On Sun, 26 Apr 1998, Florin Mateoc wrote:

> Why not something like:
> 
> Object
>   Collection
>     Bag
>       Array
>       ...
>     Set
>       Class
> 
> so why isn't Class a Set ?

You have to be careful with this sort of reasoning, I believe.  Let me 
give some concrete examples (of my own experience).

I am a mathematician, algebraic geometry, in fact.  I started designing a
few years ago (back then, as a student) a set of objects for computing
with polynomials. 

I started out by trying to design a good interface.

My reasoning was rather formal I believe : I was following the path of
using concepts like "additive semimonoid", "abelian group", "partial
ordering", "division algebra", "integral domain" etc.etc.   to 
characterize my objects and the way the various arithmetical operations 
worked.

However, I feel, after revising many times that interface, that there's
something more subtle going on, for classifying Smalltalk (or in my case: 
Objective-C) Objects, than using classical, algebraic concepts. 

There are rules, but the rules of the software engineering of a set of 
classes, are not necessarily those of e.g. algebra as developed by e.g. a
Noether or a David Hilbert.

For example, I believe the following would NOT be a good inheritance 
chain (but you may disagree) for Integer :

        SemiGroup
	  AdditiveSemiGroup
	    SemiMonoid
                Monoid
                  AdditiveMonoid
                    Group
                      AdditiveGroup (abelian)
                         ...
                          Ring
                            IntegralDomain
                               Integer

(don't panic : I am sure it is not going to happen in Smalltalk!)

Nevertheless you *could* say "Integers" are an additive group and
multiplicativily closed for multiplication, so why is this not expressed 
in the inheritance chain !?

I believe that your question about "why is Class not a subclass of Set" 
!? is similar, after all.

After struggling a few years with classes like 
"Integer-DegreeSparse-Recursive-VariableDense-Polynomial" as a subclass of 
EuclideanDomain and result of some Polynomial constructing functor, I 
just stopped doing it at that way, and I choose an interface centered 
around objects with very *simple* names :

  Polynomial, Term, Monomial, BigInt, Symbol etc.

Of course for the _algebra_ of this sort of thing, you still have to be
able to think in terms of "this is a noetherian ring" or "if I'll
construct polynomials and a quotient ring over that domain, I'll get zero
divisors etc." 

It is just that you can IMHO not carry over those concepts literally to 
an object oriented programming language.  Well, there's quite a few 
languages out there that still do it, so I suspect this posting will be 
controversial!

David.