On Mon, Mar 10, 2014 at 04:35:25AM -0700, Volker Braun wrote:
> IMHO the contained-class makes it clear what the base category is, but not
> what the axiom is. For example:
> class Cs(Category):
> class Finite(CategoryWithAxiom):
> pass
> class Ds(Category):
> class Endlich(CategoryWithAxiom):
> pass
> Now Cs.Finite implements an axiom, but Ds.Endlich does not (since you
> haven't added the "Endlich" string to a global list somewhere).
No. What makes Endlich an axiom (or not) is that some super category
has defined it (or not) [1].
As an analogy, when an abstract class C declares a method foo, and you
implement this method in some subclass D, you don't write explicitly
in D.foo that you override the method foo declared in C.
If you need that information, you either use the semantic (here the
math), or you walk the hierarchy. Of course, since the hierarchy is
built dynamically here, you need to walk the hierarchy dynamically;
introspection does that nicely for you (yes, unless Sage does not
start at all; but in that case we are speaking of the very basic
axioms and you can still use the math).
Cheers,
Nicolas
[1] The fact that Sage needs a list of the names of all the axioms
being defined is an implementation detail. Recall that it is used
mostly for printing purposes (and allowing for syntactical sugar in
some spots). We could get rid of it without changing the syntax of how
axioms are defined and implemented.
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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