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comparison agda/similar.agda @ 27:742e62fc63e4

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Define Monad-law 1-4
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Tue, 07 Oct 2014 14:53:56 +0900
parents 5ba82f107a95
children 6e6d646d7722
comparison
equal deleted inserted replaced
26:5ba82f107a95 27:742e62fc63e4
1 open import list 1 open import list
2 open import Relation.Binary.PropositionalEquality
3 open ≡-Reasoning
2 4
3 module similar where 5 module similar where
6
7 id : {A : Set} -> A -> A
8 id x = x
4 9
5 postulate String : Set 10 postulate String : Set
6 postulate show : {A : Set} -> A -> String 11 postulate show : {A : Set} -> A -> String
7 12
8 data Similar (A : Set) : Set where 13 data Similar (A : Set) : Set where
14 19
15 20
16 mu : {A : Set} -> Similar (Similar A) -> Similar A 21 mu : {A : Set} -> Similar (Similar A) -> Similar A
17 mu (similar lx (similar llx x _ _) ly (similar _ _ lly y)) = similar (lx ++ llx) x (ly ++ lly) y 22 mu (similar lx (similar llx x _ _) ly (similar _ _ lly y)) = similar (lx ++ llx) x (ly ++ lly) y
18 23
24 return : {A : Set} -> A -> Similar A
25 return x = similar [] x [] x
26
19 returnS : {A : Set} -> A -> Similar A 27 returnS : {A : Set} -> A -> Similar A
20 returnS x = similar [[ (show x) ]] x [[ (show x) ]] x 28 returnS x = similar [[ (show x) ]] x [[ (show x) ]] x
21 29
22 returnSS : {A : Set} -> A -> A -> Similar A 30 returnSS : {A : Set} -> A -> A -> Similar A
23 returnSS x y = similar [[ (show x) ]] x [[ (show y) ]] y 31 returnSS x y = similar [[ (show x) ]] x [[ (show y) ]] y
24 32
25 33
34 _∙_ : {A B C : Set} -> (A -> B) -> (B -> C) -> (A -> C)
35 f ∙ g = \x -> g (f x)
36
37 monad-law-1 : mu ∙ (fmap mu) ≡ mu ∙ mu
38 monad-law-1 = {!!}
39
40 --monad-law-2 : mu ∙ fmap return ≡ mu ∙ return ≡id
41 monad-law-2-1 : mu ∙ fmap return ≡ mu ∙ return
42 monad-law-2-1 = {!!}
43
44 monad-law-2-2 : mu ∙ return ≡ id
45 monad-law-2-2 = {!!}
46
47 monad-law-3 : ∀{f} -> return ∙ f ≡ fmap f ∙ return
48 monad-law-3 = {!!}
49
50 monad-law-4 : ∀{f} -> mu ∙ fmap (fmap f) ≡ fmap f ∙ mu
51 monad-law-4 = {!!}