Il y a un petit resume en francais a la fin.
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skaller wrote:

>         My opinion is quite different: object orientation
> cannot possibly work. It is completely unsupported by any
> coherent theory and can be so easily discredited by a single
> example that it is clear adherents were simply ignorant
> of basic theory. [no binary operator can be correctly
> represented; more generally, no n-ary relation for n>1]
>
> > Okay, so the obvious symptom of the disease is that 'a appears
> > covariantly in get_center, and contravariantly in set_center.  But
> > what's the root cause of these symptoms?
>
>         Simple. The covariance problem is a direct consequence of
> the incorrect assumption that a class can represent an abstraction.
> We know from category theory that a CATEGORY and NOT a class
> represents an abstraction, and an instance of the abstraction
> must be a functor.

I think there's some people trying to give final coalgebra semantics to
objects, certainly to "states". I have only began to understand the issue (I
look at it from the perspective of labelled transition systems), but the
landscape looks beautiful (if daunting!). Have a look at J.J.M.J. Rutten's
page

 http://www.cwi.nl/~janr/

or specifically for objects B. Jacobs:

 http://www.cwi.nl/~bjacobs/

I think you'll find this interesting:

B. Jacobs, Objects and classes, co-algebraically. In: B. Freitag, C.B.
Jones, C. Lengauer, and H.-J. Schek (eds)  Object-Orientation with
Parallelism and Persistence Kluwer Acad. Publ., 1996, p. 83--103.

Regards,

        Francisco Valverde
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Resume en (affreux) francais:

Il semble qu'on peut assigner une semantique de coalgebre finale aux objects
et ses classes. V. les URL cites en haut.