modular.hs

newtype ModularInt s = ModularInt Int

mkModularInt :: forall s . Reifies s Int => Int -> ModularInt s
mkModularInt a = ModularInt (a `mod` modulus)
  where
    modulus = reflect (Proxy :: Proxy s)

instance Reifies s Int => Num (ModularInt s) where
  ModularInt a + ModularInt b = mkModularInt (a + b)
  ModularInt a - ModularInt b = mkModularInt (a - b)
  ModularInt a * ModularInt b = mkModularInt (a * b)
  fromInteger = mkModularInt . fromInteger

withModulus :: Int -> (forall s . Reifies s Int => ModularInt s) -> Int
withModulus modulus modularInt =
  reify modulus (\(_ :: Proxy s0) ->
    case modularInt :: ModularInt s0 of
      ModularInt a -> a)

{-
ghci> withModulus 3 (2 + 3 * 4)
2

ghci> withModulus 5 (2 + 3 * 4)
4

ghci> withModulus 8 (2 + 3 * 4)
6
-}