Re: Questions on possreps

On May 29, 8:01 pm, Eric <e..._at_deptj.eu> wrote:
> On 2011-05-27, David BL <davi..._at_iinet.net.au> wrote:> On May 27, 6:55 am, Eric <e..._at_deptj.eu> wrote:
> >> On 2011-05-26, David BL <davi..._at_iinet.net.au> wrote:
>
> >> > On page 116 of An Introduction to Database Systems (8th edition) Chris
> >> > Date provides the following example:
>
> >> > TYPE POINT
> >> > POSSREP CARTESIAN { X RATIONAL, Y RATIONAL }
> >> > POSSREP POLAR { R RATIONAL, THETA RATIONAL };
>
> >> > A footnote on that page states "Tutorial D uses the more accurate
> >> > RATIONAL over the more familiar REAL".
>
> >> > I find this quite confusing, hence the following questions:
>
> Questions, answers, and subsequent responses snipped, everything is too
> interconnected for point by point answers to be sensible now.
>
> 1. Even though the real/rational thing seems to have been your main point,
> I want to ignore it for the moment. I believe that Date used "RATIONAL"
> to be consistent with somewhere else, then felt it would be questioned,
> so he added the footnote. So can we say that the declared POSSREPS
> for POINT contain numbers of a suitable type and leave the choice of
> type as a separate argument.
>
> 2. The logical model contains some types and operators sufficient for
> what we actually want to do with our model.
>
> 3. The "suitable number type" is not part of this logical model,
> because nothing is defined in terms of it, it is only used in some
> possible representations.

I don't know what you mean by "nothing is defined in terms of it". I would say the types, their possreps and various operators are all defined in terms of the "suitable number type".

> 4. A POINT is a scalar because it is not defined in terms of any other
> type in the model.

That doesn't make sense. POINT is defined in terms of two declared POSSREPS that are in turn defined in terms of the declared types for their components.

> 5. The model is abstract because we could change the names of all the
> types and it would still be a logically consistent system.
>
> 6. A POSSREP is equally abstract. All it does is specify a set of values
> of certain types such that distinct sets of values correspond to
> a unique value of the type having the POSSREP, and vice-versa. The
> types used in the POSSREP need not be either defined or used in the
> logical model.

If the types used for components of the POSSREPs are undefined, then the set of values of the type which is defined in terms of those POSSREPs is undefined as well.

> 7. There are two mappings of the logical model. The first is to objects
> and actions in the real world. The names of types and operators in
> the model are part of this mapping, as are the names and details of
> any POSSREPS.
>
> 8. The second is to the top layer of the implementation of the system
> which we use to "run" the model. Beyond this mapping is the only
> place physical representations come into it.

There are too many undefined terms in the above for me to comment.

> In spite of what you say I suspect that you are sometimes crossing the
> boundary between logical and physical. I also think you are causing
> complications by wanting "abstract" to mean "completely mathematically
> abstract".

I cannot comment on that unless you are more specific. Received on Mon May 30 2011 - 05:01:48 CEST