Re: [Caml-list] Coinductive semantics

[Andrej Bauer <Andrej.Bauer@andrej.com>]

skaller wrote:
> And of course, separate development of these things is fairly
> silly, since as the 'co' indicates the two ideas are formally
> dual.

This is claim is completely false. The theory of final coalgebras is NOT
just a dual of the theory of initial algebras.

While it is true that final coalgebras and inital algebras are dual
concepts, it is far from truth that we may translate results about one
to results about others by applying simple duality. This would only be
the case if we studied algebras and coalgebras in self-dual categories,
which usually we do not (only very special kinds of categories are
self-dual).

For example, the famous Birkhoff theorem about universal algebras says
something about initial algebras. It took a Ph.D. (by Jesse Hughes) to
figure out what the dual of Birkhoff's theorem might be. And believe me
this was not because either Jesse or his advisor failed to "apply a
simple duality principle".

Andrej