An example of type family

Arith.hs

{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE TypeFamilies #-}

class Add a b where
  type SumTy a b
  add :: a -> b -> SumTy a b

instance Add Integer Double where
  type SumTy Integer Double = Double
  add x y = fromIntegral x + y

instance Add Double Integer where
  type SumTy Double Integer = Double
  add x y = x + fromIntegral y

instance (Num a) => Add a a where
  type SumTy a a = a
  add x y = x + y