What is Aggregation? Re: grouping in tuple relational calculus

"Jan Hidders" <jan.hidders_at_REMOVETHIS.pandora.be> wrote in message news:wT8Rd.14220$hD4.1177660_at_phobos.telenet-ops.be...
> But, of course, the premisse that aggregation is based upon lattices is
> false because in essence they are operations over bags and so the
> idempotency laws don't always apply.

Well, lattices appeared in this thread as long as the order has been mentioned. For sum the defining operation is addition. Addition is clearly not a (semi)laittice operation since it violates idempotent law. Addition is not associated with any order (e.g. vectors).

So, what is the defining property of an aggregate? Is it

1. Extended projection, perhaps, with projection into the empty set of columns:

select sum(sal)
from emp
group by {}.

2. Incremental cumulative of some associative binary operation:

((3 + 2) + 5) + ...

(Ignoring the obvious exceptions like avg since they are redundant).

3. Something else?

Next, is sum the only aggregate that can't be expressed by standard means? If it is, then don't you think that justification for an aggregation syntax is too thin? Received on Fri Feb 18 2005 - 00:15:05 CET