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annotate similar.hs @ 34:b7c4e6276bcf

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Proof Monad-law-2-1
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Sat, 18 Oct 2014 14:13:00 +0900
parents b4d3960af901
children
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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 data Similar a = Similar [String] a [String] a deriving (Show)
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6 value :: (Similar a) -> a
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7 value (Similar _ x _ _) = x
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9 similar :: (Similar a) -> a
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10 similar (Similar _ _ _ y) = y
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116131b196bb Define fmap and mu
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116131b196bb Define fmap and mu
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12 instance (Eq a) => Eq (Similar a) where
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13 s == ss = (value s) == (value ss)
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15 instance Functor Similar where
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16 fmap f (Similar xs x ys y) = Similar xs (f x) ys (f y)
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18 instance Applicative Similar where
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19 pure f = Similar [] f [] f
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20 (Similar lf f lg g) <*> (Similar lx x ly y) = Similar (lf ++ lx) (f x) (lg ++ ly) (g y)
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22 mu :: Similar (Similar a) -> Similar a
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23 mu (Similar lx (Similar llx x _ _) ly (Similar _ _ lly y)) = Similar (lx ++ llx) x (ly ++ lly) y
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25 instance Monad Similar where
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26 return x = Similar [] x [] x
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27 s >>= f = mu $ fmap f s
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30 returnS :: (Show s) => s -> Similar s
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31 returnS x = Similar [(show x)] x [(show x)] x
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33 returnSS :: (Show s) => s -> s -> Similar s
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34 returnSS x y = Similar [(show x)] x [(show y)] y
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36 -- samples
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38 generator :: Int -> Similar [Int]
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39 generator x = let intList = [1..x] in
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40 returnS intList
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5e367a167382 Define samples
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42 primeFilter :: [Int] -> Similar [Int]
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43 primeFilter xs = let primeList = filter isPrime xs
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44 refactorList = filter even xs in
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45 returnSS primeList refactorList
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e8a5df54480e Define sample for Monad style
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47 count :: [Int] -> Similar Int
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48 count xs = let primeCount = length xs in
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49 returnS primeCount
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c599d2236d19 Similar as Monad
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51 primeCount :: Int -> Similar Int
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52 primeCount x = generator x >>= primeFilter >>= count