r≃l')))
lemma-insert⋘ {x = x} b≤x (ll⋘ {x = y} b≤y b'≤y' l⋘r l'⋘r' l'≃r' r≃l') | inj₂ y≤x
with lemma-insert⋘ (lexy y≤x) l⋘r
... | inj₁ lᵢ⋘r = inj₁ (ll⋘ b≤y b'≤y' lᵢ⋘r l'⋘r' l'≃r' r≃l')
... | inj₂ lᵢ⋗r = inj₁ (lr⋘ b≤y b'≤y' (lemma⋗ lᵢ⋗r) l'⋘r' l'≃r' (lemma⋗≃ lᵢ⋗r r≃l'))
lemma-insert⋘ {x = x} b≤x (lr⋘ {x = y} b≤y b'≤y' l⋙r l'⋘r' l'≃r' l⋗l')
with tot≤ x y
... | inj₁ x≤y
with lemma-insert⋙ (lexy refl≤) l⋙r
... | inj₁ l⋙rᵢ = inj₁ (lr⋘ b≤x b'≤y' (subtyping⋙ (lexy x≤y) (lexy x≤y) l⋙rᵢ) l'⋘r' l'≃r' (subtyping⋗l (lexy x≤y) l⋗l'))
... | inj₂ l≃rᵢ = inj₂ (⋗nd b≤x b'≤y' (subtyping⋘ (lexy x≤y) (lexy x≤y) (lemma≃ l≃rᵢ)) l'⋘r' (subtyping≃ (lexy x≤y) (lexy x≤y) l≃rᵢ) l'≃r' (subtyping⋗l (lexy x≤y) l⋗l'))
lemma-insert⋘ {x = x} b≤x (lr⋘ {x = y} b≤y b'≤y' l⋙r l'⋘r' l'≃r' l⋗l') | inj₂ y≤x
with lemma-insert⋙ (lexy y≤x) l⋙r
... | inj₁ l⋙rᵢ = inj₁ (lr⋘ b≤y b'≤y' l⋙rᵢ l'⋘r' l'≃r' l⋗l')
... | inj₂ l≃rᵢ = inj₂ (⋗nd b≤y b'≤y' (lemma≃ l≃rᵢ) l'⋘r' l≃rᵢ l'≃r' l⋗l')
lemma-insert⋙ : {b b' : Bound}{x : A}{h : BBHeap b}{h' : BBHeap b'} → (b'≤x : LeB b' (val x)) → h ⋙ h' → h ⋙ insert b'≤x h' ∨ h ≃ insert b'≤x h'
lemma-insert⋙ {x = x} b'≤x (⋙lf {x = y} b≤y) = inj₂ (≃nd b≤y b'≤x lf⋘ lf⋘ ≃lf ≃lf ≃lf)
lemma-insert⋙ {x = x} b'≤x (⋙rl {x' = y'} b≤y b'≤y' l⋘r l≃r l'⋘r' l⋗r')
with tot≤ x y'
... | inj₁ x≤y'
with lemma-insert⋘ (lexy refl≤) l'⋘r'
... | inj₁ l'ᵢ⋘r' = inj₁ (⋙rl b≤y b'≤x l⋘r l≃r (subtyping⋘ (lexy x≤y') (lexy x≤y') l'ᵢ⋘r') (subtyping⋗r (lexy x≤y') l⋗r'))
... | inj₂ l'ᵢ⋗r' = inj₁ (⋙rr b≤y b'≤x l⋘r l≃r (subtyping⋙ (lexy x≤y') (lexy x≤y') (lemma⋗ l'ᵢ⋗r')) (subtyping≃r (lexy x≤y') (lemma⋗⋗ l⋗r' l'ᵢ⋗r')))
lemma-insert⋙ {x = x} b'≤x (⋙rl {x' = y'} b≤y b'≤y' l⋘r l≃r l'⋘r' l⋗r') | inj₂ y'≤x
with lemma-insert⋘ (lexy y'≤x) l'⋘r'
... | inj₁ l'ᵢ⋘r' = inj₁ (⋙rl b≤y b'≤y' l⋘r l≃r l'ᵢ⋘r' l⋗r')
... | inj₂ l'ᵢ⋗r' = inj₁ (⋙rr b≤y b'≤y' l⋘r l≃r (lemma⋗ l'ᵢ⋗r') (lemma⋗⋗ l⋗r' l'ᵢ⋗r'))
lemma-insert⋙ {x = x} b'≤x (⋙rr {x' = y'} b≤y b'≤y' l⋘r l≃r l'⋙r' l≃l')
with tot≤ x y'
... | inj₁ x≤y'
with lemma-insert⋙ (lexy refl≤) l'⋙r'
... | inj₁ l'⋙r'ᵢ = inj₁ (⋙rr b≤y b'≤x l⋘r l≃r (subtyping⋙ (lexy x≤y') (lexy x≤y') l'⋙r'ᵢ) (subtyping≃r (lexy x≤y') l≃l'))
... | inj₂ l'≃r'ᵢ = inj₂ (≃nd b≤y b'≤x l⋘r (subtyping⋘ (lexy x≤y') (lexy x≤y') (lemma≃ l'≃r'ᵢ)) l≃r (subtyping≃ (lexy x≤y') (lexy x≤y') l'≃r'ᵢ) (subtyping≃r (lexy x≤y') l≃l'))
lemma-insert⋙ {x = x} b'≤x (⋙rr {x' = y'} b≤y b'≤y' l⋘r l≃r l'⋙r' l≃l') | inj₂ y'≤x
with lemma-insert⋙ (lexy y'≤x) l'⋙r'
... | inj₁ l'⋙r'ᵢ = inj₁ (⋙rr b≤y b'≤y' l⋘r l≃r l'⋙r'ᵢ l≃l')
... | inj₂ l'≃r'ᵢ = inj₂ (≃nd b≤y b'≤y' l⋘r (lemma≃ l'≃r'ᵢ) l≃r l'≃r'ᵢ l≃l')
|
{
"alphanum_fraction": 0.5014607679,
"avg_line_length": 55.7209302326,
"ext": "agda",
"hexsha": "1027768d379b3561dbba2677335e95106e5f7b27",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "b8d428bccbdd1b13613e8f6ead6c81a8f9298399",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "bgbianchi/sorting",
"max_forks_repo_path": "agda/BBHeap/Insert.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "b8d428bccbdd1b13613e8f6ead6c81a8f9298399",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "bgbianchi/sorting",
"max_issues_repo_path": "agda/BBHeap/Insert.agda",
"max_line_length": 177,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "b8d428bccbdd1b13613e8f6ead6c81a8f9298399",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "bgbianchi/sorting",
"max_stars_repo_path": "agda/BBHeap/Insert.agda",
"max_stars_repo_stars_event_max_datetime": "2021-08-24T22:11:15.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-05-21T12:50:35.000Z",
"num_tokens": 3159,
"size": 4792
}
|
------------------------------------------------------------------------
-- Some definitions related to the binary sum type former
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Equality
module Sum {c⁺} (eq : ∀ {a p} → Equality-with-J a p c⁺) where
open Derived-definitions-and-properties eq
open import Prelude
private
variable
a : Level
A B : Type a
x : A
f₁ f₂ g₁ g₂ : A → B
-- Functor laws.
⊎-map-id : ⊎-map id id x ≡ x
⊎-map-id {x = inj₁ _} = refl _
⊎-map-id {x = inj₂ _} = refl _
⊎-map-∘ :
∀ x → ⊎-map (f₁ ∘ g₁) (f₂ ∘ g₂) x ≡ ⊎-map f₁ f₂ (⊎-map g₁ g₂ x)
⊎-map-∘ = [ (λ _ → refl _) , (λ _ → refl _) ]
-- If A can be decided, then ¬ A can be decided.
dec-¬ : Dec A → Dec (¬ A)
dec-¬ (yes p) = no (_$ p)
dec-¬ (no p) = yes p
|
{
"alphanum_fraction": 0.4425087108,
"avg_line_length": 23.2702702703,
"ext": "agda",
"hexsha": "ef8c85316d8f7b20d318325b15281d1cf8d8122a",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "402b20615cfe9ca944662380d7b2d69b0f175200",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "nad/equality",
"max_forks_repo_path": "src/Sum.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "402b20615cfe9ca944662380d7b2d69b0f175200",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "nad/equality",
"max_issues_repo_path": "src/Sum.agda",
"max_line_length": 72,
"max_stars_count": 3,
"max_stars_repo_head_hexsha": "402b20615cfe9ca944662380d7b2d69b0f175200",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "nad/equality",
"max_stars_repo_path": "src/Sum.agda",
"max_stars_repo_stars_event_max_datetime": "2021-09-02T17:18:15.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-05-21T22:58:50.000Z",
"num_tokens": 291,
"size": 861
}
|
module StdLibStuff where
{-
-- Data.Empty
data ⊥ : Set where
-- Relation.Nullary.Core
infix 3 ¬_
¬_ : Set → Set
¬ P = P → ⊥
data Dec (P : Set) : Set where
yes : ( p : P) → Dec P
no : (¬p : ¬ P) → Dec P
-}
-- Relation.Binary.Core
infix 4 _≡_ -- _≢_
data _≡_ {A : Set} (x : A) : A → Set where
refl : x ≡ x
{-
_≢_ : ∀ {A : Set} → A → A → Set
x ≢ y = ¬ x ≡ y
Decidable : {A : Set} → Set
Decidable {A} = (x y : A) → Dec (x ≡ y)
-}
-- equality properties
sym : {A : Set} → {x y : A} → x ≡ y → y ≡ x
sym refl = refl
subst : {A : Set} → {x y : A} → (p : A → Set) → x ≡ y → p x → p y
subst p refl h = h
cong : {A B : Set} → {x y : A} → (f : A → B) → x ≡ y → f x ≡ f y
cong f refl = refl
trans : {A : Set} → {x y z : A} → x ≡ y → y ≡ z → x ≡ z
trans refl h = h
{-
-- Data.List
infixr 5 _∷_
data List (A : Set) : Set where
[] : List A
_∷_ : (x : A) (xs : List A) → List A
data List₁ (A : Set₁) : Set₁ where
[] : List₁ A
_∷_ : (x : A) (xs : List₁ A) → List₁ A
-}
-- Data.Bool
infixr 5 _∨_
data Bool : Set where
true : Bool
false : Bool
not : Bool → Bool
not true = false
not false = true
_∨_ : Bool → Bool → Bool
true ∨ b = true
false ∨ b = b
{-
-- Data.Product
infixr 4 _,_ _,′_
infixr 2 _×_
record Σ (A : Set) (B : A → Set) : Set where
constructor _,_
field
proj₁ : A
proj₂ : B proj₁
record Σ₁ (A : Set₁) (B : A → Set) : Set₁ where
constructor _,_
field
proj₁ : A
proj₂ : B proj₁
-- nondep product
record _×_ (A B : Set) : Set where
constructor _,_
field
proj₁ : A
proj₂ : B
open _×_ public
_,′_ : {A B : Set} → A → B → A × B
_,′_ = _,_
∃ : ∀ {A : Set} → (A → Set) → Set
∃ = Σ _
∃₁ : ∀ {A : Set₁} → (A → Set) → Set₁
∃₁ = Σ₁ _
-}
-- Data.Nat
data ℕ : Set where
zero : ℕ
suc : (n : ℕ) → ℕ
{-# BUILTIN NATURAL ℕ #-}
{-# BUILTIN ZERO zero #-}
{-# BUILTIN SUC suc #-}
-- Data.Fin
data Fin : ℕ → Set where
zero : {n : ℕ} → Fin (suc n)
suc : {n : ℕ} (i : Fin n) → Fin (suc n)
{-
-- Data.Vec
data Vec (A : Set) : ℕ → Set where
[] : Vec A zero
_∷_ : ∀ {n} (x : A) (xs : Vec A n) → Vec A (suc n)
data Vec₁ (A : Set₁) : ℕ → Set₁ where
[] : Vec₁ A zero
_∷_ : ∀ {n} (x : A) (xs : Vec₁ A n) → Vec₁ A (suc n)
lookup : ∀ {n} {A : Set} → Fin n → Vec A n → A
lookup zero (x ∷ xs) = x
lookup (suc i) (x ∷ xs) = lookup i xs
lookup₁ : ∀ {n} {A : Set₁} → Fin n → Vec₁ A n → A
lookup₁ zero (x ∷ xs) = x
lookup₁ (suc i) (x ∷ xs) = lookup₁ i xs
-- Data.Sum
infixr 1 _⊎_
data _⊎_ (A : Set) (B : Set) : Set where
inj₁ : (x : A) → A ⊎ B
inj₂ : (y : B) → A ⊎ B
[_,_]′ : ∀ {A : Set} {B : Set} {C : Set} →
(A → C) → (B → C) → (A ⊎ B → C)
[_,_]′ h₁ h₂ (inj₁ x) = h₁ x
[_,_]′ h₁ h₂ (inj₂ y) = h₂ y
--
_↔_ : Set → Set → Set
X ↔ Y = (X → Y) × (Y → X)
-- Misc
record ⊤ : Set where
-}
|
{
"alphanum_fraction": 0.4800569801,
"avg_line_length": 15.687150838,
"ext": "agda",
"hexsha": "65df98cdf67317e2408f450ef5e0858dae3975af",
"lang": "Agda",
"max_forks_count": 3,
"max_forks_repo_forks_event_max_datetime": "2022-01-15T11:51:19.000Z",
"max_forks_repo_forks_event_min_datetime": "2016-05-17T20:28:10.000Z",
"max_forks_repo_head_hexsha": "032efd5f42e4b56d436ac8e0c3c0f5127b8dc1f7",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "frelindb/agsyHOL",
"max_forks_repo_path": "soundness/StdLibStuff.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "032efd5f42e4b56d436ac8e0c3c0f5127b8dc1f7",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "frelindb/agsyHOL",
"max_issues_repo_path": "soundness/StdLibStuff.agda",
"max_line_length": 65,
"max_stars_count": 17,
"max_stars_repo_head_hexsha": "032efd5f42e4b56d436ac8e0c3c0f5127b8dc1f7",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "frelindb/agsyHOL",
"max_stars_repo_path": "soundness/StdLibStuff.agda",
"max_stars_repo_stars_event_max_datetime": "2021-03-19T20:53:45.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-09-04T14:38:28.000Z",
"num_tokens": 1267,
"size": 2808
}
|
-- Andreas, 2021-04-14, #1154
-- Andreas, 2021-04-12, BNFC/bnfc#354
-- Make sure we confirm tentative layout columns on first newline.
private private private A : Set
B : Set -- all three blocks (8,16,24) should be confirmed here
private -- the column for this block needs to be > 16
Bad : Set -- bad indentation, needs to be 0,8,16 or greater
-- Expected: Parse error after Bad
|
{
"alphanum_fraction": 0.6035242291,
"avg_line_length": 41.2727272727,
"ext": "agda",
"hexsha": "17b0320b11841040af33fd957abac005b0c59d28",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cruhland/agda",
"max_forks_repo_path": "test/Fail/Issue1145.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cruhland/agda",
"max_issues_repo_path": "test/Fail/Issue1145.agda",
"max_line_length": 87,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cruhland/agda",
"max_stars_repo_path": "test/Fail/Issue1145.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 119,
"size": 454
}
|
module LC.Base where
open import Data.Nat
--------------------------------------------------------------------------------
-- de Bruijn indexed lambda calculus
infix 5 ƛ_
infixl 7 _∙_
infix 9 var_
data Term : Set where
var_ : (x : ℕ) → Term
ƛ_ : (M : Term) → Term
_∙_ : (M : Term) → (N : Term) → Term
|
{
"alphanum_fraction": 0.446875,
"avg_line_length": 20,
"ext": "agda",
"hexsha": "c7fdd710454f970c2a86f1ddb361aff68a8f3f43",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "0c9a6e79c23192b28ddb07315b200a94ee900ca6",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "banacorn/bidirectional",
"max_forks_repo_path": "LC/Base.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "0c9a6e79c23192b28ddb07315b200a94ee900ca6",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "banacorn/bidirectional",
"max_issues_repo_path": "LC/Base.agda",
"max_line_length": 80,
"max_stars_count": 2,
"max_stars_repo_head_hexsha": "0c9a6e79c23192b28ddb07315b200a94ee900ca6",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "banacorn/bidirectional",
"max_stars_repo_path": "LC/Base.agda",
"max_stars_repo_stars_event_max_datetime": "2020-08-25T14:05:01.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-08-25T07:34:40.000Z",
"num_tokens": 102,
"size": 320
}
|
module posts.agda.typed-protocols where
open import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl)
open import Relation.Nullary using (¬_)
open import Data.Empty using (⊥; ⊥-elim)
open import Data.List
open import Data.Nat
open import Data.Unit using (⊤; tt)
open import Function.Base using (_$_; _|>_)
-- Client / server roles
--
data PeerRole : Set where
ClientRole : PeerRole
ServerRole : PeerRole
dual-role : PeerRole → PeerRole
dual-role ClientRole = ServerRole
dual-role ServerRole = ClientRole
-- Objective agency: who is responsible for sending next message.
--
data Agency : Set where
ClientAgency : Agency
ServerAgency : Agency
NobodyAgency : Agency
-- Relative agency to the current 'PeerRole'. It answer the question: are we
-- responsible for sending next message?
--
data RelativeAgency : Set where
WeHaveAgency : RelativeAgency
TheyHaveAgency : RelativeAgency
NobodyHasAgency : RelativeAgency
relative : PeerRole → Agency → RelativeAgency
relative ClientRole ClientAgency = WeHaveAgency
relative ClientRole ServerAgency = TheyHaveAgency
relative ClientRole NobodyAgency = NobodyHasAgency
relative ServerRole ClientAgency = TheyHaveAgency
relative ServerRole ServerAgency = WeHaveAgency
relative ServerRole NobodyAgency = NobodyHasAgency
-- 'relative' function obeys the following three exclusion lemmas:
--
-- * it is an absurd if client and server have agency
-- * it is an absurd if 'WeHaveAgency' and the dual role terminated
-- ('NobodyHasAgency')
-- * it is an absurd if 'TheyHaveAgency' and the dual role terminated
-- ('NobodyHasAgency')
--
-- Note that these lemmas are provided regardless of the protocol, unlike the
-- Haskell implementation which requires to prove them for each protocol.
exclusion-lemma-client-and-server-have-agency₁
: ∀ {agency : Agency}
{pr : PeerRole}
→ WeHaveAgency ≡ relative pr agency
→ WeHaveAgency ≡ relative (dual-role pr) agency
→ ⊥
exclusion-lemma-client-and-server-have-agency₁
{ClientAgency}
{ClientRole}
refl ()
exclusion-lemma-client-and-server-have-agency₁
{ServerAgency}
{ServerRole}
refl ()
exclusion-lemma-client-and-server-have-agency₂
: ∀ {agency : Agency}
{pr : PeerRole}
→ TheyHaveAgency ≡ relative pr agency
→ TheyHaveAgency ≡ relative (dual-role pr) agency
→ ⊥
exclusion-lemma-client-and-server-have-agency₂
{ServerAgency}
{ClientRole}
refl ()
exclusion-lemma-client-and-server-have-agency₂
{ClientAgency}
{ServerRole}
refl ()
exclusion-lemma-we-have-agency-and-nobody-has-agency
: ∀ {agency : Agency}
{pr : PeerRole}
{pr' : PeerRole}
→ WeHaveAgency ≡ relative pr agency
→ NobodyHasAgency ≡ relative pr' agency
→ ⊥
exclusion-lemma-we-have-agency-and-nobody-has-agency
{ClientAgency}
{ClientRole}
{ServerRole}
refl ()
exclusion-lemma-we-have-agency-and-nobody-has-agency
{ServerAgency}
{ServerRole}
{ClientRole}
refl ()
exclusion-lemma-they-have-agency-and-nobody-has-agency
: ∀ {agency : Agency}
{pr : PeerRole}
{pr' : PeerRole}
→ TheyHaveAgency ≡ relative pr agency
→ NobodyHasAgency ≡ relative pr' agency
→ ⊥
exclusion-lemma-they-have-agency-and-nobody-has-agency
{ServerAgency}
{ClientRole}
{ServerRole}
refl ()
exclusion-lemma-they-have-agency-and-nobody-has-agency
{ClientAgency}
{ServerRole}
{ClientRole}
refl ()
-----------
-- Peer API
--
-- We index each primitive with 'IsPipelined'
--
data IsPipelined : Set where
Pipelined : IsPipelined
NonPipelined : IsPipelined
-- Promised protocol transition
--
data Trans (ps : Set) : Set where
Tr : ps → ps → Trans ps
-- 'Peer' explicitly indexed by:
-- * message type
-- * objective protocol agency
-- * peer role
-- * return type
-- * 'IsPipelined'
-- * queue of unrealised transitions, due to pipelining
-- * current state
--
data Peer {ps : Set}
(msg : ps → ps → Set)
(agency : ps → Agency)
(pr : PeerRole)
(a : Set)
: IsPipelined
→ List (Trans ps)
→ ps
→ Set where
--
-- non-pipelined primitives
--
-- non-pipelined send a message
Yield : ∀ {st st' : ps}
{pl : IsPipelined}
→ WeHaveAgency ≡ relative pr (agency st)
→ msg st st'
→ Peer msg agency pr a pl [] st'
→ Peer msg agency pr a pl [] st
-- non-pipelined receive a message
Await : ∀ {st : ps}
{pl : IsPipelined}
→ TheyHaveAgency ≡ relative pr (agency st)
→ (∀ {st' : ps}
→ msg st st'
→ Peer msg agency pr a pl [] st'
)
→ Peer msg agency pr a pl [] st
-- protocol termination
Done : ∀ {st : ps}
{pl : IsPipelined}
→ NobodyHasAgency ≡ relative pr (agency st)
→ a
→ Peer msg agency pr a pl [] st
--
-- pipelining primitives
--
-- pipeline a single message
YieldPipelined
: ∀ {st st' st'' : ps}
{q : List (Trans ps)}
→ WeHaveAgency ≡ relative pr (agency st)
→ msg st st'
→ Peer msg agency pr a Pipelined (q ∷ʳ Tr st' st'') st''
→ Peer msg agency pr a Pipelined q st
-- partially collect a promissed transition
Collect
: ∀ {st st' st'' : ps}
{q : List (Trans ps)}
→ TheyHaveAgency ≡ relative pr (agency st')
→ (∀ {stNext : ps}
→ msg st' stNext
→ Peer msg agency pr a Pipelined (Tr stNext st'' ∷ q) st
)
→ Peer msg agency pr a Pipelined (Tr st' st'' ∷ q) st
-- collect the identity transition
CollectDone
: ∀ {st : ps}
{q : List (Trans ps)}
→ Peer msg agency pr a Pipelined q st
→ Peer msg agency pr a Pipelined (Tr st st ∷ q) st
--------------
-- PingPong v1
--
-- Protocol states
--
data PingPong : Set where
StIdle : PingPong
StBusy : PingPong
StDone : PingPong
-- Agency of PingPong states
--
pingPongAgency : PingPong → Agency
pingPongAgency StIdle = ClientAgency
pingPongAgency StBusy = ServerAgency
pingPongAgency StDone = NobodyAgency
-- Protocol messages
--
data PingPongMsg : ∀ (st st' : PingPong) → Set where
MsgPing : PingPongMsg StIdle StBusy
MsgPong : PingPongMsg StBusy StIdle
MsgDone : PingPongMsg StIdle StDone
--
-- PingPong v1, examples
--
-- ping client which computes unit (tt : ⊤)
--
ping : Peer PingPongMsg pingPongAgency ClientRole ⊤ NonPipelined [] StIdle
ping =
Yield refl MsgPing
$ await
$ Yield refl MsgPing
$ await
$ Yield refl MsgDone
$ Done refl tt
where
await : Peer PingPongMsg pingPongAgency ClientRole ⊤ NonPipelined [] StIdle
→ Peer PingPongMsg pingPongAgency ClientRole ⊤ NonPipelined [] StBusy
await k = Await refl λ {MsgPong → k}
-- pipelined client which computes unit (tt : ⊤)
--
pipelinedPing
: Peer PingPongMsg pingPongAgency ClientRole ⊤ Pipelined [] StIdle
pipelinedPing =
YieldPipelined refl MsgPing
$ YieldPipelined refl MsgPing
$ YieldPipelined refl MsgPing
$ collect
$ collect
$ collect
$ Yield refl MsgDone
$ Done refl tt
where
collect : ∀ {q : List (Trans PingPong)}
→ Peer PingPongMsg pingPongAgency ClientRole ⊤ Pipelined q StIdle
→ Peer PingPongMsg pingPongAgency ClientRole ⊤ Pipelined
(Tr StBusy StIdle ∷ q) StIdle
collect k =
Collect refl λ {MsgPong → CollectDone k}
--------------
-- PingPong v2
--
-- The same states and agency as PingPong v1, but with additional 'MsgBusy'
-- transition.
data PingPongMsg2 : ∀ (st st' : PingPong) → Set where
MsgPingPong : ∀ {st st' : PingPong}
→ PingPongMsg st st' → PingPongMsg2 st st'
MsgBusy : PingPongMsg2 StBusy StBusy
-- we use unbounded recursion in 'pipelinedPing2'
{-# NON_TERMINATING #-}
-- pipelined ping client which computes the number of busy messages
--
pipelinedPing2
: Peer PingPongMsg2 pingPongAgency ClientRole ℕ Pipelined [] StIdle
pipelinedPing2 =
YieldPipelined refl (MsgPingPong MsgPing)
$ YieldPipelined refl (MsgPingPong MsgPing)
$ YieldPipelined refl (MsgPingPong MsgPing)
$ collect 0
$ λ { n1 → collect n1
λ { n2 → collect n2
λ { n3 → Yield refl (MsgPingPong MsgDone)
$ Done refl n3 }}}
where
collect : ∀ {q : List (Trans PingPong)}
→ ℕ
→ (ℕ → Peer PingPongMsg2 pingPongAgency ClientRole ℕ Pipelined q StIdle)
→ Peer PingPongMsg2 pingPongAgency ClientRole ℕ Pipelined
(Tr StBusy StIdle ∷ q) StIdle
collect n k =
Collect refl
λ { MsgBusy → collect (n + 1) k
; (MsgPingPong MsgPong) → CollectDone (k n)
}
------------------------
-- Non-pipelined Duality
--
-- Termination witness
data Termination (ps : Set)
(agency : ps → Agency)
(a : Set)
(b : Set)
: Set where
Terminated : ∀ {st : ps} {pr : PeerRole}
→ a
→ b
→ NobodyHasAgency ≡ relative pr (agency st)
→ NobodyHasAgency ≡ relative (dual-role pr) (agency st)
→ Termination ps agency a b
theorem-non-pipelined-duality
: ∀ {ps : Set}
{msg : ps → ps → Set}
{agency : ps → Agency}
{pr : PeerRole}
{a : Set}
{b : Set}
{st : ps}
→ Peer msg agency pr a NonPipelined [] st
→ Peer msg agency (dual-role pr) b NonPipelined [] st
→ Termination ps agency a b
theorem-non-pipelined-duality (Yield _ msg k) (Await _ k') =
theorem-non-pipelined-duality k (k' msg)
theorem-non-pipelined-duality (Await _ k) (Yield _ msg k') =
theorem-non-pipelined-duality (k msg) k'
theorem-non-pipelined-duality (Done termA a) (Done termB b) =
Terminated a b termA termB
-- excluded cases
theorem-non-pipelined-duality (Yield weHaveAgency _ _)
(Yield theyHaveAgency _ _) =
⊥-elim (exclusion-lemma-client-and-server-have-agency₁ weHaveAgency theyHaveAgency)
theorem-non-pipelined-duality (Await theyHaveAgency _)
(Await weHaveAgency _) =
⊥-elim (exclusion-lemma-client-and-server-have-agency₂ theyHaveAgency weHaveAgency)
theorem-non-pipelined-duality (Yield weHaveAgency _ _)
(Done nobodyHasAgency _) =
⊥-elim (exclusion-lemma-we-have-agency-and-nobody-has-agency
weHaveAgency
nobodyHasAgency)
theorem-non-pipelined-duality (Done nobodyHasAgency _)
(Yield weHaveAgency _ _) =
⊥-elim (exclusion-lemma-we-have-agency-and-nobody-has-agency
weHaveAgency
nobodyHasAgency)
theorem-non-pipelined-duality (Await theyHaveAgency _)
(Done nobodyHasAgency _) =
⊥-elim (exclusion-lemma-they-have-agency-and-nobody-has-agency
theyHaveAgency
nobodyHasAgency)
theorem-non-pipelined-duality (Done nobodyHasAgency _)
(Await theyHaveAgency _) =
⊥-elim (exclusion-lemma-they-have-agency-and-nobody-has-agency
theyHaveAgency
nobodyHasAgency)
--------------
-- Un-pipeline
--
-- Transition queue which allows to transform pipelined 'Peer' into
-- non-pipelined one. Pipelined messages are pushed to the end together with
-- promised transitions to be collected.
--
data PrQueue {ps : Set}
(msg : ps → ps → Set)
(agency : ps -> Agency)
(pr : PeerRole)
: ps
→ List (Trans ps)
→ ps
→ Set where
ConsMsgQ : ∀ {st st' st'' : ps}
{q : List (Trans ps)}
→ WeHaveAgency ≡ relative pr (agency st)
→ msg st st'
→ PrQueue msg agency pr st' q st''
→ PrQueue msg agency pr st q st''
ConsTrQ : ∀ {st st' st'' : ps}
{q : List (Trans ps)}
→ PrQueue msg agency pr st' q st''
→ PrQueue msg agency pr st (Tr st st' ∷ q) st''
EmptyQ : ∀ {st : ps}
→ PrQueue msg agency pr st [] st
snockMsgQ : ∀ {ps : Set}
{msg : ps → ps → Set}
{agency : ps → Agency}
{pr : PeerRole}
{st st' st'' : ps}
{q : List (Trans ps)}
→ WeHaveAgency ≡ relative pr (agency st')
→ msg st' st''
→ PrQueue msg agency pr st q st'
→ PrQueue msg agency pr st q st''
snockMsgQ tok msg (ConsMsgQ tok' msg' q) = ConsMsgQ tok' msg' (snockMsgQ tok msg q)
snockMsgQ tok msg (ConsTrQ q) = ConsTrQ (snockMsgQ tok msg q)
snockMsgQ tok msg EmptyQ = ConsMsgQ tok msg EmptyQ
snockTrQ : ∀ {ps : Set}
{msg : ps → ps → Set}
{agency : ps → Agency}
{pr : PeerRole}
{st st' st'' : ps}
{q : List (Trans ps)}
→ PrQueue msg agency pr st q st'
→ PrQueue msg agency pr st (q ∷ʳ Tr st' st'') st''
snockTrQ (ConsMsgQ tok msg q) = ConsMsgQ tok msg (snockTrQ q)
snockTrQ (ConsTrQ q) = ConsTrQ (snockTrQ q)
snockTrQ EmptyQ = ConsTrQ EmptyQ
-- Every pipelined peer can be transformed into non-pipelined one, by
-- preserving the order of all transition.
--
theorem-unpipeline
: ∀ {ps : Set}
{msg : ps → ps → Set}
{agency : ps → Agency}
{pr : PeerRole}
{pl : IsPipelined}
{a : Set}
{stInit : ps}
→ Peer msg agency pr a pl [] stInit
→ Peer msg agency pr a NonPipelined [] stInit
theorem-unpipeline = go EmptyQ
where
go : ∀ {ps : Set}
{msg : ps → ps → Set}
{agency : ps → Agency}
{pr : PeerRole}
{pl : IsPipelined}
{a : Set}
{q : List (Trans ps)}
{st st' : ps}
→ PrQueue msg agency pr st q st'
→ Peer msg agency pr a pl q st'
→ Peer msg agency pr a NonPipelined [] st
-- non-piplined primitives
go EmptyQ (Done tok a) = Done tok a
go EmptyQ (Yield tok msg k) = Yield tok msg (go EmptyQ k)
go EmptyQ (Await tok k) = Await tok λ {msg → go EmptyQ (k msg)}
-- push msg and promised transition to back of the 'PrQueue'
go q (YieldPipelined tok msg k) =
go ( q
|> snockMsgQ tok msg
|> snockTrQ
)
k
go (ConsMsgQ tok msg q) k =
Yield tok msg (go q k)
go (ConsTrQ q) (Collect tok k) =
Await tok λ {msg → go (ConsTrQ q) (k msg)}
go (ConsTrQ q) (CollectDone k) =
go q k
----------
-- Duality
--
theorem-pipelined-duality
: ∀ {ps : Set}
{msg : ps → ps → Set}
{agency : ps → Agency}
{pr : PeerRole}
{pl : IsPipelined}
{a : Set}
{b : Set}
{st : ps}
→ Peer msg agency pr a pl [] st
→ Peer msg agency (dual-role pr) b pl [] st
→ Termination ps agency a b
theorem-pipelined-duality a b =
theorem-non-pipelined-duality (theorem-unpipeline a)
(theorem-unpipeline b)
|
{
"alphanum_fraction": 0.5842030666,
"avg_line_length": 28.5330882353,
"ext": "agda",
"hexsha": "d025b34cc1a24f1b0e7b868a8422d0d8fcba44e2",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "6773b88e8bbd1cfab98ed615855d9ae9c8859e0c",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "coot/homepage",
"max_forks_repo_path": "posts/agda/typed-protocols.agda",
"max_issues_count": 5,
"max_issues_repo_head_hexsha": "6773b88e8bbd1cfab98ed615855d9ae9c8859e0c",
"max_issues_repo_issues_event_max_datetime": "2020-02-18T21:05:51.000Z",
"max_issues_repo_issues_event_min_datetime": "2020-02-18T21:05:46.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "coot/homepage",
"max_issues_repo_path": "posts/agda/typed-protocols.agda",
"max_line_length": 85,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "6773b88e8bbd1cfab98ed615855d9ae9c8859e0c",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "coot/homepage",
"max_stars_repo_path": "posts/agda/typed-protocols.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 4369,
"size": 15522
}
|
------------------------------------------------------------------------
-- The Agda standard library
--
-- This module is DEPRECATED. Please use
-- Data.Vec.Relation.Binary.Pointwise.Extensional directly.
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Vec.Relation.Pointwise.Extensional where
open import Data.Vec.Relation.Binary.Pointwise.Extensional public
{-# WARNING_ON_IMPORT
"Data.Vec.Relation.Pointwise.Extensional was deprecated in v1.0.
Use Data.Vec.Relation.Binary.Pointwise.Extensional instead."
#-}
|
{
"alphanum_fraction": 0.5857385399,
"avg_line_length": 32.7222222222,
"ext": "agda",
"hexsha": "b969bd855b8fc12c1d7ba361b60b2a0a91a09df5",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2021-11-04T06:54:45.000Z",
"max_forks_repo_forks_event_min_datetime": "2021-11-04T06:54:45.000Z",
"max_forks_repo_head_hexsha": "fb380f2e67dcb4a94f353dbaec91624fcb5b8933",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "DreamLinuxer/popl21-artifact",
"max_forks_repo_path": "agda-stdlib/src/Data/Vec/Relation/Pointwise/Extensional.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "fb380f2e67dcb4a94f353dbaec91624fcb5b8933",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "DreamLinuxer/popl21-artifact",
"max_issues_repo_path": "agda-stdlib/src/Data/Vec/Relation/Pointwise/Extensional.agda",
"max_line_length": 72,
"max_stars_count": 5,
"max_stars_repo_head_hexsha": "fb380f2e67dcb4a94f353dbaec91624fcb5b8933",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "DreamLinuxer/popl21-artifact",
"max_stars_repo_path": "agda-stdlib/src/Data/Vec/Relation/Pointwise/Extensional.agda",
"max_stars_repo_stars_event_max_datetime": "2020-10-10T21:41:32.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-10-07T12:07:53.000Z",
"num_tokens": 108,
"size": 589
}
|
open import MJ.Types
import MJ.Classtable.Core as Core
module MJ.Classtable.Code {c}(Ct : Core.Classtable c) where
open import Prelude
open import Data.Maybe as Maybe using (Maybe; just; nothing)
open import Data.Star as Star
open import Data.List
open import Data.List.Relation.Unary.All hiding (construct)
open import Data.List.Properties.Extra as List+
open import Relation.Binary.PropositionalEquality
open import Relation.Nullary.Decidable
open import Data.String
import Data.Vec.Relation.Unary.All as Vec∀
open Core c
open Classtable Ct
open import MJ.Classtable.Membership Ct
open import MJ.LexicalScope c
open import MJ.Syntax Ct
data Body (I : Ctx) : Ty c → Set where
body : ∀ {r}{O : Ctx} → Stmts I r O → Expr O r → Body I r
{-
A helper to generate the shape of the context for method bodies
-}
methodctx : Cid c → List (Ty c) → Ctx
methodctx cid as = (ref cid ∷ as)
{-
A helper to generate the shape of the context for constructors
-}
constrctx : Cid c → Ctx
constrctx cid = let cl = Σ cid in (ref cid ∷ Class.constr cl)
-- A method is either just a body, or a body prefixed by a super call.
data Method (cid : Cid c)(m : String) : Sig c → Set where
super_⟨_⟩then_ : ∀ {as b} →
let
pid = Class.parent (Σ cid)
Γ = methodctx cid as
in
-- must have a super to call, with the same signature
AccMember pid METHOD m (as , b) →
-- super call arguments
All (Expr Γ) as →
-- body
Body (Γ +local b) b → Method cid m (as , b)
body : ∀ {as b} → Body (methodctx cid as) b → Method cid m (as , b)
-- Constructors are similar
data Constructor (cid : Cid c) : Set where
super_then_ : let
pid = Class.parent (Σ cid)
pclass = Σ pid
Γ = constrctx cid
in
-- super call arguments
All (Expr Γ) (Class.constr pclass) →
-- body
Body Γ void →
Constructor cid
body : Body (constrctx cid) void → Constructor cid
{-
A class implementation consists of a constructor and a body for every
METHOD declaration.
-}
record Implementation (cid : Cid c) : Set where
constructor implementation
open Class (Σ cid) public
field
construct : Constructor cid
mbodies : All (λ{ (name , sig) → Method cid name sig }) (decls METHOD)
-- Code is a lookup table for class implementations for every class identifier
Code = ∀ cid → Implementation cid
-- Mirroring `IsMember METHOD` we define the notion of an inherited method body.
InheritedMethod : ∀ (cid : Cid c)(m : String) → Sig c → Set
InheritedMethod cid m s = ∃ λ pid → Σ ⊢ cid <: pid × Method pid m s
|
{
"alphanum_fraction": 0.622688478,
"avg_line_length": 33.0823529412,
"ext": "agda",
"hexsha": "c6d04e2fb0189d42c5aae81963f9188d229c7bda",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2021-12-28T17:38:05.000Z",
"max_forks_repo_forks_event_min_datetime": "2021-12-28T17:38:05.000Z",
"max_forks_repo_head_hexsha": "0c096fea1716d714db0ff204ef2a9450b7a816df",
"max_forks_repo_licenses": [
"Apache-2.0"
],
"max_forks_repo_name": "metaborg/mj.agda",
"max_forks_repo_path": "src/MJ/Classtable/Code.agda",
"max_issues_count": 1,
"max_issues_repo_head_hexsha": "0c096fea1716d714db0ff204ef2a9450b7a816df",
"max_issues_repo_issues_event_max_datetime": "2020-10-14T13:41:58.000Z",
"max_issues_repo_issues_event_min_datetime": "2019-01-13T13:03:47.000Z",
"max_issues_repo_licenses": [
"Apache-2.0"
],
"max_issues_repo_name": "metaborg/mj.agda",
"max_issues_repo_path": "src/MJ/Classtable/Code.agda",
"max_line_length": 80,
"max_stars_count": 10,
"max_stars_repo_head_hexsha": "0c096fea1716d714db0ff204ef2a9450b7a816df",
"max_stars_repo_licenses": [
"Apache-2.0"
],
"max_stars_repo_name": "metaborg/mj.agda",
"max_stars_repo_path": "src/MJ/Classtable/Code.agda",
"max_stars_repo_stars_event_max_datetime": "2021-09-24T08:02:33.000Z",
"max_stars_repo_stars_event_min_datetime": "2017-11-17T17:10:36.000Z",
"num_tokens": 740,
"size": 2812
}
|
-- Andreas, Jesper, 2017-05-13, issue #2578 reported by nad
-- Jesper, 2017-07-06, absurd clauses are no longer highlighted as catchall,
-- so the test case had to be changed to reproduce the intended behaviour.
data _⊎_ (A B : Set) : Set where
inj₁ : A → A ⊎ B
inj₂ : B → A ⊎ B
record ⊤ : Set where
constructor tt
data ⊥ : Set where
Maybe : Set → Set
Maybe A = ⊤ ⊎ A
pattern nothing = inj₁ tt
pattern just x = inj₂ x
Bool : Set
Bool = ⊤ ⊎ ⊤
pattern true = inj₁ tt
pattern false = inj₂ tt
x : Maybe ⊥
x = nothing
_∋_ : ∀ {ℓ} → (A : Set ℓ) (a : A) → A
A ∋ a = a
A : Set₁
A with Bool ∋ false
A | true = Set
A | false with x | x
... | nothing | nothing = Set
... | just x | _ = {!!}
... | _ | just y = {!!}
|
{
"alphanum_fraction": 0.5941828255,
"avg_line_length": 18.5128205128,
"ext": "agda",
"hexsha": "8641276269e6c0c9512ca406adb385624f40d081",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cruhland/agda",
"max_forks_repo_path": "test/interaction/Issue2578.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cruhland/agda",
"max_issues_repo_path": "test/interaction/Issue2578.agda",
"max_line_length": 76,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cruhland/agda",
"max_stars_repo_path": "test/interaction/Issue2578.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 269,
"size": 722
}
|
-- Check that errors from tactics are displayed properly.
module _ where
open import Common.Prelude hiding (_>>=_)
open import Common.Equality
open import Common.Reflection
failTactic : Term → TC ⊤
failTactic hole =
inferType hole >>= λ goal →
typeError (strErr "Surprisingly the" ∷ nameErr (quote failTactic) ∷
strErr "failed to prove" ∷ termErr goal ∷ [])
macro
proveIt = failTactic
postulate
ComplexityClass : Set
P NP : ComplexityClass
thm : P ≡ NP → ⊥
thm = proveIt
|
{
"alphanum_fraction": 0.7054108216,
"avg_line_length": 21.6956521739,
"ext": "agda",
"hexsha": "9b5c511356e110a91329b7f4e024d70fe637b293",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2019-03-05T20:02:38.000Z",
"max_forks_repo_forks_event_min_datetime": "2019-03-05T20:02:38.000Z",
"max_forks_repo_head_hexsha": "231d6ad8e77b67ff8c4b1cb35a6c31ccd988c3e9",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "Agda-zh/agda",
"max_forks_repo_path": "test/Fail/TacticFail.agda",
"max_issues_count": 3,
"max_issues_repo_head_hexsha": "aac88412199dd4cbcb041aab499d8a6b7e3f4a2e",
"max_issues_repo_issues_event_max_datetime": "2019-04-01T19:39:26.000Z",
"max_issues_repo_issues_event_min_datetime": "2018-11-14T15:31:44.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "hborum/agda",
"max_issues_repo_path": "test/Fail/TacticFail.agda",
"max_line_length": 69,
"max_stars_count": 3,
"max_stars_repo_head_hexsha": "aac88412199dd4cbcb041aab499d8a6b7e3f4a2e",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "hborum/agda",
"max_stars_repo_path": "test/Fail/TacticFail.agda",
"max_stars_repo_stars_event_max_datetime": "2015-12-07T20:14:00.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-03-28T14:51:03.000Z",
"num_tokens": 142,
"size": 499
}
|
------------------------------------------------------------------------
-- The Agda standard library
--
-- The Maybe type
------------------------------------------------------------------------
-- The definitions in this file are reexported by Data.Maybe.
module Data.Maybe.Core where
open import Level
data Maybe {a} (A : Set a) : Set a where
just : (x : A) → Maybe A
nothing : Maybe A
{-# IMPORT Data.FFI #-}
{-# COMPILED_DATA Maybe Data.FFI.AgdaMaybe Just Nothing #-}
|
{
"alphanum_fraction": 0.4701030928,
"avg_line_length": 25.5263157895,
"ext": "agda",
"hexsha": "61101097c0b86f2a7a45deba58dc4e353ad6537f",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "9d4c43b1609d3f085636376fdca73093481ab882",
"max_forks_repo_licenses": [
"Apache-2.0"
],
"max_forks_repo_name": "qwe2/try-agda",
"max_forks_repo_path": "agda-stdlib-0.9/src/Data/Maybe/Core.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "9d4c43b1609d3f085636376fdca73093481ab882",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"Apache-2.0"
],
"max_issues_repo_name": "qwe2/try-agda",
"max_issues_repo_path": "agda-stdlib-0.9/src/Data/Maybe/Core.agda",
"max_line_length": 72,
"max_stars_count": 1,
"max_stars_repo_head_hexsha": "9d4c43b1609d3f085636376fdca73093481ab882",
"max_stars_repo_licenses": [
"Apache-2.0"
],
"max_stars_repo_name": "qwe2/try-agda",
"max_stars_repo_path": "agda-stdlib-0.9/src/Data/Maybe/Core.agda",
"max_stars_repo_stars_event_max_datetime": "2016-10-20T15:52:05.000Z",
"max_stars_repo_stars_event_min_datetime": "2016-10-20T15:52:05.000Z",
"num_tokens": 97,
"size": 485
}
|
module Type.Identity.Proofs where
import Lvl
open import Structure.Function
open import Structure.Relator.Properties
open import Structure.Relator
open import Structure.Type.Identity
open import Type.Identity
open import Type
private variable ℓ ℓ₁ ℓ₂ ℓₑ ℓₑ₁ ℓₑ₂ ℓₚ : Lvl.Level
private variable T A B : Type{ℓ}
private variable P : T → Type{ℓ}
private variable _▫_ : A → B → Type{ℓ}
instance
Id-reflexivity : Reflexivity(Id{T = T})
Reflexivity.proof Id-reflexivity = intro
instance
Id-identityEliminator : IdentityEliminator{ℓₚ = ℓₚ}(Id{T = T})
IdentityEliminator.elim Id-identityEliminator = elim
instance
Id-identityEliminationOfIntro : IdentityEliminationOfIntro{ℓₘ = ℓ}(Id{T = T})(Id)
IdentityEliminationOfIntro.proof Id-identityEliminationOfIntro P p = intro
instance
Id-identityType : IdentityType(Id)
Id-identityType = intro
{-
open import Logic.Propositional
open import Logic.Propositional.Equiv
open import Relator.Equals.Proofs
open import Structure.Setoid
te : ⦃ equiv-A : Equiv{ℓₑ}(A)⦄ → ∀{f : A → Type{ℓ}} → Function ⦃ equiv-A ⦄ ⦃ [↔]-equiv ⦄ (f)
test : ⦃ equiv-A : Equiv{ℓₑ}(A)⦄ → ∀{P : A → Type{ℓ}} → UnaryRelator ⦃ equiv-A ⦄ (P)
UnaryRelator.substitution test eq p = [↔]-to-[→] (Function.congruence te eq) p
-}
|
{
"alphanum_fraction": 0.7326968974,
"avg_line_length": 29.2325581395,
"ext": "agda",
"hexsha": "99b594fab5f1fd6459489b1400ef433a4a74a8d9",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "Lolirofle/stuff-in-agda",
"max_forks_repo_path": "Type/Identity/Proofs.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "Lolirofle/stuff-in-agda",
"max_issues_repo_path": "Type/Identity/Proofs.agda",
"max_line_length": 92,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "Lolirofle/stuff-in-agda",
"max_stars_repo_path": "Type/Identity/Proofs.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-05T06:53:22.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-04-07T17:58:13.000Z",
"num_tokens": 424,
"size": 1257
}
|
-- Abstract constructors
module Issue476c where
module M where
data D : Set
abstract
data D where
c : D
x : M.D
x = M.c
|
{
"alphanum_fraction": 0.6323529412,
"avg_line_length": 11.3333333333,
"ext": "agda",
"hexsha": "e4bba07bf43628b2ccb831405b89106208e9a28a",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "70c8a575c46f6a568c7518150a1a64fcd03aa437",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "masondesu/agda",
"max_forks_repo_path": "test/fail/Issue476c.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "70c8a575c46f6a568c7518150a1a64fcd03aa437",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "masondesu/agda",
"max_issues_repo_path": "test/fail/Issue476c.agda",
"max_line_length": 24,
"max_stars_count": 1,
"max_stars_repo_head_hexsha": "aa10ae6a29dc79964fe9dec2de07b9df28b61ed5",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "asr/agda-kanso",
"max_stars_repo_path": "test/fail/Issue476c.agda",
"max_stars_repo_stars_event_max_datetime": "2018-10-10T17:08:44.000Z",
"max_stars_repo_stars_event_min_datetime": "2018-10-10T17:08:44.000Z",
"num_tokens": 42,
"size": 136
}
|
module Array.APL where
open import Array.Base
open import Array.Properties
open import Data.Nat
open import Data.Nat.DivMod hiding (_/_)
open import Data.Nat.Properties
open import Data.Fin using (Fin; zero; suc; raise; toℕ; fromℕ≤)
open import Data.Fin.Properties using (toℕ<n)
open import Data.Vec
open import Data.Vec.Properties
open import Data.Product
open import Agda.Builtin.Float
open import Function
open import Relation.Binary.PropositionalEquality hiding (Extensionality)
open import Relation.Nullary
open import Relation.Nullary.Decidable
open import Relation.Nullary.Negation
--open import Relation.Binary
-- Now we start to introduce APL operators trying
-- to maintain syntactic rules and semantics.
-- We won't be able to mimic explicit concatenations
-- like 2 3 4 is a vector [2, 3, 4], as we would have
-- to overload the " " somehow.
-- This relation describes promotion of the scalar element in
-- dyadic operations.
data dy-args : ∀ n m k → (Vec ℕ n) → (Vec ℕ m) → (Vec ℕ k) → Set where
instance
n-n : ∀ {n}{s} → dy-args n n n s s s
n-0 : ∀ {n}{s}{s₁} → dy-args n 0 n s s₁ s
0-n : ∀ {n}{s}{s₁} → dy-args 0 n n s s₁ s₁
dyadic-type : ∀ a → Set a → Set a
dyadic-type a X = ∀ {n m k}{s s₁ s₂}{{c : dy-args n m k s s₁ s₂}}
→ Ar X n s → Ar X m s₁ → Ar X k s₂
lift-binary-op : ∀ {a}{X : Set a} → ∀ (op : X → X → X) → dyadic-type a X
lift-binary-op op ⦃ c = n-n ⦄ (imap f) (imap g) = imap λ iv → op (f iv) (g iv)
lift-binary-op op {s₁ = []} ⦃ c = n-0 ⦄ (imap f) (imap g) = imap λ iv → op (f iv) (g [])
lift-binary-op op {s = [] } ⦃ c = 0-n ⦄ (imap f) (imap g) = imap λ iv → op (f []) (g iv)
lift-unary-op : ∀ {a}{X : Set a} → ∀ (op : X → X)
→ ∀ {n s} → Ar X n s → Ar X n s
lift-unary-op f (imap g) = imap (λ iv → f (g iv))
dyadic-type-c : ∀ a → Set a → Set a
dyadic-type-c a X = ∀ {n m k}{s s₁ s₂}
→ Ar X n s → dy-args n m k s s₁ s₂ → Ar X m s₁ → Ar X k s₂
-- Nat operations
infixr 20 _+ₙ_
infixr 20 _×ₙ_
_+ₙ_ = lift-binary-op _+_
_×ₙ_ = lift-binary-op _*_
_-safe-_ : (a : ℕ) → (b : ℕ) .{≥ : a ≥ b} → ℕ
a -safe- b = a ∸ b
-- FIXME As _-ₙ_ requires a proof, we won't consider yet
-- full dyadic types for _-ₙ_, as it would require us
-- to define dyadic types for ≥a.
infixr 20 _-ₙ_
_-ₙ_ : ∀ {n}{s}
→ (a : Ar ℕ n s) → (b : Ar ℕ n s)
→ .{≥ : a ≥a b}
→ Ar ℕ n s
(imap f -ₙ imap g) {≥} = imap λ iv → (f iv -safe- g iv) {≥ = ≥ iv}
--≢-sym : ∀ {X : Set}{a b : X} → a ≢ b → b ≢ a
--≢-sym pf = pf ∘ sym
infixr 20 _÷ₙ_
_÷ₙ_ : ∀ {n}{s}
→ (a : Ar ℕ n s) → (b : Ar ℕ n s)
→ {≥0 : cst 0 <a b}
→ Ar ℕ n s
_÷ₙ_ (imap f) (imap g) {≥0} = imap λ iv → (f iv div g iv) {≢0 = fromWitnessFalse (≢-sym $ <⇒≢ $ ≥0 iv) }
infixr 20 _+⟨_⟩ₙ_
infixr 20 _×⟨_⟩ₙ_
_+⟨_⟩ₙ_ : dyadic-type-c _ _
a +⟨ c ⟩ₙ b = _+ₙ_ {{c = c}} a b
_×⟨_⟩ₙ_ : dyadic-type-c _ _
a ×⟨ c ⟩ₙ b = _×ₙ_ {{c = c}} a b
-- Float operations
infixr 20 _+ᵣ_
_+ᵣ_ = lift-binary-op primFloatPlus
infixr 20 _-ᵣ_
_-ᵣ_ = lift-binary-op primFloatMinus
infixr 20 _×ᵣ_
_×ᵣ_ = lift-binary-op primFloatTimes
-- XXX we can request the proof that the right argument is not zero.
-- However, the current primFloatDiv has the type Float → Float → Float, so...
infixr 20 _÷ᵣ_
_÷ᵣ_ = lift-binary-op primFloatDiv
infixr 20 _×⟨_⟩ᵣ_
_×⟨_⟩ᵣ_ : dyadic-type-c _ _
a ×⟨ c ⟩ᵣ b = _×ᵣ_ {{c = c}} a b
infixr 20 _+⟨_⟩ᵣ_
_+⟨_⟩ᵣ_ : dyadic-type-c _ _
a +⟨ c ⟩ᵣ b = _+ᵣ_ {{c = c}} a b
infixr 20 _-⟨_⟩ᵣ_
_-⟨_⟩ᵣ_ : dyadic-type-c _ _
a -⟨ c ⟩ᵣ b = _-ᵣ_ {{c = c}} a b
infixr 20 _÷⟨_⟩ᵣ_
_÷⟨_⟩ᵣ_ : dyadic-type-c _ _
a ÷⟨ c ⟩ᵣ b = _÷ᵣ_ {{c = c}} a b
infixr 20 *ᵣ_
*ᵣ_ = lift-unary-op primFloatExp
module xx where
a : Ar ℕ 2 (3 ∷ 3 ∷ [])
a = cst 1
s : Ar ℕ 0 []
s = cst 2
test₁ = a +ₙ a
test₂ = a +ₙ s
test₃ = s +ₙ a
--test = (s +ₙ s)
test₄ = s +⟨ n-n ⟩ₙ s
test₅ : ∀ {n s} → Ar ℕ n s → Ar ℕ 0 [] → Ar ℕ n s
test₅ = _+ₙ_
infixr 20 ρ_
ρ_ : ∀ {ℓ}{X : Set ℓ}{d s} → Ar X d s → Ar ℕ 1 (d ∷ [])
ρ_ {s = s} _ = s→a s
infixr 20 ,_
,_ : ∀ {a}{X : Set a}{n s} → Ar X n s → Ar X 1 (prod s ∷ [])
,_ {s = s} (p) = imap λ iv → unimap p (off→idx s iv)
-- Reshape
infixr 20 _ρ_
_ρ_ : ∀ {a}{X : Set a}{n}{sa}
→ (s : Ar ℕ 1 (n ∷ []))
→ (a : Ar X n sa)
-- if the `sh` is non-empty, `s` must be non-empty as well.
→ {s≢0⇒ρa≢0 : prod (a→s s) ≢ 0 → prod sa ≢ 0}
→ Ar X n (a→s s)
_ρ_ {sa = sa} s a {s≢0⇒ρa≢0} with prod sa ≟ 0 | prod (a→s s) ≟ 0
_ρ_ {sa = sa} s a {s≢0⇒ρa≢0} | _ | yes s≡0 = mkempty (a→s s) s≡0
_ρ_ {sa = sa} s a {s≢0⇒ρa≢0} | yes ρa≡0 | no s≢0 = contradiction ρa≡0 (s≢0⇒ρa≢0 s≢0)
_ρ_ {sa = sa} s a {s≢0⇒ρa≢0} | no ρa≢0 | _ = imap from-flat
where
from-flat : _
from-flat iv = let
off = idx→off (a→s s) iv --{!!} -- (ix-lookup iv zero)
flat = unimap $ , a
ix = (toℕ (ix-lookup off zero) mod prod sa)
{≢0 = fromWitnessFalse ρa≢0}
in
flat (ix ∷ [])
reduce-1d : ∀ {a}{X : Set a}{n} → Ar X 1 (n ∷ []) → (X → X → X) → X → X
reduce-1d {n = zero} (imap p) op neut = neut
reduce-1d {n = suc n} (imap p) op neut = op (p $ zero ∷ [])
(reduce-1d (imap (λ iv → p (suc (ix-lookup iv zero) ∷ []))) op neut)
{-
This goes right to left if we want to
reduce-1d (imap λ iv → p ((raise 1 $ ix-lookup iv zero) ∷ []))
op (op neut (p $ zero ∷ []))
-}
Scal : ∀ {a} → Set a → Set a
Scal X = Ar X 0 []
scal : ∀ {a}{X : Set a} → X → Scal X
scal = cst
unscal : ∀ {a}{X : Set a} → Scal X → X
unscal (imap f) = f []
module true-reduction where
thm : ∀ {a}{X : Set a}{n m} → (s : Vec X (n + m)) → s ≡ take n s ++ drop n s
thm {n = n} s with splitAt n s
thm {n = n} .(xs ++ ys) | xs , ys , refl = refl
thm2 : ∀ {a}{X : Set a} → (v : Vec X 1) → v ≡ head v ∷ []
thm2 (x ∷ []) = refl
-- This is a variant with take
_/⟨_⟩_ : ∀ {a}{X : Set a}{n}{s : Vec ℕ (n + 1)}
→ (X → X → X) → X
→ Ar X (n + 1) s
→ Ar X n (take n s)
_/⟨_⟩_ {n = n} {s} f neut a = let
x = nest {s = take n s} {s₁ = drop n s} $ subst (λ x → Ar _ _ x) (thm {n = n} s) a
in imap λ iv → reduce-1d (subst (λ x → Ar _ _ x) (thm2 (drop n s)) $ unimap x iv) f neut
_/₁⟨_⟩_ : ∀ {a}{X : Set a}{n}{s : Vec ℕ n}{m}
→ (X → X → X) → X
→ Ar X (n + 1) (s ++ (m ∷ []))
→ Ar X n s
_/₁⟨_⟩_ {n = n} {s} f neut a = let
x = nest {s = s} a
in imap λ iv → reduce-1d (unimap x iv) f neut
module test-reduce where
a : Ar ℕ 2 (4 ∷ 4 ∷ [])
a = cst 1
b : Ar ℕ 1 (5 ∷ [])
b = cst 2
test₁ = _/⟨_⟩_ {n = 0} _+_ 0 (, a)
test₂ = _/⟨_⟩_ {n = 0} _+_ 0 b
-- FIXME! This reduction does not implement semantics of APL,
-- as it assumes that we always reduce to scalars!
-- Instead, in APL / reduce on the last axis only,
-- i.e. ⍴ +/3 4 5 ⍴ ⍳1 = 3 4
-- This is mimicing APL's f/ syntax, but with extra neutral
-- element. We can later introduce the variant where certain
-- operations come with pre-defined neutral elements.
_/⟨_⟩_ : ∀ {a}{X : Set a}{n s}
→ (Scal X → Scal X → Scal X) → Scal X → Ar X n s → Scal X
f /⟨ neut ⟩ a = let
op x y = unscal $ f (scal x) (scal y)
a-1d = , a
neut = unscal neut
in
scal $ reduce-1d a-1d op neut
-- XXX I somehow don't understand how to make X to be an arbitrary Set a...
data reduce-neut : {X : Set} → (Scal X → Scal X → Scal X) → Scal X → Set where
instance
plus-nat : reduce-neut _+⟨ n-n ⟩ₙ_ (cst 0)
mult-nat : reduce-neut _×⟨ n-n ⟩ₙ_ (cst 1)
plus-flo : reduce-neut (_+ᵣ_ {{c = n-n}}) (cst 0.0)
mult-flo : reduce-neut (_×ᵣ_ {{c = n-n}}) (cst 1.0)
infixr 20 _/_
_/_ : ∀ {X : Set}{n s neut}
→ (op : Scal X → Scal X → Scal X) → {{c : reduce-neut op neut}}
→ Ar X n s → Scal X
_/_ {neut = neut} f a = f /⟨ neut ⟩ a
module test-reduce where
a = s→a $ 1 ∷ 2 ∷ 3 ∷ 4 ∷ []
test₁ : reduce-1d a _+_ 0 ≡ 10
test₁ = refl
test₂ : _+⟨ n-n ⟩ₙ_ /⟨ scal 0 ⟩ a ≡ scal 10
test₂ = refl
test₃ : _+ₙ_ / a ≡ scal 10
test₃ = refl
-- This is somewhat semi-useful dot-product expressed
-- pretty close to what you'd write in APL.
dotp : ∀ {n s} → Ar ℕ n s → Ar ℕ n s → Scal ℕ
dotp a b = _+ₙ_ / a ×ₙ b
test₄ : dotp a a ≡ scal (1 + 4 + 9 + 16)
test₄ = refl
-- The size of the leading axis.
infixr 20 ≢_
≢_ : ∀ {a}{X : Set a}{n s} → Ar X n s → Scal ℕ
≢_ {n = zero} a = scal 1
≢_ {n = suc n} {s} a = scal $ head s
data iota-type : (d : ℕ) → (n : ℕ) → (Vec ℕ d) → Set where
instance
iota-scal : iota-type 0 1 []
iota-vec : ∀ {n} → iota-type 1 n (n ∷ [])
iota-res-t : ∀ {d n s} → iota-type d n s → (sh : Ar ℕ d s) → Set
iota-res-t {n = n} iota-scal sh = Ar (Σ ℕ λ x → x < unscal sh)
1 (unscal sh ∷ [])
iota-res-t {n = n} iota-vec sh = Ar (Σ (Ar ℕ 1 (n ∷ []))
λ v → v <a sh)
n (a→s sh)
a<b⇒b≡c⇒a<c : ∀ {a b c} → a < b → b ≡ c → a < c
a<b⇒b≡c⇒a<c a<b refl = a<b
infixr 20 ι_
ι_ : ∀ {d n s}{{c : iota-type d n s}}
→ (sh : Ar ℕ d s)
→ iota-res-t c sh
ι_ ⦃ c = iota-scal ⦄ s = (imap λ iv → (toℕ $ ix-lookup iv zero) , toℕ<n (ix-lookup iv zero))
ι_ {n = n} {s = s ∷ []} ⦃ c = iota-vec ⦄ (imap sh) = imap cast-ix→a
where
cast-ix→a : _
cast-ix→a iv = let
ix , pf = ix→a iv
in ix , λ jv → a<b⇒b≡c⇒a<c (pf jv) (s→a∘a→s (imap sh) jv)
-- Zilde and comma
⍬ : ∀ {a}{X : Set a} → Ar X 1 (0 ∷ [])
⍬ = imap λ iv → magic-fin $ ix-lookup iv zero
-- XXX We are going to use _·_ instead of _,_ as the
-- latter is a constructor of dependent sum. Renaming
-- all the occurrences to something else would take
-- a bit of work which we should do later.
infixr 30 _·_
_·_ : ∀ {a}{X : Set a}{n} → X → Ar X 1 (n ∷ []) → Ar X 1 (suc n ∷ [])
x · (imap p) = imap λ iv → case ix-lookup iv zero of λ where
zero → x
(suc j) → p (j ∷ [])
-- Note that two dots in an upper register combined with
-- the underscore form the _̈ symbol. When the symbol is
-- used on its own, it looks like ̈ which is the correct
-- "spelling".
infixr 20 _̈_
_̈_ : ∀ {a}{X Y : Set a}{n s}
→ (X → Y)
→ Ar X n s
→ Ar Y n s
f ̈ imap p = imap λ iv → f $ p iv
-- Take and Drop
ax+sh<s : ∀ {n}
→ (ax sh s : Ar ℕ 1 (n ∷ []))
→ (s≥sh : s ≥a sh)
→ (ax <a (s -ₙ sh) {≥ = s≥sh})
→ (ax +ₙ sh) <a s
ax+sh<s (imap ax) (imap sh) (imap s) s≥sh ax<s-sh iv =
let
ax+sh<s-sh+sh = +-monoˡ-< (sh iv) (ax<s-sh iv)
s-sh+sh≡s = m∸n+n≡m (s≥sh iv)
in a<b⇒b≡c⇒a<c ax+sh<s-sh+sh s-sh+sh≡s
_↑_ : ∀ {a}{X : Set a}{n s}
→ (sh : Ar ℕ 1 (n ∷ []))
→ (a : Ar X n s)
→ {pf : s→a s ≥a sh}
→ Ar X n $ a→s sh
_↑_ {s = s} sh (imap f) {pf} with (prod $ a→s sh) ≟ 0
_↑_ {s = s} sh (imap f) {pf} | yes Πsh≡0 = mkempty _ Πsh≡0
_↑_ {s = s} (imap q) (imap f) {pf} | no Πsh≢0 = imap mtake
where
mtake : _
mtake iv = let
ai , ai< = ix→a iv
ix<q jv = a<b⇒b≡c⇒a<c (ai< jv) (s→a∘a→s (imap q) jv)
ix = a→ix ai (s→a s) λ jv → ≤-trans (ix<q jv) (pf jv)
in f (subst-ix (a→s∘s→a s) ix)
_↓_ : ∀ {a}{X : Set a}{n s}
→ (sh : Ar ℕ 1 (n ∷ []))
→ (a : Ar X n s)
→ {pf : (s→a s) ≥a sh}
→ Ar X n $ a→s $ (s→a s -ₙ sh) {≥ = pf}
_↓_ {s = s} sh (imap x) {pf} with
let p = prod $ a→s $ (s→a s -ₙ sh) {≥ = pf}
in p ≟ 0
_↓_ {s = s} sh (imap f) {pf} | yes Π≡0 = mkempty _ Π≡0
_↓_ {s = s} (imap q) (imap f) {pf} | no Π≢0 = imap mkdrop
where
mkdrop : _
mkdrop iv = let
ai , ai< = ix→a iv
ax = ai +ₙ (imap q)
thmx = ax+sh<s
ai (imap q) (s→a s) pf
λ jv → a<b⇒b≡c⇒a<c (ai< jv)
(s→a∘a→s ((s→a s -ₙ (imap q)) {≥ = pf}) jv)
ix = a→ix ax (s→a s) thmx
in f (subst-ix (a→s∘s→a s) ix)
_̈⟨_⟩_ : ∀ {a}{X Y Z : Set a}{n s}
→ Ar X n s
→ (X → Y → Z)
→ Ar Y n s → Ar Z n s
--(imap p) ̈⟨ f ⟩ (imap p₁) = imap λ iv → f (p iv) (p₁ iv)
p ̈⟨ f ⟩ p₁ = imap λ iv → f (unimap p iv) (unimap p₁ iv)
|
{
"alphanum_fraction": 0.4847927005,
"avg_line_length": 29.9616306954,
"ext": "agda",
"hexsha": "a5c600364f638ce71be5c1ea39f401130664aebb",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2020-10-12T07:19:48.000Z",
"max_forks_repo_forks_event_min_datetime": "2020-10-12T07:19:48.000Z",
"max_forks_repo_head_hexsha": "584fedb30552f820c0668cedae53ec3d926860b5",
"max_forks_repo_licenses": [
"0BSD"
],
"max_forks_repo_name": "ashinkarov/agda-array",
"max_forks_repo_path": "Array/APL.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "584fedb30552f820c0668cedae53ec3d926860b5",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"0BSD"
],
"max_issues_repo_name": "ashinkarov/agda-array",
"max_issues_repo_path": "Array/APL.agda",
"max_line_length": 112,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "584fedb30552f820c0668cedae53ec3d926860b5",
"max_stars_repo_licenses": [
"0BSD"
],
"max_stars_repo_name": "ashinkarov/agda-array",
"max_stars_repo_path": "Array/APL.agda",
"max_stars_repo_stars_event_max_datetime": "2021-06-15T14:21:32.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-05-09T13:53:46.000Z",
"num_tokens": 5425,
"size": 12494
}
|
module Numeral.Natural.Coprime.Proofs where
open import Functional
open import Logic
open import Logic.Classical
open import Logic.Propositional
open import Logic.Propositional.Theorems
import Lvl
open import Numeral.Finite
open import Numeral.Natural
open import Numeral.Natural.Coprime
open import Numeral.Natural.Decidable
open import Numeral.Natural.Function.GreatestCommonDivisor
open import Numeral.Natural.Relation.Divisibility.Proofs
open import Numeral.Natural.Oper
open import Numeral.Natural.Prime
open import Numeral.Natural.Prime.Proofs
open import Numeral.Natural.Relation.Divisibility
open import Numeral.Natural.Relation.Order
open import Numeral.Natural.Relation.Order.Proofs
open import Relator.Equals
open import Structure.Relator.Properties
open import Type.Properties.Decidable.Proofs
open import Type
private variable n x y d p : ℕ
-- 1 is the only number coprime to itself because it does not have any divisors except for itself.
Coprime-reflexivity-condition : Coprime(n)(n) ↔ (n ≡ 1)
Coprime-reflexivity-condition {n} = [↔]-intro l (r{n}) where
l : Coprime(n)(n) ← (n ≡ 1)
Coprime.proof(l [≡]-intro) {a} a1 _ = [1]-only-divides-[1] (a1)
r : ∀{n} → Coprime(n)(n) → (n ≡ 1)
r {𝟎} (intro z1) = z1 Div𝟎 Div𝟎
r {𝐒(𝟎)} _ = [≡]-intro
r {𝐒(𝐒(n))} (intro ssn1) = ssn1 {𝐒(𝐒(n))} divides-reflexivity divides-reflexivity
instance
Coprime-symmetry : Symmetry(Coprime)
Coprime.proof(Symmetry.proof Coprime-symmetry (intro proof)) {n} nx ny = proof {n} ny nx
-- The only number coprime to 0 is 1 because while all numbers divide 0, only 1 divides 1.
Coprime-of-0-condition : ∀{x} → Coprime(0)(x) → (x ≡ 1)
Coprime-of-0-condition {0} (intro n1) = n1 Div𝟎 Div𝟎
Coprime-of-0-condition {1} (intro n1) = [≡]-intro
Coprime-of-0-condition {𝐒(𝐒(x))} (intro n1) = n1 Div𝟎 divides-reflexivity
-- 1 is coprime to all numbers because only 1 divides 1.
Coprime-of-1 : Coprime(1)(x)
Coprime.proof (Coprime-of-1 {x}) {n} n1 nx = [1]-only-divides-[1] n1
Coprime-of-[+] : Coprime(x)(y) → Coprime(x)(x + y)
Coprime.proof (Coprime-of-[+] {x}{y} (intro proof)) {n} nx nxy = proof {n} nx ([↔]-to-[→] (divides-without-[+] nxy) nx)
-- Coprimality is obviously equivalent to the greatest common divisor being 1 by definition.
Coprime-gcd : Coprime(x)(y) ↔ (gcd(x)(y) ≡ 1)
Coprime-gcd = [↔]-transitivity ([↔]-intro l r) Gcd-gcd-value where
l : Coprime(x)(y) ← Gcd(x)(y) 1
Coprime.proof (l p) nx ny = [1]-only-divides-[1] (Gcd.maximum₂ p nx ny)
r : Coprime(x)(y) → Gcd(x)(y) 1
Gcd.divisor(r (intro coprim)) 𝟎 = [1]-divides
Gcd.divisor(r (intro coprim)) (𝐒 𝟎) = [1]-divides
Gcd.maximum(r (intro coprim)) dv with [≡]-intro ← coprim (dv 𝟎) (dv(𝐒 𝟎)) = [1]-divides
-- A smaller number and a greater prime number is coprime.
-- If the greater number is prime, then no smaller number will divide it except for 1, and greater numbers never divide smaller ones.
-- Examples (y = 7):
-- The prime factors of 7 is only itself (because it is prime).
-- Then the only alternatives for x are:
-- x ∈ {1,2,3,4,5,6}
-- None of them is able to have 7 as a prime factor because it is greater:
-- 1=1, 2=2, 3=3, 4=2⋅2, 5=5, 6=2⋅3
Coprime-of-Prime : (𝐒(x) < y) → Prime(y) → Coprime(𝐒(x))(y)
Coprime.proof (Coprime-of-Prime (succ(succ lt)) prim) nx ny with prime-only-divisors prim ny
Coprime.proof (Coprime-of-Prime (succ(succ lt)) prim) nx ny | [∨]-introₗ n1 = n1
Coprime.proof (Coprime-of-Prime (succ(succ lt)) prim) nx ny | [∨]-introᵣ [≡]-intro with () ← [≤]-to-[≯] lt ([≤]-without-[𝐒] (divides-upper-limit nx))
-- A prime number either divides a number or forms a coprime pair.
-- If a prime number does not divide a number, then it cannot share any divisors because by definition, a prime only has 1 as a divisor.
Prime-to-div-or-coprime : Prime(x) → ((x ∣ y) ∨ Coprime(x)(y))
Prime-to-div-or-coprime {y = y} (intro {x} prim) = [¬→]-disjunctive-formᵣ ⦃ decider-to-classical ⦄ (intro ∘ coprim) where
coprim : (𝐒(𝐒(x)) ∤ y) → ∀{n} → (n ∣ 𝐒(𝐒(x))) → (n ∣ y) → (n ≡ 1)
coprim nxy {𝟎} nx ny with () ← [0]-divides-not nx
coprim nxy {𝐒 n} nx ny with prim nx
... | [∨]-introₗ [≡]-intro = [≡]-intro
... | [∨]-introᵣ [≡]-intro with () ← nxy ny
divides-to-converse-coprime : ∀{x y z} → (x ∣ y) → Coprime(y)(z) → Coprime(x)(z)
divides-to-converse-coprime xy (intro yz) = intro(nx ↦ nz ↦ yz (transitivity(_∣_) nx xy) nz)
|
{
"alphanum_fraction": 0.6731951719,
"avg_line_length": 47.7282608696,
"ext": "agda",
"hexsha": "413ff184849b348eb82f57f9e41d58bf8017ec31",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "Lolirofle/stuff-in-agda",
"max_forks_repo_path": "Numeral/Natural/Coprime/Proofs.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "Lolirofle/stuff-in-agda",
"max_issues_repo_path": "Numeral/Natural/Coprime/Proofs.agda",
"max_line_length": 149,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "70f4fba849f2fd779c5aaa5af122ccb6a5b271ba",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "Lolirofle/stuff-in-agda",
"max_stars_repo_path": "Numeral/Natural/Coprime/Proofs.agda",
"max_stars_repo_stars_event_max_datetime": "2022-02-05T06:53:22.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-04-07T17:58:13.000Z",
"num_tokens": 1672,
"size": 4391
}
|
{-# OPTIONS --universe-polymorphism #-}
-- {-# OPTIONS --verbose tc.records.ifs:15 #-}
-- {-# OPTIONS --verbose tc.constr.findInScope:15 #-}
-- {-# OPTIONS --verbose tc.term.args.ifs:15 #-}
-- {-# OPTIONS --verbose cta.record.ifs:15 #-}
-- {-# OPTIONS --verbose tc.section.apply:25 #-}
-- {-# OPTIONS --verbose tc.mod.apply:100 #-}
-- {-# OPTIONS --verbose scope.rec:15 #-}
-- {-# OPTIONS --verbose tc.rec.def:15 #-}
module 04-equality where
record ⊤ : Set where
constructor tt
data Bool : Set where
true : Bool
false : Bool
or : Bool → Bool → Bool
or true _ = true
or _ true = true
or false false = false
and : Bool → Bool → Bool
and false _ = false
and _ false = false
and true true = false
not : Bool → Bool
not true = false
not false = true
id : {A : Set} → A → A
id v = v
primEqBool : Bool → Bool → Bool
primEqBool true = id
primEqBool false = not
record Eq (A : Set) : Set where
field eq : A → A → Bool
eqBool : Eq Bool
eqBool = record { eq = primEqBool }
open Eq {{...}}
neq : {t : Set} → {{eqT : Eq t}} → t → t → Bool
neq a b = not (eq a b)
test = eq false false
-- Instance arguments will also resolve to candidate instances which
-- still require hidden arguments. This allows us to define a
-- reasonable instance for Fin types
data ℕ : Set where
zero : ℕ
suc : ℕ → ℕ
{-# BUILTIN NATURAL ℕ #-}
data Fin : ℕ → Set where
zero : {n : ℕ} → Fin (suc n)
suc : {n : ℕ} → Fin n → Fin (suc n)
primEqFin : {n : ℕ} → Fin n → Fin n → Bool
primEqFin zero zero = true
primEqFin zero (suc y) = false
primEqFin (suc y) zero = false
primEqFin (suc x) (suc y) = primEqFin x y
eqFin : {n : ℕ} → Eq (Fin n)
eqFin = record { eq = primEqFin }
-- eqFin′ : Eq (Fin 3)
-- eqFin′ = record { eq = primEqFin }
-- eqFinSpecial : {n : ℕ} → Prime n → Eq (Fin n)
-- eqFinSpecial
fin1 : Fin 3
fin1 = zero
fin2 : Fin 3
fin2 = suc (suc zero)
testFin : Bool
testFin = eq fin1 fin2
|
{
"alphanum_fraction": 0.6177707676,
"avg_line_length": 20.2340425532,
"ext": "agda",
"hexsha": "8c4a3b4f7249620cee4f11bf54b82eb0620754ff",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2022-03-12T11:35:18.000Z",
"max_forks_repo_forks_event_min_datetime": "2022-03-12T11:35:18.000Z",
"max_forks_repo_head_hexsha": "477c8c37f948e6038b773409358fd8f38395f827",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "larrytheliquid/agda",
"max_forks_repo_path": "examples/instance-arguments/04-equality.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "477c8c37f948e6038b773409358fd8f38395f827",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "larrytheliquid/agda",
"max_issues_repo_path": "examples/instance-arguments/04-equality.agda",
"max_line_length": 68,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "477c8c37f948e6038b773409358fd8f38395f827",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "larrytheliquid/agda",
"max_stars_repo_path": "examples/instance-arguments/04-equality.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 621,
"size": 1902
}
|
------------------------------------------------------------------------
-- The Agda standard library
--
-- The Stream type and some operations
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe --sized-types #-}
module Codata.Stream where
open import Size
open import Codata.Thunk as Thunk using (Thunk; force)
open import Data.Nat.Base
open import Data.List.Base using (List; []; _∷_)
open import Data.List.NonEmpty using (List⁺; _∷_)
open import Data.Vec using (Vec; []; _∷_)
open import Data.Product as P hiding (map)
open import Function
------------------------------------------------------------------------
-- Definition
data Stream {ℓ} (A : Set ℓ) (i : Size) : Set ℓ where
_∷_ : A → Thunk (Stream A) i → Stream A i
module _ {ℓ} {A : Set ℓ} where
repeat : ∀ {i} → A → Stream A i
repeat a = a ∷ λ where .force → repeat a
head : ∀ {i} → Stream A i → A
head (x ∷ xs) = x
tail : Stream A ∞ → Stream A ∞
tail (x ∷ xs) = xs .force
lookup : ℕ → Stream A ∞ → A
lookup zero xs = head xs
lookup (suc k) xs = lookup k (tail xs)
splitAt : (n : ℕ) → Stream A ∞ → Vec A n × Stream A ∞
splitAt zero xs = [] , xs
splitAt (suc n) (x ∷ xs) = P.map₁ (x ∷_) (splitAt n (xs .force))
take : (n : ℕ) → Stream A ∞ → Vec A n
take n xs = proj₁ (splitAt n xs)
drop : ℕ → Stream A ∞ → Stream A ∞
drop n xs = proj₂ (splitAt n xs)
infixr 5 _++_ _⁺++_
_++_ : ∀ {i} → List A → Stream A i → Stream A i
[] ++ ys = ys
(x ∷ xs) ++ ys = x ∷ λ where .force → xs ++ ys
_⁺++_ : ∀ {i} → List⁺ A → Thunk (Stream A) i → Stream A i
(x ∷ xs) ⁺++ ys = x ∷ λ where .force → xs ++ ys .force
cycle : ∀ {i} → List⁺ A → Stream A i
cycle xs = xs ⁺++ λ where .force → cycle xs
concat : ∀ {i} → Stream (List⁺ A) i → Stream A i
concat (xs ∷ xss) = xs ⁺++ λ where .force → concat (xss .force)
interleave : ∀ {i} → Stream A i → Thunk (Stream A) i → Stream A i
interleave (x ∷ xs) ys = x ∷ λ where .force → interleave (ys .force) xs
chunksOf : (n : ℕ) → Stream A ∞ → Stream (Vec A n) ∞
chunksOf n = chunksOfAcc n id module ChunksOf where
chunksOfAcc : ∀ {i} k (acc : Vec A k → Vec A n) →
Stream A ∞ → Stream (Vec A n) i
chunksOfAcc zero acc xs = acc [] ∷ λ where .force → chunksOfAcc n id xs
chunksOfAcc (suc k) acc (x ∷ xs) = chunksOfAcc k (acc ∘ (x ∷_)) (xs .force)
module _ {ℓ ℓ′} {A : Set ℓ} {B : Set ℓ′} where
map : ∀ {i} → (A → B) → Stream A i → Stream B i
map f (x ∷ xs) = f x ∷ λ where .force → map f (xs .force)
ap : ∀ {i} → Stream (A → B) i → Stream A i → Stream B i
ap (f ∷ fs) (x ∷ xs) = f x ∷ λ where .force → ap (fs .force) (xs .force)
unfold : ∀ {i} → (A → A × B) → A → Stream B i
unfold next seed =
let (seed′ , b) = next seed in
b ∷ λ where .force → unfold next seed′
scanl : ∀ {i} → (B → A → B) → B → Stream A i → Stream B i
scanl c n (x ∷ xs) = n ∷ λ where .force → scanl c (c n x) (xs .force)
module _ {ℓ ℓ₁ ℓ₂} {A : Set ℓ} {B : Set ℓ₁} {C : Set ℓ₂} where
zipWith : ∀ {i} → (A → B → C) → Stream A i → Stream B i → Stream C i
zipWith f (a ∷ as) (b ∷ bs) = f a b ∷ λ where .force → zipWith f (as .force) (bs .force)
module _ {a} {A : Set a} where
iterate : (A → A) → A → Stream A ∞
iterate f = unfold < f , id >
|
{
"alphanum_fraction": 0.5206485164,
"avg_line_length": 32.0490196078,
"ext": "agda",
"hexsha": "6f1991dec5440695db800954d6fd70920ea0325b",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "0debb886eb5dbcd38dbeebd04b34cf9d9c5e0e71",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "omega12345/agda-mode",
"max_forks_repo_path": "test/asset/agda-stdlib-1.0/Codata/Stream.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "0debb886eb5dbcd38dbeebd04b34cf9d9c5e0e71",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "omega12345/agda-mode",
"max_issues_repo_path": "test/asset/agda-stdlib-1.0/Codata/Stream.agda",
"max_line_length": 89,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "0debb886eb5dbcd38dbeebd04b34cf9d9c5e0e71",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "omega12345/agda-mode",
"max_stars_repo_path": "test/asset/agda-stdlib-1.0/Codata/Stream.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 1172,
"size": 3269
}
|
------------------------------------------------------------------------------
-- ABP auxiliary lemma
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module FOT.FOTC.Program.ABP.StrongerInductionPrinciple.LemmaATP where
open import Common.FOL.Relation.Binary.EqReasoning
open import FOTC.Base
open import FOTC.Base.PropertiesI
open import FOTC.Base.List
open import FOTC.Base.List.PropertiesATP
open import FOTC.Base.Loop
open import FOTC.Data.Bool
open import FOTC.Data.Bool.PropertiesATP
open import FOTC.Data.List
open import FOTC.Data.List.PropertiesATP
open import FOTC.Program.ABP.ABP
open import FOTC.Program.ABP.Fair.Type
open import FOTC.Program.ABP.Fair.PropertiesATP
open import FOTC.Program.ABP.PropertiesI
open import FOTC.Program.ABP.Terms
------------------------------------------------------------------------------
-- Helper function for the auxiliary lemma
module Helper where
-- 30 November 2013. If we don't have the following definitions
-- outside the where clause, the ATPs cannot prove the theorems.
as^ : ∀ b i' is' ds → D
as^ b i' is' ds = await b i' is' ds
{-# ATP definition as^ #-}
bs^ : D → D → D → D → D → D
bs^ b i' is' ds os₁^ = corrupt os₁^ · (as^ b i' is' ds)
{-# ATP definition bs^ #-}
cs^ : D → D → D → D → D → D
cs^ b i' is' ds os₁^ = ack b · (bs^ b i' is' ds os₁^)
{-# ATP definition cs^ #-}
ds^ : D → D → D → D → D → D → D
ds^ b i' is' ds os₁^ os₂^ = corrupt os₂^ · cs^ b i' is' ds os₁^
{-# ATP definition ds^ #-}
os₁^ : D → D → D
os₁^ os₁' ft₁^ = ft₁^ ++ os₁'
{-# ATP definition os₁^ #-}
os₂^ : D → D
os₂^ os₂ = tail₁ os₂
{-# ATP definition os₂^ #-}
helper : ∀ {b i' is' os₁ os₂ as bs cs ds js} →
Bit b →
Fair os₂ →
S b (i' ∷ is') os₁ os₂ as bs cs ds js →
∀ ft₁ os₁' → F*T ft₁ → Fair os₁' → os₁ ≡ ft₁ ++ os₁' →
∃[ js' ] js ≡ i' ∷ js'
helper {b} {i'} {is'} {os₁} {os₂} {as} {bs} {cs} {ds} {js} Bb Fos₂
(asS , bsS , csS , dsS , jsS)
.(T ∷ []) os₁' f*tnil Fos₁' os₁-eq = prf
where
postulate prf : ∃[ js' ] js ≡ i' ∷ js'
{-# ATP prove prf #-}
helper {b} {i'} {is'} {os₁} {os₂} {as} {bs} {cs} {ds} {js}
Bb Fos₂ (asS , bsS , csS , dsS , jsS)
.(F ∷ ft₁^) os₁' (f*tcons {ft₁^} FTft₁^) Fos₁' os₁-eq =
helper Bb (tail-Fair Fos₂) ihS ft₁^ os₁' FTft₁^ Fos₁' refl
where
postulate os₁-eq-helper : os₁ ≡ F ∷ os₁^ os₁' ft₁^
{-# ATP prove os₁-eq-helper #-}
postulate as-eq : as ≡ < i' , b > ∷ (as^ b i' is' ds)
{-# ATP prove as-eq #-}
postulate bs-eq : bs ≡ error ∷ (bs^ b i' is' ds (os₁^ os₁' ft₁^))
{-# ATP prove bs-eq os₁-eq-helper as-eq #-}
postulate cs-eq : cs ≡ not b ∷ cs^ b i' is' ds (os₁^ os₁' ft₁^)
{-# ATP prove cs-eq bs-eq #-}
postulate
ds-eq-helper₁ :
os₂ ≡ T ∷ tail₁ os₂ →
ds ≡ ok (not b) ∷ ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂)
{-# ATP prove ds-eq-helper₁ cs-eq #-}
postulate
ds-eq-helper₂ : os₂ ≡ F ∷ tail₁ os₂ →
ds ≡ error ∷ ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂)
{-# ATP prove ds-eq-helper₂ cs-eq #-}
ds-eq : ds ≡ ok (not b) ∷ ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂)
∨ ds ≡ error ∷ ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂)
ds-eq = case (λ h → inj₁ (ds-eq-helper₁ h))
(λ h → inj₂ (ds-eq-helper₂ h))
(head-tail-Fair Fos₂)
postulate
as^-eq-helper₁ :
ds ≡ ok (not b) ∷ ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂) →
as^ b i' is' ds ≡
send b · (i' ∷ is') · ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂)
{-# ATP prove as^-eq-helper₁ x≢not-x #-}
postulate
as^-eq-helper₂ :
ds ≡ error ∷ ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂) →
as^ b i' is' ds ≡
send b · (i' ∷ is') · ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂)
{-# ATP prove as^-eq-helper₂ #-}
as^-eq : as^ b i' is' ds ≡
send b · (i' ∷ is') · ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂)
as^-eq = case as^-eq-helper₁ as^-eq-helper₂ ds-eq
postulate js-eq : js ≡ out b · bs^ b i' is' ds (os₁^ os₁' ft₁^)
{-# ATP prove js-eq bs-eq #-}
ihS : S b
(i' ∷ is')
(os₁^ os₁' ft₁^)
(os₂^ os₂)
(as^ b i' is' ds)
(bs^ b i' is' ds (os₁^ os₁' ft₁^))
(cs^ b i' is' ds (os₁^ os₁' ft₁^))
(ds^ b i' is' ds (os₁^ os₁' ft₁^) (os₂^ os₂))
js
ihS = as^-eq , refl , refl , refl , js-eq
------------------------------------------------------------------------------
-- From Dybjer and Sander's paper: From the assumption that os₁ ∈ Fair
-- and hence by unfolding Fair, we conclude that there are ft₁ : F*T
-- and os₁' : Fair, such that os₁ = ft₁ ++ os₁'.
--
-- We proceed by induction on ft₁ : F*T using helper.
open Helper
lemma : ∀ {b i' is' os₁ os₂ as bs cs ds js} →
Bit b →
Fair os₁ →
Fair os₂ →
S b (i' ∷ is') os₁ os₂ as bs cs ds js →
∃[ js' ] js ≡ i' ∷ js'
lemma Bb Fos₁ Fos₂ s with Fair-out Fos₁
... | ft , os₁' , FTft , prf , Fos₁' = helper Bb Fos₂ s ft os₁' FTft Fos₁' prf
|
{
"alphanum_fraction": 0.4923564504,
"avg_line_length": 34.6064516129,
"ext": "agda",
"hexsha": "cedb91a2b509b6889335c654152bbab7e37ef273",
"lang": "Agda",
"max_forks_count": 3,
"max_forks_repo_forks_event_max_datetime": "2018-03-14T08:50:00.000Z",
"max_forks_repo_forks_event_min_datetime": "2016-09-19T14:18:30.000Z",
"max_forks_repo_head_hexsha": "2fc9f2b81052a2e0822669f02036c5750371b72d",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "asr/fotc",
"max_forks_repo_path": "notes/FOT/FOTC/Program/ABP/StrongerInductionPrinciple/LemmaATP.agda",
"max_issues_count": 2,
"max_issues_repo_head_hexsha": "2fc9f2b81052a2e0822669f02036c5750371b72d",
"max_issues_repo_issues_event_max_datetime": "2017-01-01T14:34:26.000Z",
"max_issues_repo_issues_event_min_datetime": "2016-10-12T17:28:16.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "asr/fotc",
"max_issues_repo_path": "notes/FOT/FOTC/Program/ABP/StrongerInductionPrinciple/LemmaATP.agda",
"max_line_length": 79,
"max_stars_count": 11,
"max_stars_repo_head_hexsha": "2fc9f2b81052a2e0822669f02036c5750371b72d",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "asr/fotc",
"max_stars_repo_path": "notes/FOT/FOTC/Program/ABP/StrongerInductionPrinciple/LemmaATP.agda",
"max_stars_repo_stars_event_max_datetime": "2021-09-12T16:09:54.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-09-03T20:53:42.000Z",
"num_tokens": 2017,
"size": 5364
}
|
-- Andreas, 2019-02-24, issue #3457
-- Error messages for illegal as-clause
import Agda.Builtin.Nat Fresh-name as _
-- Previously, this complained about a duplicate module definition
-- with unspeakable name.
-- Expected error:
-- Not in scope: Fresh-name
|
{
"alphanum_fraction": 0.7451737452,
"avg_line_length": 23.5454545455,
"ext": "agda",
"hexsha": "ae4ce2f8fe4252a6e321016a0a67038f319090d7",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "231d6ad8e77b67ff8c4b1cb35a6c31ccd988c3e9",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "Agda-zh/agda",
"max_forks_repo_path": "test/Fail/Issue3457.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "shlevy/agda",
"max_issues_repo_path": "test/Fail/Issue3457.agda",
"max_line_length": 66,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "ed8ac6f4062ea8a20fa0f62d5db82d4e68278338",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "shlevy/agda",
"max_stars_repo_path": "test/Fail/Issue3457.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 66,
"size": 259
}
|
module Classes where
open import Agda.Primitive
open import Agda.Builtin.Equality
open import Relation.Binary.PropositionalEquality.Core
open ≡-Reasoning
id : ∀ {ℓ} {A : Set ℓ} → A → A
id x = x
_$_ : ∀ {ℓ} {A B : Set ℓ} → (A → B) → A → B
_$_ = id
_∘_ : ∀ {ℓ} {A B C : Set ℓ} → (B → C) → (A → B) → A → C
f ∘ g = λ x → f (g x)
record Functor {ℓ} (F : Set ℓ → Set ℓ) : Set (lsuc ℓ) where
field
fmap : ∀ {A B} → (A → B) → F A → F B
F-id : ∀ {A} → (a : F A) → fmap id a ≡ a
F-∘ : ∀ {A B C} → (g : B → C) (f : A → B) (a : F A) → fmap (g ∘ f) a ≡ (fmap g ∘ fmap f) a
_<$>_ : ∀ {A B} → (A → B) → F A → F B
_<$>_ = fmap
infixl 20 _<$>_
open Functor {{...}} public
record Applicative (F : Set → Set) : Set₁ where
field
{{funF}} : Functor F
pure : {A : Set} → A → F A
_<*>_ : {A B : Set} → F (A → B) → F A → F B
A-id : ∀ {A} → (v : F A) → pure id <*> v ≡ v
A-∘ : ∀ {A B C} → (u : F (B → C)) (v : F (A → B)) (w : F A) → pure _∘_ <*> u <*> v <*> w ≡ u <*> (v <*> w)
A-hom : ∀ {A B} → (f : A → B) (x : A) → pure f <*> pure x ≡ pure (f x)
A-ic : ∀ {A B} → (u : F (A → B)) (y : A) → u <*> pure y ≡ pure (_$ y) <*> u
infixl 20 _<*>_
open Applicative {{...}} public
postulate
-- this is from parametricity: fmap is universal w.r.t. the functor laws
appFun : ∀ {A B F} {{aF : Applicative F}} → (f : A → B) (x : F A) → pure f <*> x ≡ fmap f x
record Monad (F : Set → Set) : Set₁ where
field
{{appF}} : Applicative F
_>>=_ : ∀ {A B} → F A → (A → F B) → F B
return : ∀ {A} → A → F A
return = pure
_>=>_ : {A B C : Set} → (A → F B) → (B → F C) → A → F C
f >=> g = λ a → f a >>= g
infixl 10 _>>=_
infixr 10 _>=>_
field
left-1 : ∀ {A B} → (a : A) (k : A → F B) → return a >>= k ≡ k a
right-1 : ∀ {A} → (m : F A) → m >>= return ≡ m
assoc : ∀ {A B C D} → (f : A → F B) (g : B → F C) (h : C → F D) (a : A) → (f >=> (g >=> h)) a ≡ ((f >=> g) >=> h) a
open Monad {{...}} public
|
{
"alphanum_fraction": 0.4264853978,
"avg_line_length": 25.1392405063,
"ext": "agda",
"hexsha": "f32936682a378b9415385a7b071518eb03186425",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "1b019ce3d7b978c369fcc82c97ccafdde8f7fd02",
"max_forks_repo_licenses": [
"BSD-3-Clause"
],
"max_forks_repo_name": "samuelhklumpers/strong-vector",
"max_forks_repo_path": "proofs/Classes.agda",
"max_issues_count": 3,
"max_issues_repo_head_hexsha": "1b019ce3d7b978c369fcc82c97ccafdde8f7fd02",
"max_issues_repo_issues_event_max_datetime": "2022-03-10T10:24:40.000Z",
"max_issues_repo_issues_event_min_datetime": "2022-03-09T10:24:33.000Z",
"max_issues_repo_licenses": [
"BSD-3-Clause"
],
"max_issues_repo_name": "samuelhklumpers/strong-vector",
"max_issues_repo_path": "proofs/Classes.agda",
"max_line_length": 119,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "1b019ce3d7b978c369fcc82c97ccafdde8f7fd02",
"max_stars_repo_licenses": [
"BSD-3-Clause"
],
"max_stars_repo_name": "samuelhklumpers/strong-vector",
"max_stars_repo_path": "proofs/Classes.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 898,
"size": 1986
}
|
data Bool : Set where
true false : Bool
record Top : Set where
foo : Top
foo with true
... | true = _
... | false = top
where
top = record{ } -- the only purpose of this was to force
-- evaluation of the with function clauses
-- which were in an __IMPOSSIBLE__ state
|
{
"alphanum_fraction": 0.5776397516,
"avg_line_length": 21.4666666667,
"ext": "agda",
"hexsha": "6ecc96880e9b431dc9b0935a4b9040489db4ff9f",
"lang": "Agda",
"max_forks_count": 371,
"max_forks_repo_forks_event_max_datetime": "2022-03-30T19:00:30.000Z",
"max_forks_repo_forks_event_min_datetime": "2015-01-03T14:04:08.000Z",
"max_forks_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "cruhland/agda",
"max_forks_repo_path": "test/Succeed/Issue1031.agda",
"max_issues_count": 4066,
"max_issues_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_issues_repo_issues_event_max_datetime": "2022-03-31T21:14:49.000Z",
"max_issues_repo_issues_event_min_datetime": "2015-01-10T11:24:51.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "cruhland/agda",
"max_issues_repo_path": "test/Succeed/Issue1031.agda",
"max_line_length": 63,
"max_stars_count": 1989,
"max_stars_repo_head_hexsha": "7f58030124fa99dfbf8db376659416f3ad8384de",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "cruhland/agda",
"max_stars_repo_path": "test/Succeed/Issue1031.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-30T18:20:48.000Z",
"max_stars_repo_stars_event_min_datetime": "2015-01-09T23:51:16.000Z",
"num_tokens": 82,
"size": 322
}
|
open import Prelude
open import Nat
open import dynamics-core
open import contexts
module lemmas-disjointness where
-- disjointness is commutative
##-comm : {A : Set} {Δ1 Δ2 : A ctx} → Δ1 ## Δ2 → Δ2 ## Δ1
##-comm (π1 , π2) = π2 , π1
-- the empty context is disjoint from any context
empty-disj : {A : Set} (Γ : A ctx) → ∅ ## Γ
empty-disj Γ = ed1 , ed2
where
ed1 : {A : Set} (n : Nat) → dom {A} ∅ n → n # Γ
ed1 n (π1 , ())
ed2 : {A : Set} (n : Nat) → dom Γ n → _#_ {A} n ∅
ed2 _ _ = refl
-- two singleton contexts with different indices are disjoint
disjoint-singles : {A : Set} {x y : A} {u1 u2 : Nat} →
u1 ≠ u2 →
(■ (u1 , x)) ## (■ (u2 , y))
disjoint-singles {_} {x} {y} {u1} {u2} neq = ds1 , ds2
where
ds1 : (n : Nat) → dom (■ (u1 , x)) n → n # (■ (u2 , y))
ds1 n d with lem-dom-eq d
ds1 .u1 d | refl with natEQ u2 u1
ds1 .u1 d | refl | Inl xx = abort (neq (! xx))
ds1 .u1 d | refl | Inr x₁ = refl
ds2 : (n : Nat) → dom (■ (u2 , y)) n → n # (■ (u1 , x))
ds2 n d with lem-dom-eq d
ds2 .u2 d | refl with natEQ u1 u2
ds2 .u2 d | refl | Inl x₁ = abort (neq x₁)
ds2 .u2 d | refl | Inr x₁ = refl
apart-noteq : {A : Set} (p r : Nat) (q : A) → p # (■ (r , q)) → p ≠ r
apart-noteq p r q apt with natEQ r p
apart-noteq p .p q apt | Inl refl = abort (somenotnone apt)
apart-noteq p r q apt | Inr x₁ = flip x₁
-- if singleton contexts are disjoint, their indices must be disequal
singles-notequal : {A : Set} {x y : A} {u1 u2 : Nat} →
(■ (u1 , x)) ## (■ (u2 , y)) →
u1 ≠ u2
singles-notequal {A} {x} {y} {u1} {u2} (d1 , d2) = apart-noteq u1 u2 y (d1 u1 (lem-domsingle u1 x))
-- dual of lem2 above; if two indices are disequal, then either is apart
-- from the singleton formed with the other
apart-singleton : {A : Set} → ∀{x y} → {τ : A} →
x ≠ y →
x # (■ (y , τ))
apart-singleton {A} {x} {y} {τ} neq with natEQ y x
apart-singleton neq | Inl x₁ = abort ((flip neq) x₁)
apart-singleton neq | Inr x₁ = refl
-- if an index is apart from two contexts, it's apart from their union as
-- well. used below and in other files, so it's outside the local scope.
apart-parts : {A : Set} (Γ1 Γ2 : A ctx) (n : Nat) → n # Γ1 → n # Γ2 → n # (Γ1 ∪ Γ2)
apart-parts Γ1 Γ2 n apt1 apt2 with Γ1 n
apart-parts _ _ n refl apt2 | .None = apt2
-- this is just for convenience; it shows up a lot.
apart-extend1 : {A : Set} → ∀{x y τ} → (Γ : A ctx) → x ≠ y → x # Γ → x # (Γ ,, (y , τ))
apart-extend1 {A} {x} {y} {τ} Γ neq apt with natEQ y x
... | Inl refl = abort (neq refl)
... | Inr y≠x = apt
-- if an index is in the domain of a union, it's in the domain of one or
-- the other unand
dom-split : {A : Set} → (Γ1 Γ2 : A ctx) (n : Nat) → dom (Γ1 ∪ Γ2) n → dom Γ1 n + dom Γ2 n
dom-split Γ4 Γ5 n (π1 , π2) with Γ4 n
dom-split Γ4 Γ5 n (π1 , π2) | Some x = Inl (x , refl)
dom-split Γ4 Γ5 n (π1 , π2) | None = Inr (π1 , π2)
-- if both parts of a union are disjoint with a target, so is the union
disjoint-parts : {A : Set} {Γ1 Γ2 Γ3 : A ctx} → Γ1 ## Γ3 → Γ2 ## Γ3 → (Γ1 ∪ Γ2) ## Γ3
disjoint-parts {_} {Γ1} {Γ2} {Γ3} D13 D23 = d31 , d32
where
d31 : (n : Nat) → dom (Γ1 ∪ Γ2) n → n # Γ3
d31 n D with dom-split Γ1 Γ2 n D
d31 n D | Inl x = π1 D13 n x
d31 n D | Inr x = π1 D23 n x
d32 : (n : Nat) → dom Γ3 n → n # (Γ1 ∪ Γ2)
d32 n D = apart-parts Γ1 Γ2 n (π2 D13 n D) (π2 D23 n D)
apart-union1 : {A : Set} (Γ1 Γ2 : A ctx) (n : Nat) → n # (Γ1 ∪ Γ2) → n # Γ1
apart-union1 Γ1 Γ2 n aprt with Γ1 n
apart-union1 Γ1 Γ2 n () | Some x
apart-union1 Γ1 Γ2 n aprt | None = refl
apart-union2 : {A : Set} (Γ1 Γ2 : A ctx) (n : Nat) → n # (Γ1 ∪ Γ2) → n # Γ2
apart-union2 Γ1 Γ2 n aprt with Γ1 n
apart-union2 Γ3 Γ4 n () | Some x
apart-union2 Γ3 Γ4 n aprt | None = aprt
-- if a union is disjoint with a target, so is the left unand
disjoint-union1 : {A : Set} {Γ1 Γ2 Δ : A ctx} → (Γ1 ∪ Γ2) ## Δ → Γ1 ## Δ
disjoint-union1 {Γ1 = Γ1} {Γ2 = Γ2} {Δ = Δ} (ud1 , ud2) = du11 , du12
where
dom-union1 : {A : Set} (Γ1 Γ2 : A ctx) (n : Nat) → dom Γ1 n → dom (Γ1 ∪ Γ2) n
dom-union1 Γ1 Γ2 n (π1 , π2) with Γ1 n
dom-union1 Γ1 Γ2 n (π1 , π2) | Some x = x , refl
dom-union1 Γ1 Γ2 n (π1 , ()) | None
du11 : (n : Nat) → dom Γ1 n → n # Δ
du11 n dom = ud1 n (dom-union1 Γ1 Γ2 n dom)
du12 : (n : Nat) → dom Δ n → n # Γ1
du12 n dom = apart-union1 Γ1 Γ2 n (ud2 n dom)
-- if a union is disjoint with a target, so is the right unand
disjoint-union2 : {A : Set} {Γ1 Γ2 Δ : A ctx} → (Γ1 ∪ Γ2) ## Δ → Γ2 ## Δ
disjoint-union2 {Γ1 = Γ1} {Γ2 = Γ2} {Δ = Δ} (ud1 , ud2) = du21 , du22
where
dom-union2 : {A : Set} (Γ1 Γ2 : A ctx) (n : Nat) → dom Γ2 n → dom (Γ1 ∪ Γ2) n
dom-union2 Γ1 Γ2 n (π1 , π2) with Γ1 n
dom-union2 Γ3 Γ4 n (π1 , π2) | Some x = x , refl
dom-union2 Γ3 Γ4 n (π1 , π2) | None = π1 , π2
du21 : (n : Nat) → dom Γ2 n → n # Δ
du21 n dom = ud1 n (dom-union2 Γ1 Γ2 n dom)
du22 : (n : Nat) → dom Δ n → n # Γ2
du22 n dom = apart-union2 Γ1 Γ2 n (ud2 n dom)
-- if x isn't in a context and y is then they can't be equal
lem-dom-apt : {A : Set} {G : A ctx} {x y : Nat} → x # G → dom G y → x ≠ y
lem-dom-apt {x = x} {y = y} apt dom with natEQ x y
lem-dom-apt apt dom | Inl refl = abort (somenotnone (! (π2 dom) · apt))
lem-dom-apt apt dom | Inr x₁ = x₁
|
{
"alphanum_fraction": 0.5275787966,
"avg_line_length": 41.362962963,
"ext": "agda",
"hexsha": "f7408472e80f85bfa8ac49b2592c69ba285666cf",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "a3640d7b0f76cdac193afd382694197729ed6d57",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "hazelgrove/hazelnut-agda",
"max_forks_repo_path": "lemmas-disjointness.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "a3640d7b0f76cdac193afd382694197729ed6d57",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "hazelgrove/hazelnut-agda",
"max_issues_repo_path": "lemmas-disjointness.agda",
"max_line_length": 101,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "a3640d7b0f76cdac193afd382694197729ed6d57",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "hazelgrove/hazelnut-agda",
"max_stars_repo_path": "lemmas-disjointness.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 2349,
"size": 5584
}
|
{-# OPTIONS --safe #-}
module Cubical.Algebra.Group.Properties where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Structure
open import Cubical.Foundations.GroupoidLaws hiding (assoc)
open import Cubical.Data.Sigma
open import Cubical.Algebra.Semigroup
open import Cubical.Algebra.Monoid.Base
open import Cubical.Algebra.Group.Base
private
variable
ℓ : Level
G : Type ℓ
isPropIsGroup : (1g : G) (_·_ : G → G → G) (inv : G → G)
→ isProp (IsGroup 1g _·_ inv)
isPropIsGroup 1g _·_ inv =
isOfHLevelRetractFromIso 1 IsGroupIsoΣ
(isPropΣ (isPropIsMonoid 1g _·_)
λ mono → isProp× (isPropΠ λ _ → mono .is-set _ _)
(isPropΠ λ _ → mono .is-set _ _))
where
open IsMonoid
module GroupTheory (G : Group ℓ) where
open GroupStr (snd G)
abstract
·CancelL : (a : ⟨ G ⟩) {b c : ⟨ G ⟩} → a · b ≡ a · c → b ≡ c
·CancelL a {b} {c} p =
b ≡⟨ sym (·IdL b) ∙ cong (_· b) (sym (·InvL a)) ∙ sym (·Assoc _ _ _) ⟩
inv a · (a · b) ≡⟨ cong (inv a ·_) p ⟩
inv a · (a · c) ≡⟨ ·Assoc _ _ _ ∙ cong (_· c) (·InvL a) ∙ ·IdL c ⟩
c ∎
·CancelR : {a b : ⟨ G ⟩} (c : ⟨ G ⟩) → a · c ≡ b · c → a ≡ b
·CancelR {a} {b} c p =
a ≡⟨ sym (·IdR a) ∙ cong (a ·_) (sym (·InvR c)) ∙ ·Assoc _ _ _ ⟩
(a · c) · inv c ≡⟨ cong (_· inv c) p ⟩
(b · c) · inv c ≡⟨ sym (·Assoc _ _ _) ∙ cong (b ·_) (·InvR c) ∙ ·IdR b ⟩
b ∎
invInv : (a : ⟨ G ⟩) → inv (inv a) ≡ a
invInv a = ·CancelL (inv a) (·InvR (inv a) ∙ sym (·InvL a))
inv1g : inv 1g ≡ 1g
inv1g = ·CancelL 1g (·InvR 1g ∙ sym (·IdL 1g))
1gUniqueL : {e : ⟨ G ⟩} (x : ⟨ G ⟩) → e · x ≡ x → e ≡ 1g
1gUniqueL {e} x p = ·CancelR x (p ∙ sym (·IdL _))
1gUniqueR : (x : ⟨ G ⟩) {e : ⟨ G ⟩} → x · e ≡ x → e ≡ 1g
1gUniqueR x {e} p = ·CancelL x (p ∙ sym (·IdR _))
invUniqueL : {g h : ⟨ G ⟩} → g · h ≡ 1g → g ≡ inv h
invUniqueL {g} {h} p = ·CancelR h (p ∙ sym (·InvL h))
invUniqueR : {g h : ⟨ G ⟩} → g · h ≡ 1g → h ≡ inv g
invUniqueR {g} {h} p = ·CancelL g (p ∙ sym (·InvR g))
invDistr : (a b : ⟨ G ⟩) → inv (a · b) ≡ inv b · inv a
invDistr a b = sym (invUniqueR γ) where
γ : (a · b) · (inv b · inv a) ≡ 1g
γ = (a · b) · (inv b · inv a)
≡⟨ sym (·Assoc _ _ _) ⟩
a · b · (inv b) · (inv a)
≡⟨ cong (a ·_) (·Assoc _ _ _ ∙ cong (_· (inv a)) (·InvR b)) ⟩
a · (1g · inv a)
≡⟨ cong (a ·_) (·IdL (inv a)) ∙ ·InvR a ⟩
1g ∎
congIdLeft≡congIdRight : (_·G_ : G → G → G) (-G_ : G → G)
(0G : G)
(rUnitG : (x : G) → x ·G 0G ≡ x)
(lUnitG : (x : G) → 0G ·G x ≡ x)
→ (r≡l : rUnitG 0G ≡ lUnitG 0G)
→ (p : 0G ≡ 0G) →
cong (0G ·G_) p ≡ cong (_·G 0G) p
congIdLeft≡congIdRight _·G_ -G_ 0G rUnitG lUnitG r≡l p =
rUnit (cong (0G ·G_) p)
∙∙ ((λ i → (λ j → lUnitG 0G (i ∧ j)) ∙∙ cong (λ x → lUnitG x i) p ∙∙ λ j → lUnitG 0G (i ∧ ~ j))
∙∙ cong₂ (λ x y → x ∙∙ p ∙∙ y) (sym r≡l) (cong sym (sym r≡l))
∙∙ λ i → (λ j → rUnitG 0G (~ i ∧ j)) ∙∙ cong (λ x → rUnitG x (~ i)) p ∙∙ λ j → rUnitG 0G (~ i ∧ ~ j))
∙∙ sym (rUnit (cong (_·G 0G) p))
|
{
"alphanum_fraction": 0.473603906,
"avg_line_length": 36.8202247191,
"ext": "agda",
"hexsha": "6a9f4e7fc3aa383d210b391d1da0df717b7667ce",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "58c0b83bb0fed0dc683f3d29b1709effe51c1689",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "thomas-lamiaux/cubical",
"max_forks_repo_path": "Cubical/Algebra/Group/Properties.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "58c0b83bb0fed0dc683f3d29b1709effe51c1689",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "thomas-lamiaux/cubical",
"max_issues_repo_path": "Cubical/Algebra/Group/Properties.agda",
"max_line_length": 110,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "58c0b83bb0fed0dc683f3d29b1709effe51c1689",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "thomas-lamiaux/cubical",
"max_stars_repo_path": "Cubical/Algebra/Group/Properties.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 1494,
"size": 3277
}
|
{-# OPTIONS --safe #-}
module Cubical.HITs.Cost where
open import Cubical.HITs.Cost.Base
|
{
"alphanum_fraction": 0.7333333333,
"avg_line_length": 18,
"ext": "agda",
"hexsha": "6e9e6dc9658d64934da675dc9d67feeed5f9de20",
"lang": "Agda",
"max_forks_count": 134,
"max_forks_repo_forks_event_max_datetime": "2022-03-23T16:22:13.000Z",
"max_forks_repo_forks_event_min_datetime": "2018-11-16T06:11:03.000Z",
"max_forks_repo_head_hexsha": "53e159ec2e43d981b8fcb199e9db788e006af237",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "marcinjangrzybowski/cubical",
"max_forks_repo_path": "Cubical/HITs/Cost.agda",
"max_issues_count": 584,
"max_issues_repo_head_hexsha": "53e159ec2e43d981b8fcb199e9db788e006af237",
"max_issues_repo_issues_event_max_datetime": "2022-03-30T12:09:17.000Z",
"max_issues_repo_issues_event_min_datetime": "2018-10-15T09:49:02.000Z",
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "marcinjangrzybowski/cubical",
"max_issues_repo_path": "Cubical/HITs/Cost.agda",
"max_line_length": 34,
"max_stars_count": 301,
"max_stars_repo_head_hexsha": "53e159ec2e43d981b8fcb199e9db788e006af237",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "marcinjangrzybowski/cubical",
"max_stars_repo_path": "Cubical/HITs/Cost.agda",
"max_stars_repo_stars_event_max_datetime": "2022-03-24T02:10:47.000Z",
"max_stars_repo_stars_event_min_datetime": "2018-10-17T18:00:24.000Z",
"num_tokens": 26,
"size": 90
}
|
{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020, 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import Level using (0ℓ)
open import Util.Prelude
-- This module incldes various Agda lemmas that are independent of the project's domain
module Util.Lemmas where
cong₃ : ∀{a b c d}{A : Set a}{B : Set b}{C : Set c}{D : Set d}
→ (f : A → B → C → D) → ∀{x y u v m n} → x ≡ y → u ≡ v → m ≡ n
→ f x u m ≡ f y v n
cong₃ f refl refl refl = refl
≡-pi : ∀{a}{A : Set a}{x y : A}(p q : x ≡ y) → p ≡ q
≡-pi refl refl = refl
Unit-pi : {u1 u2 : Unit}
→ u1 ≡ u2
Unit-pi {unit} {unit} = refl
++-inj : ∀{a}{A : Set a}{m n o p : List A}
→ length m ≡ length n → m ++ o ≡ n ++ p
→ m ≡ n × o ≡ p
++-inj {m = []} {x ∷ n} () hip
++-inj {m = x ∷ m} {[]} () hip
++-inj {m = []} {[]} lhip hip
= refl , hip
++-inj {m = m ∷ ms} {n ∷ ns} lhip hip
with ++-inj {m = ms} {ns} (suc-injective lhip) (proj₂ (∷-injective hip))
...| (mn , op) rewrite proj₁ (∷-injective hip)
= cong (n ∷_) mn , op
++-abs : ∀{a}{A : Set a}{n : List A}(m : List A)
→ 1 ≤ length m → [] ≡ m ++ n → ⊥
++-abs [] ()
++-abs (x ∷ m) imp ()
filter-++-[]
: ∀ {a p} {A : Set a} {P : (a : A) → Set p}
→ ∀ xs ys (p : (a : A) → Dec (P a))
→ List-filter p xs ≡ [] → List-filter p ys ≡ []
→ List-filter p (xs ++ ys) ≡ []
filter-++-[] xs ys p pf₁ pf₂ rewrite List-filter-++ p xs ys | pf₁ | pf₂ = refl
filter-∪?-[]₁
: ∀ {a p} {A : Set a} {P Q : (a : A) → Set p}
→ ∀ xs (p : (a : A) → Dec (P a)) (q : (a : A) → Dec (Q a))
→ List-filter (p ∪? q) xs ≡ []
→ List-filter p xs ≡ []
filter-∪?-[]₁ [] p q pf = refl
filter-∪?-[]₁ (x ∷ xs) p q pf
with p x
...| no proof₁
with q x
...| no proof₂ = filter-∪?-[]₁ xs p q pf
filter-∪?-[]₁ (x ∷ xs) p q () | no proof₁ | yes proof₂
filter-∪?-[]₁ (x ∷ xs) p q () | yes proof
filter-∪?-[]₂
: ∀ {a p} {A : Set a} {P Q : (a : A) → Set p}
→ ∀ xs (p : (a : A) → Dec (P a)) (q : (a : A) → Dec (Q a))
→ List-filter (p ∪? q) xs ≡ []
→ List-filter q xs ≡ []
filter-∪?-[]₂ [] p q pf = refl
filter-∪?-[]₂ (x ∷ xs) p q pf
with p x
...| no proof₁
with q x
...| no proof₂ = filter-∪?-[]₂ xs p q pf
filter-∪?-[]₂ (x ∷ xs) p q () | no proof₁ | yes proof₂
filter-∪?-[]₂ (x ∷ xs) p q () | yes proof
noneOfKind⇒¬Any
: ∀ {a p} {A : Set a} {P : A → Set p}
xs (p : (a : A) → Dec (P a))
→ NoneOfKind xs p
→ ¬ Any P xs
noneOfKind⇒¬Any (x ∷ xs) p none ∈xs
with p x
noneOfKind⇒¬Any (x ∷ xs) p none (here px) | no ¬px = ¬px px
noneOfKind⇒¬Any (x ∷ xs) p none (there ∈xs) | no ¬px =
noneOfKind⇒¬Any xs p none ∈xs
noneOfKind⇒All¬
: ∀ {a p} {A : Set a} {P : A → Set p}
xs (p : (a : A) → Dec (P a))
→ NoneOfKind xs p
→ All (¬_ ∘ P) xs
noneOfKind⇒All¬ xs p none = ¬Any⇒All¬ xs (noneOfKind⇒¬Any xs p none)
++-NoneOfKind : ∀ {ℓA} {A : Set ℓA} {ℓ} {P : A → Set ℓ} xs ys (p : (a : A) → Dec (P a))
→ NoneOfKind xs p → NoneOfKind ys p → NoneOfKind (xs ++ ys) p
++-NoneOfKind xs ys p nok₁ nok₂ = filter-++-[] xs ys p nok₁ nok₂
data All-vec {ℓ} {A : Set ℓ} (P : A → Set ℓ) : ∀ {n} → Vec {ℓ} A n → Set (Level.suc ℓ) where
[] : All-vec P []
_∷_ : ∀ {x n} {xs : Vec A n} (px : P x) (pxs : All-vec P xs) → All-vec P (x ∷ xs)
≤-unstep : ∀{m n} → suc m ≤ n → m ≤ n
≤-unstep (s≤s ss) = ≤-step ss
≡⇒≤ : ∀{m n} → m ≡ n → m ≤ n
≡⇒≤ refl = ≤-refl
∈-cong : ∀{a b}{A : Set a}{B : Set b}{x : A}{l : List A}
→ (f : A → B) → x ∈ l → f x ∈ List-map f l
∈-cong f (here px) = here (cong f px)
∈-cong f (there hyp) = there (∈-cong f hyp)
All-self : ∀{a}{A : Set a}{xs : List A} → All (_∈ xs) xs
All-self = All-tabulate (λ x → x)
All-reduce⁺
: ∀{a b}{A : Set a}{B : Set b}{Q : A → Set}{P : B → Set}
→ { xs : List A }
→ (f : ∀{x} → Q x → B)
→ (∀{x} → (prf : Q x) → P (f prf))
→ (all : All Q xs)
→ All P (All-reduce f all)
All-reduce⁺ f hyp [] = []
All-reduce⁺ f hyp (ax ∷ axs) = (hyp ax) ∷ All-reduce⁺ f hyp axs
All-reduce⁻
: ∀{a b}{A : Set a}{B : Set b}
{Q : A → Set}
→ { xs : List A }
→ ∀ {vdq}
→ (f : ∀{x} → Q x → B)
→ (all : All Q xs)
→ vdq ∈ All-reduce f all
→ ∃[ v ] ∃[ v∈xs ] (vdq ≡ f {v} v∈xs)
All-reduce⁻ {Q = Q} {(h ∷ _)} {vdq} f (px ∷ pxs) (here refl) = h , px , refl
All-reduce⁻ {Q = Q} {(_ ∷ t)} {vdq} f (px ∷ pxs) (there vdq∈) = All-reduce⁻ {xs = t} f pxs vdq∈
List-index : ∀ {A : Set} → (_≟A_ : (a₁ a₂ : A) → Dec (a₁ ≡ a₂)) → A → (l : List A) → Maybe (Fin (length l))
List-index _≟A_ x l with break (_≟A x) l
...| not≡ , _ with length not≡ <? length l
...| no _ = nothing
...| yes found = just ( fromℕ< {length not≡} {length l} found)
nats : ℕ → List ℕ
nats 0 = []
nats (suc n) = (nats n) ++ (n ∷ [])
_ : nats 4 ≡ 0 ∷ 1 ∷ 2 ∷ 3 ∷ []
_ = refl
_ : Maybe-map toℕ (List-index _≟_ 2 (nats 4)) ≡ just 2
_ = refl
_ : Maybe-map toℕ (List-index _≟_ 4 (nats 4)) ≡ nothing
_ = refl
allDistinct : ∀ {A : Set} → List A → Set
allDistinct l = ∀ (i j : Fin (length l))
→ i ≡ j ⊎ List-lookup l i ≢ List-lookup l j
postulate -- TODO-1: currently unused; prove it, if needed
allDistinct? : ∀ {A : Set} → {≟A : (a₁ a₂ : A) → Dec (a₁ ≡ a₂)} → (l : List A) → Dec (allDistinct l)
-- Extends an arbitrary relation to work on the head of
-- the supplied list, if any.
data OnHead {A : Set}(P : A → A → Set) (x : A) : List A → Set where
[] : OnHead P x []
on-∷ : ∀{y ys} → P x y → OnHead P x (y ∷ ys)
-- Establishes that a list is sorted according to the supplied
-- relation.
data IsSorted {A : Set}(_<_ : A → A → Set) : List A → Set where
[] : IsSorted _<_ []
_∷_ : ∀{x xs} → OnHead _<_ x xs → IsSorted _<_ xs → IsSorted _<_ (x ∷ xs)
OnHead-prop : ∀{A}(P : A → A → Set)(x : A)(l : List A)
→ Irrelevant P
→ isPropositional (OnHead P x l)
OnHead-prop P x [] hyp [] [] = refl
OnHead-prop P x (x₁ ∷ l) hyp (on-∷ x₂) (on-∷ x₃) = cong on-∷ (hyp x₂ x₃)
IsSorted-prop : ∀{A}(_<_ : A → A → Set)(l : List A)
→ Irrelevant _<_
→ isPropositional (IsSorted _<_ l)
IsSorted-prop _<_ [] hyp [] [] = refl
IsSorted-prop _<_ (x ∷ l) hyp (x₁ ∷ a) (x₂ ∷ b)
= cong₂ _∷_ (OnHead-prop _<_ x l hyp x₁ x₂)
(IsSorted-prop _<_ l hyp a b)
IsSorted-map⁻ : {A : Set}{_≤_ : A → A → Set}
→ {B : Set}(f : B → A)(l : List B)
→ IsSorted (λ x y → f x ≤ f y) l
→ IsSorted _≤_ (List-map f l)
IsSorted-map⁻ f .[] [] = []
IsSorted-map⁻ f .(_ ∷ []) (x ∷ []) = [] ∷ []
IsSorted-map⁻ f .(_ ∷ _ ∷ _) (on-∷ x ∷ (x₁ ∷ is)) = (on-∷ x) ∷ IsSorted-map⁻ f _ (x₁ ∷ is)
transOnHead : ∀ {A} {l : List A} {y x : A} {_<_ : A → A → Set}
→ Transitive _<_
→ OnHead _<_ y l
→ x < y
→ OnHead _<_ x l
transOnHead _ [] _ = []
transOnHead trans (on-∷ y<f) x<y = on-∷ (trans x<y y<f)
++-OnHead : ∀ {A} {xs ys : List A} {y : A} {_<_ : A → A → Set}
→ OnHead _<_ y xs
→ OnHead _<_ y ys
→ OnHead _<_ y (xs ++ ys)
++-OnHead [] y<y₁ = y<y₁
++-OnHead (on-∷ y<x) _ = on-∷ y<x
h∉t : ∀ {A} {t : List A} {h : A} {_<_ : A → A → Set}
→ Irreflexive _<_ _≡_ → Transitive _<_
→ IsSorted _<_ (h ∷ t)
→ h ∉ t
h∉t irfl trans (on-∷ h< ∷ sxs) (here refl) = ⊥-elim (irfl h< refl)
h∉t irfl trans (on-∷ h< ∷ (x₁< ∷ sxs)) (there h∈t)
= h∉t irfl trans ((transOnHead trans x₁< h<) ∷ sxs) h∈t
≤-head : ∀ {A} {l : List A} {x y : A} {_<_ : A → A → Set} {_≤_ : A → A → Set}
→ Reflexive _≤_ → Trans _<_ _≤_ _≤_
→ y ∈ (x ∷ l) → IsSorted _<_ (x ∷ l)
→ _≤_ x y
≤-head ref≤ trans (here refl) _ = ref≤
≤-head ref≤ trans (there y∈) (on-∷ x<x₁ ∷ sl) = trans x<x₁ (≤-head ref≤ trans y∈ sl)
-- TODO-1 : Better name and/or replace with library property
Any-sym : ∀ {a b}{A : Set a}{B : Set b}{tgt : B}{l : List A}{f : A → B}
→ Any (λ x → tgt ≡ f x) l
→ Any (λ x → f x ≡ tgt) l
Any-sym (here x) = here (sym x)
Any-sym (there x) = there (Any-sym x)
Any-lookup-correct : ∀ {a b}{A : Set a}{B : Set b}{tgt : B}{l : List A}{f : A → B}
→ (p : Any (λ x → f x ≡ tgt) l)
→ Any-lookup p ∈ l
Any-lookup-correct (here px) = here refl
Any-lookup-correct (there p) = there (Any-lookup-correct p)
Any-lookup-correctP : ∀ {a}{A : Set a}{l : List A}{P : A → Set}
→ (p : Any P l)
→ Any-lookup p ∈ l
Any-lookup-correctP (here px) = here refl
Any-lookup-correctP (there p) = there (Any-lookup-correctP p)
Any-witness : ∀ {a b} {A : Set a} {l : List A} {P : A → Set b}
→ (p : Any P l) → P (Any-lookup p)
Any-witness (here px) = px
Any-witness (there x) = Any-witness x
-- TODO-1: there is probably a library property for this.
∈⇒Any : ∀ {A : Set}{x : A}
→ {xs : List A}
→ x ∈ xs
→ Any (_≡ x) xs
∈⇒Any {x = x} (here refl) = here refl
∈⇒Any {x = x} {h ∷ t} (there xxxx) = there (∈⇒Any {xs = t} xxxx)
false≢true : false ≢ true
false≢true ()
witness : {A : Set}{P : A → Set}{x : A}{xs : List A}
→ x ∈ xs → All P xs → P x
witness x y = All-lookup y x
maybe-⊥ : ∀{a}{A : Set a}{x : A}{y : Maybe A}
→ y ≡ just x
→ y ≡ nothing
→ ⊥
maybe-⊥ () refl
Maybe-map-cool : ∀ {S S₁ : Set} {f : S → S₁} {x : Maybe S} {z}
→ Maybe-map f x ≡ just z
→ x ≢ nothing
Maybe-map-cool {x = nothing} ()
Maybe-map-cool {x = just y} prf = λ x → ⊥-elim (maybe-⊥ (sym x) refl)
Maybe-map-cool-1 : ∀ {S S₁ : Set} {f : S → S₁} {x : Maybe S} {z}
→ Maybe-map f x ≡ just z
→ Σ S (λ x' → f x' ≡ z)
Maybe-map-cool-1 {x = nothing} ()
Maybe-map-cool-1 {x = just y} {z = z} refl = y , refl
Maybe-map-cool-2 : ∀ {S S₁ : Set} {f : S → S₁} {x : S} {z}
→ f x ≡ z
→ Maybe-map f (just x) ≡ just z
Maybe-map-cool-2 {S}{S₁}{f}{x}{z} prf rewrite prf = refl
T⇒true : ∀ {a : Bool} → T a → a ≡ true
T⇒true {true} _ = refl
isJust : ∀ {A : Set}{aMB : Maybe A}{a : A}
→ aMB ≡ just a
→ Is-just aMB
isJust refl = just tt
to-witness-isJust-≡ : ∀ {A : Set}{aMB : Maybe A}{a prf}
→ to-witness (isJust {aMB = aMB} {a} prf) ≡ a
to-witness-isJust-≡ {aMB = just a'} {a} {prf}
with to-witness-lemma (isJust {aMB = just a'} {a} prf) refl
...| xxx = just-injective (trans (sym xxx) prf)
deMorgan : ∀ {A B : Set} → (¬ A) ⊎ (¬ B) → ¬ (A × B)
deMorgan (inj₁ ¬a) = λ a×b → ¬a (proj₁ a×b)
deMorgan (inj₂ ¬b) = λ a×b → ¬b (proj₂ a×b)
¬subst : ∀ {ℓ₁ ℓ₂} {A : Set ℓ₁} {P : A → Set ℓ₂}
→ {x y : A}
→ ¬ (P x)
→ y ≡ x
→ ¬ (P y)
¬subst px refl = px
∸-suc-≤ : ∀ (x w : ℕ) → suc x ∸ w ≤ suc (x ∸ w)
∸-suc-≤ x zero = ≤-refl
∸-suc-≤ zero (suc w) rewrite 0∸n≡0 w = z≤n
∸-suc-≤ (suc x) (suc w) = ∸-suc-≤ x w
m∸n≤o⇒m∸o≤n : ∀ (x z w : ℕ) → x ∸ z ≤ w → x ∸ w ≤ z
m∸n≤o⇒m∸o≤n x zero w p≤ rewrite m≤n⇒m∸n≡0 p≤ = z≤n
m∸n≤o⇒m∸o≤n zero (suc z) w p≤ rewrite 0∸n≡0 w = z≤n
m∸n≤o⇒m∸o≤n (suc x) (suc z) w p≤ = ≤-trans (∸-suc-≤ x w) (s≤s (m∸n≤o⇒m∸o≤n x z w p≤))
tail-⊆ : ∀ {A : Set} {x} {xs ys : List A}
→ (x ∷ xs) ⊆List ys
→ xs ⊆List ys
tail-⊆ xxs⊆ys x∈xs = xxs⊆ys (there x∈xs)
allDistinctTail : ∀ {A : Set} {x} {xs : List A}
→ allDistinct (x ∷ xs)
→ allDistinct xs
allDistinctTail allDist i j
with allDist (suc i) (suc j)
...| inj₁ refl = inj₁ refl
...| inj₂ lookup≢ = inj₂ lookup≢
∈-Any-Index-elim : ∀ {A : Set} {x y} {ys : List A} (x∈ys : x ∈ ys)
→ x ≢ y → y ∈ ys
→ y ∈ ys ─ Any-index x∈ys
∈-Any-Index-elim (here refl) x≢y (here refl) = ⊥-elim (x≢y refl)
∈-Any-Index-elim (here refl) _ (there y∈ys) = y∈ys
∈-Any-Index-elim (there _) _ (here refl) = here refl
∈-Any-Index-elim (there x∈ys) x≢y (there y∈ys) = there (∈-Any-Index-elim x∈ys x≢y y∈ys)
∉∧⊆List⇒∉ : ∀ {A : Set} {x} {xs ys : List A}
→ x ∉ xs → ys ⊆List xs
→ x ∉ ys
∉∧⊆List⇒∉ x∉xs ys∈xs x∈ys = ⊥-elim (x∉xs (ys∈xs x∈ys))
allDistinctʳʳ : ∀ {A : Set} {x x₁ : A} {xs : List A}
→ allDistinct (x ∷ x₁ ∷ xs)
→ allDistinct (x ∷ xs)
allDistinctʳʳ _ zero zero = inj₁ refl
allDistinctʳʳ allDist zero (suc j)
with allDist zero (suc (suc j))
...| inj₂ x≢lookup
= inj₂ λ x≡lkpxs → ⊥-elim (x≢lookup x≡lkpxs)
allDistinctʳʳ allDist (suc i) zero
with allDist (suc (suc i)) zero
...| inj₂ x≢lookup
= inj₂ λ x≡lkpxs → ⊥-elim (x≢lookup x≡lkpxs)
allDistinctʳʳ allDist (suc i) (suc j)
with allDist (suc (suc i)) (suc (suc j))
...| inj₁ refl = inj₁ refl
...| inj₂ lookup≡ = inj₂ lookup≡
allDistinct⇒∉ : ∀ {A : Set} {x} {xs : List A}
→ allDistinct (x ∷ xs)
→ x ∉ xs
allDistinct⇒∉ allDist (here x≡x₁)
with allDist zero (suc zero)
... | inj₂ x≢x₁ = ⊥-elim (x≢x₁ x≡x₁)
allDistinct⇒∉ allDist (there x∈xs)
= allDistinct⇒∉ (allDistinctʳʳ allDist) x∈xs
sumListMap : ∀ {A : Set} {x} {xs : List A} (f : A → ℕ) → (x∈xs : x ∈ xs)
→ f-sum f xs ≡ f x + f-sum f (xs ─ Any-index x∈xs)
sumListMap _ (here refl) = refl
sumListMap {_} {x} {x₁ ∷ xs} f (there x∈xs)
rewrite sumListMap f x∈xs
| sym (+-assoc (f x) (f x₁) (f-sum f (xs ─ Any-index x∈xs)))
| +-comm (f x) (f x₁)
| +-assoc (f x₁) (f x) (f-sum f (xs ─ Any-index x∈xs)) = refl
lookup⇒Any : ∀ {A : Set} {xs : List A} {P : A → Set} (i : Fin (length xs))
→ P (List-lookup xs i) → Any P xs
lookup⇒Any {_} {_ ∷ _} zero px = here px
lookup⇒Any {_} {_ ∷ _} (suc i) px = there (lookup⇒Any i px)
x∉→AllDistinct : ∀ {A : Set} {x} {xs : List A}
→ allDistinct xs
→ x ∉ xs
→ allDistinct (x ∷ xs)
x∉→AllDistinct _ _ zero zero = inj₁ refl
x∉→AllDistinct _ x∉xs zero (suc j)
= inj₂ λ x≡lkp → x∉xs (lookup⇒Any j x≡lkp)
x∉→AllDistinct _ x∉xs (suc i) (zero)
= inj₂ λ x≡lkp → x∉xs (lookup⇒Any i (sym x≡lkp))
x∉→AllDistinct allDist x∉xs (suc i) (suc j)
with allDist i j
...| inj₁ refl = inj₁ refl
...| inj₂ lkup≢ = inj₂ lkup≢
cast-injective : ∀ {n m} {i j : Fin n} {eq : n ≡ m}
→ cast eq i ≡ cast eq j → i ≡ j
cast-injective {_} {_} {zero} {zero} {refl} _ = refl
cast-injective {_} {_} {suc i} {suc j} {refl} ci≡cj
= cong suc (cast-injective {eq = refl} (Fin-suc-injective ci≡cj))
List-lookup-map : ∀ {A B : Set} (xs : List A) (f : A → B) (α : Fin (length xs))
→ let cα = cast (sym (List-length-map f xs)) α
in f (List-lookup xs α) ≡ List-lookup (List-map f xs) cα
List-lookup-map (x ∷ xs) f zero = refl
List-lookup-map (x ∷ xs) f (suc α) = List-lookup-map xs f α
allDistinct-Map : ∀ {A B : Set} {xs : List A} {α₁ α₂ : Fin (length xs)} (f : A → B)
→ allDistinct (List-map f xs) → α₁ ≢ α₂
→ f (List-lookup xs α₁) ≢ f (List-lookup xs α₂)
allDistinct-Map {_} {_} {xs} {α₁} {α₂} f all≢ α₁≢α₂ flkp≡
with all≢ (cast (sym (List-length-map f xs)) α₁)
(cast (sym (List-length-map f xs)) α₂)
...| inj₁ cα₁≡cα₂ = ⊥-elim (α₁≢α₂ (cast-injective {eq = sym (List-length-map f xs)} cα₁≡cα₂))
...| inj₂ lkpα₁α₂≢ = ⊥-elim (lkpα₁α₂≢ (trans (sym (List-lookup-map xs f α₁))
(trans flkp≡ (List-lookup-map xs f α₂))))
filter⊆ : ∀ {A : Set} {P : A → Set} {P? : (a : A) → Dec (P a)} {xs : List A}
→ List-filter P? xs ⊆List xs
filter⊆ {P? = P?} x∈fxs = Any-filter⁻ P? x∈fxs
⊆⇒filter⊆ : ∀ {A : Set} {P : A → Set} {P? : (a : A) → Dec (P a)} {xs ys : List A}
→ xs ⊆List ys
→ List-filter P? xs ⊆List List-filter P? ys
⊆⇒filter⊆ {P? = P?} {xs = xs} {ys = ys} xs∈ys x∈fxs
with List-∈-filter⁻ P? {xs = xs} x∈fxs
...| x∈xs , px = List-∈-filter⁺ P? (xs∈ys x∈xs) px
map∘filter : ∀ {A B : Set} (xs : List A) (ys : List B) (f : A → B)
{P : B → Set} (P? : (b : B) → Dec (P b))
→ List-map f xs ≡ ys
→ List-map f (List-filter (P? ∘ f) xs) ≡ List-filter P? ys
map∘filter [] [] _ _ _ = refl
map∘filter (x ∷ xs) (.(f x) ∷ .(List-map f xs)) f P? refl
with P? (f x)
...| yes prf = cong (f x ∷_) (map∘filter xs (List-map f xs) f P? refl)
...| no imp = map∘filter xs (List-map f xs) f P? refl
allDistinct-Filter : ∀ {A : Set} {P : A → Set} {P? : (a : A) → Dec (P a)} {xs : List A}
→ allDistinct xs
→ allDistinct (List-filter P? xs)
allDistinct-Filter {P? = P?} {xs = x ∷ xs} all≢ i j
with P? x
...| no imp = allDistinct-Filter {P? = P?} {xs = xs} (allDistinctTail all≢) i j
...| yes prf = let all≢Tail = allDistinct-Filter {P? = P?} {xs = xs} (allDistinctTail all≢)
x∉Tail = allDistinct⇒∉ all≢
in x∉→AllDistinct all≢Tail (∉∧⊆List⇒∉ x∉Tail filter⊆) i j
sum-f∘g : ∀ {A B : Set} (xs : List A) (g : B → ℕ) (f : A → B)
→ f-sum (g ∘ f) xs ≡ f-sum g (List-map f xs)
sum-f∘g xs g f = cong sum (List-map-compose xs)
map-lookup-allFin : ∀ {A : Set} (xs : List A)
→ List-map (List-lookup xs) (allFin (length xs)) ≡ xs
map-lookup-allFin xs = trans (map-tabulate id (List-lookup xs)) (tabulate-lookup xs)
list-index : ∀ {A B : Set} {P : A → B → Set} (_∼_ : Decidable P)
(xs : List A) → B → Maybe (Fin (length xs))
list-index _∼_ [] x = nothing
list-index _∼_ (x ∷ xs) y
with x ∼ y
...| yes x≡y = just zero
...| no x≢y
with list-index _∼_ xs y
...| nothing = nothing
...| just i = just (suc i)
module DecLemmas {A : Set} (_≟D_ : Decidable {A = A} (_≡_)) where
_∈?_ : ∀ (x : A) → (xs : List A) → Dec (Any (x ≡_) xs)
x ∈? xs = Any-any (x ≟D_) xs
y∉xs⇒Allxs≢y : ∀ {xs : List A} {x y}
→ y ∉ (x ∷ xs)
→ x ≢ y × y ∉ xs
y∉xs⇒Allxs≢y {xs} {x} {y} y∉
with y ∈? xs
...| yes y∈xs = ⊥-elim (y∉ (there y∈xs))
...| no y∉xs
with x ≟D y
...| yes x≡y = ⊥-elim (y∉ (here (sym x≡y)))
...| no x≢y = x≢y , y∉xs
⊆List-Elim : ∀ {x} {xs ys : List A} (x∈ys : x ∈ ys)
→ x ∉ xs → xs ⊆List ys
→ xs ⊆List ys ─ Any-index x∈ys
⊆List-Elim (here refl) x∉xs xs∈ys x₂∈xs
with xs∈ys x₂∈xs
...| here refl = ⊥-elim (x∉xs x₂∈xs)
...| there x∈xs = x∈xs
⊆List-Elim (there x∈ys) x∉xs xs∈ys x₂∈xxs
with x₂∈xxs
...| there x₂∈xs
= ⊆List-Elim (there x∈ys) (proj₂ (y∉xs⇒Allxs≢y x∉xs)) (tail-⊆ xs∈ys) x₂∈xs
...| here refl
with xs∈ys x₂∈xxs
...| here refl = here refl
...| there x₂∈ys
= there (∈-Any-Index-elim x∈ys (≢-sym (proj₁ (y∉xs⇒Allxs≢y x∉xs))) x₂∈ys)
sum-⊆-≤ : ∀ {ys} (xs : List A) (f : A → ℕ)
→ allDistinct xs
→ xs ⊆List ys
→ f-sum f xs ≤ f-sum f ys
sum-⊆-≤ [] _ _ _ = z≤n
sum-⊆-≤ (x ∷ xs) f dxs xs⊆ys
rewrite sumListMap f (xs⊆ys (here refl))
= let x∉xs = allDistinct⇒∉ dxs
xs⊆ysT = tail-⊆ xs⊆ys
xs⊆ys-x = ⊆List-Elim (xs⊆ys (here refl)) x∉xs xs⊆ysT
disTail = allDistinctTail dxs
in +-monoʳ-≤ (f x) (sum-⊆-≤ xs f disTail xs⊆ys-x)
⊆-allFin : ∀ {n} {xs : List (Fin n)} → xs ⊆List allFin n
⊆-allFin {x = x} _ = Any-tabulate⁺ x refl
intersect : List A → List A → List A
intersect xs [] = []
intersect xs (y ∷ ys)
with y ∈? xs
...| yes _ = y ∷ intersect xs ys
...| no _ = intersect xs ys
union : List A → List A → List A
union xs [] = xs
union xs (y ∷ ys)
with y ∈? xs
...| yes _ = union xs ys
...| no _ = y ∷ union xs ys
∈-intersect : ∀ (xs ys : List A) {α}
→ α ∈ intersect xs ys
→ α ∈ xs × α ∈ ys
∈-intersect xs (y ∷ ys) α∈int
with y ∈? xs | α∈int
...| no y∉xs | α∈ = ×-map₂ there (∈-intersect xs ys α∈)
...| yes y∈xs | here refl = y∈xs , here refl
...| yes y∈xs | there α∈ = ×-map₂ there (∈-intersect xs ys α∈)
x∉⇒x∉intersect : ∀ {x} {xs ys : List A}
→ x ∉ xs ⊎ x ∉ ys
→ x ∉ intersect xs ys
x∉⇒x∉intersect {x} {xs} {ys} x∉ x∈int
= contraposition (∈-intersect xs ys) (deMorgan x∉) x∈int
intersectDistinct : ∀ (xs ys : List A)
→ allDistinct xs → allDistinct ys
→ allDistinct (intersect xs ys)
intersectDistinct xs (y ∷ ys) dxs dys
with y ∈? xs
...| yes y∈xs = let distTail = allDistinctTail dys
intDTail = intersectDistinct xs ys dxs distTail
y∉intTail = x∉⇒x∉intersect (inj₂ (allDistinct⇒∉ dys))
in x∉→AllDistinct intDTail y∉intTail
...| no y∉xs = intersectDistinct xs ys dxs (allDistinctTail dys)
x∉⇒x∉union : ∀ {x} {xs ys : List A}
→ x ∉ xs × x ∉ ys
→ x ∉ union xs ys
x∉⇒x∉union {_} {_} {[]} (x∉xs , _) x∈∪ = ⊥-elim (x∉xs x∈∪)
x∉⇒x∉union {x} {xs} {y ∷ ys} (x∉xs , x∉ys) x∈union
with y ∈? xs | x∈union
...| yes y∈xs | x∈∪
= ⊥-elim (x∉⇒x∉union (x∉xs , (proj₂ (y∉xs⇒Allxs≢y x∉ys))) x∈∪)
...| no y∉xs | here refl
= ⊥-elim (proj₁ (y∉xs⇒Allxs≢y x∉ys) refl)
...| no y∉xs | there x∈∪
= ⊥-elim (x∉⇒x∉union (x∉xs , (proj₂ (y∉xs⇒Allxs≢y x∉ys))) x∈∪)
unionDistinct : ∀ (xs ys : List A)
→ allDistinct xs → allDistinct ys
→ allDistinct (union xs ys)
unionDistinct xs [] dxs dys = dxs
unionDistinct xs (y ∷ ys) dxs dys
with y ∈? xs
...| yes y∈xs = unionDistinct xs ys dxs (allDistinctTail dys)
...| no y∉xs = let distTail = allDistinctTail dys
uniDTail = unionDistinct xs ys dxs distTail
y∉intTail = x∉⇒x∉union (y∉xs , allDistinct⇒∉ dys)
in x∉→AllDistinct uniDTail y∉intTail
sumIntersect≤ : ∀ (xs ys : List A) (f : A → ℕ)
→ f-sum f (intersect xs ys) ≤ f-sum f (xs ++ ys)
sumIntersect≤ _ [] _ = z≤n
sumIntersect≤ xs (y ∷ ys) f
with y ∈? xs
...| yes y∈xs rewrite map-++-commute f xs (y ∷ ys)
| sum-++-commute (List-map f xs) (List-map f (y ∷ ys))
| sym (+-assoc (f-sum f xs) (f y) (f-sum f ys))
| +-comm (f-sum f xs) (f y)
| +-assoc (f y) (f-sum f xs) (f-sum f ys)
| sym (sum-++-commute (List-map f xs) (List-map f ys))
| sym (map-++-commute f xs ys)
= +-monoʳ-≤ (f y) (sumIntersect≤ xs ys f)
...| no y∉xs rewrite map-++-commute f xs (y ∷ ys)
| sum-++-commute (List-map f xs) (List-map f (y ∷ ys))
| +-comm (f y) (f-sum f ys)
| sym (+-assoc (f-sum f xs) (f-sum f ys) (f y))
| sym (sum-++-commute (List-map f xs) (List-map f ys))
| sym (map-++-commute f xs ys)
= ≤-stepsʳ (f y) (sumIntersect≤ xs ys f)
index∘lookup-id : ∀ {B : Set} (xs : List B) (f : B → A)
→ allDistinct (List-map f xs) → {α : Fin (length xs)}
→ list-index (_≟D_ ∘ f) xs ((f ∘ List-lookup xs) α) ≡ just α
index∘lookup-id (x ∷ xs) f all≢ {zero}
with f x ≟D f x
...| yes fx≡fx = refl
...| no fx≢fx = ⊥-elim (fx≢fx refl)
index∘lookup-id (x ∷ xs) f all≢ {suc α}
with f x ≟D f (List-lookup xs α)
...| yes fx≡lkp = ⊥-elim (allDistinct⇒∉ all≢ (Any-map⁺ (lookup⇒Any α fx≡lkp)))
...| no fx≢lkp
with list-index (_≟D_ ∘ f) xs (f (List-lookup xs α))
| index∘lookup-id xs f (allDistinctTail all≢) {α}
...| just .α | refl = refl
lookup∘index-id : ∀ {B : Set} (xs : List B) (f : B → A)
→ allDistinct (List-map f xs) → {α : Fin (length xs)} {x : A}
→ list-index (_≟D_ ∘ f) xs x ≡ just α
→ (f ∘ List-lookup xs) α ≡ x
lookup∘index-id (x₁ ∷ xs) f all≢ {α} {x} lkp≡α
with f x₁ ≟D x
...| yes fx≡nId rewrite sym (just-injective lkp≡α) = fx≡nId
...| no fx≢nId
with list-index (_≟D_ ∘ f) xs x | inspect (list-index (_≟D_ ∘ f) xs) x
...| just _ | [ eq ] rewrite sym (just-injective lkp≡α)
= lookup∘index-id xs f (allDistinctTail all≢) eq
|
{
"alphanum_fraction": 0.4793307087,
"avg_line_length": 37.4562211982,
"ext": "agda",
"hexsha": "190f73a32f235fa878903d90a17fb2c68eab7645",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "a4674fc473f2457fd3fe5123af48253cfb2404ef",
"max_forks_repo_licenses": [
"UPL-1.0"
],
"max_forks_repo_name": "LaudateCorpus1/bft-consensus-agda",
"max_forks_repo_path": "src/Util/Lemmas.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "a4674fc473f2457fd3fe5123af48253cfb2404ef",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"UPL-1.0"
],
"max_issues_repo_name": "LaudateCorpus1/bft-consensus-agda",
"max_issues_repo_path": "src/Util/Lemmas.agda",
"max_line_length": 111,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "a4674fc473f2457fd3fe5123af48253cfb2404ef",
"max_stars_repo_licenses": [
"UPL-1.0"
],
"max_stars_repo_name": "LaudateCorpus1/bft-consensus-agda",
"max_stars_repo_path": "src/Util/Lemmas.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 10357,
"size": 24384
}
|
module Cats.Category.Setoids.Facts where
open import Cats.Category
open import Cats.Category.Setoids using (Setoids)
open import Cats.Category.Setoids.Facts.Exponentials using (hasExponentials)
open import Cats.Category.Setoids.Facts.Initial using (hasInitial)
open import Cats.Category.Setoids.Facts.Products
using (hasProducts ; hasBinaryProducts)
open import Cats.Category.Setoids.Facts.Terminal using (hasTerminal)
instance
isCCC : ∀ l → IsCCC (Setoids l l)
isCCC l = record { hasFiniteProducts = record {} } -- [1]
-- [1] For no discernible reason, `record {}` doesn't work.
|
{
"alphanum_fraction": 0.7715736041,
"avg_line_length": 32.8333333333,
"ext": "agda",
"hexsha": "5f50f7ff9c4c72350f595d5d449d111a30332837",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "a3b69911c4c6ec380ddf6a0f4510d3a755734b86",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "alessio-b-zak/cats",
"max_forks_repo_path": "Cats/Category/Setoids/Facts.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "a3b69911c4c6ec380ddf6a0f4510d3a755734b86",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "alessio-b-zak/cats",
"max_issues_repo_path": "Cats/Category/Setoids/Facts.agda",
"max_line_length": 76,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "a3b69911c4c6ec380ddf6a0f4510d3a755734b86",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "alessio-b-zak/cats",
"max_stars_repo_path": "Cats/Category/Setoids/Facts.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 145,
"size": 591
}
|
module AML where
open import Level
open import Data.Product
data satisfied (a : Set) (m : Set → Set) : Set where
s : m a → satisfied a m
data reachability (m₀ : Set → Set) (m : Set → Set) : Set where
tt : reachability m₀ m
data necessarity (m₀ : Set → Set) (a : Set) : Set₁ where
n : ∀ m → (reachability m₀ m) → satisfied a m → necessarity m₀ a
□_ : Set → Set₁
□_ = necessarity {!!}
data posibility (m₀ : Set → Set) (a : Set) : Set₁ where
p : ∃[ m ](reachability m₀ m → satisfied a m) → posibility m₀ a
◇_ : Set → Set₁
◇_ = posibility {!!}
|
{
"alphanum_fraction": 0.6216216216,
"avg_line_length": 24.1304347826,
"ext": "agda",
"hexsha": "4369bd472794f97584559c9cf0ed26c6b4c2ea3c",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2019-12-13T04:50:46.000Z",
"max_forks_repo_forks_event_min_datetime": "2019-12-13T04:50:46.000Z",
"max_forks_repo_head_hexsha": "eb2cef0556efb9a4ce11783f8516789ea48cc344",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "Brethland/LEARNING-STUFF",
"max_forks_repo_path": "Agda/AML.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "eb2cef0556efb9a4ce11783f8516789ea48cc344",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "Brethland/LEARNING-STUFF",
"max_issues_repo_path": "Agda/AML.agda",
"max_line_length": 66,
"max_stars_count": 2,
"max_stars_repo_head_hexsha": "eb2cef0556efb9a4ce11783f8516789ea48cc344",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "Brethland/LEARNING-STUFF",
"max_stars_repo_path": "Agda/AML.agda",
"max_stars_repo_stars_event_max_datetime": "2020-03-11T10:35:42.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-02-03T05:05:52.000Z",
"num_tokens": 199,
"size": 555
}
|
module Array.Properties where
open import Array.Base
open import Data.Fin using (Fin; zero; suc; raise; fromℕ≤; fromℕ<; fromℕ)
open import Data.Nat
open import Data.Nat.Properties
open import Data.Vec
open import Data.Vec.Properties
open import Relation.Binary.PropositionalEquality
open import Function using (_$_; _∘_; case_of_)
open import Data.Product
open import Relation.Nullary
open import Relation.Nullary.Decidable
open import Relation.Nullary.Negation
open import Relation.Binary using (Decidable; Rel)
open import Data.Maybe
open import Data.Sum
sel-ext : ∀ {a}{X : Set a}{d s} → (f : Ix d s → X)
→ (iv jv : Ix d s)
→ iv =ix jv
→ f iv ≡ f jv
sel-ext {d = zero} f [] [] pf = refl
sel-ext {d = suc d} f (i ∷ iv) (j ∷ jv) pf rewrite (pf zero) = sel-ext (f ∘ (j ∷_)) iv jv (pf ∘ suc)
s→a∘a→s : ∀ {n} → (a : Ar ℕ 1 (n ∷ [])) → s→a (a→s a) =a a
s→a∘a→s (imap x) (i ∷ []) = lookup∘tabulate _ i
a→s∘s→a : ∀ {n} → (v : Vec ℕ n) → a→s (s→a v) =s v
a→s∘s→a v i = lookup∘tabulate _ i
refl-=a : ∀ {a}{X : Set a}{d s}{x : Ar X d s}
→ x =a x
refl-=a {x = imap x} iv = refl
sym-=a : ∀ {a}{X : Set a}{d s}{l r : Ar X d s}
→ l =a r → r =a l
sym-=a {l = imap f} {imap g} l=r = sym ∘ l=r
trans-=a : ∀ {a}{X : Set a}{d s}{x y z : Ar X d s}
→ x =a y → y =a z → x =a z
trans-=a {x = imap x} {imap y} {imap z} x=y y=z iv
= trans (x=y iv) (y=z iv)
_<v?_ : ∀ {n} → Decidable (_<s_ {n = n})
[] <v? [] = yes λ ()
(x ∷ xs) <v? (y ∷ ys) = case _,_ {B = λ x₂ → Dec (xs <s ys) }(x <? y) (xs <v? ys) of λ where
(yes pf-xy , yes pf-xsys) → yes λ where
zero → pf-xy
(suc i) → pf-xsys i
(no pf-xy , _) → no (not-head pf-xy)
(_ , no pf-xsys) → no (not-tail pf-xsys)
where
p1 : ∀ {n}{x y}{xs ys : Vec ℕ n} → (x ∷ xs) <s (y ∷ ys) → x < y
p1 pf = pf zero
p2 : ∀ {n}{x y}{xs ys : Vec ℕ n} → (x ∷ xs) <s (y ∷ ys) → xs <s ys
p2 pf = pf ∘ (raise 1)
not-head : ∀ {n}{x y}{xs ys : Vec ℕ n} → ¬ (x < y) → ¬ ((x ∷ xs) <s (y ∷ ys))
not-head pf-xy pf-xxs-yys = contradiction (p1 pf-xxs-yys) pf-xy
not-tail : ∀ {n}{x y}{xs ys : Vec ℕ n} → ¬ (xs <s ys) → ¬ ((x ∷ xs) <s (y ∷ ys))
not-tail pf-xsys pf-xxs-yys = contradiction (p2 pf-xxs-yys) pf-xsys
-- Index curry makes it possible to fix the first position of
-- the index vector and select a sub-array.
ix-curry : ∀ {a}{X : Set a}{d s ss} → (f : Ix (suc d) (s ∷ ss) → X) → (Fin s) → (Ix d ss → X)
ix-curry f x xs = f (x ∷ xs)
ARel : ∀ {a}{A : Set a} → (P : Rel A a) -- → Decidable P
→ ∀ {d s} → Ar A d s → Ar A d s → Set a
ARel p (imap x) (imap y) = ∀ iv → p (x iv) (y iv)
--test = ARel _≥_
-- If a < b, then sub-arays a[i] < b[i], where a[i] and b[i]
-- is non-scalar selection where the head of index-vector is
-- fixed to i.
all-subarrays : ∀ {d s ss}{a}{X : Set a}{_~_ : Rel X a}
→ let _~a_ = ARel _~_ in
(a b : Ix (suc d) (suc s ∷ ss) → X)
→ imap a ~a imap b
→ ∀ i → (imap (ix-curry a i) ~a imap (ix-curry b i))
all-subarrays a b pf i iv = pf (i ∷ iv)
-- If all a[i] < b[i], then a < b.
from-subarrays : ∀ {d s ss}{a}{X : Set a}{_~_ : Rel X a}
→ let _~a_ = ARel _~_ in
(a b : Ix (suc d) (suc s ∷ ss) → X)
→ (∀ i → (imap (ix-curry a i) ~a imap (ix-curry b i)))
→ imap a ~a imap b
from-subarrays a b pf (x ∷ iv) = pf x iv
-- If there exists i such that ¬ a[i] < b[i], then ¬ a < b.
not-subarrays : ∀ {d s ss}{a}{X : Set a}{_~_ : Rel X a}
→ let _~a_ = ARel _~_ in
(a b : Ix (suc d) (suc s ∷ ss) → X)
→ (i : Fin (suc s))
→ ¬ imap (ix-curry a i) ~a imap (ix-curry b i)
→ ¬ imap a ~a imap b
not-subarrays a b i ¬p pp = contradiction pp λ z → ¬p (λ iv → z (i ∷ iv))
module not-needed where
unmaybe : ∀ {a}{X : Set a}{n}
→ (x : Vec (Maybe X) n)
→ (∀ i → lookup x i ≢ nothing)
→ Vec X n
unmaybe {n = zero} x pf = []
unmaybe {n = suc n} (just x ∷ xs) pf = x ∷ unmaybe xs (pf ∘ suc)
unmaybe {n = suc n} (nothing ∷ x₁) pf = contradiction refl $ pf zero
check-all-nothing : ∀ {a}{X : Set a}{n}
→ (x : Vec (Maybe X) n)
→ Maybe ((i : Fin n) → lookup x i ≢ nothing)
check-all-nothing {n = zero} x = nothing
check-all-nothing {n = suc n} (just x ∷ xs) with check-all-nothing xs
check-all-nothing {n = suc n} (just x ∷ xs) | just f = just λ { zero → λ () ; (suc k) → f k }
check-all-nothing {n = suc n} (just x ∷ xs) | nothing = nothing
check-all-nothing {n = suc n} _ = nothing
check-all-subarrays : ∀ {d s ss}{a}{X : Set a}{_~_ : Rel X a}
→ let _~a_ = ARel _~_ in
(a b : Ix (suc d) (suc s ∷ ss) → X)
→ (∀ i → Dec (imap (ix-curry a i) ~a imap (ix-curry b i)))
→ (Σ (Fin (suc s)) λ i → ¬ (imap (ix-curry a i) ~a imap (ix-curry b i)))
⊎ (∀ i → (imap (ix-curry a i) ~a imap (ix-curry b i)))
check-all-subarrays {s = zero} a b pf with (pf zero)
check-all-subarrays {_} {zero} a b pf | yes p = inj₂ λ { zero → p }
check-all-subarrays {_} {zero} a b pf | no ¬p = inj₁ (zero , ¬p)
check-all-subarrays {s = suc s} {_~_ = _~_} a b pf with check-all-subarrays {_~_ = _~_}
(λ { (i ∷ iv) → a (suc i ∷ iv)})
(λ { (i ∷ iv) → b (suc i ∷ iv)})
(pf ∘ suc)
-- If we have a subarray that is not <
-- simply propagate it further, updating the index
check-all-subarrays {_} {suc s} a b pf | inj₁ (i , a≁b) = inj₁ (suc i , a≁b)
check-all-subarrays {_} {suc s} a b pf | inj₂ y with (pf zero)
check-all-subarrays {_} {suc s} a b pf | inj₂ y | yes p = inj₂ λ { zero → p ; (suc k) → y k }
check-all-subarrays {_} {suc s} a b pf | inj₂ y | no ¬p = inj₁ (zero , ¬p)
{-
-- For arrays a and b, if f : ∀ i → Dec (a[i] < b[i]),
-- check whether:
-- 1. There exists i, for which ¬ a[i] < b[i]
-- 2. Otherwise construct a function of type ∀ i → a[i] < b[i]
check-all-subarrays : ∀ {d s ss}
→ (a b : Ix (suc d) (suc s ∷ ss) → ℕ)
→ (∀ i → Dec (imap (ix-curry a i) <a imap (ix-curry b i)))
→ (Σ (Fin (suc s)) λ i → ¬ (imap (ix-curry a i) <a imap (ix-curry b i)))
⊎ (∀ i → (imap (ix-curry a i) <a imap (ix-curry b i)))
check-all-subarrays {s = zero} a b pf with (pf zero)
check-all-subarrays {_} {zero} a b pf | yes p = inj₂ λ { zero → p }
check-all-subarrays {_} {zero} a b pf | no ¬p = inj₁ (zero , ¬p)
check-all-subarrays {s = suc s} a b pf with check-all-subarrays (λ { (i ∷ iv) → a (suc i ∷ iv)})
(λ { (i ∷ iv) → b (suc i ∷ iv)})
(pf ∘ suc)
-- If we have a subarray that is not <
-- simply propagate it further, updating the index
check-all-subarrays {_} {suc s} a b pf | inj₁ (i , a≮b) = inj₁ (suc i , a≮b)
check-all-subarrays {_} {suc s} a b pf | inj₂ y with (pf zero)
check-all-subarrays {_} {suc s} a b pf | inj₂ y | yes p = inj₂ λ { zero → p ; (suc k) → y k }
check-all-subarrays {_} {suc s} a b pf | inj₂ y | no ¬p = inj₁ (zero , ¬p)
-}
mk-dec-arel : ∀ {a}{X : Set a} → (p : Rel X a) → Decidable p → ∀ {d s} → Decidable (ARel p {d = d} {s = s})
mk-dec-arel _~_ _~?_ {zero} {[]} (imap x) (imap x₁) with x [] ~? x₁ []
mk-dec-arel _~_ _~?_ {zero} {[]} (imap x) (imap x₁) | yes p = yes λ { [] → p }
mk-dec-arel _~_ _~?_ {zero} {[]} (imap x) (imap x₁) | no ¬p = no λ p → contradiction (p []) ¬p
mk-dec-arel _~_ _~?_ {suc d} {zero ∷ ss} (imap x) (imap x₁) = yes λ iv → magic-fin $ ix-lookup iv zero
mk-dec-arel _~_ _~?_ {suc d} {suc s ∷ ss} (imap x) (imap x₁) = case-analysis
where
case-analysis : _ -- Dec ((i : Ix (suc d) (suc s ∷ ss)) → suc (x i) ≤ x₁ i)
case-analysis = let _~a?_ = mk-dec-arel _~_ _~?_
in case check-all-subarrays {_~_ = _~_}
x x₁ (λ i → imap (ix-curry x i)
~a? imap (ix-curry x₁ i)) of λ where
-- In this case we have an index and a proof that
-- subarray at this index is not <
(inj₁ (i , x≁x₁)) → no $ not-subarrays {_~_ = _~_} x x₁ i x≁x₁
-- In this case we have a function that for every index
-- returns a proof that sub-arrays are <
(inj₂ f) → yes (from-subarrays {_~_ = _~_} x x₁ f)
_<a?_ = mk-dec-arel _<_ _<?_
_≥a?_ = mk-dec-arel _≥_ _≥?_
{-
_<a?_ : ∀ {d s} → Decidable (_<a_ {d = d} {s = s})
_<a?_ {zero} {[]} (imap x) (imap x₁) with x [] <? x₁ []
_<a?_ {zero} {[]} (imap x) (imap x₁) | yes p = yes λ { [] → p }
_<a?_ {zero} {[]} (imap x) (imap x₁) | no ¬p = no λ p → contradiction (p []) ¬p
_<a?_ {suc d} {0 ∷ ss} (imap x) (imap x₁) = yes λ iv → magic-fin $ ix-lookup iv zero
_<a?_ {suc d} {(suc s) ∷ ss} (imap x) (imap x₁) = case-analysis
where
case-analysis : _ -- Dec ((i : Ix (suc d) (suc s ∷ ss)) → suc (x i) ≤ x₁ i)
case-analysis = case check-all-subarrays {_~_ = _<_}
x x₁ (λ i → imap (ix-curry x i)
<a? imap (ix-curry x₁ i)) of λ where
-- In this case we have an index and a proof that
-- subarray at this index is not <
(inj₁ (i , x≮x₁)) → no $ not-subarrays {_~_ = _<_} x x₁ i x≮x₁
-- In this case we have a function that for every index
-- returns a proof that sub-arrays are <
(inj₂ f) → yes (from-subarrays {_~_ = _<_} x x₁ f)
_≥a?_ : ∀ {d s} → Decidable (_≥a_ {d = d} {s = s})
_≥a?_ {zero} {[]} (imap x) (imap x₁) with x [] ≥? x₁ []
_≥a?_ {zero} {[]} (imap x) (imap x₁) | yes p = yes λ { [] → p }
_≥a?_ {zero} {[]} (imap x) (imap x₁) | no ¬p = no λ p → contradiction (p []) ¬p
_≥a?_ {suc d} {s} (imap x) (imap x₁) = {!!}
-}
private
thm : ∀ { i s } → i < s → s ∸ i ∸ 1 + suc i ≡ s
thm {i} {s} pf = begin
s ∸ i ∸ 1 + suc i ≡⟨ cong (_+ (suc i)) (∸-+-assoc s i 1) ⟩
s ∸ (i + 1) + suc i ≡⟨ cong (_+ (suc i)) (cong (s ∸_) (+-comm i 1)) ⟩
s ∸ suc i + suc i ≡⟨ m∸n+n≡m pf ⟩
s
∎
where open ≡-Reasoning
-- XXX can we do this simpler?
≮a⇒∃ : ∀ {d s}{a b : Ar _ d s} → ¬ a <a b → Σ (Ix d s) λ iv → ¬ (unimap a iv < unimap b iv)
≮a⇒∃ {zero} {[]} {imap f} {imap g} ¬a<b with f [] <? g []
≮a⇒∃ {zero} {[]} {imap f} {imap g} ¬a<b | yes p = contradiction (λ { [] → p}) ¬a<b
≮a⇒∃ {zero} {[]} {imap f} {imap g} ¬a<b | no ¬p = [] , ¬p
≮a⇒∃ {suc d} {zero ∷ ss} {imap f} {imap g} ¬a<b = contradiction (λ iv → magic-fin $ ix-lookup iv zero) ¬a<b
≮a⇒∃ {suc d} {suc s ∷ ss} {imap f} {imap g} ¬a<b = case-analysis
where
case-analysis : _
case-analysis = case check-all-subarrays {_~_ = _<_}
f g (λ i → imap (ix-curry f i)
<a? imap (ix-curry g i)) of λ where
(inj₁ (i , f≮g)) → let
iv , pf = ≮a⇒∃ f≮g
in (i ∷ iv) , λ pp → contradiction pp pf
(inj₂ pf) → contradiction (from-subarrays {_~_ = _<_} f g pf) ¬a<b
module try-irrelevant where
-- XXX this shouldn't be here, this is for now to avoid
-- dependencies in the modules.
-- Inverse of the above
a→ix : ∀ {d} --{s : Fin d → ℕ}
→ (ax sh : Ar ℕ 1 (d ∷ []))
-- XXX we can make this inequality irrelevant
-- and recompute it when it is needed, as <a
-- is decideable.
→ .(ax <a sh)
→ Ix d (a→s sh)
a→ix {d} (imap axf) (imap shf) ax<sh = ix-tabulate from-pf
where
pf : _
pf = recompute (imap axf <a? imap shf) ax<sh
from-pf : _
from-pf i rewrite (lookup∘tabulate (shf ∘ (_∷ [])) i)
= let
ix : Ix 1 (d ∷ [])
ix = i ∷ []
r = raise (shf ix ∸ axf ix ∸ 1) $ fromℕ (axf ix)
in subst Fin (thm (pf ix)) r --fromℕ≤ (ax<sh (i ∷ []))
a→ix : ∀ {d} --{s : Fin d → ℕ}
→ (ax sh : Ar ℕ 1 (d ∷ []))
→ (ax <a sh)
→ Ix d (a→s sh)
a→ix {d} (imap axf) (imap shf) ax<sh = ix-tabulate from-pf
where
from-pf : _
from-pf i rewrite (lookup∘tabulate (shf ∘ (_∷ [])) i)
= fromℕ< (ax<sh (i ∷ []))
|
{
"alphanum_fraction": 0.4587155963,
"avg_line_length": 43.5268456376,
"ext": "agda",
"hexsha": "a94b383f3a4feb5a4be6b4ecfae351ccec00c064",
"lang": "Agda",
"max_forks_count": 1,
"max_forks_repo_forks_event_max_datetime": "2020-10-12T07:19:48.000Z",
"max_forks_repo_forks_event_min_datetime": "2020-10-12T07:19:48.000Z",
"max_forks_repo_head_hexsha": "584fedb30552f820c0668cedae53ec3d926860b5",
"max_forks_repo_licenses": [
"0BSD"
],
"max_forks_repo_name": "ashinkarov/agda-array",
"max_forks_repo_path": "Array/Properties.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "584fedb30552f820c0668cedae53ec3d926860b5",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"0BSD"
],
"max_issues_repo_name": "ashinkarov/agda-array",
"max_issues_repo_path": "Array/Properties.agda",
"max_line_length": 107,
"max_stars_count": 6,
"max_stars_repo_head_hexsha": "584fedb30552f820c0668cedae53ec3d926860b5",
"max_stars_repo_licenses": [
"0BSD"
],
"max_stars_repo_name": "ashinkarov/agda-array",
"max_stars_repo_path": "Array/Properties.agda",
"max_stars_repo_stars_event_max_datetime": "2021-06-15T14:21:32.000Z",
"max_stars_repo_stars_event_min_datetime": "2020-05-09T13:53:46.000Z",
"num_tokens": 4788,
"size": 12971
}
|
module Oscar.Class.Symmetry where
open import Oscar.Class.Extensionality
open import Oscar.Function
open import Oscar.Level
record Symmetry {a} {A : Set a} {ℓ} (_≤_ : A → A → Set ℓ) : Set (a ⊔ ℓ) where
field
⦃ ′extensionality ⦄ : Extensionality _≤_ (λ ⋆ → flip _≤_ ⋆) id id
symmetry : ∀ {x y} → x ≤ y → y ≤ x
symmetry = extension (λ ⋆ → flip _≤_ ⋆)
open Symmetry ⦃ … ⦄ public hiding (′extensionality)
instance
Symmetry⋆ : ∀
{a} {A : Set a} {ℓ} {_≤_ : A → A → Set ℓ}
⦃ _ : Extensionality _≤_ (λ ⋆ → flip _≤_ ⋆) id id ⦄
→ Symmetry _≤_
Symmetry.′extensionality Symmetry⋆ = it
|
{
"alphanum_fraction": 0.6072607261,
"avg_line_length": 25.25,
"ext": "agda",
"hexsha": "19652ee6937dec5b44356358f243a4a52b180b84",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "52e1cdbdee54d9a8eaee04ee518a0d7f61d25afb",
"max_forks_repo_licenses": [
"RSA-MD"
],
"max_forks_repo_name": "m0davis/oscar",
"max_forks_repo_path": "archive/agda-2/Oscar/Class/Symmetry.agda",
"max_issues_count": 1,
"max_issues_repo_head_hexsha": "52e1cdbdee54d9a8eaee04ee518a0d7f61d25afb",
"max_issues_repo_issues_event_max_datetime": "2019-05-11T23:33:04.000Z",
"max_issues_repo_issues_event_min_datetime": "2019-04-29T00:35:04.000Z",
"max_issues_repo_licenses": [
"RSA-MD"
],
"max_issues_repo_name": "m0davis/oscar",
"max_issues_repo_path": "archive/agda-2/Oscar/Class/Symmetry.agda",
"max_line_length": 77,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "52e1cdbdee54d9a8eaee04ee518a0d7f61d25afb",
"max_stars_repo_licenses": [
"RSA-MD"
],
"max_stars_repo_name": "m0davis/oscar",
"max_stars_repo_path": "archive/agda-2/Oscar/Class/Symmetry.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 252,
"size": 606
}
|
import cedille-options
module elaboration (options : cedille-options.options) where
open import lib
options' = record options
{during-elaboration = tt;
erase-types = ff;
show-qualified-vars = ff}
open import general-util
open import monad-instances
open import cedille-types
open import classify options' {id}
open import ctxt
open import constants
open import conversion
open import is-free
open import meta-vars options' {id}
open import spans options {IO}
open import subst
open import syntax-util
open import toplevel-state options {IO}
open import to-string options'
open import rename
open import rewriting
open import elaboration-helpers options
open import templates
import spans options' {id} as id-spans
{- Datatypes -}
mendler-encoding : datatype-encoding
mendler-encoding =
let functorₓ = "Functor"
castₓ = "cast"
fixpoint-typeₓ = "CVFixIndM"
fixpoint-inₓ = "cvInFixIndM"
fixpoint-indₓ = "cvIndFixIndM" in
record {
template = MendlerTemplate;
functor = functorₓ;
cast = castₓ;
fixpoint-type = fixpoint-typeₓ;
fixpoint-in = fixpoint-inₓ;
fixpoint-ind = fixpoint-indₓ;
elab-mu = λ {
(Data x ps is cs)
(mk-encoded-datatype-names data-functorₓ data-fmapₓ data-functor-indₓ castₓ
fixpoint-typeₓ fixpoint-inₓ fixpoint-indₓ)
Γ t oT ms → record {
elab-check-mu = λ ihₓ T → nothing;
elab-synth-mu = case oT of λ {
NoType ihₓ → nothing;
(SomeType Tₘ) ihₓ → nothing
};
elab-check-mu' = λ T → nothing;
elab-synth-mu' = case oT of λ {
NoType → nothing;
(SomeType Tₘ) → nothing
}
}
}
}
mendler-simple-encoding : datatype-encoding
mendler-simple-encoding =
let functorₓ = "RecFunctor"
castₓ = "cast"
fixpoint-typeₓ = "FixM"
fixpoint-inₓ = "inFix"
fixpoint-indₓ = "IndFixM" in
record {
template = MendlerSimpleTemplate;
functor = functorₓ;
cast = castₓ;
fixpoint-type = fixpoint-typeₓ;
fixpoint-in = fixpoint-inₓ;
fixpoint-ind = fixpoint-indₓ;
elab-mu = λ {
(Data x ps is cs)
(mk-encoded-datatype-names data-functorₓ data-fmapₓ data-functor-indₓ castₓ
fixpoint-typeₓ fixpoint-inₓ fixpoint-indₓ)
Γ t oT ms → record {
elab-check-mu = λ ihₓ T →
-- let Tₘ = case oT of λ {(SomeType Tₘ) → Tₘ; NoType → indices-to-tplams is $ TpLambda posinfo-gen posinfo-gen ignored-var (Tkt {!!}) T} in
nothing;
elab-synth-mu = case oT of λ {
NoType ihₓ → nothing;
(SomeType Tₘ) ihₓ → nothing
};
elab-check-mu' = λ T → nothing;
elab-synth-mu' = case oT of λ {
NoType → nothing;
(SomeType Tₘ) → nothing
}
}
}
}
selected-encoding = mendler-simple-encoding
-- TODO: ^ Add option so user can choose encoding ^
{-# TERMINATING #-}
elab-check-term : ctxt → term → type → maybe term
elab-synth-term : ctxt → term → maybe (term × type)
elab-pure-term : ctxt → term → maybe term
elab-type : ctxt → type → maybe (type × kind)
elab-pure-type : ctxt → type → maybe type
elab-kind : ctxt → kind → maybe kind
elab-pure-kind : ctxt → kind → maybe kind
elab-tk : ctxt → tk → maybe tk
elab-pure-tk : ctxt → tk → maybe tk
elab-typeh : ctxt → type → 𝔹 → maybe (type × kind)
elab-kindh : ctxt → kind → 𝔹 → maybe kind
elab-tkh : ctxt → tk → 𝔹 → maybe tk
elab-type-arrow : type → type
elab-kind-arrow : kind → kind
elab-tk-arrow : tk → tk
elab-hnf-type : ctxt → type → 𝔹 → maybe type
elab-hnf-kind : ctxt → kind → 𝔹 → maybe kind
elab-hnf-tk : ctxt → tk → 𝔹 → maybe tk
elab-app-term : ctxt → term → prototype → 𝔹 → maybe ((meta-vars → maybe term) × spine-data)
elab-type Γ T = elab-typeh Γ T tt
elab-kind Γ k = elab-kindh Γ k tt
elab-tk Γ atk = elab-tkh Γ atk tt
elab-pure-type Γ T = maybe-map fst (elab-typeh Γ T ff)
elab-pure-kind Γ k = elab-kindh Γ k ff
elab-pure-tk Γ atk = elab-tkh Γ atk ff
elab-type-arrow (Abs pi b pi' x atk T) = Abs pi b pi' x (elab-tk-arrow atk) (elab-type-arrow T)
elab-type-arrow (Iota pi pi' x T T') = Iota pi pi' x (elab-type-arrow T) (elab-type-arrow T')
elab-type-arrow (Lft pi pi' x t lT) = Lft pi pi' x t lT
elab-type-arrow (NoSpans T pi) = elab-type-arrow T
elab-type-arrow (TpLet pi (DefTerm pi' x NoType t) T') = TpLet pi (DefTerm pi x NoType t) (elab-type-arrow T')
elab-type-arrow (TpLet pi (DefTerm pi' x (SomeType T) t) T') = TpLet pi (DefTerm pi x (SomeType (elab-type-arrow T)) t) T'
elab-type-arrow (TpLet pi (DefType pi' x k T) T') = TpLet pi (DefType pi' x (elab-kind-arrow k) (elab-type-arrow T)) (elab-type-arrow T')
elab-type-arrow (TpApp T T') = TpApp (elab-type-arrow T) (elab-type-arrow T')
elab-type-arrow (TpAppt T t) = TpAppt (elab-type-arrow T) t
elab-type-arrow (TpArrow T a T') = Abs posinfo-gen a posinfo-gen "_" (Tkt (elab-type-arrow T)) (elab-type-arrow T')
elab-type-arrow (TpEq pi t t' pi') = TpEq pi (erase-term t) (erase-term t') pi'
elab-type-arrow (TpHole pi) = TpHole pi
elab-type-arrow (TpLambda pi pi' x atk T) = TpLambda pi pi' x (elab-tk-arrow atk) (elab-type-arrow T)
elab-type-arrow (TpParens pi T pi') = elab-type-arrow T
elab-type-arrow (TpVar pi x) = TpVar pi x
elab-kind-arrow (KndArrow k k') = KndPi posinfo-gen posinfo-gen "_" (Tkk (elab-kind-arrow k)) (elab-kind-arrow k')
elab-kind-arrow (KndParens pi k pi') = elab-kind-arrow k
elab-kind-arrow (KndPi pi pi' x atk k) = KndPi pi pi' x (elab-tk-arrow atk) (elab-kind-arrow k)
elab-kind-arrow (KndTpArrow T k) = KndPi posinfo-gen posinfo-gen "_" (Tkt (elab-type-arrow T)) (elab-kind-arrow k)
elab-kind-arrow k = k
elab-tk-arrow (Tkt T) = Tkt (elab-type-arrow T)
elab-tk-arrow (Tkk k) = Tkk (elab-kind-arrow k)
elab-hnf-type Γ T b = just (elab-type-arrow (substh-type {TYPE} Γ empty-renamectxt empty-trie (hnf Γ (unfolding-set-erased unfold-head (~ b)) T tt)))
elab-hnf-kind Γ k b = just (elab-kind-arrow (substh-kind {KIND} Γ empty-renamectxt empty-trie (hnf Γ (unfolding-set-erased unfold-head (~ b)) k tt)))
elab-hnf-tk Γ (Tkt T) b = elab-hnf-type Γ T b ≫=maybe (just ∘ Tkt)
elab-hnf-tk Γ (Tkk k) b = elab-hnf-kind Γ k b ≫=maybe (just ∘ Tkk)
elab-check-term Γ (App t me t') T =
elab-app-term Γ (App t me t') (proto-maybe (just T)) tt ≫=maybe uncurry λ where
tf (mk-spine-data Xs T' _) → tf Xs
elab-check-term Γ (AppTp t T) T' =
elab-synth-term Γ t ≫=maybe uncurry λ t T'' →
elab-type Γ T ≫=maybe uncurry λ T k →
just (AppTp t T)
elab-check-term Γ (Beta pi ot ot') T =
let ot'' = case ot' of λ where NoTerm → just (fresh-id-term Γ); (SomeTerm t _) → elab-pure-term Γ (erase-term t) in
case ot of λ where
NoTerm → elab-hnf-type Γ T tt ≫=maybe λ where
(TpEq _ t₁ t₂ _) → ot'' ≫=maybe (just ∘ mbeta t₁)
_ → nothing
(SomeTerm t _) →
elab-pure-term Γ (erase-term t) ≫=maybe λ t →
ot'' ≫=maybe (just ∘ mbeta t)
elab-check-term Γ (Chi pi mT t) T = case mT of λ where
NoType → maybe-map fst (elab-synth-term Γ t)
(SomeType T') →
elab-pure-type Γ (erase-type T') ≫=maybe λ T' →
let id = fresh-id-term Γ in
elab-check-term Γ t T' ≫=maybe
(just ∘ mrho (mbeta id id) "_" T')
elab-check-term Γ (Delta pi mT t) T =
elab-pure-type Γ (erase-type T) ≫=maybe λ T →
elab-synth-term Γ t ≫=maybe uncurry λ where
t (TpEq _ t1 t2 _) →
rename "x" from Γ for λ x →
rename "y" from Γ for λ y →
rename "z" from Γ for λ z →
let ρ = renamectxt-insert (renamectxt-insert (renamectxt-insert empty-renamectxt x x) y y) z z
tt-term = mlam x (mlam y (mvar x))
ff-term = mlam x (mlam y (mvar y)) in
if conv-term Γ t1 tt-term && conv-term Γ t2 ff-term
then just (Delta posinfo-gen (SomeType T) t)
else
delta-contra (hnf Γ unfold-head t1 tt) (hnf Γ unfold-head t2 tt) ≫=maybe λ f →
let f = substh-term {TERM} Γ ρ empty-trie f in
elab-pure-term Γ (erase-term t) ≫=maybe λ pt →
just (Delta posinfo-gen (SomeType T)
(mrho t z (mtpeq (mapp f t1) (mapp f (mvar z))) (mbeta tt-term pt)))
t T → nothing
elab-check-term Γ (Epsilon pi lr mm t) T =
elab-hnf-type Γ T tt ≫=maybe λ where
(TpEq _ t₁ t₂ _) → elab-check-term Γ (Chi posinfo-gen
(SomeType (check-term-update-eq Γ lr mm posinfo-gen t₁ t₂ posinfo-gen)) t) T
_ → nothing
elab-check-term Γ (Hole pi) T = nothing
elab-check-term Γ (IotaPair pi t t' og pi') T =
elab-hnf-type Γ T tt ≫=maybe λ where
(Iota _ pi x T' T'') →
elab-check-term Γ t T' ≫=maybe λ t →
elab-check-term Γ t' (subst Γ t x T'') ≫=maybe λ t' →
rename x from Γ for λ x' →
just (IotaPair posinfo-gen t t' (Guide posinfo-gen x' T'') posinfo-gen)
_ → nothing
elab-check-term Γ (IotaProj t n pi) T =
elab-synth-term Γ t ≫=maybe uncurry λ t T' →
just (IotaProj t n posinfo-gen)
elab-check-term Γ (Lam pi l pi' x oc t) T =
(elab-hnf-type Γ T tt ≫=maybe to-abs) ≫=maybe λ where
(mk-abs b x' atk free T') →
rename (if x =string "_" && free then x' else x) from Γ for λ x'' →
elab-tk Γ atk ≫=maybe λ tk →
elab-check-term (ctxt-tk-decl' pi' x'' atk Γ) (rename-var Γ x x'' t)
(rename-var Γ x' x'' T') ≫=maybe λ t →
just (Lam posinfo-gen l posinfo-gen x'' (SomeClass atk) t)
elab-check-term Γ (Let pi d t) T =
case d of λ where
(DefTerm pi' x NoType t') →
rename x from Γ for λ x' →
elab-synth-term Γ t' ≫=maybe uncurry λ t' T' →
elab-check-term (ctxt-let-term-def pi' x' t' T' Γ) (rename-var Γ x x' t) T ≫=maybe λ t →
just (Let posinfo-gen (DefTerm posinfo-gen x' NoType t') t)
(DefTerm pi' x (SomeType T') t') →
rename x from Γ for λ x' →
elab-type Γ T' ≫=maybe uncurry λ T' k →
elab-check-term Γ t' T' ≫=maybe λ t' →
elab-check-term (ctxt-let-term-def pi' x' t' T' Γ) (rename-var Γ x x' t) T ≫=maybe λ t →
just (Let posinfo-gen (DefTerm posinfo-gen x' NoType t') t)
(DefType pi' x k T') →
rename x from Γ for λ x' →
elab-type Γ T' ≫=maybe uncurry λ T' k' →
elab-check-term (ctxt-let-type-def pi' x' T' k' Γ) (rename-var Γ x x' t) T ≫=maybe λ t →
just (Let posinfo-gen (DefType posinfo-gen x' k' T') t)
elab-check-term Γ (Open pi x t) T =
ctxt-clarify-def Γ x ≫=maybe uncurry λ _ Γ →
elab-check-term Γ t T
elab-check-term Γ (Parens pi t pi') T = elab-check-term Γ t T
elab-check-term Γ (Phi pi t t₁ t₂ pi') T =
elab-pure-term Γ (erase-term t₁) ≫=maybe λ t₁' →
elab-pure-term Γ (erase-term t₂) ≫=maybe λ t₂ →
elab-check-term Γ t₁ T ≫=maybe λ t₁ →
elab-check-term Γ t (mtpeq t₁' t₂) ≫=maybe λ t →
just (Phi posinfo-gen t t₁ t₂ posinfo-gen)
elab-check-term Γ (Rho pi op on t og t') T =
elab-synth-term Γ t ≫=maybe uncurry λ t T' →
elab-hnf-type Γ (erase-type T') ff ≫=maybe λ where
(TpEq _ t₁ t₂ _) → case og of λ where
NoGuide →
elab-hnf-type Γ T tt ≫=maybe λ T →
rename "x" from Γ for λ x →
let ns = fst (optNums-to-stringset on)
Γ' = ctxt-var-decl x Γ
rT = fst (rewrite-type T Γ' (is-rho-plus op) ns t t₁ x 0)
rT' = post-rewrite Γ x t t₂ rT in
elab-hnf-type Γ rT' tt ≫=maybe λ rT' →
elab-check-term Γ t' rT' ≫=maybe
(just ∘ mrho (Sigma posinfo-gen t) x (erase-type rT))
(Guide pi' x T') →
let Γ' = ctxt-var-decl x Γ in
elab-pure-type Γ' (erase-type T') ≫=maybe λ T' →
elab-check-term Γ t' (post-rewrite Γ' x t t₂ (rewrite-at Γ' x t tt T T')) ≫=maybe
(just ∘ mrho t x T')
_ → nothing
elab-check-term Γ (Sigma pi t) T =
elab-hnf-type Γ T tt ≫=maybe λ where
(TpEq _ t₁ t₂ _) →
elab-check-term Γ t (mtpeq t₂ t₁) ≫=maybe λ t →
just (Sigma posinfo-gen t)
_ → nothing
elab-check-term Γ (Theta pi θ t ts) T =
elab-synth-term Γ t ≫=maybe uncurry λ t T' →
let x = case hnf Γ unfold-head t tt of λ {(Var _ x) → x; _ → "_"} in
rename x from Γ for λ x' →
motive x x' T T' θ ≫=maybe λ mtv →
elab-check-term Γ (lterms-to-term θ (AppTp t mtv) ts) T where
wrap-var : var → type → maybe type
wrap-var x T =
rename x from Γ for λ x' →
env-lookup Γ x ≫=maybe λ where
(term-decl T' , loc) → just (mtplam x' (Tkt T') (rename-var Γ x x' T))
(type-decl k , loc) → just (mtplam x' (Tkk k) (rename-var Γ x x' T))
(term-def ps _ _ T' , loc) → just (mtplam x' (Tkt T') (rename-var Γ x x' T))
(type-def ps _ _ k , loc) → just (mtplam x' (Tkk k) (rename-var Γ x x' T))
_ → nothing
wrap-vars : vars → type → maybe type
wrap-vars (VarsStart x) T = wrap-var x T
wrap-vars (VarsNext x xs) T = wrap-vars xs T ≫=maybe wrap-var x
motive : var → var → type → type → theta → maybe type
motive x x' T T' Abstract = just (mtplam x' (Tkt T') (rename-var Γ x x' T))
motive x x' T T' AbstractEq = just (mtplam x' (Tkt T') (TpArrow (mtpeq t (mvar x')) Erased (rename-var Γ x x' T)))
motive x x' T T' (AbstractVars vs) = wrap-vars vs T
elab-check-term Γ (Var pi x) T = just (mvar x)
elab-check-term Γ (Mu pi x t ot pi' cs pi'') T = nothing
elab-check-term Γ (Mu' pi t ot pi' cs pi'') T = nothing
elab-synth-term Γ (App t me t') =
elab-app-term Γ (App t me t') (proto-maybe nothing) tt ≫=maybe uncurry λ where
tf (mk-spine-data Xs T _) →
tf Xs ≫=maybe λ t'' →
elab-hnf-type Γ (meta-vars-subst-type' ff Γ Xs (decortype-to-type T)) tt ≫=maybe λ T →
just (t'' , T)
elab-synth-term Γ (AppTp t T) =
elab-synth-term Γ t ≫=maybe uncurry λ t T' →
elab-hnf-type Γ T' tt ≫=maybe λ where
(Abs _ _ _ x (Tkk k) T'') →
elab-type Γ T ≫=maybe uncurry λ T k' →
just (AppTp t T , subst Γ T x T'')
_ → nothing
elab-synth-term Γ (Beta pi ot ot') =
let ot'' = case ot' of λ where NoTerm → just (fresh-id-term Γ); (SomeTerm t _) → elab-pure-term Γ (erase-term t) in
case ot of λ where
(SomeTerm t _) →
elab-pure-term Γ (erase-term t) ≫=maybe λ t →
ot'' ≫=maybe λ t' →
just (mbeta t t' , mtpeq t t)
NoTerm → nothing
elab-synth-term Γ (Chi pi mT t) = case mT of λ where
NoType → elab-synth-term Γ t
(SomeType T') →
let id = fresh-id-term Γ in
elab-pure-type Γ (erase-type T') ≫=maybe λ T' →
elab-check-term Γ t T' ≫=maybe λ t →
just (mrho (mbeta id id) "_" T' t , T')
elab-synth-term Γ (Delta pi mT t) = (case mT of λ where
NoType → just compileFailType
(SomeType T) → elab-pure-type Γ (erase-type T)) ≫=maybe λ T →
elab-synth-term Γ t ≫=maybe uncurry λ where
t (TpEq _ t1 t2 _) →
elab-pure-term Γ (erase-term t) ≫=maybe λ pt →
rename "x" from Γ for λ x →
rename "y" from Γ for λ y →
rename "z" from Γ for λ z →
let ρ = renamectxt-insert (renamectxt-insert (renamectxt-insert empty-renamectxt x x) y y) z z
tt-term = mlam x (mlam y (mvar x))
ff-term = mlam x (mlam y (mvar y)) in
if conv-term Γ t1 tt-term && conv-term Γ t2 ff-term
then just (Delta posinfo-gen (SomeType T) t , T)
else
delta-contra (hnf Γ unfold-head t1 tt) (hnf Γ unfold-head t2 tt) ≫=maybe λ f →
let f = substh-term {TERM} Γ ρ empty-trie f in
just (Delta posinfo-gen (SomeType T)
(mrho t z (mtpeq (mapp f t1) (mapp f (mvar z))) (mbeta tt-term pt)) , T)
t T → nothing
elab-synth-term Γ (Epsilon pi lr mm t) =
elab-synth-term Γ t ≫=maybe uncurry λ where
t (TpEq _ t₁ t₂ _) →
let id = fresh-id-term Γ
T = check-term-update-eq Γ lr mm posinfo-gen t₁ t₂ posinfo-gen in
elab-pure-type Γ T ≫=maybe λ T →
just (mrho (mbeta id id) "_" T t , T)
_ _ → nothing
elab-synth-term Γ (Hole pi) = nothing
elab-synth-term Γ (IotaPair pi t₁ t₂ og pi') = case og of λ where
NoGuide → nothing
(Guide pi'' x T₂) →
rename x from Γ for λ x' →
elab-type (ctxt-var-decl x' Γ) (rename-var Γ x x' T₂) ≫=maybe uncurry λ T₂ k₂ →
elab-synth-term Γ t₁ ≫=maybe uncurry λ t₁ T₁ →
elab-check-term Γ t₂ (subst Γ t₁ x' T₂) ≫=maybe λ t₂ →
just (IotaPair posinfo-gen t₁ t₂ (Guide posinfo-gen x' T₂) posinfo-gen ,
Iota posinfo-gen posinfo-gen x' T₁ T₂)
elab-synth-term Γ (IotaProj t n pi) =
elab-synth-term Γ t ≫=maybe uncurry λ where
t (Iota _ pi' x T₁ T₂) →
case n of λ where
"1" → elab-hnf-type Γ T₁ tt ≫=maybe λ T₁ →
just (IotaProj t n posinfo-gen , T₁)
"2" → elab-hnf-type Γ (subst Γ (IotaProj t "1" posinfo-gen) x T₂) tt ≫=maybe λ T₂ →
just (IotaProj t n posinfo-gen , subst Γ (IotaProj t "1" posinfo-gen) x T₂) -- , T₂)
_ → nothing
_ _ → nothing
elab-synth-term Γ (Lam pi l pi' x oc t) = (case (l , oc) of λ where
(Erased , SomeClass atk) → elab-tk Γ atk
(NotErased , SomeClass (Tkt T)) → elab-tk Γ (Tkt T)
_ → nothing) ≫=maybe λ atk →
rename x from Γ for λ x' →
elab-synth-term (ctxt-tk-decl' pi' x' atk Γ) (rename-var Γ x x' t) ≫=maybe uncurry λ t T →
just (Lam posinfo-gen l posinfo-gen x' (SomeClass atk) t , Abs posinfo-gen l posinfo-gen x' atk T)
elab-synth-term Γ (Let pi d t) = case d of λ where
(DefTerm pi' x NoType t') →
rename x from Γ for λ x' →
elab-synth-term Γ t' ≫=maybe uncurry λ t' T' →
elab-synth-term (ctxt-let-term-def pi' x' t' T' Γ) (rename-var Γ x x' t) ≫=maybe uncurry λ t T →
just (Let posinfo-gen (DefTerm posinfo-gen x' NoType t') t , subst Γ t' x' T)
(DefTerm pi' x (SomeType T') t') →
rename x from Γ for λ x' →
elab-type Γ T' ≫=maybe uncurry λ T' k →
elab-check-term Γ t' T' ≫=maybe λ t' →
elab-synth-term (ctxt-let-term-def pi' x' t' T' Γ) (rename-var Γ x x' t) ≫=maybe uncurry λ t T →
just (Let posinfo-gen (DefTerm posinfo-gen x' NoType t') t , subst Γ t' x' T)
(DefType pi' x k T') →
rename x from Γ for λ x' →
elab-type Γ T' ≫=maybe uncurry λ T' k' →
elab-synth-term (ctxt-let-type-def pi' x' T' k' Γ) (rename-var Γ x x' t) ≫=maybe uncurry λ t T →
just (Let posinfo-gen (DefType pi' x' k' T') t , subst Γ T' x' T)
elab-synth-term Γ (Open pi x t) =
ctxt-clarify-def Γ x ≫=maybe uncurry λ _ Γ →
elab-synth-term Γ t
elab-synth-term Γ (Parens pi t pi') = elab-synth-term Γ t
elab-synth-term Γ (Phi pi t t₁ t₂ pi') =
elab-pure-term Γ (erase-term t₁) ≫=maybe λ t₁' →
elab-pure-term Γ (erase-term t₂) ≫=maybe λ t₂ →
elab-synth-term Γ t₁ ≫=maybe uncurry λ t₁ T →
elab-check-term Γ t (mtpeq t₁' t₂) ≫=maybe λ t →
just (Phi posinfo-gen t t₁ t₂ posinfo-gen , T)
elab-synth-term Γ (Rho pi op on t og t') =
elab-synth-term Γ t ≫=maybe uncurry λ t T →
elab-synth-term Γ t' ≫=maybe uncurry λ t' T' →
elab-hnf-type Γ (erase-type T) ff ≫=maybe λ where
(TpEq _ t₁ t₂ _) → case og of λ where
NoGuide →
rename "x" from Γ for λ x →
let ns = fst (optNums-to-stringset on)
Γ' = ctxt-var-decl x Γ
rT = fst (rewrite-type T' Γ' (is-rho-plus op) ns t t₁ x 0)
rT' = post-rewrite Γ' x t t₂ rT in
-- elab-hnf-type Γ rT' tt ≫=maybe λ rT' →
just (mrho t x (erase-type rT) t' , rT')
(Guide pi' x T'') →
let Γ' = ctxt-var-decl x Γ in
elab-pure-type Γ' (erase-type T'') ≫=maybe λ T'' →
just (mrho t x T'' t' , post-rewrite Γ' x t t₂ (rewrite-at Γ' x t tt T' T''))
_ → nothing
elab-synth-term Γ (Sigma pi t) =
elab-synth-term Γ t ≫=maybe uncurry λ where
t (TpEq _ t₁ t₂ _) → just (Sigma posinfo-gen t , mtpeq t₂ t₁)
_ _ → nothing
elab-synth-term Γ (Theta pi θ t ts) = nothing
elab-synth-term Γ (Var pi x) =
ctxt-lookup-term-var' Γ x ≫=maybe λ T →
elab-hnf-type Γ T tt ≫=maybe λ T →
just (mvar x , T)
elab-synth-term Γ (Mu pi x t ot pi' cs pi'') = nothing
elab-synth-term Γ (Mu' pi t ot pi' cs pi'') = nothing
elab-typeh Γ (Abs pi b pi' x atk T) b' =
elab-tkh Γ atk b' ≫=maybe λ atk →
rename x from Γ for λ x' →
elab-typeh (ctxt-tk-decl' pi' x' atk Γ) (rename-var Γ x x' T) b' ≫=maybe uncurry λ T k →
just (Abs posinfo-gen b posinfo-gen x' atk T , star)
elab-typeh Γ (Iota pi pi' x T T') b =
elab-typeh Γ T b ≫=maybe uncurry λ T k →
rename x from Γ for λ x' →
elab-typeh (ctxt-term-decl' pi' x' T Γ) (rename-var Γ x x' T') b ≫=maybe uncurry λ T' k' →
just (Iota posinfo-gen posinfo-gen x' T T' , star)
elab-typeh Γ (Lft pi pi' x t lT) b = nothing
elab-typeh Γ (NoSpans T pi) b = nothing
elab-typeh Γ (TpApp T T') b =
elab-typeh Γ T b ≫=maybe uncurry λ T k →
elab-typeh Γ T' b ≫=maybe uncurry λ T' k' →
case k of λ where
(KndPi _ pi x (Tkk _) k'') → just (TpApp T T' , subst Γ T' x k'')
_ → nothing
elab-typeh Γ (TpAppt T t) b =
elab-typeh Γ T b ≫=maybe uncurry λ where
T (KndPi _ pi x (Tkt T') k) →
(if b then elab-check-term Γ t T' else elab-pure-term Γ (erase-term t)) ≫=maybe λ t →
just (TpAppt T t , subst Γ t x k)
_ _ → nothing
elab-typeh Γ (TpArrow T a T') b =
elab-typeh Γ T b ≫=maybe uncurry λ T k →
elab-typeh Γ T' b ≫=maybe uncurry λ T' k' →
just (Abs posinfo-gen a posinfo-gen "_" (Tkt T) T' , star)
elab-typeh Γ (TpEq pi t t' pi') b =
elab-pure-term Γ (erase-term t) ≫=maybe λ t →
elab-pure-term Γ (erase-term t') ≫=maybe λ t' →
just (mtpeq t t' , star)
elab-typeh Γ (TpHole pi) b = nothing
elab-typeh Γ (TpLambda pi pi' x atk T) b =
elab-tkh Γ atk b ≫=maybe λ atk →
rename x from Γ for λ x' →
elab-typeh (ctxt-tk-decl' pi' x' atk Γ) (rename-var Γ x x' T) b ≫=maybe uncurry λ T k →
just (mtplam x' atk T , KndPi posinfo-gen posinfo-gen x' atk k)
elab-typeh Γ (TpParens pi T pi') b = elab-typeh Γ T b
elab-typeh Γ (TpVar pi x) b =
ctxt-lookup-type-var' Γ x ≫=maybe λ k →
elab-kindh Γ k b ≫=maybe λ k →
just (mtpvar x , k)
elab-typeh Γ (TpLet pi (DefTerm pi' x ot t) T) = elab-typeh Γ (subst Γ (Chi posinfo-gen ot t) x T)
elab-typeh Γ (TpLet pi (DefType pi' x k T') T) = elab-typeh Γ (subst Γ T' x T)
elab-kindh Γ (KndArrow k k') b =
elab-kindh Γ k b ≫=maybe λ k →
elab-kindh Γ k' b ≫=maybe λ k' →
just (KndPi posinfo-gen posinfo-gen "_" (Tkk k) k')
elab-kindh Γ (KndParens pi k pi') b = elab-kindh Γ k b
elab-kindh Γ (KndPi pi pi' x atk k) b =
elab-tkh Γ atk b ≫=maybe λ atk →
rename x from Γ for λ x' →
elab-kindh (ctxt-tk-decl' pi' x' atk Γ) (rename-var Γ x x' k) b ≫=maybe λ k →
just (KndPi posinfo-gen posinfo-gen x' atk k)
elab-kindh Γ (KndTpArrow T k) b =
elab-typeh Γ T b ≫=maybe uncurry λ T _ →
elab-kindh Γ k b ≫=maybe λ k →
just (KndPi posinfo-gen posinfo-gen "_" (Tkt T) k)
elab-kindh Γ (KndVar pi x as) b =
ctxt-lookup-kind-var-def Γ x ≫=maybe uncurry (do-subst as)
where
do-subst : args → params → kind → maybe kind
do-subst (ArgsCons (TermArg _ t) ys) (ParamsCons (Decl _ _ _ x _ _) ps) k = do-subst ys ps (subst Γ t x k)
do-subst (ArgsCons (TypeArg t) ys) (ParamsCons (Decl _ _ _ x _ _) ps) k = do-subst ys ps (subst Γ t x k)
do-subst ArgsNil ParamsNil k = elab-kindh Γ k b
do-subst _ _ _ = nothing
elab-kindh Γ (Star pi) b = just star
elab-tkh Γ (Tkt T) b = elab-typeh Γ T b ≫=maybe uncurry λ T _ → just (Tkt T)
elab-tkh Γ (Tkk k) b = elab-kindh Γ k b ≫=maybe λ k → just (Tkk k)
elab-pure-term Γ (Var pi x) = just (mvar x)
elab-pure-term Γ (App t NotErased t') =
elab-pure-term Γ t ≫=maybe λ t →
elab-pure-term Γ t' ≫=maybe λ t' →
just (App t NotErased t')
elab-pure-term Γ (Lam pi NotErased pi' x NoClass t) =
rename x from Γ for λ x' →
elab-pure-term (ctxt-var-decl x' Γ) (rename-var Γ x x' t) ≫=maybe λ t →
just (mlam x' t)
elab-pure-term Γ (Let pi (DefTerm pi' x NoType t) t') =
elab-pure-term Γ t ≫=maybe λ t →
elab-pure-term Γ (subst Γ t x t')
elab-pure-term _ _ = nothing -- should be erased
elab-app-term Γ (App t me t') pt max =
elab-app-term Γ t (proto-arrow me pt) ff ≫=maybe uncurry λ where
tf (mk-spine-data Xs dt locl) →
case fst (meta-vars-unfold-tmapp' Γ ("" , "" , "") Xs dt Γ id-spans.empty-spans) of uncurry λ where
Ys (not-tpabsd _) → nothing
Ys (inj₂ arr) →
elab-app-term' Xs Ys t t' arr (islocl locl) ≫=maybe uncurry λ where
t' (check-term-app-return Xs' Tᵣ arg-mode _) →
fst (check-spine-locality Γ Xs' (decortype-to-type Tᵣ) max (pred locl) Γ id-spans.empty-spans) ≫=maybe uncurry' λ Xs'' locl' is-loc →
just ((λ Xs → tf (if is-loc then Xs' else Xs) ≫=maybe λ t → fill-meta-vars t (if is-loc then Xs' else Xs) Ys ≫=maybe λ t → just (App t me t')) ,
mk-spine-data Xs'' Tᵣ locl')
where
islocl = (max ||_) ∘ (iszero ∘ pred)
fill-meta-vars : term → meta-vars → 𝕃 meta-var → maybe term
fill-meta-vars t Xs = flip foldl (just t) λ where
(meta-var-mk x _ _) tₘ → tₘ ≫=maybe λ t → meta-vars-lookup Xs x ≫=maybe λ where
(meta-var-mk _ (meta-var-tp k Tₘ) _) → Tₘ ≫=maybe λ T → just (AppTp t (meta-var-sol.sol T))
(meta-var-mk _ (meta-var-tm T tₘ) _) → nothing
elab-app-term' : (Xs : meta-vars) → (Ys : 𝕃 meta-var) → (t₁ t₂ : term) → is-tmabsd → 𝔹 → maybe (term × check-term-app-ret)
elab-app-term' Xs Zs t₁ t₂ (mk-tmabsd dt me x dom occurs cod) is-locl =
let Xs' = meta-vars-add* Xs Zs
T = decortype-to-type dt in
if ~ meta-vars-are-free-in-type Xs' dom
then (elab-check-term Γ t₂ dom ≫=maybe λ t₂ →
let rdt = fst $ subst-decortype Γ t₂ x cod Γ id-spans.empty-spans in
just (t₂ , check-term-app-return Xs' (if occurs then rdt else cod) checking []))
else (elab-synth-term Γ t₂ ≫=maybe uncurry λ t₂ T₂ →
case fst (match-types Xs' empty-trie match-unfolding-both dom T₂ Γ id-spans.empty-spans) of λ where
(match-error _) → nothing
(match-ok Xs) →
let rdt = fst $ subst-decortype Γ t₂ x cod Γ id-spans.empty-spans
rdt' = fst $ meta-vars-subst-decortype Γ Xs (if occurs then rdt else cod) Γ id-spans.empty-spans in
just (t₂ , check-term-app-return Xs rdt' synthesizing []))
elab-app-term Γ (AppTp t T) pt max =
elab-app-term Γ t pt max ≫=maybe uncurry λ where
tf (mk-spine-data Xs dt locl) →
let Tₕ = decortype-to-type dt in
case fst (meta-vars-unfold-tpapp' Γ Xs dt Γ id-spans.empty-spans) of λ where
(not-tpabsd _) → nothing
(yes-tpabsd dt me x k sol rdt) →
elab-type Γ T ≫=maybe uncurry λ T k' →
just ((λ Xs → tf Xs ≫=maybe λ t → just (AppTp t T)) ,
mk-spine-data Xs (fst $ subst-decortype Γ T x rdt Γ id-spans.empty-spans) locl)
elab-app-term Γ (Parens _ t _) pt max =
elab-app-term Γ t pt max
elab-app-term Γ t pt max =
elab-synth-term Γ t ≫=maybe uncurry λ t T →
let locl = num-arrows-in-type Γ T
ret = fst $ match-prototype meta-vars-empty ff T pt Γ id-spans.empty-spans
dt = match-prototype-data.match-proto-dectp ret in
just ((λ Xs → just t) , mk-spine-data meta-vars-empty dt locl)
{- ################################ IO ###################################### -}
private
ie-set-span-ast : include-elt → ctxt → start → include-elt
ie-set-span-ast ie Γ ast = record ie
{ss = inj₁ (regular-spans nothing
[ mk-span "" "" "" [ "" , strRun Γ (file-to-string ast) , [] ] nothing ])}
ie-get-span-ast : include-elt → maybe rope
ie-get-span-ast ie with include-elt.ss ie
...| inj₁ (regular-spans nothing (mk-span "" "" ""
(("" , r , []) :: []) nothing :: [])) = just r
...| _ = nothing
elab-t : Set → Set
elab-t X = toplevel-state → (var-mapping file-mapping : renamectxt) → trie encoded-datatype →
X → maybe (X × toplevel-state × renamectxt × renamectxt × trie encoded-datatype)
{-# TERMINATING #-}
elab-file' : elab-t string
elab-cmds : elab-t cmds
elab-params : elab-t params
elab-args : elab-t (args × params)
elab-imports : elab-t imports
elab-params ts ρ φ μ ParamsNil = just (ParamsNil , ts , ρ , φ , μ)
elab-params ts ρ φ μ (ParamsCons (Decl _ pi me x atk _) ps) =
let Γ = toplevel-state.Γ ts in
elab-tk Γ (subst-qualif Γ ρ atk) ≫=maybe λ atk →
rename x - x from ρ for λ x' ρ →
elab-params (record ts {Γ = ctxt-param-decl x x' atk Γ}) ρ φ μ ps ≫=maybe uncurry λ ps ω →
just (ParamsCons (Decl posinfo-gen posinfo-gen me x' atk posinfo-gen) ps , ω)
elab-args ts ρ φ μ (ArgsNil , ParamsNil) = just ((ArgsNil , ParamsNil) , ts , ρ , φ , μ)
elab-args ts ρ φ μ (_ , ParamsNil) = nothing -- Too many arguments
elab-args ts ρ φ μ (ArgsNil , ParamsCons p ps) = just ((ArgsNil , ParamsCons p ps) , ts , ρ , φ , μ)
elab-args ts ρ φ μ (ArgsCons a as , ParamsCons (Decl _ _ me x atk _) ps) =
let Γ = toplevel-state.Γ ts in
case (a , atk) of λ where
(TermArg me' t , Tkt T) →
elab-type Γ (subst-qualif Γ ρ T) ≫=maybe uncurry λ T k →
elab-check-term Γ (subst-qualif Γ ρ t) T ≫=maybe λ t →
rename qualif-new-var Γ x - x lookup ρ for λ x' ρ →
let ts = record ts {Γ = ctxt-term-def' x x' t T OpacTrans Γ} in
elab-args ts ρ φ μ (as , ps) ≫=maybe (uncurry ∘ uncurry) λ as ps ω →
just ((ArgsCons (TermArg me' t) as , ParamsCons (Decl posinfo-gen posinfo-gen me x' (Tkt T) posinfo-gen) ps) , ω)
(TypeArg T , Tkk _) →
elab-type Γ (subst-qualif Γ ρ T) ≫=maybe uncurry λ T k →
rename qualif-new-var Γ x - x lookup ρ for λ x' ρ →
let ts = record ts {Γ = ctxt-type-def' x x' T k OpacTrans Γ} in
elab-args ts ρ φ μ (as , ps) ≫=maybe (uncurry ∘ uncurry) λ as ps ω →
just ((ArgsCons (TypeArg T) as , ParamsCons (Decl posinfo-gen posinfo-gen me x' (Tkk k) posinfo-gen) ps) , ω)
_ → nothing
elab-imports ts ρ φ μ ImportsStart = just (ImportsStart , ts , ρ , φ , μ)
elab-imports ts ρ φ μ (ImportsNext (Import _ op _ ifn oa as _) is) =
let Γ = toplevel-state.Γ ts
fn = ctxt-get-current-filename Γ
mod = ctxt-get-current-mod Γ in
get-include-elt-if ts fn ≫=maybe λ ie →
trie-lookup (include-elt.import-to-dep ie) ifn ≫=maybe λ ifn' →
elab-file' ts ρ φ μ ifn' ≫=maybe uncurry''' λ fn ts ρ φ μ →
lookup-mod-params (toplevel-state.Γ ts) ifn' ≫=maybe λ ps →
elab-args ts ρ φ μ (as , ps) ≫=maybe (uncurry''' ∘ uncurry) λ as ps ts ρ φ μ →
elim-pair (scope-file (record ts {Γ = ctxt-set-current-mod (toplevel-state.Γ ts) mod}) fn ifn' oa as) λ ts _ →
elab-imports ts ρ φ μ is ≫=maybe uncurry''' λ is ts ρ φ μ →
add-imports ts φ (stringset-strings $ get-all-deps ifn' empty-stringset) (just is) ≫=maybe λ is →
let i = Import posinfo-gen NotPublic posinfo-gen fn NoOptAs ArgsNil posinfo-gen in
just (ImportsNext i is , ts , ρ , φ , μ)
where
get-all-deps : filepath → stringset → stringset
get-all-deps fp fs = maybe-else fs (foldr get-all-deps $ stringset-insert fs fp)
((maybe-not $ trie-lookup fs fp) ≫=maybe λ _ →
get-include-elt-if ts fp ≫=maybe
(just ∘ include-elt.deps))
add-imports : toplevel-state → renamectxt → 𝕃 string → maybe imports → maybe imports
add-imports ts φ = flip $ foldl λ fn isₘ → renamectxt-lookup φ fn ≫=maybe λ ifn → isₘ ≫=maybe
(just ∘ ImportsNext (Import posinfo-gen NotPublic posinfo-gen ifn NoOptAs ArgsNil posinfo-gen))
elab-cmds ts ρ φ μ CmdsStart = just (CmdsStart , ts , ρ , φ , μ)
elab-cmds ts ρ φ μ (CmdsNext (DefTermOrType op (DefTerm _ x NoType t) _) cs) =
let Γ = toplevel-state.Γ ts in
elab-synth-term Γ (subst-qualif Γ ρ t) ≫=maybe uncurry λ t T →
rename qualif-new-var Γ x - x from ρ for λ x' ρ →
let ts = record ts {Γ = ctxt-term-def' x x' t T op Γ} in
elab-cmds ts ρ φ μ cs ≫=maybe uncurry λ cs ω →
just (CmdsNext (DefTermOrType OpacTrans (DefTerm posinfo-gen x' NoType t) posinfo-gen) cs , ω)
elab-cmds ts ρ φ μ (CmdsNext (DefTermOrType op (DefTerm _ x (SomeType T) t) _) cs) =
let Γ = toplevel-state.Γ ts in
elab-type Γ (subst-qualif Γ ρ T) ≫=maybe uncurry λ T k →
elab-check-term Γ (subst-qualif Γ ρ t) T ≫=maybe λ t →
rename qualif-new-var Γ x - x from ρ for λ x' ρ →
let ts = record ts {Γ = ctxt-term-def' x x' t T op Γ} in
elab-cmds ts ρ φ μ cs ≫=maybe uncurry λ cs ω →
just (CmdsNext (DefTermOrType OpacTrans (DefTerm posinfo-gen x' NoType t) posinfo-gen) cs , ω)
elab-cmds ts ρ φ μ (CmdsNext (DefTermOrType op (DefType _ x _ T) _) cs) =
let Γ = toplevel-state.Γ ts in
elab-type Γ (subst-qualif Γ ρ T) ≫=maybe uncurry λ T k →
rename qualif-new-var Γ x - x from ρ for λ x' ρ →
let ts = record ts {Γ = ctxt-type-def' x x' T k op Γ} in
elab-cmds ts ρ φ μ cs ≫=maybe uncurry λ cs ω →
just (CmdsNext (DefTermOrType OpacTrans (DefType posinfo-gen x' k T) posinfo-gen) cs , ω)
elab-cmds ts ρ φ μ (CmdsNext (DefKind _ x ps k _) cs) =
let Γ = toplevel-state.Γ ts
x' = fresh-var (qualif-new-var Γ x) (λ _ → ff) ρ
ρ = renamectxt-insert ρ x x'
ts = record ts {Γ = ctxt-kind-def' x x' ps k Γ} in
elab-cmds ts ρ φ μ cs
elab-cmds ts ρ φ μ (CmdsNext (ImportCmd i) cs) =
elab-imports ts ρ φ μ (ImportsNext i ImportsStart) ≫=maybe uncurry''' λ is ts ρ φ μ →
elab-cmds ts ρ φ μ cs ≫=maybe uncurry λ cs ω →
just (append-cmds (imps-to-cmds is) cs , ω)
elab-cmds ts ρ φ μ (CmdsNext (DefDatatype (Datatype pi pi' x ps k dcs pi'') _) cs) =
let Γ = toplevel-state.Γ ts
x' = rename qualif-new-var Γ x - x from ρ for λ x' ρ' → x'
-- Still need to use x (not x') so constructors work,
-- but we need to know what it will be renamed to later for μ
d = defDatatype-to-datatype Γ (Datatype pi pi' x ps k dcs pi'') in
elim-pair (datatype-encoding.mk-defs selected-encoding Γ d) λ cs' d →
elab-cmds ts ρ φ (trie-insert μ x' d) (append-cmds cs' cs)
elab-file' ts ρ φ μ fn =
get-include-elt-if ts fn ≫=maybe λ ie →
case include-elt.need-to-add-symbols-to-context ie of λ where
ff → rename fn - base-filename (takeFileName fn) lookup φ for λ fn' φ → just (fn' , ts , ρ , φ , μ)
tt → include-elt.ast ie ≫=maybe λ where
(File _ is _ _ mn ps cs _) →
rename fn - base-filename (takeFileName fn) from φ for λ fn' φ →
let ie = record ie {need-to-add-symbols-to-context = ff; do-type-check = ff; inv = refl} in
elab-imports (record (set-include-elt ts fn ie)
{Γ = ctxt-set-current-file (toplevel-state.Γ ts) fn mn}) ρ φ μ is ≫=maybe uncurry''' λ is ts ρ φ μ →
elab-params ts ρ φ μ ps ≫=maybe uncurry''' λ ps' ts ρ φ μ →
let Γ = toplevel-state.Γ ts
Γ = ctxt-add-current-params (ctxt-set-current-mod Γ (fn , mn , ps' , ctxt-get-qualif Γ)) in
elab-cmds (record ts {Γ = Γ}) ρ φ μ cs ≫=maybe uncurry' λ cs ts ω →
let ast = File posinfo-gen ImportsStart posinfo-gen posinfo-gen mn ParamsNil
(remove-dup-imports empty-stringset (append-cmds (imps-to-cmds is) cs)) posinfo-gen in
just (fn' , set-include-elt ts fn (ie-set-span-ast ie (toplevel-state.Γ ts) ast) , ω)
where
remove-dup-imports : stringset → cmds → cmds
remove-dup-imports is CmdsStart = CmdsStart
remove-dup-imports is (CmdsNext c @ (ImportCmd (Import _ _ _ fp _ _ _)) cs) =
if stringset-contains is fp
then remove-dup-imports is cs
else CmdsNext c (remove-dup-imports (stringset-insert is fp) cs)
remove-dup-imports is (CmdsNext c cs) = CmdsNext c $ remove-dup-imports is cs
{-# TERMINATING #-}
elab-all : toplevel-state → (from-fp to-fp : string) → IO ⊤
elab-all ts fm to =
elab-file' prep-ts empty-renamectxt empty-renamectxt empty-trie fm err-code 1 else h
where
_err-code_else_ : ∀ {X : Set} → maybe X → ℕ → (X → IO ⊤) → IO ⊤
nothing err-code n else f = putStrLn (ℕ-to-string n)
just x err-code n else f = f x
prep-ts : toplevel-state
prep-ts = record ts
{Γ = new-ctxt fm "[unknown]";
is = trie-map (λ ie → record ie
{need-to-add-symbols-to-context = tt;
do-type-check = ff;
inv = refl})
(toplevel-state.is ts)}
get-file-imports : toplevel-state → (filename : string) → stringset → maybe stringset
get-file-imports ts fn is =
get-include-elt-if ts fn ≫=maybe λ ie →
foldr
(λ fn' is → if fn =string fn' then is else
(is ≫=maybe λ is →
get-file-imports ts fn' is ≫=maybe λ is →
just (stringset-insert is fn')))
(just is)
(include-elt.deps ie)
h : (string × toplevel-state × renamectxt × renamectxt × trie encoded-datatype) → IO ⊤
h' : toplevel-state → renamectxt → stringset → IO ⊤
h (_ , ts , _ , φ , μ) =
get-file-imports ts fm (trie-single fm triv) err-code 3 else h' ts φ
h' ts φ is = foldr
(λ fn x → x >>= λ e →
maybe-else
(return ff)
(uncurry λ fn ie →
writeRopeToFile (combineFileNames to fn ^ ".ced")
(maybe-else [[ "Error lookup up elaborated data" ]] id (ie-get-span-ast ie)) >>
return e)
(renamectxt-lookup φ fn ≫=maybe λ fn' →
get-include-elt-if ts fn ≫=maybe λ ie →
include-elt.ast ie ≫=maybe λ ast → just (fn' , ie)))
(createDirectoryIfMissing tt to >> return tt)
(stringset-strings is) >>= λ e →
putStrLn (if e then "0" else "2")
elab-file : toplevel-state → (filename : string) → maybe rope
elab-file ts fn =
elab-file' ts empty-renamectxt empty-renamectxt empty-trie fn ≫=maybe uncurry'' λ fn' ts ρ φ →
get-include-elt-if ts fn ≫=maybe ie-get-span-ast
|
{
"alphanum_fraction": 0.6140322229,
"avg_line_length": 45.531598513,
"ext": "agda",
"hexsha": "0141fa4384318cf8482cdbaa9411608c3b45f3bc",
"lang": "Agda",
"max_forks_count": null,
"max_forks_repo_forks_event_max_datetime": null,
"max_forks_repo_forks_event_min_datetime": null,
"max_forks_repo_head_hexsha": "acf691e37210607d028f4b19f98ec26c4353bfb5",
"max_forks_repo_licenses": [
"MIT"
],
"max_forks_repo_name": "xoltar/cedille",
"max_forks_repo_path": "src/elaboration.agda",
"max_issues_count": null,
"max_issues_repo_head_hexsha": "acf691e37210607d028f4b19f98ec26c4353bfb5",
"max_issues_repo_issues_event_max_datetime": null,
"max_issues_repo_issues_event_min_datetime": null,
"max_issues_repo_licenses": [
"MIT"
],
"max_issues_repo_name": "xoltar/cedille",
"max_issues_repo_path": "src/elaboration.agda",
"max_line_length": 158,
"max_stars_count": null,
"max_stars_repo_head_hexsha": "acf691e37210607d028f4b19f98ec26c4353bfb5",
"max_stars_repo_licenses": [
"MIT"
],
"max_stars_repo_name": "xoltar/cedille",
"max_stars_repo_path": "src/elaboration.agda",
"max_stars_repo_stars_event_max_datetime": null,
"max_stars_repo_stars_event_min_datetime": null,
"num_tokens": 13635,
"size": 36744
}
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.