{-# LANGUAGE DataKinds, TypeApplications#-}

import GHC.TypeLits (KnownNat, natVal)
import Data.Proxy (Proxy (..))

newtype Mod n = Mod Integer
  deriving (Eq, Ord)

instance (KnownNat n) => Num (Mod n) where
  fromInteger i = Mod $ i `mod` natVal (Proxy @n)
  (Mod a) + (Mod b) = Mod $ (a + b) `mod` natVal (Proxy @n)
  (Mod a) * (Mod b) = Mod $ (a * b) `mod`  natVal (Proxy @n)
  (Mod a) - (Mod b) = Mod $ (a - b) `mod` natVal (Proxy @n)
  abs = id
  signum = id

instance (KnownNat n) => Show (Mod n) where
  show (Mod i) = show i <> " (mod " <> show (natVal $ Proxy @n) <> ")"