diff options
| -rw-r--r-- | FinMap.agda | 8 | ||||
| -rw-r--r-- | Precond.agda | 11 |
2 files changed, 5 insertions, 14 deletions
diff --git a/FinMap.agda b/FinMap.agda index fa13144..b2db8f4 100644 --- a/FinMap.agda +++ b/FinMap.agda @@ -38,7 +38,7 @@ fromAscList [] = empty fromAscList ((f , a) ∷ xs) = insert f a (fromAscList xs) fromFunc : {A : Set} {n : ℕ} → (Fin n → A) → FinMapMaybe n A -fromFunc = mapV just ∘ tabulate +fromFunc = tabulate ∘ _∘_ just reshape : {n : ℕ} {A : Set} → FinMapMaybe n A → (l : ℕ) → FinMapMaybe l A reshape m zero = [] @@ -103,10 +103,6 @@ lemma-lookupM-fromFunc : {n : ℕ} {A : Set} → (f : Fin n → A) → flip look lemma-lookupM-fromFunc f zero = refl lemma-lookupM-fromFunc f (suc i) = lemma-lookupM-fromFunc (f ∘ suc) i -lemma-fromFunc-tabulate : {n : ℕ} {A : Set} → (f : Fin n → A) → fromFunc f ≡ tabulate (Maybe.just ∘ f) -lemma-fromFunc-tabulate {zero} f = refl -lemma-fromFunc-tabulate {suc _} f = cong (_∷_ (just (f zero))) (lemma-fromFunc-tabulate (f ∘ suc)) - lemma-lookupM-delete : {n : ℕ} {A : Set} {i j : Fin n} → (f : FinMapMaybe n A) → i ≢ j → lookupM i (delete j f) ≡ lookupM i f lemma-lookupM-delete {i = zero} {j = zero} (_ ∷ _) p = contradiction refl p lemma-lookupM-delete {i = zero} {j = suc j} (_ ∷ _) p = refl @@ -118,7 +114,7 @@ lemma-reshape-id [] = refl lemma-reshape-id (x ∷ xs) = cong (_∷_ x) (lemma-reshape-id xs) lemma-disjoint-union : {n m : ℕ} {A : Set} → (f : Fin n → A) → (t : Vec (Fin n) m) → union (restrict f (toList t)) (delete-many t (fromFunc f)) ≡ fromFunc f -lemma-disjoint-union {n} {m} f t = trans (lemma-tabulate-∘ (lemma-inner t)) (sym (lemma-fromFunc-tabulate f)) +lemma-disjoint-union {n} {m} f t = lemma-tabulate-∘ (lemma-inner t) where lemma-inner : {m : ℕ} → (t : Vec (Fin n) m) → (x : Fin n) → maybe′ just (lookupM x (delete-many t (fromFunc f))) (lookupM x (restrict f (toList t))) ≡ just (f x) lemma-inner [] x = begin maybe′ just (lookupM x (fromFunc f)) (lookupM x empty) diff --git a/Precond.agda b/Precond.agda index 3e4c219..3a48757 100644 --- a/Precond.agda +++ b/Precond.agda @@ -41,23 +41,18 @@ lemma-maybe-just a (just x) = refl lemma-maybe-just a nothing = refl lemma-union-delete-fromFunc : {m n : ℕ} {A : Set} {is : Vec (Fin n) m} {h : FinMapMaybe n A} {g : Fin n → A} → (toList 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 = _ , (begin - union h (fromFunc g) - ≡⟨ lemma-tabulate-∘ (λ f → begin +lemma-union-delete-fromFunc {is = []} {h = h} {g = g} p = _ , (lemma-tabulate-∘ (λ f → begin maybe′ just (lookupM f (fromFunc g)) (lookupM f h) ≡⟨ cong (flip (maybe′ just) (lookupM f h)) (lemma-lookupM-fromFunc 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)) ∎) ⟩ - tabulate (λ f → just (maybe′ id (g f) (lookup f h))) - ≡⟨ tabulate-∘ just (λ f → maybe′ id (g f) (lookup f h)) ⟩ - map just (tabulate (λ f → maybe′ id (g f) (lookup f h))) ∎) + just (maybe′ id (g f) (lookupM f h)) ∎)) lemma-union-delete-fromFunc {n = n} {is = i ∷ is} {h = h} {g = g} (Data.List.All._∷_ (x , px) ps) = _ , (begin union h (delete i (delete-many is (fromFunc g))) ≡⟨ lemma-tabulate-∘ inner ⟩ union h (delete-many is (fromFunc g)) ≡⟨ proj₂ (lemma-union-delete-fromFunc ps) ⟩ - map just _ ∎) + _ ∎) where inner : (f : Fin n) → maybe′ just (lookupM f (delete i (delete-many is (fromFunc g)))) (lookup f h) ≡ maybe′ just (lookupM f (delete-many is (fromFunc g))) (lookup f h) inner f with f ≟ i inner .i | yes refl = begin |