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  1. import Prelude hiding (const, id, (.))
  2. import Control.Category
  3.  
  4. data St a b = St (a -> (b, St a b))
  5.  
  6. ap :: St a b -> [a] -> [b]
  7. ap _ [] = []
  8. ap (St f) (a:as) = let (b, nSt) = f a in b : ap nSt as
  9.  
  10. const :: a -> St b a
  11. const x = St $ \_ -> (x, const x)
  12.  
  13. integral :: Num a => St a a
  14. integral = from 0 where
  15.   from n = St $ \x -> st x where
  16.     st x = let s = x + n in (s, from s)
  17.  
  18. instance Category St where
  19.   --  id :: St a a
  20.   id = St $ (\x -> (x, id))
  21.   --  (.) :: St b c -> St a b -> St a c
  22.   (.) (St f) (St g) = St $ \x -> compose x where
  23.     compose x = (x2, f1 . g1) where
  24.       (x1, g1) = g x
  25.       (x2, f1) = f x1
  26.  
  27. main = do
  28.   print $ ap (integral . id) [0,1,2] == ap (id . integral) [0,1,2]
  29.   print $ ap (integral . (const 42 . integral)) [0,1,2] == ap ((integral . const 42) . integral) [0,1,2]
  30.   print $ ap (const 42) [0,1,2]  == [42,42,42]
  31.   print $ ap integral [0,1,2,3] == [0,1,3,6]
  32.  
Success #stdin #stdout 0s 8388607KB
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https://ideone.com/ivPNU3
language:
Haskell (ghc 8.4.4)
created:
8 years ago
visibility:
public

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