Re: grouping in tuple relational calculus

Mikito Harakiri wrote:
> "Paul" <paul_at_test.com> wrote in message
> news:4213e7b7$0$53482$ed2619ec_at_ptn-nntp-reader03.plus.net...
> > Mikito Harakiri wrote:
> > > Speaking of aggregates, I always wondered why some aggregates are
> > > expressable by standard means (min, max can be expressed as
antijoins),
> > > while the others aren't (sum).
> >
> > I guess that min and max only require an ordering, which is a more
> > fundamental concept than addition, which is required for sum.
>
> That's right, on one hand, aggregate min and max are based upon
lattice join
> and meet binary operators, similar to sum based upon binary addition.
This
> makes all of them to fit into aggregate framework. On the other hand,
> lattice implies order, and with order one can leverage antijoin.

Not quite. In a lattice that is not a total order, we can have both max(a,b)!=a and max(a,b)!=b. Therefore, no antijoin can help producing those new values. Thus, it is essential for the order to be total. Why? Received on Thu Feb 17 2005 - 02:59:04 CET