gadt constructor

Hello everybody,

I'm trying to convert a structure data into gadt, and do not know how to 
build them :

Here is a little example :

(* The gadt I want to build *)
type _ data =
   | Num : int -> int data
   | Str : string -> string data

type values = [
     | `Num of int
     | `Other
]

(* Build the gadt *)
let builder : type a. values -> a data = begin function
   | `Num n -> Num n
   | _ -> Str ""
end

But this gives me an error :

Error: This expression has type int data
        but an expression was expected of type a data
        Type int is not compatible with type a

Do you know how I can tell the compiler that the type is polymorphic ?

Thanks a lot