Re: On Formal IS-A definition

On May 10, 7:29 pm, David BL <davi..._at_iinet.net.au> wrote:
> On May 10, 2:06 pm, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
>
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>
>
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> > On May 8, 9:44 pm, David BL <davi..._at_iinet.net.au> wrote:
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> > > On May 9, 2:34 am, Nilone <rea..._at_gmail.com> wrote:
>
> > > > On May 8, 7:11 am, David BL <davi..._at_iinet.net.au> wrote:
>
> > > > > Values are immutable. Variables accessed by imperative programs are
> > > > > usually mutable. Sets are values. If a set contained a variable then
> > > > > it wouldn't be immutable.
>
> > > > We can generalize values and variables to elements of domains, where a
> > > > value is any element of a domain while a variable is an element of a
> > > > domain for which a homomorphism to another domain is defined.
> > > > Assigning to a variable would reduce to modification of the
> > > > homomorphism, so sets containing variables would not be modified by
> > > > assignment to a variable.
>
> > Mathematically there is no "modification" or "mutation" nor
> > any such anthropomorphic passage of time sense. A variable is a
> > symbol. That symbol might have a binding. That binding is also a
> > relation whose key is the variable symbol and in the case of an
> > imperative interpretation if the variable is "mutable" also the
> > "time" or "program counter" or similar is part of the key. For
> > example the variable X might have the following binding relation
>
> > S T V
> > X 0 0
> > X 1 0
> > X 2 5
> > X 3 5
> > ...
>
> > where S is the variable symbol, T is the "time", and V is the
> > bound value. But note that nothing "changes" at T=2 from this meta
> > perspective of math where "time" is just yet-another dimension.
>
> > > Wrong. You can't modify a homomorphism just like you can't modify a
> > > number or a set. Homomorphisms are values and are therefore
> > > immutable. You have invented a homomorphism variable to hold a
> > > homomorphism value. What you claimed were variables were just values
> > > intended to act as inputs to a homomorphism function.
>
> > Except his error is irrelevant. Variables are symbols and are
> > representable by sets. Their bindings (regardless of extent ie
> > dependence on "time") can be represented by relations which are
> > sets just as their interpretations are relations which are sets.
>
> I haven't seen a variable yet. All you have provided are symbol
> values and relation values. I'll agree there's a variable when I see
> one! There needs to be an imperative statement, a quantification in
> a formula, a lambda expression, an integral etc.

I almost don't have time to refute these inane flimflam "objections". But this one is so lame and easy as to nearly answer itself:

   var X = 0 ;
   var Y = 5 ;
   X = Y ;
   Y = 0 ;

which exactly reflects the binding relation above. Do you still not comprehend? { X, Y } is a set of variables. For gods sake just google "set of variables" and see that the world of mathematics is replete with this concept. What are you smoking down there (besides pride)?

(Your other post is so chock full of flimflam hot-air that refuting would take more time than I have right now, due to the Principle of Incoherence.)

KHD Received on Tue May 11 2010 - 05:00:27 CEST