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annotate delta.hs @ 116:f02c5ad4a327

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Prove association-law for DeltaM by (S O) pattern with definition changes
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Sun, 01 Feb 2015 17:55:39 +0900
parents 29c54b0197fb
children f2187ad63791
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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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4
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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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279ebcf670c4 Define Similar as Applicative
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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)
47
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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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27
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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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40
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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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53
84
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54 returnDD :: (Show s) => s -> s -> Delta s
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55 returnDD x y = (return x) `deltaAppend` (return y)
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56
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57 deltaFromList :: [a] -> Delta a
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58 deltaFromList = (foldl1 deltaAppend) . (fmap return)
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59
23
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60
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61 -- samples
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62
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63 generator :: Int -> Delta [Int]
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64 generator x = let intList = [1..x] in
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65 return intList
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66
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67 primeFilter :: [Int] -> Delta [Int]
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68 primeFilter xs = let primeList = filter isPrime xs
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69 refactorList = filter even xs in
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8c7bd8bf8092 Define DeltaWithLog
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70 returnDD primeList refactorList
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71
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72 count :: [Int] -> Delta Int
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73 count xs = let primeCount = length xs in
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74 return primeCount
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c599d2236d19 Similar as Monad
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75
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76 primeCount :: Int -> Delta Int
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77 primeCount x = generator x >>= primeFilter >>= count
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cb5c190aa45d Define bubble sort
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78
cb5c190aa45d Define bubble sort
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79 bubbleSort :: [Int] -> Delta [Int]
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80 bubbleSort [] = return []
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81 bubbleSort xs = bubbleSort remainValue >>= (\xs -> returnDD (sortedValueL : xs)
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82 (sortedValueR ++ xs))
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83 where
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84 maximumValue = maximum xs
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85 sortedValueL = maximumValue
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86 sortedValueR = replicate (length $ filter (== maximumValue) xs) maximumValue
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87 remainValue = filter (/= maximumValue) xs
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1339772b2e36 Define DeltaM. Delta with Monad
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91 -- DeltaM definition (Delta with Monad)
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92
1339772b2e36 Define DeltaM. Delta with Monad
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93 data DeltaM m a = DeltaM (Delta (m a)) deriving (Show)
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94
1339772b2e36 Define DeltaM. Delta with Monad
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95
1339772b2e36 Define DeltaM. Delta with Monad
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96 -- DeltaM utils
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97
1339772b2e36 Define DeltaM. Delta with Monad
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98 headDeltaM :: DeltaM m a -> m a
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99 headDeltaM (DeltaM d) = headDelta d
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100
1339772b2e36 Define DeltaM. Delta with Monad
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101 tailDeltaM :: DeltaM m a -> DeltaM m a
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102 tailDeltaM (DeltaM d) = DeltaM $ tailDelta d
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103
1339772b2e36 Define DeltaM. Delta with Monad
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104 appendDeltaM :: DeltaM m a -> DeltaM m a -> DeltaM m a
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105 appendDeltaM (DeltaM d) (DeltaM dd) = DeltaM (deltaAppend d dd)
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106
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107 checkOut :: Int -> DeltaM m a -> m a
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108 checkOut 0 (DeltaM (Mono x)) = x
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109 checkOut 0 (DeltaM (Delta x _)) = x
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110 checkOut n (DeltaM (Mono x)) = x
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111 checkOut n (DeltaM (Delta _ d)) = checkOut (n-1) (DeltaM d)
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112
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113
1339772b2e36 Define DeltaM. Delta with Monad
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114 -- DeltaM instance definitions
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115
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116 instance (Functor m) => Functor (DeltaM m) where
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117 fmap f (DeltaM d) = DeltaM $ fmap (fmap f) d
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118
1339772b2e36 Define DeltaM. Delta with Monad
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119 instance (Applicative m) => Applicative (DeltaM m) where
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120 pure f = DeltaM $ Mono $ pure f
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121 (DeltaM (Mono f)) <*> (DeltaM (Mono x)) = DeltaM $ Mono $ f <*> x
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122 df@(DeltaM (Mono f)) <*> (DeltaM (Delta x d)) = appendDeltaM (DeltaM $ Mono $ f <*> x) (df <*> (DeltaM d))
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123 (DeltaM (Delta f df)) <*> dx@(DeltaM (Mono x)) = appendDeltaM (DeltaM $ Mono $ f <*> x) ((DeltaM df) <*> dx)
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124 (DeltaM (Delta f df)) <*> (DeltaM (Delta x dx)) = appendDeltaM (DeltaM $ Mono $ f <*> x) ((DeltaM df) <*> (DeltaM dx))
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125
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126
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127 mu' :: (Functor m, Monad m) => DeltaM m (DeltaM m a) -> DeltaM m a
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128 mu' (DeltaM (Mono x)) = DeltaM $ Mono $ (>>= id) $ fmap headDeltaM x
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129 mu' (DeltaM (Delta x d)) = appendDeltaM (mu' $ DeltaM $ Mono x)
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130 (mu' $ fmap tailDeltaM $ DeltaM d )
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131
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132 instance (Functor m, Monad m) => Monad (DeltaM m) where
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133 return x = DeltaM $ Mono $ return x
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134 d >>= f = mu' $ fmap f d
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135
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136
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137
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138 -- DeltaM examples
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139
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140 -- DeltaM example utils
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141 type DeltaLog = Writer [String]
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142 type DeltaWithLog = DeltaM DeltaLog
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143
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144 returnW :: (Show a) => a -> DeltaLog a
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145 returnW x = do tell $ [show x]
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146 return x
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147
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148 dmap :: (m a -> b) -> DeltaM m a -> Delta b
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149 dmap f (DeltaM d) = fmap f d
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150
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151 deltaWithLogFromList :: (Show a) => [a] -> DeltaWithLog a
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152 deltaWithLogFromList xs = DeltaM $ deltaFromList $ fmap returnW xs
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153
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154
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155 -- example : prime filter
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156 -- usage : runWriter $ checkOut 0 $ primeCountM 30 -- run specific version
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157 -- : dmap runWriter $ primeCountM 30 -- run all version
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158
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159 generatorM :: Int -> DeltaWithLog [Int]
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160 generatorM x = let intList = [1..x] in
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161 DeltaM $ deltaFromList $ fmap returnW $ replicate 2 intList
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162
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163 primeFilterM :: [Int] -> DeltaWithLog [Int]
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164 primeFilterM xs = let primeList = filter isPrime xs
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165 refactorList = filter even xs in
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166 DeltaM $ deltaFromList $ fmap returnW [primeList, refactorList]
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167
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168
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169 countM :: [Int] -> DeltaWithLog Int
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170 countM xs = let primeCount = length xs in
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171 DeltaM $ deltaFromList $ fmap returnW $ replicate 2 primeCount
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172
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173 primeCountM :: Int -> DeltaWithLog Int
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174 primeCountM x = generatorM x >>= primeFilterM >>= countM