Num instance functions: Num a => Num (a -> a)

NumFunction.hs

{-# LANGUAGE FlexibleInstances #-}
module NumFunction where

instance Num a => Num (a -> a) where
 (f + g) x = f x + g x
 (f * g) x = f x * g x
 abs f = abs . f
 signum f = signum . f
 fromInteger x = const (fromInteger x)
 negate f = negate . f

instance Fractional a => Fractional (a -> a) where
  (f / g) x = f x / g x
  fromRational x = const (fromRational x)

-- Example
f x = x * x
g x = x + 2

h = f + g
u = f / g

test1 = h 0 == 2
test2 = h 1 == 4
test3 = u 0 == 0
test4 = u 1 == 1/3

testAll = and [test1, test2, test2, test4]