Ticket #89: D.hs

{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies,
  UndecidableInstances, FlexibleInstances #-}

module D where

instance (Num a, Num b, TypeCast b a, TypeCast a b) => Num (a,b) where
    (x,y) * (u,v) = (typeCast x * typeCast u -
                     typeCast y * typeCast v, 
                     typeCast x * typeCast v +
                     typeCast y * typeCast u)

test1 = (1,1) * (2,2)    -- (1+i)*(2+2*i) where i^2 = -1

class TypeCast   a b   | a -> b, b->a   where
        typeCast :: a -> b
class TypeCast'  t a b | t a -> b, t b -> a where
        typeCast'  :: t->a->b
class TypeCast'' t a b | t a -> b, t b -> a where
        typeCast'' :: t->a->b

instance TypeCast'  () a b => TypeCast a b where
        typeCast x = typeCast' () x
instance TypeCast'' t a b => TypeCast' t a b where
        typeCast' = typeCast''
instance TypeCast'' () a a where typeCast'' _ x  = x