The C3 algorithm¶
The C3 algorithm is used as method resolution order for new style classes in Python. The implementation here is used to order the list of super categories of a category.
AUTHOR:
 Simon King (201111): initial version.

sage.misc.c3.
C3_algorithm
(start, bases, attribute, proper)¶ An implementation of the C3 algorithm.
C3 is the algorithm used by Python to construct the method resolution order for new style classes involving multiple inheritance.
After trac ticket #11943 this implementation was used to compute the list of super categories of a category; see
all_super_categories()
. The purpose is to ensure that list of super categories matches with the method resolution order of the parent or element classes of a category.Since trac ticket #13589, this implementation is superseded by that in
sage.misc.c3_controlled
, that puts theC3
algorithm under control of some total order on categories. This guarantees thatC3
always finds a consistent Method Resolution Order. For background, seesage.misc.c3_controlled
.INPUT:
start
– an object; the returned list is built upon data provided by certain attributes ofstart
.bases
– a string; the name of an attribute ofstart
providing a list of objects.attribute
– a string; the name of an attribute of the objects provided ingetattr(start,bases)
. That attribute is supposed to provide a list.
ASSUMPTIONS:
Our implementation of the algorithm only works on lists of objects that compare equal if and only if they are identical.
OUTPUT:
A list, the result of the C3 algorithm applied to the list
[getattr(X,attribute) for X in getattr(start,bases)]
.EXAMPLES:
We create a class for elements in a hierarchy that uses the
C3
algorithm to compute, for each element, a linear extension of the elements above it:.. TODO:: Move back the __init__ at the beginning
sage: from sage.misc.c3 import C3_algorithm sage: class HierarchyElement(UniqueRepresentation): ….: @lazy_attribute ….: def _all_bases(self): ….: return C3_algorithm(self, ‘_bases’, ‘_all_bases’, False) ….: def __repr__(self): ….: return self._name ….: def __init__(self, name, bases): ….: self._name = name ….: self._bases = list(bases)We construct a little hierarchy:
sage: T = HierarchyElement("T", ()) sage: X = HierarchyElement("X", (T,)) sage: Y = HierarchyElement("Y", (T,)) sage: A = HierarchyElement("A", (X, Y)) sage: B = HierarchyElement("B", (Y, X)) sage: Foo = HierarchyElement("Foo", (A, B))
And inspect the linear extensions associated to each element:
sage: T._all_bases [T] sage: X._all_bases [X, T] sage: Y._all_bases [Y, T] sage: A._all_bases [A, X, Y, T] sage: B._all_bases [B, Y, X, T]
So far so good. However:
sage: Foo._all_bases Traceback (most recent call last): ... ValueError: Can not merge the items X, Y.
The
C3
algorithm is not able to create a consistent linear extension. Indeed, its specifications impose that, ifX
andY
appear in a certain order in the linear extension for an element of the hierarchy, then they should appear in the same order for any lower element. This is clearly not possibly forFoo
, sinceA
andB
impose incompatible orders. If the above was a hierarchy of classes, Python would complain that it cannot calculate a consistent Method Resolution Order.