Hi Martin,
> (By the way, are you absolutely sure that SetSpecies is necessary?)
Read the documentation. I have tried to explain why I had to introduce
SetSpecies. But maybe it is not "absolut". In particular, SetSpecies
came up when I thought more carefully how to implement Compose.
But there are actually two issues.
1) SetSpecies L as an argument of a species F. For example, in Compose
we have
Rep == Record(
tag: SetPartition L,
left: F SetSpecies L,
right: SetSpecies G L
);
which is pretty near to the actual definition in BLL.
2) SetSpecies now appears in
<<exports: CombinatorialSpecies>>=
structures: SetSpecies L -> Generator %;
@
The reason was that I want to be close to BLL. And there a species is a
functor from the category of sets to the category of sets. If we keep
structures: List L -> Generator %;
then "structures" would have to check whether the input list is, in
fact, a set. I wanted to avoid that checking and thus put the
information into the type.
BUT... I am not so convinced that this is the best possible design. I
think already to change that signature back to List or to Array instead
of SetSpecies, first I have to check the consequences.
I would impose a different meaning than it was before.
So, let me open a discussion on that idea. It is as follows.
Let F be a species and U be a set and then F[U] is the set of
structures. That is perfectly fine in mathematics, but there are some
people who like to do ranking and unranking (and I don't even know
whether it would be interesting to provide different generation
orderings for one species). So in order to get some order on F[U], U has
to be ordered.
In that idea I would like to have
structures: List L -> Generator %
or
structures: Array L -> Generator %
with the meaning that
structures([a,b,c]) is the "same" as structures([1,2,3]) but in each
structure 1 is replaced by a, 2 by b, and 3 by c. With that in the
documentation, it would mean that structures([a,a,a]) is perfectly
defined. It gives as many structures as applied to [1,2,3]. And not the
same as applied to [a].
It basically means, if f is a function from {1,2,...,n} to an arbitrary
set s (where not necessarily #s=n) then structures(l) generates the
elements f(F[{1,2,...,}]) in a predefined order. Here l is the list
[f(1), f(2), ..., f(n)]. I hope, it is clear, that in f(F[{1,2,...,}]) f
is actually applied to the elements of F[{1,2,...,}] in the sense of
applying a bijection \sigma to a structure.
Would someone like that more than what I have written near the
introduction of SetSpecies in trunk?
All the best
Ralf
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