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Re: Object Class and Data Type

From: D Guntermann <guntermann_at_hotmail.com>
Date: Fri, 2 Apr 2004 22:33:14 GMT
Message-ID: <HvKEnE.4uD@news.boeing.com>


The abstraction class expression (y | p} in the logical sense could also be interpreted as a view or query, both of which operate on and are substitutable over relation types.

"D Guntermann" <guntermann_at_hotmail.com> wrote in message news:HvJ1Fs.FFt_at_news.boeing.com...
> In logic, an abstraction class (A) is defined: A is defined as the
> expression {y | p }, where y is the universal set of sets and p is a
> well-formed formula. All sets are classes, but the opposite is not true.
A
> class might not ever exist as a set or set of sets. A real-world example
of
> a class based on logic would be the collection of ordinal numbers.
>
> This definition would correspond to your assertion in terms of
> generalization, except that equating the object-oriented programming class
> to a logical abstraction class as an extension to sets is only half the
> battle. Where do types fit in to the logical model, as sets?
>
> It's too bad OOP didn't start out with rigorous definitions from the
> beginning.
>
> Interesting stuff. Hopefully I'll learn more.
>
> Regards,
>
> - Dan
> "Tom Hester" <$$tom_at_metadata.com> wrote in message
> news:35e25$406cb235$45033832$6792_at_msgid.meganewsservers.com...
> I apologize. I did not intend to mislead. But, you're right the cutting
> and pasting was misleading.
> "D Guntermann" <guntermann_at_hotmail.com> wrote in message
> news:HvIGCy.IKo_at_news.boeing.com...
> I found this quote on wikipedia.org, in reference to computer science
> related programming classes (versus class definition in logic). Page
> history indicates that there is some doubts as to whether information
> included is irrefutably correct or neutral:
>
> "A class also describes a set of invariants that are preserved by every
> method in the class. An invariant is a constraint on the state of an
object
> that should be satisfied by every object of the class. The main purpose of
> the invariants is to establish what objects belong to the class. An
> invariant is what distinguishes datatypes and classes from each other."
>
> My apologies to Dr. Pierce for attributing a degree speciousness to him
> personally. Quotation attribution was misleading, a correction was not
> forthcoming, and my suspicion that the quote was out of context was indeed
> correct.
>
> - Dan
>
> References: Wikipedia.Org. Available: http://en.wikipedia.org/wiki/Class
>
> "Tom Hester" <$$tom_at_metadata.com> wrote in message
> news:a8b99$406a148a$45033832$30830_at_msgid.meganewsservers.com...
> No they are not the same. Perhaps understanding the difference should be
a
> prerequisite to contributing to a theory group. "[A type system is a]
> tractable syntactic method for proving the absence of certain program
> behaviors by classifying phrases according to the kinds of values they
> compute."
> (Types and Programming Languages, MIT Press, 2002) "A class contains a
> description of data ("state") stored in the objects of the class. A
class
> implements its interfaces by specifying methods that describe what
> operations can be performed on the data stored in the objects of the
class.
> A class also describes a set of invariants that are preserved by every
> method in the class. An invariant is a constraint on the state of an
object
> that should be satisfied by every object of the class. The main purpose of
> the invariants is to establish what objects belong to the class. An
> invariant is what distinguishes datatypes and classes from each other. "
>
> As I said before, the purpose of a type is to highlight differences
> (absences of behavior) whereas a class hierarchy is intended to highlight
> similarities (invariants).
> "D Guntermann" <guntermann_at_hotmail.com> wrote in message
> news:HvEx8L.9tC_at_news.boeing.com...
> >
> > "Tom Hester" <$$tom_at_metadata.com> wrote in message
> > news:d2b19$406990ec$45033832$24651_at_msgid.meganewsservers.com...
> > > Of course you are right. The purpose of class and type are entirely
> > > different. A class hierarchy is intended to relate entities based on
> > common
> > > behavior; however, a set of data types is intended to elaborate the
> > > differences between sets of values.
> >
> > So I guess real numbers, rational numbers, and integers are not part of
> the
> > same class hierarchy since they are data *types* versus your precious
> > classes. What kind of reasoning is this? There are still basic
> properties
> > of numbers shared, whether its called class or type.
> >
> > Isn't the set of engineer objects in some context a subset of person
> > objects? The set of values are different based on semantics and rules,
> but
> > they are drawn from the same generalized set - the same as numbers.
> >
> >
> > So, for example, it is common for a
> > > class hierarchy to have a single root; often called object or entity.
> But
> > > data types rarely if ever inherit from a single basic data type.
> > > Furthermore, class itself is typically defined as an object with
certain
> > > behaviors. On the other hand, one never sees data type, a base type,
> > > defined as a data type!
> >
> > You are getting data type and built-in data type confused. You are also
> > confusing low-level constructs with higher levels of abstraction.
> >
> > - Dan
> > >
> > > "Laconic2" <laconic2_at_comcast.net> wrote in message
> > > news:0fudnaF9l9x-kvXdRVn-uQ_at_comcast.com...
> > > > Over in the OTLT thread, I saw where someone used the name "CLASS"
to
> > > > describe the code_type. It seems to me that many people use "class"
> and
> > > > "type" as though they were synonyms. It seems to me that they are
> not.
> > > >
> > > > Any thoughts?
> > > >
> > > >
> > > >
> > > >
> > >
> > >
> >
> >
>
>
Received on Fri Apr 02 2004 - 16:33:14 CST

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