Mercurial > hg > Members > atton > delta_monad

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

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
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
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
87
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
1 open import delta
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
2 open import basic
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
3 open import laws
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
4
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
5 open import Level
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
6 open import Relation.Binary.PropositionalEquality
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
7
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
8
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
9 module delta.functor where
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
10
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
11 -- Functor-laws
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
12
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
13 -- Functor-law-1 : T(id) = id'
89
5411ce26d525 Defining DeltaM in Agda...
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents: 87
diff changeset
14 functor-law-1 : {l : Level} {A : Set l} -> (d : Delta A) -> (delta-fmap id) d ≡ id d
87
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
15 functor-law-1 (mono x) = refl
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
16 functor-law-1 (delta x d) = cong (delta x) (functor-law-1 d)
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
17
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
18 -- Functor-law-2 : T(f . g) = T(f) . T(g)
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
19 functor-law-2 : {l ll lll : Level} {A : Set l} {B : Set ll} {C : Set lll} ->
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
20 (f : B -> C) -> (g : A -> B) -> (d : Delta A) ->
89
5411ce26d525 Defining DeltaM in Agda...
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents: 87
diff changeset
21 (delta-fmap (f ∙ g)) d ≡ (delta-fmap f) (delta-fmap g d)
87
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
22 functor-law-2 f g (mono x) = refl
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
23 functor-law-2 f g (delta x d) = cong (delta (f (g x))) (functor-law-2 f g d)
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
24
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
25 delta-is-functor : {l : Level} -> Functor (Delta {l})
89
5411ce26d525 Defining DeltaM in Agda...
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents: 87
diff changeset
26 delta-is-functor = record { fmap = delta-fmap ;
87
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
27 preserve-id = functor-law-1;
6789c65a75bc Split functor-proofs into delta.functor
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents:
diff changeset
28 covariant = \f g -> functor-law-2 g f}