Use abstract module as part of type definition separate from module - ocaml

Question

I'm trying to use the module type Partial_information which is constructed via the functor Make_partial_information as the type of the field contents in the type Cell.t. However, I'm getting the error Unbound module Partial_information.
open Core
(* module which is used as argument to functor *)
module type Partial_type = sig
type t
val merge : old:t -> new_:t -> t
end
(* type of result from functor *)
module type Partial_information = sig
type a
type t = a option
val merge : old:t -> new_:t -> t
val is_nothing : t -> bool
end
(* The functor *)
module Make_partial_information(Wrapping : Partial_type):
(Partial_information with type a = Wrapping.t)
= struct
type a = Wrapping.t
type t = a option
let merge ~(old : t) ~(new_ : t) =
match (old, new_) with
| (None, None) -> None
| (None, Some a) -> Some a
| (Some a, None) -> Some a
| (Some a, Some b) -> (Wrapping.merge ~old:a ~new_:b) |> Some
let is_nothing (it: t) : bool = (is_none it)
end
(* Checking to make sure understanding of functor is correct *)
module Int_partial_type = struct
type t = int
let merge ~old ~new_ = new_ [##warning "-27"]
end
module Int_partial_information = Make_partial_information(Int_partial_type)
(* Trying to use _any_ type which might have been created by the functor as a field in the record *)
module Cell = struct
type id = { name : string ; modifier : int }
type t = {
(* Error is here stating `Unbound module Partial_information` *)
contents : Partial_information.t ;
id : id
}
end

Answer 1

Module types are specifications for modules. They do not define types by themselves. They are also not constructed by functors in any way.
Consequently, it is hard to tell what you are trying to do.
As far I can see, you can simply define your cell type with a functor:
module Cell(P : Partial_information) = struct
type id = { name : string ; modifier : int }
type partial
type t = {
contents : P.t;
id : id
}
end
Or it might be even simpler to make the cell type polymorphic:
type 'a cell = {
contents : 'a;
id : id
}
since the type in itself is not particularly interesting nor really dependent upon
the type of contents.
P.S:
It is possible to use first class modules and GADTs to existentially quantify over a specific implementation of a module type. But it is unclear if it is worthwhile to explode your complexity budget here:
type 'a partial_information = (module Partial_information with type a = 'a)
module Cell = struct
type id = { name : string ; modifier : int }
type t = E: {
contents : 'a ;
partial_information_implementation: 'a partial_information;
id : id
} -> t
end