#11943: The category graph should comply with Python's method resolution order
---------------------------+------------------------------------------------
Reporter: SimonKing | Owner: nthiery
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.8
Component: categories | Keywords: category graph, method resolution
order
Work_issues: | Upstream: N/A
Reviewer: | Author: Simon King
Merged: | Dependencies: #11900
---------------------------+------------------------------------------------
Changes (by SimonKing):
* status: needs_work => needs_review
* work_issues: Remove dead code =>
Old description:
> 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.
>
> Apply:
>
> [attachment:trac11943_mro_for_all_super_categories_lazy_hook.patch]
New description:
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].
What my patch does:
* 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.
Apply:
[attachment:trac11943_mro_for_all_super_categories_lazy_hook.patch]
--
Comment:
Dead code is removed, ticket description updated.
Apply trac11943_mro_for_all_super_categories_lazy_hook.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11943#comment:42>
Sage <http://www.sagemath.org>
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