Defining a family of functors
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Date:  20090126 (15:08) 
From:  Michaël_Grünewald <michaelgrunewald@y...> 
Subject:  Defining a family of functors 
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.  Thanks for your suggestions, Michaël