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Re: Idempotence and "Replication Insensitivity" are equivalent ?

From: Chris Smith <cdsmith_at_twu.net>
Date: Sat, 23 Sep 2006 12:16:43 -0600
Message-ID: <MPG.1f7f27f2687453ae989733@news.altopia.net>


vc <boston103_at_hotmail.com> wrote:
> What is the standard formulation of aggregate functions ? Where can one
> find such formulations (private attempts do not qualify) ?

I was mainly working from memory in this thread. Jan's first post in this thread referred to a few considerations of the question in journal's, and it appears that the structural recursion formulation in the first article is mainly equivalent to the definitions given here, except that there may be a few technical details, they give a sufficient criteria for well-definedness in terms that I have heard but don't understand (something about initial algebras), and they then go on to expand their formulation to give it additional operations that allow computation of other transformations on relations. I've only skimmed the paper, though, and I lack the understanding of category theory to confidently tell you what it says.

> Do you have a reference for the non-acceptance of the median function ?

I am having trouble sorting through all the requests for median in SQLbased  DBMS systems; Google doesn't seem to turn up much from the database theory side in the first two or three pages.

> What about standard deviation ?

As has been mentioned, it is possible to compute standard deviation from the sums of the values and their squares, respectively; so it's fairly simple to define as an aggregate.

> What is a "reasonable implementation of any aggregate function" and
> assuming there is such, what has the implementation got to do with the
> abstract notion of aggregate function ?

The difference in implementation is a consequence of the abstract notions.

-- 
Chris Smith
Received on Sat Sep 23 2006 - 13:16:43 CDT

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