diff options
Diffstat (limited to 'Instances.agda')
| -rw-r--r-- | Instances.agda | 15 |
1 files changed, 8 insertions, 7 deletions
diff --git a/Instances.agda b/Instances.agda index 3f69627..a09e30d 100644 --- a/Instances.agda +++ b/Instances.agda @@ -3,14 +3,15 @@ module Instances where open import Level using () renaming (zero to ℓ₀) open import Category.Functor using (RawFunctor) open import Data.Maybe as M using (Maybe) +import Data.Maybe.Categorical open import Data.Nat using (ℕ) open import Data.Product using (_×_ ; _,_ ; proj₁ ; proj₂) open import Data.Vec using (Vec) -import Data.Vec.Equality -open Data.Vec.Equality.PropositionalEquality using () renaming (to-≡ to VecEq-to-≡) +open import Data.Vec.Relation.Pointwise.Inductive using (Pointwise-≡⇒≡) open import Function using (_∘_ ; id) open import Relation.Binary using (Setoid ; module Setoid) -open import Relation.Binary.Indexed using (_at_) renaming (Setoid to ISetoid) +open import Relation.Binary.Indexed.Heterogeneous using () renaming (IndexedSetoid to ISetoid) +open import Relation.Binary.Indexed.Heterogeneous.Construct.At using (_atₛ_) open import Relation.Binary.PropositionalEquality as P using (_≡_ ; _≗_ ; module ≡-Reasoning) open Setoid using () renaming (_≈_ to _∋_≈_) @@ -20,14 +21,14 @@ open import Structures using (Functor ; Shaped ; module Shaped) MaybeFunctor : Functor Maybe MaybeFunctor = record - { rawfunctor = M.functor + { rawfunctor = Data.Maybe.Categorical.functor ; isFunctor = record { cong = cong ; identity = identity ; composition = composition } } where _<$>_ : {α β : Set} → (α → β) → Maybe α → Maybe β - _<$>_ = RawFunctor._<$>_ M.functor + _<$>_ = RawFunctor._<$>_ Data.Maybe.Categorical.functor cong : {α β : Set} {g h : α → β} → g ≗ h → _<$>_ g ≗ _<$>_ h cong g≗h (M.just x) = P.cong M.just (g≗h x) @@ -61,12 +62,12 @@ ShapedISetoid S {C} ShapeT α = record ; trans = λ p q → Setoid.trans S (proj₁ p) (proj₁ q) , ISetoid.trans (VecISetoid α) (proj₂ p) (proj₂ q) } } where open Shaped ShapeT -Shaped≈-to-≡ : {S : Set} {C : Set → S → Set} → (ShapeT : Shaped S C) → (α : Set) → {s : S} {x y : C α s} → ShapedISetoid (P.setoid S) ShapeT (P.setoid α) at s ∋ x ≈ y → x ≡ y +Shaped≈-to-≡ : {S : Set} {C : Set → S → Set} → (ShapeT : Shaped S C) → (α : Set) → {s : S} {x y : C α s} → ShapedISetoid (P.setoid S) ShapeT (P.setoid α) atₛ s ∋ x ≈ y → x ≡ y Shaped≈-to-≡ ShapeT α {s} {x} {y} (shape≈ , content≈) = begin x ≡⟨ P.sym (content-fill x) ⟩ fill s (content x) - ≡⟨ P.cong (fill s) (VecEq-to-≡ content≈) ⟩ + ≡⟨ P.cong (fill s) (Pointwise-≡⇒≡ content≈) ⟩ fill s (content y) ≡⟨ content-fill y ⟩ y ∎ |