Mercurial > hg > Members > atton > delta_monad
diff agda/delta/functor.agda @ 104:ebd0d6e2772c
Trying redenition Delta with length constraints
author | Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp> |
---|---|
date | Mon, 26 Jan 2015 23:00:05 +0900 |
parents | f26a954cd068 |
children | e6499a50ccbd |
line wrap: on
line diff
--- a/agda/delta/functor.agda Mon Jan 26 14:08:46 2015 +0900 +++ b/agda/delta/functor.agda Mon Jan 26 23:00:05 2015 +0900 @@ -1,28 +1,32 @@ -open import delta -open import basic -open import laws - open import Level open import Relation.Binary.PropositionalEquality +open import basic +open import delta +open import laws +open import nat +open import revision + + + module delta.functor where -- Functor-laws -- Functor-law-1 : T(id) = id' -functor-law-1 : {l : Level} {A : Set l} -> (d : Delta A) -> (delta-fmap id) d ≡ id d +functor-law-1 : {l : Level} {A : Set l} {n : Rev} -> (d : Delta A n) -> (delta-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 : Level} {A B C : Set l} -> - (f : B -> C) -> (g : A -> B) -> (d : Delta A) -> +functor-law-2 : {l : Level} {n : Rev} {A B C : Set l} -> + (f : B -> C) -> (g : A -> B) -> (d : Delta A n) -> (delta-fmap (f ∙ g)) d ≡ ((delta-fmap f) ∙ (delta-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 {l} Delta +delta-is-functor : {l : Level} {n : Rev} -> Functor {l} (\A -> Delta A n) delta-is-functor = record { fmap = delta-fmap ; preserve-id = functor-law-1; covariant = \f g -> functor-law-2 g f}