"Bob Badour" <·······@golden.net> wrote in message
··························@radon.golden.net...
>
> >However, is it necessary to have all three constructs (relations, tuples
and
> >domains) that the relational model provides? For example, the Lisp model
> >provides two (atoms and lists) and the Smalltalk object model gets by
with
> >one (objects).
>
> Relations are mathematical constructs. One can think of them as points in
an
> N-dimensional space. One can think of them as sets of propositions. One
can
> think of them simply as sets.
>
> As a result, one can use first order predicate logic to improve the
> understanding of the data model, to query databases, to transform queries
> into useful logical equivalents etc. One can apply set theory to all of
the
> same uses.
>
> How is the Lisp model of atoms and lists equivalent to or derived from any
> branch of mathematics?
I am not a Lisp expert, but I will go out on a limb and say that the Lisp
model, like any logical or mathematical model, has primitive constructs and
formal rules from which statements of truth or valid expressions can be
derived. I have added comp.lang.lisp to the distribution in case there is
some interest from those folks in answering your question.
Why do we need to have a formal model from any particular branch of
mathematics to be applied in the (decidedly formal) domain of computation?
> SmallTalk does not get by with one logical construct. It has object
classes,
> object variables, references (ie. pointers) etc. While I do not know the
> details of the language, I am sure it also has at least one repeating
group
> type such as array or collection. Does it have extents?
Smalltalk classes are objects, collections are also objects. That Smalltalk
is able to get by without having any special types for "repeating groups" is
due to some cleverness in the virtual machine that hides any such
distinction. I suppose you could think of it as a way of providing logical
independence in a general-purpose programming language.
By extent do you mean the set of all instances of a class? If so, it does
not, but user-defined classes can keep track of their instances if they need
to (classes are instances of their metaclasses and therefore can have
user-defined behavior).
Here is a postscript paper on the Smalltalk object model (with reference to
the Lisp model):
http://www.emn.fr/dept_info/perso/rivard/pub/reflection/reflex96.ps (493K)
Note that this paper is more oriented toward language design than it is
toward "modeling reality". The diagram on p.4 will help to explain the
metaclass concept, but it doesn't speak to the issues on the collection
classes that you are likely to be concerned about.
> Stealing heavily from Chris Date (and Hugh Darwen) again: Think of domains
> (object classes) as the things we want to talk about and think of
relations
> as what we want to say about them. I think it is reasonable to want to
make
> statements regarding multiple things at once; hence, the tuple. I think it
> is reasonable to want to make the same statement about different
> combinations of things; hence, the relation.
This sounds fine, except I am not sure why a distinction is made between
domains and tuples. It also seems reasonable to want to aggregate things at
multiple levels and make statements on that basis. Why limit yourself to two
levels? Just to make the math easier?
--
Regards,
Steve (steve at wart dot ca ICQ 50919689)
>> How is the Lisp model of atoms and lists equivalent to or derived from
any
>> branch of mathematics?
>
>I am not a Lisp expert, but I will go out on a limb and say that the Lisp
>model, like any logical or mathematical model, has primitive constructs and
>formal rules from which statements of truth or valid expressions can be
>derived. I have added comp.lang.lisp to the distribution in case there is
>some interest from those folks in answering your question.
>
>Why do we need to have a formal model from any particular branch of
>mathematics to be applied in the (decidedly formal) domain of computation?
We don't. We only need to have a useful formal model. Dr. Codd successfully
applied a couple different branches of mathematics to the problem of
database management. Over the last thirty years, they have certainly proved
their worth.
What other formalisms has anyone applied to the problem of database
management? How have they proved their worth?
>> Stealing heavily from Chris Date (and Hugh Darwen) again: Think of
domains
>> (object classes) as the things we want to talk about and think of
>relations
>> as what we want to say about them. I think it is reasonable to want to
>make
>> statements regarding multiple things at once; hence, the tuple. I think
it
>> is reasonable to want to make the same statement about different
>> combinations of things; hence, the relation.
>
>This sounds fine, except I am not sure why a distinction is made between
>domains and tuples.
Because they are fundamentally different things. One is a statement of fact
and the other is a data type. Why do we make a distinction between nouns and
sentences?
>It also seems reasonable to want to aggregate things at
>multiple levels and make statements on that basis. Why limit yourself to
two
>levels?
I haven't limited myself to two levels. Domains can have arbitrary
complexity including relation valued attributes. I can derive further
statements of fact by combining multiple statements thereby extending a
statements to additional aggregates.