Polymorphic type inside a module (OCaml)

Question

I just define a Matrix module as follows:

module Matrix =
  struct
    type element
    type t = element array array

    let make (nr: int) (nc: int) (init: element) : t =
      let result = Array.make nr (Array.make nc init) in
      for i = 0 to nr - 1 do
        result.(i) <- Array.make nc init
      done;
      result
  end

And let m = Matrix.make 3 4 0 gives me an error Error: This expression has type int but an expression was expected of type Matrix.element. Then I added 'a:

module Matrix =
  struct
    type element = 'a
    type t = element array array

    let make (nr: int) (nc: int) (init: element) : t =
      let result = Array.make nr (Array.make nc init) in
      for i = 0 to nr - 1 do
        result.(i) <- Array.make nc init
      done;
      result
  end

The compilation of the module gives an error Error: Unbound type parameter 'a.

Could anyone tell me how to define the type inside of my module?

Answer 1

Two problems: (1) type variables cannot be named by a binding, like you tried with element, and (2) your type t needs to have all type variables as parameters if it is supposed to be polymorphic. That is, you either want to write

type 'a t = 'a array array

or you have to turn the module into a functor, where you take element as a parameter of the entire module.