OCaml repeating entire signature in implementation

Question

Suppose I have a module A, with the following interface and implementation files:

(* a.mli *)
module type A_SIG =
sig
    val f: int -> int
    ...
end

(* a.ml *)
module A : A_SIG =
struct
    let f x = x + 1
    ...
end

Compiling a.mli followed by a.ml fails, with error Unbound module type A_SIG. Duplicating the entire signature in the implementation file fixes it.

Why is this the case? It seems that the following works in SML:

(* a.sig *)
signature A_SIG =
sig
    val f: int -> int
    ...
end

(* a.sml *)
structure A : A_SIG =
struct
   fun f x = x+1
   ...
end

I've seen this similar post, but its answer is unclear to me.

Answer 1

The file a.ml is implicitly wrapped as the module A and the file a.mli is implicitly wrapped as the module type A.

So the following works

(* A.mli *)
val f : int -> int

(* A.ml *)
let f x = x + 1

And you would access f from another module as A.f.

Or if you really want submodules you could write

(* a.mli *)
module type A_SIG =
sig
    val f: int -> int
end

module A : A_SIG

(* a.ml *)
module type A_SIG =
sig
    val f: int -> int
end

module A : A_SIG =
struct
    let f x = x + 1
end

And you would access f from another module as A.A.f and the module A would also contain the signature A_SIG, in addition to the (sub)module A.

Implementations of Standard ML do not normally implicitly wrap the contents of a file as a module.

For completeness, note that OCaml has a feature to "generate" a module type from a module:

(* a.mli *)
module type A_SIG =
sig
    val f: int -> int
end

module A : A_SIG

(* a.ml *)
module A =
struct
    let f x = x + 1
end

module type A_SIG = module type of A