diff options
Diffstat (limited to 'Generic.agda')
| -rw-r--r-- | Generic.agda | 18 |
1 files changed, 8 insertions, 10 deletions
diff --git a/Generic.agda b/Generic.agda index a734ec2..c458483 100644 --- a/Generic.agda +++ b/Generic.agda @@ -8,13 +8,13 @@ open import Data.Nat using (ℕ ; zero ; suc) open import Data.Product using (_×_ ; _,_) open import Data.Vec using (Vec ; toList ; fromList ; map) renaming ([] to []V ; _∷_ to _∷V_) open import Data.Vec.Equality using () renaming (module Equality to VecEq) -open import Function using (_∘_ ; id) +open import Function using (_∘_ ; id ; flip) open import Function.Equality using (_⟶_) open import Level using () renaming (zero to ℓ₀) open import Relation.Binary using (Setoid ; module Setoid) open import Relation.Binary.Core using (_≡_ ; refl) open import Relation.Binary.Indexed using (_at_) renaming (Setoid to ISetoid) -open import Relation.Binary.PropositionalEquality using (_≗_ ; cong ; subst ; trans) renaming (setoid to EqSetoid) +open import Relation.Binary.PropositionalEquality using (_≗_ ; cong ; subst ; trans ; cong₂) renaming (setoid to EqSetoid) open Setoid using () renaming (_≈_ to _∋_≈_) open Category.Functor.RawFunctor {Level.zero} Data.Maybe.functor using (_<$>_) @@ -35,14 +35,12 @@ mapMV f []V = just []V mapMV f (x ∷V xs) = (f x) >>= (λ y → (_∷V_ y) <$> (mapMV f xs)) mapMV-cong : {A B : Set} {f g : A → Maybe B} → f ≗ g → {n : ℕ} → mapMV {n = n} f ≗ mapMV g -mapMV-cong f≗g []V = refl -mapMV-cong {f = f} {g = g} f≗g (x ∷V xs) with f x | g x | f≗g x -mapMV-cong f≗g (x ∷V xs) | just y | .(just y) | refl = cong (_<$>_ (_∷V_ y)) (mapMV-cong f≗g xs) -mapMV-cong f≗g (x ∷V xs) | nothing | .nothing | refl = refl +mapMV-cong f≗g []V = refl +mapMV-cong f≗g (x ∷V xs) = cong₂ _>>=_ (f≗g x) (cong (flip (_<$>_ ∘ _∷V_)) (mapMV-cong f≗g xs)) -mapMV-purity : {A B : Set} {n : ℕ} → (f : A → B) → (v : Vec A n) → mapMV (just ∘ f) v ≡ just (map f v) -mapMV-purity f []V = refl -mapMV-purity f (x ∷V xs) rewrite mapMV-purity f xs = refl +mapMV-purity : {A B : Set} {n : ℕ} → (f : A → B) → (v : Vec A n) → mapMV (Maybe.just ∘ f) v ≡ just (map f v) +mapMV-purity f []V = refl +mapMV-purity f (x ∷V xs) = cong (_<$>_ (_∷V_ (f x))) (mapMV-purity f xs) maybeEq-from-≡ : {A : Set} {a b : Maybe A} → a ≡ b → MaybeEq (EqSetoid A) ∋ a ≈ b maybeEq-from-≡ {a = just x} {b = .(just x)} refl = just refl @@ -84,7 +82,7 @@ toList-subst v refl = refl VecISetoid : Setoid ℓ₀ ℓ₀ → ISetoid ℕ ℓ₀ ℓ₀ VecISetoid S = record { Carrier = Vec (Setoid.Carrier S) - ; _≈_ = λ x → S VecEq.≈ x + ; _≈_ = λ x → VecEq._≈_ S x ; isEquivalence = record { refl = VecEq.refl S _ ; sym = VecEq.sym S |