Re: choice of character for relational division

On Apr 1, 7:40 am, "Cimode" <cim..._at_hotmail.com> wrote:
> On 31 mar, 23:23, "Marshall" <marshall.spi..._at_gmail.com> wrote:
>
> > 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.

I accept the "subjective choice" part. In fact, I see that as inescapable when designing a formal language, whether for mathematical or computational usage. *Design* is exactly the process of making those subjective choices, those "tradeoffs" that Joel Spolsky is always talking about.

And I really believe that some designs are better than others. We have all complained about SQL here; what we are complaining about is not exclusively mathematical problems but also design problems.

It is like writing a sonnet*. One the one hand we have the restrictive, unforgiving, necessary structure. On the other hand within that structure, the poet is free to create any image he wishes. Some sonnets are exquisite (Shakespeare's,) and some are as bad as anything you might find on a bathroom wall (mine.) I compare these to mathematical soundness and the design choices made by the author of the formalism.

Marshall

• Does the sonnet exist as a poetic form in French? I have made some modest attempts at French literature, but admit to being completely ignorant of French poetry or poetic forms.