Scope of constructors of a module in OCaml

Question

I have defined the following interface and module:

module type TYPE =
  sig
    type t
  end

module Type = (struct
  type t =
    | TBot
    | T of int
    | TTop
end: TYPE)

Now I realize that If I write outside Type.T 5, the compiler will give me en error Error: Unbound constructor Type.T. If I remove the signature and keep the module, the error will disappear.

1) So my first question is, how to change the signature such that I can use the constructors outside?

2) One way is to define a constructor explicitly as follows, do you think it is a conventional way? One disadvantage I can see now is it does not allow to construct TBot or TTop.

module type TYPE =
  sig
    type t
    val make : int -> t
  end

module Type = (struct
  ...
  let make (i: int) : t =
      T i
end: TYPE)

3) Is it always necessary to let outside be able to construct a value inside a module?

Answer 1

1) You have to export the type declaration, otherwise, t is considered as abstract and then you need to define and export constructors (see 2)):

module type TYPE = sig
  type t =
    | TBot
    | T of int
    | TTop
end

module Type : TYPE = struct
  type t =
    | TBot
    | T of int
    | TTop
end

2) Yes, it is a perfectly fine way. To define top and bottom, you just have to define (and export) new constructors:

module type TYPE = sig
  ...
  val top: t
  val bot: t
end

module Type = struct
  ...
  let bot = TBot
  let top = TTop
end

3) I don't get your question