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annotate agda/similar.agda @ 29:e0ba1bf564dd

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Apply level to some functions
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Tue, 07 Oct 2014 15:09:17 +0900
parents 6e6d646d7722
children c2f40b6d4027
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5ba82f107a95 Define Similar in Agda
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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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e0ba1bf564dd Apply level to some functions
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e0ba1bf564dd Apply level to some functions
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4 open import Level
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5 open import Relation.Binary.PropositionalEquality
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6 open ≡-Reasoning
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8 module similar where
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10 data Similar {l : Level} (A : Set l) : (Set (suc l)) where
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11 similar : List String -> A -> List String -> A -> Similar A
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13 fmap : {l ll : Level} {A : Set l} {B : Set ll} -> (A -> B) -> (Similar A) -> (Similar B)
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14 fmap f (similar xs x ys y) = similar xs (f x) ys (f y)
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16 mu : {l : Level} {A : Set l} -> Similar (Similar A) -> Similar A
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17 mu (similar lx (similar llx x _ _) ly (similar _ _ lly y)) = similar (lx ++ llx) x (ly ++ lly) y
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19 return : {A : Set} -> A -> Similar A
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20 return x = similar [] x [] x
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22 returnS : {A : Set} -> A -> Similar A
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23 returnS x = similar [[ (show x) ]] x [[ (show x) ]] x
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25 returnSS : {A : Set} -> A -> A -> Similar A
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26 returnSS x y = similar [[ (show x) ]] x [[ (show y) ]] y
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28 --monad-law-1 : mu ∙ (fmap mu) ≡ mu ∙ mu
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30 monad-law-1 : {l : Level} {A : Set l} -> (s : Similar (Similar (Similar A))) -> ((mu ∙ (fmap mu)) s) ≡ ((mu ∙ mu) s)
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31 monad-law-1 s = begin
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32 ((mu ∙ (fmap mu)) s)
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33 ≡⟨⟩
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34 mu (fmap mu s)
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35 ≡⟨ {!!} ⟩
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36 mu (mu s)
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37 ≡⟨⟩
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38 ((mu ∙ mu) s)
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39 ∎
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e0ba1bf564dd Apply level to some functions
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e0ba1bf564dd Apply level to some functions
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44 {-
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45 --monad-law-2 : mu ∙ fmap return ≡ mu ∙ return ≡id
742e62fc63e4 Define Monad-law 1-4
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46 monad-law-2-1 : mu ∙ fmap return ≡ mu ∙ return
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47 monad-law-2-1 = {!!}
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49 monad-law-2-2 : mu ∙ return ≡ id
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50 monad-law-2-2 = {!!}
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52 monad-law-3 : ∀{f} -> return ∙ f ≡ fmap f ∙ return
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53 monad-law-3 = {!!}
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55 monad-law-4 : ∀{f} -> mu ∙ fmap (fmap f) ≡ fmap f ∙ mu
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56 monad-law-4 = {!!}
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57 -}