I don't follow. Doesn't

  module MakeBetter (K : sig include Map.OrderedType val show : t ->
string end) =
  struct
    include Map.Make(K)
    let show show_val m = List.show (Pair.show K.show show_val) (bindings m)
  end

suit your need?

The extensibility problem I see is that you cannot use the map's
internal representation because it is an abstract type -- which
prevents from efficiently implementing certain operations -- but this
is unrelated to being a functor.

On Thu, Aug 27, 2015 at 3:29 PM, Yotam Barnoy <yotambarnoy@gmail.com> wrote:
> One problem I've commonly encountered in OCaml is the inability to expand
> the interface of functors after they've been created (I'm not talking about
> post-application). For example, Map.Make in the stdlib takes an OrderedType
> module which contains only the compare function. What happens if I want to
> add something to this interface, such as a show function? I have to copy the
> whole implementation of Map.Make into my own file to modify it. Compare this
> to the ability to 'include' a regular module and just add the new
> functionality, and to take the type of a module and expand that type as
> needed. Functors are severely lacking in this regard.
>
> What do people think of this idea -- of allowing functors to be expanded?
> Ideally, expanding a functor would allow for both replacing its argument
> type (as in the example I gave) and for adding a second/third functor
> argument type (so Map.Make(OrderedType) would become
> Map.Make(OrderedType)(Show).
>
> -Yotam