[FOM] Object-Oriented Formal Mathematical Languages

[Dennis E. Hamilton]

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.