#11943: The category graph should comply with Python's method resolution order
---------------------------+------------------------------------------------
Reporter: SimonKing | Owner: nthiery
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.7.3
Component: categories | Keywords: category graph, method resolution
order
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Let C be a category. `C.all_super_categories()` starts with
`C.super_categories()` and finds all super categories inductively.
Unfortunately, the algorithm of `C.all_super_categories()` does not comply
with the C3 algorithm, that is used by Python to determine the method
resolution order for `C.parent_class` and `C.element_class`.
The aim of this ticket is to be more consistent. Eventually, for any
category C (perhaps with modifications for hom categories), one should
have
{{{
sage: C.parent_class.mro() == [X.parent_class for X in
C.all_super_categories()] + [object]
True
sage: C.element_class.mro() == [X.element_class for X in
C.all_super_categories()] + [object]
True
}}}
and that test should become part of the test suite.
At #11900, the implementation of `all_super_categories()` has been
changed, so, work should rely on #11900.
Unfortunately, it seems that the C3 algorithm can not simply be imported
from Python, even though Python uses it internally, namely in
`Objects/typeobject.c`. Looking at the implementation, it requires that
one gets a list of types, while we want to use it on a list of objects.
Therefore, we need to implement C3 from scratch. Implementing C3 is easy,
but if it shall be fast, one needs to be careful.
In particular, one needs to be able to `L.pop(0)` quickly, where L is a
list. Unfortunately, `L.pop(0)` is slow, even in Cython. I found that, if
the lists are not too long, it is best to revert L and do `L.pop()`
instead, which is optimized in Cython. See the discussion at
[http://groups.google.com/group/sage-
support/browse_thread/thread/317aecee64ddab48 sage-devel].
My plan is:
* Provide the C3 algorithm in a new extension module `sage.misc.c3`
* Use it to compute `all_super_categories()`
* Add a test `_test_category_graph`, asserting that
`self.parent_class.mro()` and `self.all_super_categories()` are
compatible.
First tests indicate that the change of order on
`C.all_super_categories()` is fine (sage does not crash, and most tests in
sage.categories pass. However, one really needs to look at the
performance.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11943>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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