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  1. {-# LANGUAGE  ScopedTypeVariables, EmptyDataDecls #-}
  2. import Data.Function
  3. data Zero 
  4. data Succ a 
  5.  
  6. class Nat a where
  7.  toInt::a->Int
  8.  
  9. instance Nat Zero where
  10.  toInt = const 0
  11.  
  12. instance (Nat a) => Nat (Succ a) where
  13.  toInt = const $ toInt (undefined::a) + 1
  14.  
  15.  
  16. type One = Succ Zero
  17. type Two = Succ One
  18. type Three = Succ Two
  19. type Four = Succ Three
  20. type Five = Succ Four
  21.  
  22. data ModNInt mod = MN {int::Int} deriving ( Eq, Ord)
  23.  
  24. instance Show (ModNInt mod) where
  25.   show = show . int
  26.  
  27. instance (Nat mod) => Enum (ModNInt mod) where
  28.   toEnum = MN . (`mod` toInt (undefined::mod))
  29.   fromEnum = int
  30.  
  31. convop2 p x y = toEnum $ (p `on` fromEnum) x y
  32.  
  33. instance (Nat mod) => Num (ModNInt mod) where
  34.  (+) = convop2 (+)
  35.  (-) = convop2 (-)
  36.  (*) = convop2 (*)
  37.  fromInteger = toEnum . fromInteger
  38.  
  39. a = fromInteger 2 :: ModNInt Five
  40. b = fromInteger 3 :: ModNInt Five
  41. c = fromInteger 19 :: ModNInt Five
  42. main = print [a-b, a*b, a+b-c]
Success #stdin #stdout 0s 5700KB
comments (?)
stdin 
Standard input is empty
stdout 
[4,1,1]
https://ideone.com/O243Zk
language:
Haskell (ghc 8.4.4)
created:
11 years ago
visibility:
public

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