Question

I want to make functions Double -> Double an instance of the Num typeclass.
I want to define the sum of two functions as sum of their images.
So I wrote

instance Num Function where

f + g = (\ x -> (f x) + (g x))

Here the compiler complains he can´t tell whether I´m using Prelude.+ or Module.+
in the lambda expression.
So I imported Prelude qualified as P and wrote

instance Num Function where

f + g = (\ x -> (f x) P.+ (g x))

This compiles just fine, but when I try to add two functions in GHCi
the interpreter complains again he can´t tell whether I´m using Prelude.+ or
Module.+.
Is there any way I can solve this problem?

Answer 1

The compiler is complaining because you’re defining a new function named +, rather than defining an implementation of + for a class instance. Are you forgetting to indent the function definition? You want something like this:

instance Num (Double -> Double) where
    f + g = (\ x -> (f x) + (g x))

Not like this:

instance Num (Double -> Double) where

f + g = (\ x -> (f x) + (g x))

That said, a Num instance for a function type isn’t really going to work properly for various reasons, most significantly that Num instances are required to also be instances of Eq and Show, neither of which can really be defined on functions in a way that makes sense.