> In your case you got it wrong when you quantified 'a in the object p.

> # let p = object method map =  fun f -> List.map f [1;2;3] end;;
> val p : < map : (int -> 'a) -> 'a list > = <obj>

Perhaps I oversimplified my example.
Indeed I want to make p a function like

let p1 l = object 
  method map : 'a.(int -> 'a) -> 'a list =  fun f -> List.map f l
end;;

let o1 = p1 [1;2;3];;
- val o1 : < map : 'a. (int -> 'a) -> 'a list > = <obj>

Then I need type annotations

let p2 l = object 
  method map =  fun f -> List.map f l
end;;
let o2 = p2 [1;2;3];;
- val o2 : < map : (int -> '_a) -> '_a list > = <obj>


With best,
keiko