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Home -> Community -> Usenet -> comp.databases.theory -> Re: Idempotence and "Replication Insensitivity" are equivalent ?
paul c wrote:
> David Cressey wrote:
>
>> "paul c" <toledobythesea_at_oohay.ac> wrote in message >> news:od0Rg.12923$1T2.10076_at_pd7urf2no... >> >>> David Cressey wrote: >>> >>>> "Chris Smith" <cdsmith_at_twu.net> wrote in message
>> It's probably me. I'm trying to use the term "domain" the way some of >> the >> mathematicians seem to be using it. >> >> Here's what I think I got by making inferences from other posts: the >> domain >> of a relation is the cartesian product of the domains of each of its >> attributes. >> >> I probably misinterpreted something I read in here. That'll teach me to >> learn things in c.d.t.!
For the relation, F(x,y) = { x in R, x > 0, y in R | y = log x }, R (as in a real number) corresponds to the type, but the domain of x is positive reals only.
If one has specialization by constraint, one could argue that positive real is a subtype of real, though.
Thus, it is arguable either way whether domain is identical to type.
> If you just mean project in some mathematical sense that is apart from
> the RM, then I suppose the domain formed that way could still have the
> same name as the relation (at least that would be convenient).
Project in the RM is the mathematical sense. It is limited, however, to what for now I will call 'orthogonal project'. Arguably, one could project onto a subspace that is neither orthogonal nor parallel to any of the dimensions of the relation. However, one could argue that such a project is an orthogonal project following some other transformation including rotation.
> But I'm also thinking that when you say 'project a relation onto its
> attributes', if such a thing were permitted by some RM impl'n, what
> *could* actually happen is that a relation with a single relation-valued
> attribute would be formed and I suppose that attribute's 'type' would be
> the name of the relation. But join is usually the operator we expect to
> be able to undo a projection, so if an impl'n did this, then I suppose
> it might want to undo the rva-creating projection, and that might entail
> that it also have a way of equating a relation with several attributes
> against a single-attribute rva equivalent.
Such as the relational equality operation?
> In this admittedly oddball view of things, I wonder if the name of an
> rva really matters? That's as far as I've got.
What's oddball about it? Received on Mon Sep 25 2006 - 07:36:28 CDT