Re: Sets and Lists, again

"dawn" <dawnwolthuis_at_gmail.com> wrote in message news:1148166734.465140.31870_at_i39g2000cwa.googlegroups.com...
> Bob Badour wrote:
> > David Cressey wrote:
> >
> > > "dawn" <dawnwolthuis_at_gmail.com> wrote in message
> > > news:1148097777.431200.106670_at_j55g2000cwa.googlegroups.com...
> > >
> > >>David Cressey wrote:
> > >>
> > >>>Recently, in a thread on implementing both threads and lists in a
> > >>>programming language, the example of lists or sets of Presidents
arose.
> <snip>

> > What if we want to use ordered operations like the above to determine
> > the median age at first election? How does the list help us if it is
> > ordered by year of first election? If we re-order the list by age, how
> > do we put it back to the original order?

If we re-order the list by age it is a different list. The same thing happens when we rename the attributes of a relation. married( Man, Woman) ------> deirram(Woman, Man) by the rename Man <----> Woman.
The two relations are two very different relations. The same thing with lists.
A perfect lists DBMS will only allow content addressing. For example for retrieving the list [1,2,3] from the database, the only way available must be to ask the DBMS if it's true that [1,2,3] in Db.

> The list order is but one possible ordering. You can represent the
> list as a set ordered by age instead without affecting the logical
> list. The list is logically equivalent to adding an ordinal attribute
> in a relation. Working with that relation ordered by something other
> than what could be implemented in the RM as an ordinal attribute can be
> done without losing the list order. --dawn

If we have a set V and an operation , with the following: x,x=x
x,y=y,x
((x,y),z)=(x,(y,z))
define a normal form for the 1,2,1,2,3,1,3,2,1,1,2,3

When Date&Darwen follower say a list IS just a set with a total order you should be aware that IS has an exact meaning in Tutorial D. Received on Mon May 22 2006 - 11:07:02 CEST