Hi, The recent discussions about Axiom/Aldor being object-oriented or not, whether Axiom could be made to be "truly categorial" or not reminded be of a curiosity I found in Axiom's hierarchy for mathematical structures.
In the impressive diagram titled "Basic Agebra Hierarchy" displayed in the Axiom Book (I only have a copy of the edition copyrighted 1992, NAG), AbelianSemiGroup is not "derived" from SemiGroup, and similarly AbelianMonoid is not "derived" from Monoid. I find that curious as it goes counter the mathematical fact that an AbelianMonoid *is* a Monoid, with an additional algebraic law (commutation). Does anyone know the reason of those curiosities? (A year or so ago, in a discussion with a friend I attributed those anomalies to object-orientation artifacts. I would be glad to see that disproved...) Thanks, -- Gaby PS: libalgebra has similar curiosities _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
