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annotate delta.hs @ 79:7307e43a3c76

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Prove monad-law-4
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Mon, 01 Dec 2014 17:25:59 +0900
parents 0ad0ae7a3cbe
children 1339772b2e36
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17
279ebcf670c4 Define Similar as Applicative
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1 import Control.Applicative
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2 import Data.Numbers.Primes -- $ cabal install primes
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4 -- delta definition
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6 data Delta a = Mono a | Delta a (Delta a) deriving Show
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279ebcf670c4 Define Similar as Applicative
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8 instance (Eq a) => Eq (Delta a) where
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9 (Mono x) == (Mono y) = x == y
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10 (Mono _) == (Delta _ _) = False
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11 (Delta x xs) == (Delta y ys) = (x == y) && (xs == ys)
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13 -- basic functions
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15 deltaAppend :: Delta a -> Delta a -> Delta a
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16 deltaAppend (Mono x) d = Delta x d
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17 deltaAppend (Delta x d) ds = Delta x (deltaAppend d ds)
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19 headDelta :: Delta a -> a
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20 headDelta (Mono x) = x
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21 headDelta (Delta x _) = x
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116131b196bb Define fmap and mu
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23 tailDelta :: Delta a -> Delta a
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24 tailDelta d@(Mono _) = d
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25 tailDelta (Delta _ ds) = ds
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27 -- instance definitions
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29 instance Functor Delta where
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30 fmap f (Mono x) = Mono (f x)
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31 fmap f (Delta x d) = Delta (f x) (fmap f d)
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32
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33 instance Applicative Delta where
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34 pure f = Mono f
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35 (Mono f) <*> (Mono x) = Mono (f x)
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36 df@(Mono f) <*> (Delta x d) = Delta (f x) (df <*> d)
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37 (Delta f df) <*> d@(Mono x) = Delta (f x) (df <*> d)
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38 (Delta f df) <*> (Delta x d) = Delta (f x) (df <*> d)
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39
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40 bind :: (Delta a) -> (a -> Delta b) -> (Delta b)
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41 bind (Mono x) f = f x
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42 bind (Delta x d) f = Delta (headDelta (f x)) (bind d (tailDelta . f))
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43
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44 mu :: (Delta (Delta a)) -> (Delta a)
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45 mu d = bind d id
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46
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47 instance Monad Delta where
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48 return x = Mono x
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49 d >>= f = mu $ fmap f d
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53 -- utils
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54
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55 returnS :: (Show s) => s -> Delta s
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56 returnS x = Mono x
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58 returnSS :: (Show s) => s -> s -> Delta s
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59 returnSS x y = (returnS x) `deltaAppend` (returnS y)
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61 deltaFromList :: [a] -> Delta a
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62 deltaFromList = (foldl1 deltaAppend) . (fmap return)
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65 -- samples
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67 generator :: Int -> Delta [Int]
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68 generator x = let intList = [1..x] in
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69 returnS intList
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71 primeFilter :: [Int] -> Delta [Int]
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72 primeFilter xs = let primeList = filter isPrime xs
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73 refactorList = filter even xs in
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74 returnSS primeList refactorList
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76 count :: [Int] -> Delta Int
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77 count xs = let primeCount = length xs in
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78 returnS primeCount
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80 primeCount :: Int -> Delta Int
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81 primeCount x = generator x >>= primeFilter >>= count
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cb5c190aa45d Define bubble sort
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cb5c190aa45d Define bubble sort
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83 bubbleSort :: [Int] -> Delta [Int]
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84 bubbleSort [] = returnS []
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85 bubbleSort xs = bubbleSort remainValue >>= (\xs -> returnSS (sortedValueL : xs)
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86 (sortedValueR ++ xs))
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87 where
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88 maximumValue = maximum xs
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89 sortedValueL = maximumValue
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90 sortedValueR = replicate (length $ filter (== maximumValue) xs) maximumValue
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91 remainValue = filter (/= maximumValue) xs