Tansel Ersavas wrote:
> 
> Florin Mateoc wrote:
> >
> > At 08:54 PM 24/04/98 -0700, Alan wrote:
> [... Alan's good stuff deleted]
> > Alan,
> >
> > Thank you for your reply. I would say though that math looks to me like it
> > is still ticking, even if it is much more formal than in its early days.
> > And I think that the efforts towards formalization have helped its
> > progress. Metamathematics or, more general, thinking about the thought
> > process, are still very useful tools, even if not universal panaceas (sigh...)
> 
> Florin,
> 
> Alan is known to be 20 to 50 years ahead of his time. I know where his
> heart is but by his own words in last years OOPSLA opening speech we are
> not "there" where we reach anywhere near the complexity of biological
> systems yet. Still computer programs are the most complex systems human
> beings have ever created so far.
> 
> I agree with Alan that the current mathematics hasn't got sufficient
> tools that can make sense of object oriented systems. The reason for
> this is an average object oriented system in terms of its combinatorial
> complexity makes up a non-linear system far beyond the reach of current
> mathematical techniques.
> 
> Mathematics as is today does not have the techniques that can be applied
> to an arbitrary non-trivial non-linear system. When mathematicians face
> a complex non-linear system they either try to go into messy
> linearization techniques to convert the darn thing into something that
> they can apply their techniques to, or all together call it a yucky
> system and avoid it; and I am afraid most non-trivial OO systems are in
> this second category.
> 
> I suspect what you're looking for is something in the lines of
> relational database theory so that by means of something or some
> mechanism similar to "normal forms" so that one can apply the magic of
> formulas to prove a design's correctness; in fact OO was long criticized
> (yawn) that it didn't have something similar to that.
> 
> If this is an assignment, then you can fake it by finding some attempts
> to address the issue such as [1] and [2]. You can also look at FOOD
> (formal OO development) FOOM (formal OO methodology) or even very
> appropriately named FOOL (Yes, you guessed it, formal OO language:). If
> you are genuinely looking for an answer then I recommend that you look
> far beyond the existing mathematical techniques, because you won't find
> the answers there.
> 
> [1] Formal Object-Oriented Development,Springer-Verlag, Formal
> Approaches to Computing and Information Technology Series Editor:
> Professor S.A.Schuman
> [2] Formal Object-Oriented Development of Software Systems using LOTOS
> , Paul Gibson
> 
 
Another reference is 
"Theoretical Aspects of Object Oriented Programming"
MIT-Press

Markus


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