Ralf Hemmecke <[EMAIL PROTECTED]> writes: > > Yes. In Categorial Language, I have functors from the category of multisets > > with bijections to the category of sets with bijections, I > > guess. > > Maybe. > > > Unfortunately, BLL use "multiensemble" (in french, what do they use in > > english?) for something different, namely, a k-tuple of sets. A > > k-multisorted > > species is a functor from the category of k-tuples of sets and bijections to > > the category of sets with bijections... > > Ha, it seems you stepped over the same problem as me. ;-) For some time I was > wondering, why they call something like "k-tuple of sets" a "k-multiset". I > could not see equal elements. After a while I realized that if you have a > BLL-multiset U1+U2+...+Uk and factor out any permutations of the components, > you basically make all elements of U1 equal (same for U2,...,Uk). And that is > a > multiset as we are used to it.
YES! Good remark. > >> In fact, I would not throw away your code, because basically you > >> implemented the ground algorithm which must be adapted to > >> multisort. (Whatever we decide what "multisort" should look like in AC.) > > I didn't intend to throw away my code. I think it's quite ok. And in fact, > > very likely we will need - to generate isomorphismtypes of compositions of > > multisorted species - functors from the category of k-tuples of multisets > > to the category of sets... > > Rather, a multisort species M is a functor M: B^k -> B. (k-tuples of "sets", > not "multisets") Yes, but: to generate isomorphismtypes of unisort species I need to be able to produce structures with labels from a (usual) multiset. It is highly unlikely that this is not necessary for multisort species. Thus, we really need functors MultiSet^k -> B (It is "highly unlikely", since for k=1 we have the current situation. However, it may well be the case that I overlooked something and composition can be done without considering multisets. On the other hand, this generalisation looks quite interesting to me!) > How does M: B^k -> B look like to you? I don't understand this question. Martin ------------------------------------------------------------------------- Take Surveys. Earn Cash. Influence the Future of IT Join SourceForge.net's Techsay panel and you'll get the chance to share your opinions on IT & business topics through brief surveys-and earn cash http://www.techsay.com/default.php?page=join.php&p=sourceforge&CID=DEVDEV _______________________________________________ Aldor-combinat-devel mailing list Aldor-combinat-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/aldor-combinat-devel
