module Modulus where

import TypeVal

default (Integer)

data Mod s a = Mod {value::a} deriving (Eq, Show)

data Modulus a = forall s. TypeVal a s => Modulus (a -> Mod s a) (Mod s a -> a)

mkModulus :: (ValToType a, Integral a) => a -> Modulus a
mkModulus x = case valToType x of {Wrapper y ->
	      case y of {(_ :: t) ->
	      Modulus normalize (value :: Mod t a -> a)}}

normalize :: (TypeVal a s, Integral a) => a -> Mod s a
normalize x :: (Mod s a) = Mod (x `mod` typeToVal (undefined::s))

inModulus :: Modulus a -> (forall s . TypeVal a s =>  Mod s a -> Mod s a)
	        -> a -> a
inModulus (Modulus in_ out) f x = out (f (in_ x))

instance (TypeVal a s, Integral a) => Num (Mod s a) where
    Mod x + Mod y = normalize (x + y)
    Mod x - Mod y = normalize (x - y)
    negate (Mod x) = normalize (negate x)
    Mod x * Mod y = normalize (x * y)
    fromInteger a = normalize (fromInteger a)