Re: choice of character for relational division

On 31 mar, 23:23, "Marshall" <marshall.spi..._at_gmail.com> wrote:
> On Mar 31, 9:55 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>
>
>
> > Bob Badour wrote:
> > > Marshall wrote:
>
> > >> Let us consider the choice of characters to use for
> > >> relational operators. It might be desirable to use
> > >> different characters for the relational operators from
> > >> the scalar ones, so we avoid using * for join, even
> > >> though it is in some sense a product operator.
>
> > >> Set subtraction already has a standard character
> > >> in common usage: \
>
> > >> But we also need a character for relational division.
> > >> The / character is often used, but that's the same
> > >> as numerical division. Bummer.
>
> > >> So, if you had to choose an ascii character for
> > >> relational division, which one would you use
> > >> and why?
>
> > > Does a unique relational "division" exist? If "product" has a completely
> > > different name "join", why should a "divide" use the same name?
>
> > > If we have an equality operation for relations, does a "divide"
> > > operation give us all that much?
>
> > Hmmmm... and division isn't really the inverse of join. It is the
> > inverse of cross product which is a special case of join. Is the divide
> > operation you contemplate the inverse of cross product or a more general
> > operation which is the inverse of join?
>
> More general. It encompasses the relation-relation operator that
> gets us "suppliers that supply all parts" as well as aggregation.
> Aggregate functions are a mapping from a collection type
> to a result type. Thus, integer sum() is a mapping from a
> bag of integers to an int. (It's the only application that seems
> to require bags that I've run into. I don't much like bags.)
> The operation of applying aggregate functions is the same
> operator as dividing two relations. Not that I would expect
> syntax to especially reflect that, since the mathematically
> cleanest way of thinking about it is for once not the most
> convenient way of doing it. I'd expect to have a group-by
> that behaved in a more convenient way, but that was
> defined in terms of relational division.
>
> So ... what character would you use? :-)
I do not think this is a simple as a matter of preference. I am afraid the equation of *group by* is inherently bound to Codd's choice of table/attribute formalism for relation structuralization. Such choice inherently breaks the possibility of directly equating mathematical operators and computing operators without the risk of making a subjective choice. In other words, I would like to emit the hypothesis that there is here a case of conflict between computing formalism and mathematical formalism for relation operation.

> Marshall
Received on Sun Apr 01 2007 - 16:40:12 CEST