Dear Axiom and Aldor users/developers; Here is an example of something that I would really like to work on in Axiom and/or Aldor:
"Hopf Algebra = Group + Monad" http://sigfpe.blogspot.com/2008/08/hopf-algebra-group-monad.html by 'sigfpe' on the blog: "A Neighborhood of Infinity". This work is done using the programming language Haskell which although it does have a strong formal definition is not nearly as "categorical" as Axiom about the way it expressions mathematics. I hope that someday that people interested in this subject will be able to use Axiom and Aldor this way. In general I believe that computer algebra systems have not yet begun to catch up with recent developments in formal mathematics and in particular the ideas aboout co-algebra. The subject of co-algebra (and co-data) however has been a hot topic in programming language design and leads naturally semantics based on co-induction appropriate to "infinite" objects such as streams and generators. This leads back to the subject of exact real numbers and even p-adic numbers in computer algebra. For example it seems clear that support for concepts like "stream calculus" Elements of stream calculus (an extensive exercise in coinduction) by J. J.M.M. Rutten, 2001 http://portal.acm.org/citation.cfm?id=869620 could be easily added to the mathematical libraries implemented in strongly-typed computer algebra systems like Axiom and Aldor since they already support Stream and Generator data structures. The failure to treat co-algebraic properties on a par with algebraic properties is beginning to seem like a serious limitation for advanced applications of these systems especially since dual notions such as these arise naturally in the category theoretic treatment of almost any subject. Perhaps you know some other people working on this sort of thing? It would be very good to work together. Regards, Bill Page. ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
