Re: More on lists and sets

From: Jan Hidders <hidders_at_gmail.com>
Date: 27 Mar 2006 04:54:25 -0800
Message-ID: <1143464065.895510.300720_at_t31g2000cwb.googlegroups.com>


Marshall Spight wrote:

>

> So I would propose that we need to consider sorting with partial
> orders and sorting with totals orders separately. In the total order
> case, we end up with a list whose element type is the same as
> the element type of the set. In the partial order case, we end up
> with a list-of-sets, where the set has cardinality-1 in the no-ties
> case and cardinality > 1 in the case of ties.

Such a grouping seems more logical to me if you are sorting with a preorder (a partial order except antisymmetry is not required). For a partial order such a grouping is not so easy to define nor is it immedeately clear what it would mean.

> It is interesting that we see list-of-sets emerging directly from the
> nature of ordered data.

Indeed, and let me add to this that there is already in fact some theory on pomsets (partially ordered multisets) as they are a natural generalization of sets, bags, lists and trees. The work is rather technical and not more than a first dip in the pool, but it might give you an idea of how theorists think about these things:

http://citeseer.ist.psu.edu/grumbach95algebra.html

  • Jan Hidders
Received on Mon Mar 27 2006 - 14:54:25 CEST

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