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annotate agda/similar.agda @ 28:6e6d646d7722

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Split basic functions to file
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Tue, 07 Oct 2014 14:55:40 +0900
parents 742e62fc63e4
children e0ba1bf564dd
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5ba82f107a95 Define Similar in Agda
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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1 open import list
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6e6d646d7722 Split basic functions to file
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2 open import basic
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3 open import Relation.Binary.PropositionalEquality
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4 open ≡-Reasoning
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6 module similar where
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8 data Similar (A : Set) : Set where
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9 similar : List String -> A -> List String -> A -> Similar A
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11 fmap : {A B : Set} -> (A -> B) -> (Similar A) -> (Similar B)
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12 fmap f (similar xs x ys y) = similar xs (f x) ys (f y)
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14 mu : {A : Set} -> Similar (Similar A) -> Similar A
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15 mu (similar lx (similar llx x _ _) ly (similar _ _ lly y)) = similar (lx ++ llx) x (ly ++ lly) y
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17 return : {A : Set} -> A -> Similar A
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18 return x = similar [] x [] x
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20 returnS : {A : Set} -> A -> Similar A
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21 returnS x = similar [[ (show x) ]] x [[ (show x) ]] x
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23 returnSS : {A : Set} -> A -> A -> Similar A
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24 returnSS x y = similar [[ (show x) ]] x [[ (show y) ]] y
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27 monad-law-1 : mu ∙ (fmap mu) ≡ mu ∙ mu
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28 monad-law-1 = {!!}
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30 --monad-law-2 : mu ∙ fmap return ≡ mu ∙ return ≡id
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31 monad-law-2-1 : mu ∙ fmap return ≡ mu ∙ return
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32 monad-law-2-1 = {!!}
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34 monad-law-2-2 : mu ∙ return ≡ id
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35 monad-law-2-2 = {!!}
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37 monad-law-3 : ∀{f} -> return ∙ f ≡ fmap f ∙ return
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38 monad-law-3 = {!!}
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40 monad-law-4 : ∀{f} -> mu ∙ fmap (fmap f) ≡ fmap f ∙ mu
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41 monad-law-4 = {!!}