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>
> 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.
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.
- Jan Hidders