Re: header part of the value?
Date: Sun, 2 Mar 2008 12:08:23 -0800 (PST)
On 29 feb, 15:49, Marshall <marshall.spi..._at_gmail.com> wrote:
> On Feb 29, 1:23 am, Jan Hidders <hidd..._at_gmail.com> wrote:
> > On 29 feb, 08:02, Marshall <marshall.spi..._at_gmail.com> wrote:
> > > On Feb 27, 11:56 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
> > > > On 24 feb, 19:48, Marshall <marshall.spi..._at_gmail.com> wrote:
> > > > > Occasionally the question has come up as to whether a
> > > > > relation value is the body, or the body+the header. In the past
> > > > > I've sided with the just-the-body approach, but today I decided
> > > > > that I don't think that anymore.
> > > > > Consider the algorithm to perform a natural join on two
> > > > > relation values. Just values: not tables in a database
> > > > > with a known schema or whatever. Just two plain relation
> > > > > values. The natural join specification *requires* the header;
> > > > > it is defined (in part) in terms of the header. So the header
> > > > > must be part of the value.
> > > > That is not correct. The natural join can be defined without referring
> > > > to the header.
> > > I am skeptical, however my intuition is that we might not be
> > > speaking the same language here.
> > > Natural join is defined to be an equijoin on pairs of attributes
> > > in each operand with the same name, yes?
> > Depends on your definition of equijoin. The natural join leaves only
> > one of the homonymous columns, equijoins do not under all definitions
> > do that.
> > > So how do you
> > > know which attributes have the same name without access
> > > to the header? How do you even know that there *are*
> > > attributes, without the header?
> > Since we are working in the named perspective, they are included in
> > the tuples. I'm frankly a bit surprised that I have to point this out
> > to you. See the standard definitions in the Alice book.
> This point was addressed earlier in the thread. My perspective
> is that if you are going to say you can produce the header
> by examining the tuples, and the tuples are part of the
> relation, then if you have the tuples you have the header:
I'm not sure how you mean this exactly. If the relation is empty, i.e, there are no tuples, then you cannot derive the header from that empty set. That's why for the relational lattice, where you really need the header to define the semantics, you cannot get around defining relations formally as consisting of both a separate header and a body that contains a set of tuples.
- Jan Hidders