[Numpy-discussion] [Python-3000] PEP 31XX: A Type Hierarchy for Numbers (and other algebraic entities)

Jim Jewett jimjjewett@gmail....
Sun Apr 29 20:51:52 CDT 2007

On 4/29/07, Guido van Rossum <guido@python.org> wrote:

> Hmm... Maybe the conclusion to draw from this is that we shouldn't
> make Ring a class? Maybe it ought to be a metaclass, so we could ask
> isinstance(Complex, Ring)?

Yes; all the ABCs are assertions about the class.  (Zope interfaces do
support instance-specific interfaces, which has been brought up as a
relative weakness of ABCs.)

The only thing two subclasses of an *Abstract* class need to have in
common is that they both (independently) meet the requirements of the
ABC.  If not for complexity of implementation, that would be better
described as a common metaclass.

Using a metaclass would also solve the "when to gripe" issue; the
metaclass would gripe if it couldn't make every method concrete.  If
this just used the standard metaclass machinery, then it would mean a
much deeper metaclass hierarchy than we're used to; MutableSet would a
have highly dervived metaclass.

> The more I think about it, it sounds like the right thing to do. To
> take PartiallyOrdered (let's say PO for brevity) as an example, the
> Set class should specify PO as a metaclass. The PO metaclass could
> require that the class implement __lt__ and __le__. If it found a
> class that didn't implement them, it could make the class abstract by
> adding the missing methods to its __abstractmethods__ attribute.

Or by making it a sub(meta)class, instead of a (regular instance) class.

> if it found that the class implemented one but not the other, it could
> inject a default implementation of the other in terms of the one and
> __eq__.

This also allows greater freedom in specifying which subsets of
methods must be defined.

> Now, you could argue that Complex should also be a metaclass. While
> that may mathematically meaningful (for all I know there are people
> doing complex number theory using Complex[Z/n]), for Python's numeric
> classes I think it's better to make Complex a regular class
> representing all the usual complex numbers (i.e. a pair of Real
> numbers).

complex already meets that need.  Complex would be the metaclass
representing the restrictions on the class, so that independing
implementations wouldn't have to fake-inherit from complex.

> I expect that the complex subclasses used in practice are
> all happy under mixed arithmetic using the usual definition of mixed
> arithmetic: convert both arguments to a common base class and compute
> the operation in that domain.

It is reasonable to insist that all Complex classes have a way to
tranform their instances into (builtin) complex instances, if only as
a final fallback.  There is no need for complex to be a base class.


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