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comparison agda/delta/functor.agda @ 89:5411ce26d525

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Defining DeltaM in Agda...
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Mon, 19 Jan 2015 11:48:41 +0900
parents 6789c65a75bc
children 55d11ce7e223
comparison
equal deleted inserted replaced
88:526186c4f298 89:5411ce26d525
9 module delta.functor where 9 module delta.functor where
10 10
11 -- Functor-laws 11 -- Functor-laws
12 12
13 -- Functor-law-1 : T(id) = id' 13 -- Functor-law-1 : T(id) = id'
14 functor-law-1 : {l : Level} {A : Set l} -> (d : Delta A) -> (fmap id) d ≡ id d 14 functor-law-1 : {l : Level} {A : Set l} -> (d : Delta A) -> (delta-fmap id) d ≡ id d
15 functor-law-1 (mono x) = refl 15 functor-law-1 (mono x) = refl
16 functor-law-1 (delta x d) = cong (delta x) (functor-law-1 d) 16 functor-law-1 (delta x d) = cong (delta x) (functor-law-1 d)
17 17
18 -- Functor-law-2 : T(f . g) = T(f) . T(g) 18 -- Functor-law-2 : T(f . g) = T(f) . T(g)
19 functor-law-2 : {l ll lll : Level} {A : Set l} {B : Set ll} {C : Set lll} -> 19 functor-law-2 : {l ll lll : Level} {A : Set l} {B : Set ll} {C : Set lll} ->
20 (f : B -> C) -> (g : A -> B) -> (d : Delta A) -> 20 (f : B -> C) -> (g : A -> B) -> (d : Delta A) ->
21 (fmap (f ∙ g)) d ≡ (fmap f) (fmap g d) 21 (delta-fmap (f ∙ g)) d ≡ (delta-fmap f) (delta-fmap g d)
22 functor-law-2 f g (mono x) = refl 22 functor-law-2 f g (mono x) = refl
23 functor-law-2 f g (delta x d) = cong (delta (f (g x))) (functor-law-2 f g d) 23 functor-law-2 f g (delta x d) = cong (delta (f (g x))) (functor-law-2 f g d)
24 24
25 delta-is-functor : {l : Level} -> Functor (Delta {l}) 25 delta-is-functor : {l : Level} -> Functor (Delta {l})
26 delta-is-functor = record { fmap = fmap ; 26 delta-is-functor = record { fmap = delta-fmap ;
27 preserve-id = functor-law-1; 27 preserve-id = functor-law-1;
28 covariant = \f g -> functor-law-2 g f} 28 covariant = \f g -> functor-law-2 g f}