.hs

data Number = forall a . Number (TypeEnum a) a
higherPred :: forall dict . (forall a . TypeEnum a -> dict) -> Number -> Number -> dict
higherPred f (Number e1 _) (Number e2 _) = if ordering e1 >= ordering e2 then f e1 else f e2

data NumDict = forall a . Num a => NumDict (TypeEnum a)
matchNum :: forall a . TypeEnum a -> NumDict
matchNum  Integer  = NumDict Integer
matchNum  Rational = NumDict Rational
matchNum  Real     = NumDict Real
matchNum  Complex  = NumDict Complex
liftNum :: (forall a. Num a => a -> a -> a) -> Number -> Number -> Number
liftNum f a b = case higherPred matchNum a b of
    NumDict d -> Number d $ to d a `f` to d b