Re: [Caml-list] Locally abstract parameterized types?

[Kenichi Asai <asai@is.ocha.ac.jp>]

Thank you, Gabriel.

> No, this is currently not supported. For this use-case you will have to use
> modules, typically a functor (in some circumstances a first-class module
> parameter may work as well, if the return type does not depend on the
> parameter).

Let me ask a possibly related question.  I want to define types
similar to the following:

type 'v pair_t = {pair : 'a. 'a * ('a -> 'v t)}
and 'v t =
  A of 'v pair_t
| V of 'v

but where the type 'a of the pair field should be existential, rather
than universal.  Since the above definition is universal, I get an
error for the following definition:

let test : bool t = A {pair = (3, fun x -> V true)}

Error: This field value has type int * (int -> bool t)
       which is less general than 'a. 'a * ('a -> 'v t)

To implement an existential type, we need to use modules.  Let me try.
If 'v pair_t does not depend on 'v t, for example, if the second
element of the pair has type 'a -> 'v (rather than 'a -> 'v t), I
could write as follows:

module type Pair1_t = sig
  type a
  type v
  val pair : a * (a -> v)   (* not a -> v t *)
end

type 'v t1 =
  A of (module Pair1_t with type v = 'v)
| V of 'v

Now I can define (3, fun x -> true) as follows:

let test1 : bool t1 =
  let module Pair1 = struct
    type a = int
    type v = bool
    let pair = (3, fun x -> true)
  end in
  A (module Pair1)

On the other hand, if pair_t did not have a type parameter, for
example, if the parameter is fixed to bool, I could write as follows:

module type Pair2_t = sig
  type a
  type t
  val pair : a * (a -> t)   (* not a -> v t *)
end

type t2 =
  A of (module Pair2_t with type t = t2)
| V of bool

Now I can define (3, fun x -> V true) as follows:

let test2 : t2 =
  let module Pair2 = struct
    type a = int
    type t = t2
    let pair = (3, fun x -> V true)
  end in
  A (module Pair2)

My question is if we can combine these two to achieve my original
goal.  I first write:

module type Pair3_t = sig
  type a
  type v
  type 'a t
  val pair : a * (a -> v t)
end

and tried to define:

type 'v t3 =
  A of (module Pair3_t with type v = 'v and type 'a t = 'a t3)
| V of 'v

but I got the following error:

Error: invalid package type: parametrized types are not supported

If mutual recursion between Pair3_t and t3 is allowed, that would also
be OK.  But if I try to connect the two definitons with "and", I get a
syntax error.

You mention a functor, which is suggestive.  I tried to use a
functor, but so far without success.  Can I define my types using a
functor?

Thank you in advance.  Sincerely,

-- 
Kenichi Asai