{-# LANGUAGE  ScopedTypeVariables, EmptyDataDecls #-}
import Data.Function
data Zero 
data Succ a 

class Nat a where
 toInt::a->Int

instance Nat Zero where
 toInt = const 0

instance (Nat a) => Nat (Succ a) where
 toInt = const $ toInt (undefined::a) + 1


type One = Succ Zero
type Two = Succ One
type Three = Succ Two
type Four = Succ Three
type Five = Succ Four

data ModNInt mod = MN {int::Int} deriving ( Eq, Ord)

instance Show (ModNInt mod) where
  show = show . int

instance (Nat mod) => Enum (ModNInt mod) where
  toEnum = MN . (`mod` toInt (undefined::mod))
  fromEnum = int

convop2 p x y = toEnum $ (p `on` fromEnum) x y

instance (Nat mod) => Num (ModNInt mod) where
 (+) = convop2 (+)
 (-) = convop2 (-)
 (*) = convop2 (*)
 fromInteger = toEnum . fromInteger

a = fromInteger 2 :: ModNInt Five
b = fromInteger 3 :: ModNInt Five
c = fromInteger 19 :: ModNInt Five
main = print [a-b, a*b, a+b-c]