Haskell function型

Question

I'm trying to understand Haskell function types right now. Let's say I want to compose two functions f1 and f2 (suppose I don't know their definition). The function signature of f2. f1 is:

f1 . f2 :: (Fractional (a -> a), Num a) => a -> (a -> a) -> a -> a

How do I read this signature and more specifically, how do I know how to apply arguments to this composition?

eg how can I read the type information of f1. f2 to be able to write valid expressions like

(f1 . f2 2) 3 4
(f1 2. f2 2) 4

Answer 1

That signature means you haven't composed them correctly. You don't get a type error , because in theory some madman might give functions a Num instance, but in real life that never happens. So there is no set of arguments you can apply to (f1. f2) that will typecheck.

Instead, back up and look at the types of f1 and f2 . What are they? I predict that they are both two-argument functions, because your type is the one I get when I write

:t (/) . (+)
(/) . (+)
  :: (Fractional (a -> a), Num a) => a -> (a -> a) -> a -> a

You can't really compose a two-argument function, because composition is for one-argument functions. But you can partially apply the functions before composing, if you like, to make them into one-argument functions. And that's exactly what you've done in your last example, which works fine:

Prelude> f1 = (/)
Prelude> f2 = (+)
Prelude> (f1 2 . f2 2) 4
0.3333333333333333