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annotate delta.hs @ 82:1339772b2e36

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Define DeltaM. Delta with Monad
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Sun, 04 Jan 2015 16:31:17 +0900
parents 0ad0ae7a3cbe
children 6635a513f81a
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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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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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18
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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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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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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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51 -- utils
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53 returnS :: (Show s) => s -> Delta s
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54 returnS x = Mono x
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56 returnSS :: (Show s) => s -> s -> Delta s
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57 returnSS x y = (returnS x) `deltaAppend` (returnS y)
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59 deltaFromList :: [a] -> Delta a
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60 deltaFromList = (foldl1 deltaAppend) . (fmap return)
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62
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63 -- samples
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64
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65 generator :: Int -> Delta [Int]
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66 generator x = let intList = [1..x] in
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67 returnS intList
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69 primeFilter :: [Int] -> Delta [Int]
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70 primeFilter xs = let primeList = filter isPrime xs
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71 refactorList = filter even xs in
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72 returnSS primeList refactorList
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74 count :: [Int] -> Delta Int
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75 count xs = let primeCount = length xs in
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76 returnS primeCount
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78 primeCount :: Int -> Delta Int
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79 primeCount x = generator x >>= primeFilter >>= count
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80
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81 bubbleSort :: [Int] -> Delta [Int]
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82 bubbleSort [] = returnS []
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83 bubbleSort xs = bubbleSort remainValue >>= (\xs -> returnSS (sortedValueL : xs)
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84 (sortedValueR ++ xs))
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85 where
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86 maximumValue = maximum xs
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87 sortedValueL = maximumValue
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88 sortedValueR = replicate (length $ filter (== maximumValue) xs) maximumValue
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89 remainValue = filter (/= maximumValue) xs
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91 -- DeltaM Definition (Delta with Monad)
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92
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93 data DeltaM m a = DeltaM (Delta (m a)) deriving (Show)
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96 -- DeltaM utils
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97
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98 headDeltaM :: DeltaM m a -> m a
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99 headDeltaM (DeltaM (Mono x)) = x
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100 headDeltaM (DeltaM (Delta x _ )) = x
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101
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102 tailDeltaM :: DeltaM m a -> DeltaM m a
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103 tailDeltaM d@(DeltaM (Mono _)) = d
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104 tailDeltaM (DeltaM (Delta _ d)) = DeltaM d
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105
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106 appendDeltaM :: DeltaM m a -> DeltaM m a -> DeltaM m a
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107 appendDeltaM (DeltaM d) (DeltaM dd) = DeltaM (deltaAppend d dd)
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108
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109
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110 -- DeltaM instance definitions
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111
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112 instance (Functor m) => Functor (DeltaM m) where
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113 fmap f (DeltaM d) = DeltaM $ fmap (fmap f) d
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114
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115 instance (Applicative m) => Applicative (DeltaM m) where
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116 pure f = DeltaM $ Mono $ pure f
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117 (DeltaM (Mono f)) <*> (DeltaM (Mono x)) = DeltaM $ Mono $ f <*> x
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118 df@(DeltaM (Mono f)) <*> (DeltaM (Delta x d)) = appendDeltaM (DeltaM $ Mono $ f <*> x) (df <*> (DeltaM d))
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119 (DeltaM (Delta f df)) <*> dx@(DeltaM (Mono x)) = appendDeltaM (DeltaM $ Mono $ f <*> x) ((DeltaM df) <*> dx)
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120 (DeltaM (Delta f df)) <*> (DeltaM (Delta x dx)) = appendDeltaM (DeltaM $ Mono $ f <*> x) ((DeltaM df) <*> (DeltaM dx))
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121
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122 instance (Monad m) => Monad (DeltaM m) where
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123 return x = DeltaM $ Mono $ return x
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124 (DeltaM (Mono x)) >>= f = DeltaM $ Mono $ (x >>= headDeltaM . f)
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125 (DeltaM (Delta x d)) >>= f = appendDeltaM ((DeltaM $ Mono x) >>= f)
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126 ((DeltaM d) >>= tailDeltaM . f)
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127
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128
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129 -- DeltaM examples
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130
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131 val :: DeltaM [] Int
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132 val = DeltaM $ deltaFromList [[10, 20], [1, 2, 3], [100,200,300], [0]]
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133
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134 func :: Int -> DeltaM [] Int
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135 func x = DeltaM $ deltaFromList [[x+1, x+2, x+3],
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136 [x*x],
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137 [x, x, x, x]]