diff options
Diffstat (limited to 'Precond.agda')
| -rw-r--r-- | Precond.agda | 42 |
1 files changed, 21 insertions, 21 deletions
diff --git a/Precond.agda b/Precond.agda index bc54cd5..85c955c 100644 --- a/Precond.agda +++ b/Precond.agda @@ -25,7 +25,7 @@ open import Relation.Binary.PropositionalEquality using (refl ; cong ; inspect ; open Relation.Binary.PropositionalEquality.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎) open import Relation.Nullary using (yes ; no) -open import Structures using (IsFunctor) +open import Structures using (IsFunctor ; Shaped) open import FinMap using (FinMapMaybe ; lookupM ; union ; fromFunc ; empty ; insert ; lemma-lookupM-empty ; delete-many ; lemma-tabulate-∘ ; delete ; lemma-lookupM-delete ; lemma-lookupM-fromFunc ; reshape ; lemma-reshape-id) import CheckInsert open CheckInsert (decSetoid deq) using (checkInsert ; lemma-checkInsert-new ; lemma-lookupM-checkInsert-other) @@ -33,7 +33,7 @@ import BFF import Bidir open Bidir (decSetoid deq) using (_in-domain-of_ ; lemma-assoc-domain) import GetTypes -open GetTypes.PartialShapeVec using (Get ; module Get) +open GetTypes.PartialShapeShape using (Get ; module Get) open BFF.PartialShapeBFF (decSetoid deq) using (assoc ; enumerate ; denumerate ; bff) lemma-maybe-just : {A : Set} → (a : A) → (ma : Maybe A) → maybe′ Maybe.just (just a) ma ≡ Maybe.just (maybe′ id a ma) @@ -63,32 +63,32 @@ lemma-union-delete-fromFunc {n = n} {is = i ∷ is} {h = h} {g = g} (Data.List.A maybe′ just (lookupM i (delete-many is (fromFunc g))) (lookup i h) ∎ inner f | no f≢i = cong (flip (maybe′ just) (lookup f h)) (lemma-lookupM-delete (delete-many is (fromFunc g)) f≢i) -assoc-enough : (G : Get) → {i : Get.|I| G} → (j : Get.|I| G) → (s : Get.Container G Carrier (Get.|gl₁| G i)) → (v : Vec Carrier (Get.|gl₂| G j)) → ∃ (λ h → assoc (Get.get G (enumerate (Get.ShapeT G) (Get.|gl₁| G j))) v ≡ just h) → ∃ λ u → bff G j s v ≡ just u -assoc-enough G {i} j s v (h , p) = _ , cong (_<$>_ ((λ f → fmap f t) ∘ flip lookupM) ∘ _<$>_ (flip union (reshape g′ (arity (|gl₁| j))))) p +assoc-enough : (G : Get) → {i : Get.|I| G} → (j : Get.|I| G) → (s : Get.SourceContainer G Carrier (Get.|gl₁| G i)) → (v : Get.ViewContainer G Carrier (Get.|gl₂| G j)) → ∃ (λ h → assoc (Shaped.content (Get.ViewShapeT G) (Get.get G (enumerate (Get.SourceShapeT G) (Get.|gl₁| G j)))) (Shaped.content (Get.ViewShapeT G) v) ≡ just h) → ∃ λ u → bff G j s v ≡ just u +assoc-enough G {i} j s v (h , p) = _ , cong (_<$>_ ((λ f → fmapS f t) ∘ flip lookupM) ∘ _<$>_ (flip union (reshape g′ (Shaped.arity SourceShapeT (|gl₁| j))))) p where open Get G - g′ = delete-many (get (enumerate ShapeT (|gl₁| i))) (fromFunc (denumerate ShapeT s)) - t = enumerate ShapeT (|gl₁| j) + g′ = delete-many (Shaped.content ViewShapeT (get (enumerate SourceShapeT (|gl₁| i)))) (fromFunc (denumerate SourceShapeT s)) + t = enumerate SourceShapeT (|gl₁| j) -assoc-enough′ : (G : Get) → {i : Get.|I| G} → (s : Get.Container G Carrier (Get.|gl₁| G i)) → (v : Vec Carrier (Get.|gl₂| G i)) → ∃ (λ h → assoc (Get.get G (enumerate (Get.ShapeT G) (Get.|gl₁| G i))) v ≡ just h) → ∃ λ u → bff G i s v ≡ just (Get.fmap G just u) +assoc-enough′ : (G : Get) → {i : Get.|I| G} → (s : Get.SourceContainer G Carrier (Get.|gl₁| G i)) → (v : Get.ViewContainer G Carrier (Get.|gl₂| G i)) → ∃ (λ h → assoc (Shaped.content (Get.ViewShapeT G) (Get.get G (enumerate (Get.SourceShapeT G) (Get.|gl₁| G i)))) (Shaped.content (Get.ViewShapeT G) v) ≡ just h) → ∃ λ u → bff G i s v ≡ just (Get.fmapS G just u) assoc-enough′ G {i} s v (h , p) = _ , (begin bff G i s v ≡⟨ proj₂ (assoc-enough G i s v (h , p)) ⟩ - just (fmap (flip lookupM (union h (reshape g′ (arity (|gl₁| i))))) t) + just (fmapS (flip lookupM (union h (reshape g′ (Shaped.arity SourceShapeT (|gl₁| i))))) t) ≡⟨ cong just (begin _ - ≡⟨ cong ((λ f → fmap f t) ∘ flip lookupM ∘ union h) (lemma-reshape-id g′) ⟩ - fmap (flip lookupM (union h g′)) t - ≡⟨ cong ((λ f → fmap f t) ∘ flip lookupM) (proj₂ wp) ⟩ - fmap (flip lookupM (fromFunc (proj₁ wp))) t - ≡⟨ IsFunctor.cong (isFunctor (|gl₁| i)) (lemma-lookupM-fromFunc (proj₁ wp)) t ⟩ - fmap (Maybe.just ∘ proj₁ wp) t - ≡⟨ IsFunctor.composition (isFunctor (|gl₁| i)) just (proj₁ wp) t ⟩ - fmap Maybe.just (fmap (proj₁ wp) t) ∎) ⟩ _ ∎) + ≡⟨ cong ((λ f → fmapS f t) ∘ flip lookupM ∘ union h) (lemma-reshape-id g′) ⟩ + fmapS (flip lookupM (union h g′)) t + ≡⟨ 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 ⟩ + fmapS (Maybe.just ∘ proj₁ wp) t + ≡⟨ IsFunctor.composition (Shaped.isFunctor SourceShapeT (|gl₁| i)) just (proj₁ wp) t ⟩ + fmapS Maybe.just (fmapS (proj₁ wp) t) ∎) ⟩ _ ∎) where open Get G - s′ = enumerate ShapeT (|gl₁| i) - g = fromFunc (denumerate ShapeT s) - g′ = delete-many (get s′) g - t = enumerate ShapeT (|gl₁| i) - wp = lemma-union-delete-fromFunc (lemma-assoc-domain (get t) v h p) + s′ = enumerate SourceShapeT (|gl₁| i) + g = fromFunc (denumerate SourceShapeT s) + g′ = delete-many (Shaped.content ViewShapeT (get s′)) g + t = enumerate SourceShapeT (|gl₁| i) + wp = lemma-union-delete-fromFunc (lemma-assoc-domain (Shaped.content ViewShapeT (get t)) (Shaped.content ViewShapeT v) h p) data All-different {A : Set} : List A → Set where different-[] : All-different [] |