Re: "Aggregate" operators

Erwin wrote:
> Looking for a *formal* definition of the term "aggregate" operator.
>
> The term is quite familiar and the one in common use to denote SQL operators such as MIN, MAX,
> AVG that occur exclusively in connection with some GROUP BY.
>
> However, "occur exclusively in connection with SQL GROUP BY" is rather non-mathematical as a
> formal definition and so, is anyone around here aware of something more rigorous as a
> *definition* of when some operator is or is not an "aggregate" operator ?

Formally "GROUP BY a, b,..." is a partition of the table, where "table" is informal for "set of tuples".
https://en.wikipedia.org/wiki/Partition_of_a_set So the intermediate result of a GROUP BY-query is a set of those subtables of the table where the specified attributes have same values. The operators in the SELECT clause hence operate on whole non-empty columns of which MAX, MIN, etc. give the corresponding value. The attributes specified in the GROUP BY clause have equal values for each sub-table in the partition and hence are well-defined. Therefore they can be used without "aggregate".

Where did you read "occur exclusively in connection with SQL GROUP BY"? You can use aggregate operators without GROUP-BY. This can then be considered as if they acted on the trivial partition {T} of the table T. (Formally, this could have been defined as the result of a GROUP BY-clause with an empty attribute list). Received on Tue Apr 25 2017 - 11:04:23 CEST