Many wrote that the functional programming 'fold' is a good model for
relational aggregate functions. I have a few difficulties with this:
1. fold doesn't offer any type of GROUP BY, which is an essential component
of aggregation.
2. I don't believe fold can handle things like AVG() or STDDEV(). Can it?
Conversely, fold can handle non-commutative and non-associative operators,
which I don't believe can be used for aggregation.
3. fold is defined on sequences, not sets. This doesn't seem to be a
problem until you think about cases where there a duplicates of the
aggregated field. (For instance, there are 10 bags each weighing 5 lbs, and
you want SUM(weight) - you need to project weight onto a collection which
allows for 10 occurences, or define the aggregate function to work on the
whole tuple somehow... I know a man named Krug worked out a formal theory
for this...)
