OCaml: Currying without defined values

Question

I have two functions f and g and I am trying to return f(g(x)) but I do not know the value of x and I am not really sure how to go about this.

A more concrete example: if I have functions f = x + 1 and g = x * 2 and I am trying to return f(g(x)) I should get a function equal to (x*2) + 1

Answer 1

It looks like you have it right, f(g(x)) should work fine. I'm not sure why you have a return keyword there (it's not a keyword in ocaml). Here is a correct version,

let compose f g x = f (g x)

The type definition for this is,

val compose : ('b -> 'c) -> ('a -> 'b) -> 'a -> 'c = <fun>

Each, 'a,'b,'c are abstract types; we don't care what they are, they just need to be consistent in the definition (so, the domain of g must be in the range of f).

let x_plus_x_plus_1 = compose (fun x -> x + 1) (fun x -> x * 2)