[FOM] Object-Oriented Formal Mathematical Languages

[Steven Ericsson Zenith]

Object orientation is a development of structure theory - it meets certain needs of high order organization in complex, ad hoc, systems.  

It is rarely defined with the rigor necessary to allow full reduction (a rigorous OOP system should reduce to primitive structures existent in the system), a freedom from side effects, or distribution.

However, I see no particular reason why a class heirarchy cannot be defined with the transformative properties and primitives necessary to provide formal rigor.

With respect,
Steven


"Lengyel, Florian" <FLengyel at gc.cuny.edu> wrote ..
> The class hierarchy of object oriented programming seems inadequate for
> mathematics.
> 
> A nice comparison between of the use, for mathematical purposes, of
> dependent types in the language Aldor, versus class hierarchies of standard
> object oriented programming languages, appears on pages 27-29 in the talk
> "Aldor: the language and recent directions (Watt, Sophia-Antipolis, 2000)",
> available online at the URL 
> http://www.aldor.org/docs/reports/sa2000/aldortalk-sa2000.pdf.
> 
> 
> FL                 
> 
> -----Original Message-----
> From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf
> Of
> steven at pearavenue.com
> Sent: Wednesday, May 05, 2004 2:51 AM
> To: dennis.hamilton at acm.org; FOM at cs.nyu.edu
> Subject: RE: [FOM] Object-Oriented Formal Mathematical Languages
> 
> 
> In support of Tony Hoare - I worked with his group at Oxford while defining
> one of the languages based on his formalism CSP - that language was the
> Occam programming language that deals with communication and concurrency
> -
> and we were very focused on the formal verification of computer programs.
> 
> It is only a matter of economics that lets software companies get away
> with
> the liberal informality of modern programming languages.  If the penalty
> for
> shipping faultly code was equal to the penalty in the semiconductor business
> (which can amount to million of dollars) then you would see software houses
> demanding formal practice, verification, demonstration of certain properties
> (such as deadlock feeedom) and proof that a program met its specification.
> 
> As it is th cost of poor practice is simply passed to the consumer.
> 
> That computer programmers are not mathematicians is matter only of economic
> tolerance and engineering pragmatics.
> 
> With respect,
> Steven
> 
> "Dennis E. Hamilton" <dennis.hamilton at acm.org> wrote ..
> > Victor Makarov, in
> > <http://www.cs.nyu.edu/pipermail/fom/2004-May/008154.html>,
> > states, quoting Sir Tony Hoare:
> > 
> > 	"Programming is a mathematical activity. Like other branches of
> > 	 applied mathematics and engineering,its successful practice
> > 	 requires determined and meticulous application of traditional
> > 	 methods of mathematical understanding, calculation and proofs".
> > 
> > 	But what is mathematcal activity? It is creating new theories and
> > 	writing definitions and proofs in these theories.
> > 
> > Based on my extensive experience of practical programming since 1958,
> I
> > assert that this is an unfortunate over-generalization.  I see enormous
> > quantities of successful practice that shows little evidence of what
> I
> > would
> > call mathematical activity.  And I do not doubt the value of a
> mathematical
> > perspective in creation of software.
> > 
> > I am keenly interested in the connection between software and mathematics
> > (and logic and language).  I accept that it is off-purpose for FOM and
> > welcome off-list suggestions of more-appropriate forums/communities where
> > the connections might be explored.
> > 
> >  - Dennis
> >  - - - - - - - - -
> > "I don't even know how to formulate the concept that a METAFONT program
> > draws a beautiful letter A, so I couldn't possibly prove the correctness
> > of
> > such a program.  But still, somehow, the theory that I've learned while
> > doing computer science gives me more confidence in the programs that
> I
> > have
> > written."  Donald E. Knuth, Things a Computer Scientist Rarely Talks
> About,
> > pp.17-18.
> > 
> > 
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