diff options
Diffstat (limited to 'Bidir.agda')
| -rw-r--r-- | Bidir.agda | 14 |
1 files changed, 1 insertions, 13 deletions
@@ -31,25 +31,13 @@ open CheckInsert (decSetoid deq) import BFF open BFF.VecBFF Carrier deq using (assoc ; enumerate ; denumerate ; bff) -maybeSetoid-to-≡ : {A : Set} {x y : Setoid.Carrier (MaybeSetoid (≡-setoid A))} → Setoid._≈_ (MaybeSetoid (≡-setoid A)) x y → x ≡ y -maybeSetoid-to-≡ (just refl) = refl -maybeSetoid-to-≡ nothing = refl - -vecMaybeSetoid-to-≡ : {A : Set} {n : ℕ} {x y : Setoid.Carrier (vecIsSetoid (MaybeSetoid (≡-setoid A)) n)} → Setoid._≈_ (vecIsSetoid (MaybeSetoid (≡-setoid A)) n) x y → x ≡ y -vecMaybeSetoid-to-≡ VecEq.[]-cong = refl -vecMaybeSetoid-to-≡ (p₁ VecEq.∷-cong p₂) = cong₂ _∷_ (maybeSetoid-to-≡ p₁) (vecMaybeSetoid-to-≡ p₂) - -maybeVecMaybeSetoid-to-≡ : {A : Set} {n : ℕ} {x y : Setoid.Carrier (MaybeSetoid (vecIsSetoid (MaybeSetoid (≡-setoid A)) n))} → Setoid._≈_ (MaybeSetoid (vecIsSetoid (MaybeSetoid (≡-setoid A)) n)) x y → x ≡ y -maybeVecMaybeSetoid-to-≡ (just p) rewrite vecMaybeSetoid-to-≡ p = refl -maybeVecMaybeSetoid-to-≡ nothing = refl - lemma-1 : {m n : ℕ} → (f : Fin n → Carrier) → (is : Vec (Fin n) m) → assoc is (map f is) ≡ just (restrict f (toList is)) lemma-1 f [] = refl lemma-1 f (i ∷ is′) = begin (assoc is′ (map f is′) >>= checkInsert i (f i)) ≡⟨ cong (λ m → m >>= checkInsert i (f i)) (lemma-1 f is′) ⟩ checkInsert i (f i) (restrict f (toList is′)) - ≡⟨ maybeVecMaybeSetoid-to-≡ (lemma-checkInsert-restrict f i (toList is′)) ⟩ + ≡⟨ lemma-checkInsert-restrict f i (toList is′) ⟩ just (restrict f (toList (i ∷ is′))) ∎ lemma-lookupM-assoc : {m n : ℕ} → (i : Fin n) → (is : Vec (Fin n) m) → (x : Carrier) → (xs : Vec Carrier m) → (h : FinMapMaybe n Carrier) → assoc (i ∷ is) (x ∷ xs) ≡ just h → lookupM i h ≡ just x |