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Clear up vector reindexing

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-04-08 00:12:50 -07:00
parent f7ac22257e
commit 520b2b514c
1 changed files with 11 additions and 2 deletions
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13
Language.agda
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@ -14,7 +14,7 @@ open import Data.List.Membership.Propositional as MemProp using () renaming (_
open import Data.List.Relation.Unary.All using (All; []; _∷_) open import Data.List.Relation.Unary.All using (All; []; _∷_)
open import Data.List.Relation.Unary.Any as RelAny using () open import Data.List.Relation.Unary.Any as RelAny using ()
open import Data.List.Relation.Unary.Any.Properties using (++⁺ʳ) open import Data.List.Relation.Unary.Any.Properties using (++⁺ʳ)
open import Data.Fin using (Fin; suc; zero; fromℕ; inject₁; inject≤; _↑ʳ_; _↑ˡ_) renaming (_≟_ to _≟ᶠ_) open import Data.Fin using (Fin; suc; zero; fromℕ; inject₁; inject≤; _↑ʳ_; _↑ˡ_) renaming (_≟_ to _≟ᶠ_; cast to castᶠ)
open import Data.Fin.Properties using (suc-injective) open import Data.Fin.Properties using (suc-injective)
open import Relation.Binary.PropositionalEquality as Eq using (subst; cong; _≡_; sym; trans; refl) open import Relation.Binary.PropositionalEquality as Eq using (subst; cong; _≡_; sym; trans; refl)
open import Relation.Nullary using (¬_) open import Relation.Nullary using (¬_)
@ -121,6 +121,13 @@ module Graphs where
e ∈ˡ (Graph.edges g₁) → e ∈ˡ (Graph.edges g₁) →
(↑ˡ-Edge e n) ∈ˡ (subst (λ m → List (Fin m × Fin m)) sg₂≡sg₁+n (Graph.edges g₂)) (↑ˡ-Edge e n) ∈ˡ (subst (λ m → List (Fin m × Fin m)) sg₂≡sg₁+n (Graph.edges g₂))
flatten-casts : ∀ {s₁ s₂ s₃ n₁ n₂ : ℕ}
(p : s₂ +ⁿ n₂ ≡ s₃) (q : s₁ +ⁿ n₁ ≡ s₂) (r : s₁ +ⁿ (n₁ +ⁿ n₂) ≡ s₃)
(idx : Fin s₁) →
castᶠ p ((castᶠ q (idx ↑ˡ n₁)) ↑ˡ n₂) ≡ castᶠ r (idx ↑ˡ (n₁ +ⁿ n₂))
flatten-casts refl refl r zero = refl
flatten-casts {(suc s₁)} {s₂} {s₃} {n₁} {n₂} refl refl r (suc idx')
rewrite flatten-casts refl refl (sym (+-assoc s₁ n₁ n₂)) idx' = refl
⊆-trans : ∀ {g₁ g₂ g₃ : Graph} → g₁ ⊆ g₂ → g₂ ⊆ g₃ → g₁ ⊆ g₃ ⊆-trans : ∀ {g₁ g₂ g₃ : Graph} → g₁ ⊆ g₂ → g₂ ⊆ g₃ → g₁ ⊆ g₃
⊆-trans {MkGraph s₁ ns₁ es₁} {MkGraph s₂ ns₂ es₂} {MkGraph s₃ ns₃ es₃} ⊆-trans {MkGraph s₁ ns₁ es₁} {MkGraph s₂ ns₂ es₂} {MkGraph s₃ ns₃ es₃}
@ -139,7 +146,9 @@ module Graphs where
-- lookup (cast p₂ ns₃) ((Fin.cast (sym p₁) (idx ↑ˡ n₁) ↑ˡ n₂)) ≡ lookup ns₃ (Fin.cast (sym p₂) ((Fin.cast (sym p₁) (idx ↑ˡ n₁) ↑ˡ n₂))) -- by lookup-cast₂ -- lookup (cast p₂ ns₃) ((Fin.cast (sym p₁) (idx ↑ˡ n₁) ↑ˡ n₂)) ≡ lookup ns₃ (Fin.cast (sym p₂) ((Fin.cast (sym p₁) (idx ↑ˡ n₁) ↑ˡ n₂))) -- by lookup-cast₂
-- -- ?? -- lookup ns₃ (Fin.cast (sym p₂) ((Fin.cast (sym p₁) (idx ↑ˡ n₁) ↑ˡ n₂))) ≡ lookup ns₃ (Fin.cast (sym (+-assoc s₁ n₁ n₂)) (idx ↑ˡ (n₁ + n₂))) -- by flatten-casts
--
-- lookup ns₃ (Fin.cast (sym (+-assoc s₁ n₁ n₂)) (idx ↑ˡ (n₁ + n₂))) ≡ lookup (cast (+-assoc s₁ n₁ n₂) ns₃) (idx ↑ˡ (n₁ + n₂)) ∎
} }
record Relaxable (T : Graph → Set) : Set where record Relaxable (T : Graph → Set) : Set where