Martin Rubey wrote:
>
> Waldek Hebisch <[EMAIL PROTECTED]> writes:
>
> > Hmm, I still do not understand how species work but my impression was that:
>
> > 1) species lack much of functionality present in concrete domains
> > 2) species impose serious overhead compared to specialized domains
>
> Sorry, I miscommunicated - as Ralf already pointed out.
>
> The idea is only to use Species as a good "Category" (warning: SPAD meaning)
> framework, because mathematically convincing.
>
> More concretely:
>
> the domain Permutation(S: SetCategory) should stay! But, it should export
> SpeciesCategory S, in particular:
>
> structures: Set S -> Stream %
> ++ structures s returns all permutations of the set s
>
> and something like
>
> structures: (Set S, FiniteGroup S) -> Stream %
> ++ structures(s, g) returns all isomorphismtypes of permutations of the set
> s
> ++ under the action of g
>
> The domain SetOfMIntegersInOneToN should be generalised and renamed into
> Combination(n: NNI, S: SetCategory)
>
> The package PartitionsAndPermutations should go away. It's functionality
> should be moved into the two domains Partition (or possibly SetPartition) and
> Permutation.
>
> Aggregates would also export SpeciesCategory, of course.
>
> I'm not completely sure yet how to provide the domains of the isotypes,
> eg. Partition vs SetPartition. We could either have two domains, or one (in
> this case SetPartition), that is able to "produce" the other. I believe it's
> easier to have two.
>
> So, there is *no* overhead. Only for experimentation one would generate a
> species using Plus, Times, Compose, etc. However, without turning
> Permutation,
> Combination, etc. into Species, experimentation is difficult.
>
> I hope this is clearer now.
>
Yes, that looks like good plan.
--
Waldek Hebisch
[EMAIL PROTECTED]
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