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annotate delta.hs @ 83:6635a513f81a

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Add example for DeltaM
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Sun, 04 Jan 2015 17:20:33 +0900
parents 1339772b2e36
children 8c7bd8bf8092
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17
279ebcf670c4 Define Similar as Applicative
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1 import Control.Applicative
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2 import Control.Monad.Writer
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3 import Data.Numbers.Primes -- $ cabal install primes
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5 -- delta definition
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6
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7 data Delta a = Mono a | Delta a (Delta a) deriving Show
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8
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9 instance (Eq a) => Eq (Delta a) where
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10 (Mono x) == (Mono y) = x == y
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11 (Mono _) == (Delta _ _) = False
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12 (Delta x xs) == (Delta y ys) = (x == y) && (xs == ys)
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13
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14 -- basic functions
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15
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16 deltaAppend :: Delta a -> Delta a -> Delta a
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17 deltaAppend (Mono x) d = Delta x d
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18 deltaAppend (Delta x d) ds = Delta x (deltaAppend d ds)
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19
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20 headDelta :: Delta a -> a
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21 headDelta (Mono x) = x
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22 headDelta (Delta x _) = x
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23
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24 tailDelta :: Delta a -> Delta a
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25 tailDelta d@(Mono _) = d
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26 tailDelta (Delta _ ds) = ds
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28 -- instance definitions
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29
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30 instance Functor Delta where
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31 fmap f (Mono x) = Mono (f x)
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32 fmap f (Delta x d) = Delta (f x) (fmap f d)
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33
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34 instance Applicative Delta where
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35 pure f = Mono f
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36 (Mono f) <*> (Mono x) = Mono (f x)
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37 df@(Mono f) <*> (Delta x d) = Delta (f x) (df <*> d)
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38 (Delta f df) <*> d@(Mono x) = Delta (f x) (df <*> d)
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39 (Delta f df) <*> (Delta x d) = Delta (f x) (df <*> d)
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41 bind :: (Delta a) -> (a -> Delta b) -> (Delta b)
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42 bind (Mono x) f = f x
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43 bind (Delta x d) f = Delta (headDelta (f x)) (bind d (tailDelta . f))
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44
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45 mu :: (Delta (Delta a)) -> (Delta a)
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46 mu d = bind d id
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47
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48 instance Monad Delta where
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49 return x = Mono x
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50 d >>= f = mu $ fmap f d
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51
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52 -- utils
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54 returnS :: (Show s) => s -> Delta s
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55 returnS x = Mono x
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57 returnSS :: (Show s) => s -> s -> Delta s
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58 returnSS x y = (returnS x) `deltaAppend` (returnS y)
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59
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60 deltaFromList :: [a] -> Delta a
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61 deltaFromList = (foldl1 deltaAppend) . (fmap return)
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62
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63
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64 -- samples
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65
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66 generator :: Int -> Delta [Int]
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67 generator x = let intList = [1..x] in
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68 returnS intList
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70 primeFilter :: [Int] -> Delta [Int]
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71 primeFilter xs = let primeList = filter isPrime xs
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72 refactorList = filter even xs in
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73 returnSS primeList refactorList
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75 count :: [Int] -> Delta Int
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76 count xs = let primeCount = length xs in
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77 returnS primeCount
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79 primeCount :: Int -> Delta Int
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80 primeCount x = generator x >>= primeFilter >>= count
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81
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82 bubbleSort :: [Int] -> Delta [Int]
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83 bubbleSort [] = returnS []
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84 bubbleSort xs = bubbleSort remainValue >>= (\xs -> returnSS (sortedValueL : xs)
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85 (sortedValueR ++ xs))
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86 where
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87 maximumValue = maximum xs
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88 sortedValueL = maximumValue
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89 sortedValueR = replicate (length $ filter (== maximumValue) xs) maximumValue
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90 remainValue = filter (/= maximumValue) xs
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91
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92 -- DeltaM Definition (Delta with Monad)
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93
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94 data DeltaM m a = DeltaM (Delta (m a)) deriving (Show)
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95
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96
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97 -- DeltaM utils
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98
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99 headDeltaM :: DeltaM m a -> m a
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100 headDeltaM (DeltaM (Mono x)) = x
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101 headDeltaM (DeltaM (Delta x _ )) = x
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102
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103 tailDeltaM :: DeltaM m a -> DeltaM m a
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104 tailDeltaM d@(DeltaM (Mono _)) = d
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105 tailDeltaM (DeltaM (Delta _ d)) = DeltaM d
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106
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107 appendDeltaM :: DeltaM m a -> DeltaM m a -> DeltaM m a
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108 appendDeltaM (DeltaM d) (DeltaM dd) = DeltaM (deltaAppend d dd)
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109
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110 checkOut :: Int -> DeltaM m a -> m a
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111 checkOut 0 (DeltaM (Mono x)) = x
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112 checkOut 0 (DeltaM (Delta x _)) = x
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113 checkOut n (DeltaM (Mono x)) = x
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114 checkOut n (DeltaM (Delta _ d)) = checkOut (n-1) (DeltaM d)
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115
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116
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117 -- DeltaM instance definitions
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118
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119 instance (Functor m) => Functor (DeltaM m) where
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120 fmap f (DeltaM d) = DeltaM $ fmap (fmap f) d
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121
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122 instance (Applicative m) => Applicative (DeltaM m) where
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123 pure f = DeltaM $ Mono $ pure f
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124 (DeltaM (Mono f)) <*> (DeltaM (Mono x)) = DeltaM $ Mono $ f <*> x
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125 df@(DeltaM (Mono f)) <*> (DeltaM (Delta x d)) = appendDeltaM (DeltaM $ Mono $ f <*> x) (df <*> (DeltaM d))
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126 (DeltaM (Delta f df)) <*> dx@(DeltaM (Mono x)) = appendDeltaM (DeltaM $ Mono $ f <*> x) ((DeltaM df) <*> dx)
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127 (DeltaM (Delta f df)) <*> (DeltaM (Delta x dx)) = appendDeltaM (DeltaM $ Mono $ f <*> x) ((DeltaM df) <*> (DeltaM dx))
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128
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129 instance (Monad m) => Monad (DeltaM m) where
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130 return x = DeltaM $ Mono $ return x
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131 (DeltaM (Mono x)) >>= f = DeltaM $ Mono $ (x >>= headDeltaM . f)
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132 (DeltaM (Delta x d)) >>= f = appendDeltaM ((DeltaM $ Mono x) >>= f)
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133 ((DeltaM d) >>= tailDeltaM . f)
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134
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135
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136 -- DeltaM examples
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137
83
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138 -- DeltaM example utils
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139 type DeltaLog = Writer [String]
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140
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141 returnW :: (Show a) => a -> DeltaLog a
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142 returnW x = do tell $ [show x]
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143 return x
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144
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145 dmap :: (m a -> b) -> DeltaM m a -> Delta b
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146 dmap f (DeltaM (Mono mx)) = (Mono $ f mx)
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147 dmap f (DeltaM (Delta x d)) = Delta (f x) (dmap f (DeltaM d))
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148
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149
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150 -- example : prime filter
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151 -- usage : runWriter $ checkOut 0 $ primeCountM 30 -- run specific version
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152 -- : dmap runWriter $ primeCountM 30 -- run all version
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153
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154 generatorM :: Int -> DeltaM DeltaLog [Int]
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155 generatorM x = let intList = returnW [1..x] in
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156 DeltaM $ deltaFromList $ [intList, intList]
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157
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158 primeFilterM :: [Int] -> DeltaM DeltaLog [Int]
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159 primeFilterM xs = let primeList = filter isPrime xs
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160 refactorList = filter even xs in
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161 DeltaM $ deltaFromList $ fmap returnW [primeList, refactorList]
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162
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163
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164 countM :: [Int] -> DeltaM DeltaLog Int
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165 countM xs = let primeCount = length xs in
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166 DeltaM $ deltaFromList $ fmap returnW [primeCount, primeCount]
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167
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168 primeCountM :: Int -> DeltaM DeltaLog Int
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169 primeCountM x = generatorM x >>= primeFilterM >>= countM