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annotate similar.hs @ 19:003b6e58d815

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Define Similar as Monad by mu
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Mon, 22 Sep 2014 23:26:51 +0900
parents c77397d0677f
children d4aa70d94352
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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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3
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4 data Similar a = Single [String] a | Similar [String] a [String] a deriving (Show)
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279ebcf670c4 Define Similar as Applicative
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5
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6 value :: (Similar a) -> Similar a
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7 value (Similar xs x _ _) = Single xs x
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8 value s = s
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9
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10 instance (Eq a) => Eq (Similar a) where
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11 s == ss = (value s) == (value ss)
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12
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13 instance Functor Similar where
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14 fmap f (Single xs x) = Single xs (f x)
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15 fmap f (Similar xs x ys y) = Similar xs (f x) ys (f y)
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16
19
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17 mu :: Similar (Similar a) -> Similar a
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18 mu (Single ls (Single lx x)) = Single (ls ++ lx) x
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19 mu (Single ls (Similar lx x ly y)) = Similar (ls ++ lx) x (ls ++ ly) y
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20 mu (Similar lx (Single llx x) ly (Single lly y)) = Similar (lx ++ llx) x (ly ++ lly) y
003b6e58d815 Define Similar as Monad by mu
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21 mu (Similar lx (Similar llx x _ _) ly (Similar _ _ lly y)) = Similar (lx ++ llx) x (lx ++ lly) y
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22 mu _ = error "Invalid Similar"
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23
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24 instance Monad Similar where
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25 return = Single []
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26 s >>= f = mu $ fmap f s
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27
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28
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29 {-
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30
10
7c7efee7891f Define Monad style Similer
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32
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33 -- samples
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34 {-
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35
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36 generator :: Int -> Similar [Int]
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37 generator x = return [1..x]
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38
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39 primeFilter :: [Int] -> Similar [Int]
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40 primeFilter xs = return $ filter isPrime xs
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41
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42 count :: [Int] -> Similar Int
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43 count xs = return $ length xs
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44
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45 primeCount :: Int -> Int
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46 primeCount x = value $ generator x >>= primeFilter >>= count
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47 -}
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48
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49
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50 {-
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51 same :: (Eq a) => Similar a -> a
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52 same (Single x) = x
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53 same (Similar x s) = if x == (same s) then x else (error "same")
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7c7efee7891f Define Monad style Similer
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54
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55
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56 similar :: Similar a -> Similar a -> Similar a
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57 similar (Single x) ss = Similar x ss
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58 similar (Similar x s) ss = Similar x (similar s ss)
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59
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60 instance Functor Similar where
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61 fmap f (Single a) = Single (f a)
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62 fmap f (Similar a s) = Similar (f a) (fmap f s)
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63
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64 instance Applicative Similar where
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65 pure = Single
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66 (Single f) <*> s = fmap f s
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67 (Similar f s) <*> ss = similar (fmap f ss) (s <*> ss)
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68
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69 mu :: (Similar (Similar a)) -> Similar a
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70 mu (Single s) = s
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71 mu (Similar s ss) = similar s (mu ss)
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72
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73
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74
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75 -- samples
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76
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77 double :: Int -> Similar Int
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78 double x = Single (2 * x)
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79
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80 twicePlus :: Int -> Similar Int
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81 twicePlus x = Similar (x + x) (double x)
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82
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83 plusTwo :: Int -> Similar Int
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84 plusTwo x = Similar (x + 2) (double x)
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85
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86 -- samples
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87
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88 {-
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89 - Similar as Functor
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90 *Main> fmap (double ) (Single 1)
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91 Single (Single 2)
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92 *Main> fmap (twicePlus) (Single 1)
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93 Single (Similar 2 (Single 2))
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94 *Main> fmap (plusTwo) (Single 1)
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95 Single (Similar 3 (Single 2))
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96 *Main> fmap (fmap double) (fmap (plusTwo ) (Single 1))
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97 Single (Similar (Single 6) (Single (Single 4)))
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98 *Main> same $ fmap same $ fmap (fmap double) (fmap (plusTwo ) (Single 1))
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99 *** Exception: same
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100 *Main> same $ fmap same $ fmap (fmap double) (fmap (plusTwo ) (Single 2))
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101 Single 8
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102
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103 - Similar as Applicative Functor
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104 *Main> Single (\x -> x * x) <*> Single 100
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105 Single 10000
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106 *Main> Similar (\x -> x * x) (Single (\x -> x * 3)) <*> Single 100
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107 Similar 10000 (Single 300)
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108 *Main> Similar (\x -> x * x) (Single (\x -> x * 3)) <*> (Similar 100 (Single 200))
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109 Similar 10000 (Similar 40000 (Similar 300 (Single 600)))
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110
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111 - Similar as Monad
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112 *Main> return 100 >>= double >>= twicePlus
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113 Similar 400 (Single 400)
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114 *Main> return 100 >>= double >>= twicePlus >>= plusTwo
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115 Similar 402 (Similar 800 (Similar 402 (Single 800)))
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116
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117 *Main> same $ return 100 >>= double >>= twicePlus >>= plusTwo
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118 *** Exception: same
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119 *Main> same $ return 100 >>= double >>= twicePlus
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120 400
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121
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122 *Main> same $ return 100 >>= double >>= twicePlus
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123 400
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124 *Main> same $ return 100 >>= double >>= twicePlus >>= plusTwo
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125 *** Exception: same
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126 *Main> value $ return 100 >>= double >>= twicePlus >>= plusTwo
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127 800
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128
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Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents: 9
diff changeset
129 -}
18
c77397d0677f Try define Similar as Monad
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents: 17
diff changeset
130 -}
c77397d0677f Try define Similar as Monad
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
parents: 17
diff changeset
131 -}