Mercurial > hg > Members > atton > delta_monad
annotate agda/similar.agda @ 31:33b386de3f56
Proof list-associative
author | Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp> |
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date | Sat, 18 Oct 2014 13:38:29 +0900 |
parents | c2f40b6d4027 |
children | 71906644d206 |
rev | line source |
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Define Similar in Agda
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1 open import list |
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2 open import basic |
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3 |
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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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7 |
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8 module similar where |
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9 |
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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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12 |
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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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15 |
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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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18 |
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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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21 |
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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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24 |
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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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27 |
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28 --monad-law-1 : mu ∙ (fmap mu) ≡ mu ∙ mu |
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29 |
30
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30 {- |
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31 monad-law-1 : {l : Level} {A : Set l} -> (s : Similar (Similar (Similar A))) -> ((mu ∙ (fmap mu)) s) ≡ ((mu ∙ mu) s) |
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32 monad-law-1 s = begin |
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33 ((mu ∙ (fmap mu)) s) |
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34 ≡⟨⟩ |
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35 mu (fmap mu s) |
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36 ≡⟨ cong mu {!!} ⟩ |
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37 mu (mu s) |
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38 ≡⟨⟩ |
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39 ((mu ∙ mu) s) |
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40 ∎ |
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41 -} |
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42 |
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43 monad-law-1-sub : {l : Level} {A : Set l} -> (s : Similar (Similar (Similar A))) -> fmap mu s ≡ mu s |
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44 monad-law-1-sub (similar lx (similar llx (similar lllx x _ _) _ _) ly (similar _ _ lly (similar _ _ llly y))) = begin |
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45 similar lx (mu (similar llx (similar lllx x _ _) _ _)) ly |
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46 (mu (similar _ _ lly (similar _ _ llly y))) |
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47 ≡⟨ {!!} ⟩ |
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48 similar (lx ++ llx) (similar lllx x _ _) (ly ++ lly) |
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49 (similar _ _ llly y) |
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50 ∎ |
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51 |
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52 |
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53 |
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54 |
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55 |
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56 {- |
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57 --monad-law-2 : mu ∙ fmap return ≡ mu ∙ return ≡id |
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58 monad-law-2-1 : mu ∙ fmap return ≡ mu ∙ return |
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59 monad-law-2-1 = {!!} |
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60 |
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61 monad-law-2-2 : mu ∙ return ≡ id |
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62 monad-law-2-2 = {!!} |
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63 |
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64 monad-law-3 : ∀{f} -> return ∙ f ≡ fmap f ∙ return |
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65 monad-law-3 = {!!} |
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66 |
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67 monad-law-4 : ∀{f} -> mu ∙ fmap (fmap f) ≡ fmap f ∙ mu |
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68 monad-law-4 = {!!} |
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69 -} |