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module GetTypes where
open import Level using () renaming (zero to ℓ₀)
open import Data.Nat using (ℕ)
open import Data.List using (List ; map)
open import Data.Vec using (Vec) renaming (map to mapV)
open import Function using (_∘_)
open import Function.Equality using (_⟶_ ; _⟨$⟩_)
open import Function.Injection using (module Injection) renaming (Injection to _↪_ ; id to id↪)
open import Relation.Binary.PropositionalEquality using (_≗_) renaming (setoid to EqSetoid)
open import Relation.Binary using (Setoid)
open Injection using (to)
open import Generic using (≡-to-Π)
module ListList where
record Get : Set₁ where
field
get : {A : Set} → List A → List A
free-theorem : {α β : Set} → (f : α → β) → get ∘ map f ≗ map f ∘ get
module VecVec where
record Get : Set₁ where
field
getlen : ℕ → ℕ
get : {A : Set} {n : ℕ} → Vec A n → Vec A (getlen n)
free-theorem : {α β : Set} (f : α → β) {n : ℕ} → get {_} {n} ∘ mapV f ≗ mapV f ∘ get
module PartialVecVec where
record Get : Set₁ where
field
I : Setoid ℓ₀ ℓ₀
gl₁ : I ↪ EqSetoid ℕ
gl₂ : I ⟶ EqSetoid ℕ
get : {A : Set} {i : Setoid.Carrier I} → Vec A (to gl₁ ⟨$⟩ i) → Vec A (gl₂ ⟨$⟩ i)
free-theorem : {α β : Set} → (f : α → β) → {i : Setoid.Carrier I} → get {_} {i} ∘ mapV f ≗ mapV f ∘ get
VecVec-to-PartialVecVec : VecVec.Get → PartialVecVec.Get
VecVec-to-PartialVecVec G = record
{ I = EqSetoid ℕ
; gl₁ = id↪
; gl₂ = ≡-to-Π getlen
; get = get
; free-theorem = free-theorem
} where open VecVec.Get G
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