Mercurial > hg > Members > atton > delta_monad
view agda/delta/functor.agda @ 87:6789c65a75bc
Split functor-proofs into delta.functor
author | Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp> |
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date | Mon, 19 Jan 2015 11:00:34 +0900 |
parents | |
children | 5411ce26d525 |
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open import delta open import basic open import laws open import Level open import Relation.Binary.PropositionalEquality module delta.functor where -- Functor-laws -- Functor-law-1 : T(id) = id' functor-law-1 : {l : Level} {A : Set l} -> (d : Delta A) -> (fmap id) d ≡ id d functor-law-1 (mono x) = refl functor-law-1 (delta x d) = cong (delta x) (functor-law-1 d) -- Functor-law-2 : T(f . g) = T(f) . T(g) functor-law-2 : {l ll lll : Level} {A : Set l} {B : Set ll} {C : Set lll} -> (f : B -> C) -> (g : A -> B) -> (d : Delta A) -> (fmap (f ∙ g)) d ≡ (fmap f) (fmap g d) functor-law-2 f g (mono x) = refl functor-law-2 f g (delta x d) = cong (delta (f (g x))) (functor-law-2 f g d) delta-is-functor : {l : Level} -> Functor (Delta {l}) delta-is-functor = record { fmap = fmap ; preserve-id = functor-law-1; covariant = \f g -> functor-law-2 g f}