Without the projections, you can do it via a higher-order Functor which 
does a fold, ie lifting to the Functor level what one usually does to 
get an n-ary product out of a binary product.

With the projections, as this involves name-generation, I don't see how 
to do it without using camlp4.  Even my favourite sledgehammer, 
metocaml, can't help here.

Jacques

Michaël Grünewald wrote:
> I am facing a situation that could be solved by ``defining a family of 
> functors'', I describe the problem and would be very glad to get your 
> views about it.
>
> To illustrate the situation, I will suppose A1, ..., An are modules 
> implementing the same signature S, let's say S contains the usual 
> opertations on groups (mathematical groups, you can replace this by 
> vector spaces, or whatever). It is easy to write a Product2 functor
>
> Product2: A1:S -> A2:S -> S2
>
> producing an implementation for the direct product (with signature S) 
> of the groups A1 and A2, plus injections j1 : A1.t -> S2.t and j2: 
> A2.t -> S2.t and corresponding projections (the type t denotes the 
> module thingie, as usual). This extension of S is here written S2.
>
> My problem is ``how do I remove the 2'' ? Would it be possible to 
> define a functor scheme [:)]
>
> Productn: A1:S -> .. -> An:S -> Sn
>
> able to instantiate concrete functors for any value of n ?
>
> It is possible to generate automatically appropriate code for small 
> values of n, but I am looking for a better approach. It is simple to 
> get close of the solution in the object paradigm, since I can simply 
> put objects in an array and iterate over this array (IIRC this is the 
> aggregate design pattern), but I do not see an easy way to define 
> injections and projections.