OCaml functions on uncertain data types

I have a data type,

type data = IntData of int list | FloatData of float list

I want to write a function with signature map : data -> ('a -> 'a) -> data which will apply the given function to each element in the data's list.

The compiler doesn't like the following code, for understandable reasons.

let rec map dat func =  match dat with   | IntData il = IntData (List.map func il)  | FloatData fl = FloatData (List.map func fl)

Of course, the compiler can't make sense of the idea that func could have a different type in each of these cases.

On the other hand, I can't think of how to accomplish this kind of behavior, except to write a separate map function, one for IntData and another for FloatData. But that seems like the kind of wasteful duplication of code that OCaml strives to avoid.