instance Num b => Num (a -> b) where

  f + g = \x -> f x + g x

  f * g = \x -> f x * g x

  f - g = \x -> f x - g x

  negate f = \x -> negate (f x)

  abs f = \x -> abs (f x)

  signum f = \x -> signum (f x)

  fromInteger i = \x -> fromInteger (f x)