Dear list,

Suppose I define a GADT for expressions:

type _ expr =
| Int : int -> int expr
| Float : float -> float expr

Now I want to write a parser, that will build an ['a expr] from a string.
Without thinking much, I tried the following:

let parse_expr : type s. string -> s expr = fun x ->
  try Int (int_of_string x)
  with _ ->
    Float (float_of_string x)
;;

Which fails with the following error message:

Error: This expression has type int expr but an expression was expected of
type s expr

That makes sense, since [s] is a locally abstract type. I tried a couple of
variants and finally realised that I could not even write the type of
[parse_expr]: it should be [string -> 'a expr] for some ['a], but I'm not
sure that really means something.

So to put it simple, how does one construct a GADT value from a string ?

Cheers,
  ph.