Re: A Logical Model for Lists as Relations
Date: 12 May 2006 10:44:18 -0700
Message-ID: <1147455858.197917.262490_at_d71g2000cwd.googlegroups.com>
Marshall Spight wrote:
> JOG wrote:
> > Marshall Spight wrote:
> > >
> > > But a list can be described as a relation. Most simply, an infinite
> > > list is a relation from the natural numbers to the target set,
> > > and a finite list is a relation from some finite contiguous subset
> > > [0..n] of the naturals to the target set. Generalizing, we could
> > > describe an n-ary list as a relation with an index attribute and
> > > zero or more other attributes.
> >
> > Do you not find this unsatisfying though?
>
> Actually, I find it quite satisfying, since it means I can, for
> example,
> use the full power of the relational algebra for selection on lists.
>
>
> > By doing this one is altering
> > information that is ordinal in nature to being cardinal.
>
> I don't understand this statement. Can you expand?
"The order of the primeministers were Blair, major, thatcher" = "Blair was prime minister after Major." "Major was prime minister after Thatcher."
Hence A satisfying relation (to me ;) representing this list is: { (Blair, Major), (Major, Thatcher) }
This ordinal representation does not need to include cardinal indeces, and to my eyes that's a good thing as where did they exist in the original propositions?
>
>
> > Given one is
> > modelling assertions, these indexes come from the aether - they seem
> > rather implementational in nature, a physical workaround to the issue
> > of ordering.
>
> I don't see it that way. I don't see anything implementational to these
> equalities:
>
> "abc" = ['a', 'b', 'c'] = { (0,'a'), (1, 'b'), (2, 'c') }
>
> Rather, they simply provide me a way to work with lists in a
> set-theoretic way, rather than in the recursive, or worse, the customary iterative
> way. It also means I don't have to introduce a new container type to handle
> ordered data, which maintains closure and keeps the number of generic
> containers small (= 1).
>
>
> Marshall
Received on Fri May 12 2006 - 19:44:18 CEST