1 module FreeTheorems where
3 open import Data.Nat using (ℕ)
4 open import Data.List using (List ; map)
5 open import Data.Vec using (Vec) renaming (map to mapV)
6 open import Function using (_∘_)
7 open import Relation.Binary.PropositionalEquality using (_≗_)
11 get-type = {A : Set} → List A → List A
14 free-theorem : (get : get-type) → {α β : Set} → (f : α → β) → get ∘ map f ≗ map f ∘ get
17 get-type : (ℕ → ℕ) → Set₁
18 get-type getlen = {A : Set} {n : ℕ} → Vec A n → Vec A (getlen n)
21 free-theorem : {getlen : ℕ → ℕ} → (get : get-type getlen) → {α β : Set} → (f : α → β) → {n : ℕ} → get {_} {n} ∘ mapV f ≗ mapV f ∘ get