Re: Character string relation and functional dependencies

From: V.J. Kumar <vjkmail_at_gmail.com>
Date: Tue, 11 Dec 2007 20:29:41 +0100 (CET)
Message-ID: <Xns9A03938917AF7vdghher_at_194.177.96.26>


Tegiri Nenashi <TegiriNenashi_at_gmail.com> wrote in news:f7283774-a81f-417a-9942-ca25012ff6d3_at_i29g2000prf.googlegroups.com:

> On Dec 11, 6:08 am, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
>> The formulas look very cute, no doubt about that, but immediate
>> questions are:
>>
>> how do you propose to index infinite relations ?
>
> First, let's establish the idea that an index for a finite relation
> R(x,y) is a function.

First of all, if you introduce the arbitrary function as an additional primitive, deus ex machina as it were, then in many cases you do not need any of the finitely definable infinite relation apparatus. SQL already has built-in or user-defined functions that make possible evaluating queries over a finite tuple domain with embedded infinitary structures. You need to try and express query evaluation in your model with relations only -- that's the whole point !

>Given x=1 an index function returns all the
> "matching" tuples, or a single tuple if there is a functional
> dependency x->y. For an equality relation x=y this function is
> identity: given x, return x.
>
>> what do you do when you join two infinite relations and the result is
>> also an infinite relation: x < 5 join x > 1 where x ranges over
>> reals ?
>
> Well, let's not get into incountable domains, because there appeared
> no way to apply the ideas of pipelined execution flow there.

I do not know what "pipelined execution flow" is, but the uncountable case is what might actually motivate your research, as in the spacialtemporal  database area. The countable case by itself is not very interesting especially if the user "is expected to see the finite set".

If you admit first-order formulas ("extended tuples") as a legitimate query evaluation result, then your ideas coincide with Kanellakis's ideas wrt constraint databases, a tree that has yet to bear practically usable fruits !

> Also, as
> Marshal noted, it is perfectly allright for an intermediatory query
> evaluation result to be infinite; it is the final result where a user
> is expected to see the finite set.
>
Received on Tue Dec 11 2007 - 20:29:41 CET

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