diff options
Diffstat (limited to 'Precond.agda')
| -rw-r--r-- | Precond.agda | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/Precond.agda b/Precond.agda index 293f44d..3fccfe8 100644 --- a/Precond.agda +++ b/Precond.agda @@ -15,7 +15,7 @@ import Data.Maybe.Categorical open Category.Monad.RawMonad {Level.zero} Data.Maybe.Categorical.monad using (_>>=_) open Category.Functor.RawFunctor {Level.zero} Data.Maybe.Categorical.functor using (_<$>_) open import Data.Vec using (Vec ; [] ; _∷_ ; map ; lookup ; toList) -open import Data.Vec.Properties using (map-cong ; map-∘ ; tabulate-∘ ; lookup-replicate ; tabulate-cong) +open import Data.Vec.Properties using (map-cong ; map-∘ ; tabulate-∘ ; lookup-replicate ; tabulate-cong ; lookup∘tabulate) import Data.List.All open import Data.List.Any using (here ; there) open import Data.List.Membership.Setoid using (_∉_) @@ -28,7 +28,7 @@ open P.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎) open import Relation.Nullary using (yes ; no) open import Structures using (IsFunctor ; module Shaped ; Shaped) -open import FinMap using (FinMapMaybe ; lookupM ; union ; fromFunc ; empty ; insert ; delete-many ; delete ; lemma-lookupM-delete ; lemma-lookupM-fromFunc ; reshape ; lemma-reshape-id) +open import FinMap using (FinMapMaybe ; lookupM ; union ; fromFunc ; empty ; insert ; delete-many ; delete ; lemma-lookupM-delete ; reshape ; lemma-reshape-id) import CheckInsert open CheckInsert (P.decSetoid deq) using (checkInsert ; lemma-checkInsert-new ; lemma-lookupM-checkInsert-other) import BFF @@ -45,7 +45,7 @@ lemma-maybe-just a nothing = P.refl lemma-union-delete-fromFunc : {m n : ℕ} {A : Set} {is : Vec (Fin n) m} {h : FinMapMaybe n A} {g : Fin n → A} → is in-domain-of h → ∃ λ v → union h (delete-many is (fromFunc g)) ≡ fromFunc v lemma-union-delete-fromFunc {is = []} {h = h} {g = g} p = _ , (tabulate-cong (λ f → begin maybe′ just (lookupM f (fromFunc g)) (lookupM f h) - ≡⟨ P.cong (flip (maybe′ just) (lookupM f h)) (lemma-lookupM-fromFunc g f) ⟩ + ≡⟨ P.cong (flip (maybe′ just) (lookupM f h)) (lookup∘tabulate (just ∘ g) f) ⟩ maybe′ just (just (g f)) (lookupM f h) ≡⟨ lemma-maybe-just (g f) (lookupM f h) ⟩ just (maybe′ id (g f) (lookupM f h)) ∎)) @@ -88,7 +88,7 @@ module _ (G : Get) where fmapS (flip lookupM (union h g′)) t ≡⟨ P.cong ((λ f → fmapS f t) ∘ flip lookupM) (proj₂ wp) ⟩ fmapS (flip lookupM (fromFunc (proj₁ wp))) t - ≡⟨ IsFunctor.cong (Shaped.isFunctor SourceShapeT (gl₁ i)) (lemma-lookupM-fromFunc (proj₁ wp)) t ⟩ + ≡⟨ IsFunctor.cong (Shaped.isFunctor SourceShapeT (gl₁ i)) (lookup∘tabulate (just ∘ proj₁ wp)) t ⟩ fmapS (Maybe.just ∘ proj₁ wp) t ≡⟨ IsFunctor.composition (Shaped.isFunctor SourceShapeT (gl₁ i)) just (proj₁ wp) t ⟩ fmapS Maybe.just (fmapS (proj₁ wp) t) ∎) ⟩ _ ∎) |