Re: header part of the value?
Date: Fri, 29 Feb 2008 01:23:32 -0800 (PST)
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.
> > > Certainly in practice this is the sort of thing that would
> > > be almost universally a good idea. But what theoretical
> > > basis does it have?
> > Static typing goes out the window.
> Yes, certainly; that bears mentioning. That doesn't change the
> algebra at all, though, does it?
The standard relational algebra is essentially statically typed and it's formal definition is based on that. If you drop that, you will have to give new definitions that take into account that the headers might not be what you expect. I would not call that "doesn't change at all".
- Jan Hidders