Re: more closed-world chatter

On May 10, 9:32 am, Jon Heggland <jon.heggl..._at_idi.ntnu.no> wrote:
> Marshall wrote:
> > On May 9, 2:21 am, Jon Heggland <jon.heggl..._at_idi.ntnu.no> wrote:
> >> D&D's point is that intersection is a special case of join,
> >> as well as a special case of difference, so the rules
> >> for type inference ought to produce the same result
> >> in all three cases.
>
> > Right; and I disagree. "Special case" does not imply
> > logical equivalence, nor any particular obligation on
> > the codomain of functions.
>
> Seems a shame to lose the set intersection/complement identities, though.

I guess. I'm not too attached to either operator; I think closed relational operators are more interesting than ones that aren't closed.

> > (Under the relational lattice, T WHERE FALSE and
> > T JOIN TABLE_DUM are not merely equivalent,
> > but are actually the same expression. The RL
> > WHERE is JOIN, and the RL FALSE is TABLE_DUM.)
>
> As in TTM's A. But what are the types of the attributes of the result?
> The same as in T, or the bottom type? And what if you use a more complex
> expression than FALSE/TABLE_DUM.

If we are joining X with DUM, then there are necessarily no attributes in common, so we would not expect to perturb the attribute types from X. If X does have some attributes in common, then the question is exactly the sub vs. super question we've been discussing.

> The amount of type inference you will
> be able to do statically will be limited, won't it?

Dunno for sure; I'm still investigating. My intuition though, is that it is possible to produce a system that has proper superset of the capabilities of a more typical type theory.

> > As to A INTERSECT B and A \ (A \ B), I would again
> > draw an arithmetic comparison. On the natural numbers,
> > what the type of a + b? Is it natural, or integer? I would
> > say natural. However, subtraction of naturals is not
> > closed; the result type has to be integer. So
> > a - (0-b) will have the result type integer.
>
> Thanks; I see your point now.

Cool.

> > My feeling is that INTERSECT isn't worthy of
> > much inspection, because it's not a generic
> > relational operator and it can't do anything that
> > we can't already do with generic relational
> > operators. The same goes for specialized
> > MINUS. Generalized MINUS, on the other
> > hand, is worthy of attention.
>
> Is generalized minus the same as semiminus?

As Vadim mentioned, it is more traditionally called antijoin. (And has he has also mentioned, it's an unfortunate name since it's the inverse not of join but of generalized union.)

Marshall Received on Thu May 10 2007 - 22:53:02 CEST