Re: Sets and Lists, again

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 20 May 2006 16:15:53 GMT
Message-ID: <ZgHbg.10266$A26.253682@ursa-nb00s0.nbnet.nb.ca>

Marshall wrote:

> David Cressey wrote:
>

>>So, at the logical level, why isn't a list just a set of entries with some
>>natural order implied by one of its attributes?

>
> Be careful of the idea of "natural order implied by one of its
> attributes."
> It makes it sound as if there is a distinguished order when there
> isn't. (Sort of like picking one key to be the primary key.) Any order
> you can come up with for a relation is just as "natural" as any
> other order. And the existence of an order on an attribute doesn't
> make a relation a list.
>
> With a list, there *is* a distinguished order, (as well as all the
> other orders possible.)

Other than violating the information principle, what does the distinguished order buy one?

> The definition of list is: a target set (relation for our purposes) and
> a mapping from the natural numbers to the set. More useful in
> a programming context is a finite list, in which the mapping is
> from [0..n]. The map and the relation together form the list.
>
> It is important to be clear about the differences among: set, relation,
> bag, ordered set, ordered bag, list. It's also important to distinguish
> between a total order, a partial order, and a quasi order. (I will
> admit
> that I don't really understand the last of these yet.)
>
>
> Marshall
>
Received on Sat May 20 2006 - 11:15:53 CDT