[Caml-list] issue with polymorphism

[Guillaume Hennequin <g.hennequin@eng.cam.ac.uk>]

Dear caml-list,

let id x = x

is polymorphic, and indeed I can apply it to various types:

let _ = print_float (id 1.)
let _ = print_int (id 1)

Now, say you want to write a function that takes a function of the same ['a->'a] 
type as [id] above, and applies it to two different types:

let print_both f =
  print_int (f 1);
  print_float (f 1.0)

That in fact won't compile:

Error: This expression (1.0) has type float but an expression was expected of 
int

Naively trying to enforce polymorphism doesn't work either:

let print_both: 'a. ('a -> 'a) -> unit = fun f ->
  print_int (f 1);
  print_float (f 1.0)

As a matter of fact, neither will this:

let print1: 'a. ('a -> 'a) -> unit = fun f -> print_int (f 1)

Error: This definition has type (int -> int) -> unit
which is less general than 'a. ('a -> 'a) -> unit

What am I missing? How would you go about writing such a function?

Many thanks,
Guillaume