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annotate similar.hs @ 17:279ebcf670c4

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Define Similar as Applicative
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Tue, 09 Sep 2014 16:21:22 +0900
parents 4b315cf0edb9
children c77397d0677f
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279ebcf670c4 Define Similar as Applicative
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1 import Control.Applicative
279ebcf670c4 Define Similar as Applicative
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116131b196bb Define fmap and mu
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3 data Similar a = Single a | Similar a (Similar a) deriving (Show)
116131b196bb Define fmap and mu
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4
116131b196bb Define fmap and mu
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5 instance (Eq a) => Eq (Similar a) where
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6 s == ss = (same s) == (same ss)
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7c7efee7891f Define Monad style Similer
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88d6897c391a Redefine Similar. reject function in data
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8 same :: (Eq a) => Similar a -> a
88d6897c391a Redefine Similar. reject function in data
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9 same (Single x) = x
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10 same (Similar x s) = if x == (same s) then x else (error "same")
10
7c7efee7891f Define Monad style Similer
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11
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c599d2236d19 Similar as Monad
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12 value :: Similar a -> a
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13 value (Single x) = x
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14 value (Similar x s) = value s
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15
16
4b315cf0edb9 Improve mu definition
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16 similar :: Similar a -> Similar a -> Similar a
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17 similar (Single x) ss = Similar x ss
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18 similar (Similar x s) ss = Similar x (similar s ss)
10
7c7efee7891f Define Monad style Similer
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19
13
88d6897c391a Redefine Similar. reject function in data
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20 instance Functor Similar where
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21 fmap f (Single a) = Single (f a)
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22 fmap f (Similar a s) = Similar (f a) (fmap f s)
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23
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279ebcf670c4 Define Similar as Applicative
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24 instance Applicative Similar where
279ebcf670c4 Define Similar as Applicative
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25 pure = Single
279ebcf670c4 Define Similar as Applicative
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26 (Single f) <*> s = fmap f s
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27 (Similar f s) <*> ss = similar (fmap f ss) (s <*> ss)
279ebcf670c4 Define Similar as Applicative
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28
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29 mu :: (Similar (Similar a)) -> Similar a
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30 mu (Single s) = s
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31 mu (Similar s ss) = similar s (mu ss)
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7c7efee7891f Define Monad style Similer
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32
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116131b196bb Define fmap and mu
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33 instance Monad Similar where
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34 return = Single
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35 (Single x) >>= f = f x
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36 (Similar x s) >>= f = mu $ Similar (f x) (fmap f s)
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e8a5df54480e Define sample for Monad style
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37
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7a82a5e50499 Initial commit. define to Functor for Similer
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38
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39 -- samples
3
3c5fbce357af Define >>= for Similer
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40
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116131b196bb Define fmap and mu
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41 double :: Int -> Similar Int
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42 double x = Single (2 * x)
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66609010d477 Define Similer example as Functor
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43
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44 twicePlus :: Int -> Similar Int
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45 twicePlus x = Similar (x + x) (double x)
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66609010d477 Define Similer example as Functor
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46
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47 plusTwo :: Int -> Similar Int
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48 plusTwo x = Similar (x + 2) (double x)
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66609010d477 Define Similer example as Functor
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49
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e8a5df54480e Define sample for Monad style
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50 -- samples
6
5e367a167382 Define samples
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51
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52 {-
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c599d2236d19 Similar as Monad
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53 - Similar as Functor
c599d2236d19 Similar as Monad
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54 *Main> fmap (double ) (Single 1)
c599d2236d19 Similar as Monad
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55 Single (Single 2)
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56 *Main> fmap (twicePlus) (Single 1)
c599d2236d19 Similar as Monad
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57 Single (Similar 2 (Single 2))
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58 *Main> fmap (plusTwo) (Single 1)
c599d2236d19 Similar as Monad
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59 Single (Similar 3 (Single 2))
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60 *Main> fmap (fmap double) (fmap (plusTwo ) (Single 1))
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61 Single (Similar (Single 6) (Single (Single 4)))
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62 *Main> same $ fmap same $ fmap (fmap double) (fmap (plusTwo ) (Single 1))
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63 *** Exception: same
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64 *Main> same $ fmap same $ fmap (fmap double) (fmap (plusTwo ) (Single 2))
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65 Single 8
6
5e367a167382 Define samples
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66
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279ebcf670c4 Define Similar as Applicative
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67 - Similar as Applicative Functor
279ebcf670c4 Define Similar as Applicative
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68 *Main> Single (\x -> x * x) <*> Single 100
279ebcf670c4 Define Similar as Applicative
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69 Single 10000
279ebcf670c4 Define Similar as Applicative
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70 *Main> Similar (\x -> x * x) (Single (\x -> x * 3)) <*> Single 100
279ebcf670c4 Define Similar as Applicative
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71 Similar 10000 (Single 300)
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72 *Main> Similar (\x -> x * x) (Single (\x -> x * 3)) <*> (Similar 100 (Single 200))
279ebcf670c4 Define Similar as Applicative
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73 Similar 10000 (Similar 40000 (Similar 300 (Single 600)))
279ebcf670c4 Define Similar as Applicative
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74
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c599d2236d19 Similar as Monad
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75 - Similar as Monad
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76 *Main> return 100 >>= double >>= twicePlus
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77 Similar 400 (Single 400)
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78 *Main> return 100 >>= double >>= twicePlus >>= plusTwo
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79 Similar 402 (Similar 800 (Similar 402 (Single 800)))
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e8a5df54480e Define sample for Monad style
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80
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81 *Main> same $ return 100 >>= double >>= twicePlus >>= plusTwo
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82 *** Exception: same
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83 *Main> same $ return 100 >>= double >>= twicePlus
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84 400
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85
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86 *Main> same $ return 100 >>= double >>= twicePlus
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87 400
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88 *Main> same $ return 100 >>= double >>= twicePlus >>= plusTwo
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89 *** Exception: same
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90 *Main> value $ return 100 >>= double >>= twicePlus >>= plusTwo
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91 800
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92
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7c7efee7891f Define Monad style Similer
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93 -}
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158ae705cd16 Rename Similer -> Similar
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94