# Re: Aggregation (with GBY) is Relational Division

Date: Mon, 05 Jun 2006 12:07:09 GMT

Message-ID: <N7Vgg.17749$A26.412644_at_ursa-nb00s0.nbnet.nb.ca>

> vadimtro_at_gmail.com wrote:

[snip]

> Actually, I had kind of a jolt reading something Bob Badour

*> wrote recently about defining aggregates as either a fold
**> or an expression written in terms of folds. (He did not use
**> the term "fold".) Thus, avg(x) can be defined as simply
**> sum(x) / count(). And sum(x) can be defined as simply
**> fold(x,+,0).
**>
**> I like that much better. For one thing, it makes it much
**> easier to eliminate duplicate folds in a complex group-by.
**> (It's hard to explain why, so I won't bother. It's not clear
**> if this post will interest anyone anyway, the OP excepted. :-)
*

I am surprised that my comment would jolt you. I wonder how you would define standard deviation without reference to variance, for instance, or variance without reference to sums of squares etc. I cannot imagine anyone forsaking the normal definition of average to replace it with something that has to multiply by (i-1) before every i-th term and then divide by i after adding the term.

(I am not even sure how I would express that mathematically without using recursion.)

>>From a programming language standpoint, it raises the

*> question of handling the aggregate expressions. But*

> that's not any theoretical difficulty, and not necessarily

*> all that much design difficulty.*

I wonder what you would call arbitrary expressions defined in terms of aggregates if you did not call them aggregates. Received on Mon Jun 05 2006 - 14:07:09 CEST