[Edu-sig] re: Terminology question: just operator overriding?

[Arthur]

Kirby Urner wrote:

> At 06:49 PM 6/29/2003 -0400, Arthur wrote:
Kirby writes -
> 
> 
> More concretely, it's considered high level, and part of abstract
> algebra, to be able to generalize from ordinary numbers to these
> generic "types" with their group, ring and field properties.
> 
> The addition and multiplication operators become abstracted, to
> mean whatever operations follow similar patterns (e.g. you need
> identity elements).
> 
> So I hardly think the mathematicians can object that we're dumbing
> down the math curriculum or getting off on a tangent, if we look
> at an extensible type system, such as Python provides, and use
> our ability to override __add__ and __mul__ as we define one type
> after another (permutations, integers modulo N, matrices,
> polynomials, rationals -- the sets of 'math objects' people
> traditionally study in group theory and abstract algebra classes).

Override?  Overload,no?  Or I am just wrong here? Who cares, really.

More to the point:

I am more concerned about the programmers than the mathematicians. 
Aren't there those who feel strongly that object concepts are overplayed 
and dumbing down programming?

I am out of my element, and not particlarly interested, in those kinds 
of discussions.  But expect you will face them.

Here I am satisfied - with you - with the practicalities.  The object 
concept largely is what is in the real world of programming, and is 
probably somewhere at work at the grocery store.  At some level I also 
accept that it represents the survival of the fittest concept.  At this 
stage of the game, at least.

Art