Re: Extending my question. Was: The relational model and relational algebra - why did SQL become the industry standard?

From: Paul Vernon <paul.vernon_at_ukk.ibmm.comm>
Date: Tue, 25 Feb 2003 13:11:50 -0000
Message-ID: <b3fqck$u4o$2@sp15at20.hursley.ibm.com>

"Bob Badour" <bbadour_at_golden.net> wrote in message news:mnF6a.332$QR3.51347581_at_mantis.golden.net...
> "Paul Vernon" <paul.vernon_at_ukk.ibmm.comm> wrote in message
> news:b3dr5r$sss$1_at_sp15at20.hursley.ibm.com...
> > "Bob Badour" <bbadour_at_golden.net> wrote in message
> > news:zst6a.297$9O1.43758648_at_mantis.golden.net...
> > > > Let me put it this way. If a type has 2 possiable representations,
> then
> > > > A) the number of values represented by PosRep1 must equal the
> number
> > > > of values represented by PosRep2
> > > > B) each value represented by PosRep1 must 'map' to exactly one
> value
> > > > represented bt PosRep2, and versa.
> > >
> > > While desirable whenever possible and while certainly possible in an
> ideal
> > > machine, I do not require this of physical implementations.
> >
> > Yes and that is my worry. I'm not comfortable with such a fudge. If the
> > logical model cannot be implemented correctly then is there not something
> > wrong with the model?

>

> First, I would disagree that the implementation is incorrect. Second, I
> would observe that a logical data model is an ideal abstraction. Third, I
> would observe that any flaw lies in the physical implementation and not the
> logical data model.

That does seem to be the received wisdom. I don't take people's word for it however.

1. An implementation is incorrect if it does not faithfully reproduce all aspects of the model. To me it is obvious that an implementation that breaks say my A) and B) criteria is strictly incorrect.
2. I disagree with the conceit that a 'logical data model is an ideal abstraction' with all the implications that the 'real world' has forever unknowable complexities . Ask a physicist. Do they consider their theories as abstractions of the world, or rather, as I see it, the theories are how the world *actually* works.
3. But if, even in principle, no possible physical implementation could implement the logical model correctly, then quite simply the logical model is (to some extent) broken.

The received wisdom seems to suggest that it is OK to assume an infinite and continuous universe. Rubbish! Any logical model that needs to assume that is never going to be a true model of the world.

> Fourth and finally, I must ask: What other logical data
> model do you propose that addresses the specific issue of cartesian and
> polar coordinates and possible rounding in the internal physical
> representation?

Well, lets have a go shall we.

In the case of polar and catesian points, something like the following type hierarchy suggests itself to me

               POINT_Real
           /             \
         /                 \
Point_Int32_Polar    Point_Int32_Cart
         \                 /
           \             /

    Point_Int32_Polar_isect_Int32_Cart

Here POINT is an abstract type with both poss reps both using the abstact type REAL
for the components of the pos reps.

Point_Int32_Polar is the set of POINTS representable using signed 32 bit integers in the r & thera polar poss rep components. This type has only one poss rep.

Point_Int32_Cart is the set of POINTS representable using signed 32 bit integers in the r & thera cartiesian poss rep components. This type has only one poss rep.

Then Point_Int32_Polar_isect_Int32_Cart is the intersection of Point_Int32_Polar and Point_Int32_Cart. This would include all *exactly equal* points in the two representations.

    e.g. (a:0, b:0) = (r:0, theta:0), (a:1,b:0) = (r:1, theta:0) etc etc. This type has two poss reps.

Regards
Paul Vernon
Business Intelligence, IBM Global Services Received on Tue Feb 25 2003 - 07:11:50 CST