C3Linearize is a Python implementation of the C3 linearization algorithm that Python uses for its class method resolution order ("MRO"). The difference is that now we can perform this on any type of object!

That being said, I'll demonstrate by just using classes anyways. (This is using Python 2.6 syntax, but this module works with 2.3 through 3.2.)

from c3linearize import linearize, class_graph

class meta(type):
    def __repr__(cls):
        return cls.__name__

class A(object): __metaclass__ = meta
class B(object): __metaclass__ = meta
class C(object): __metaclass__ = meta
class D(object): __metaclass__ = meta
class E(object): __metaclass__ = meta
class K1(A,B,C): pass
class K2(D,B,E): pass
class K3(D,A):   pass
class Z(K1,K2,K3): pass

print 'native MRO: ', Z.__mro__
print 'c3linearize:', linearize(class_graph(Z))[Z]

This prints out:

native MRO:  (Z, K1, K2, K3, D, A, B, C, E, <type 'object'>)
c3linearize: [Z, K1, K2, K3, D, A, B, C, E, <type 'object'>]

linearize operates on a mapping that represents the dependency graph; keys map to a sequence of their dependencies. It will then return a dictionary mapping each and every object to its linearization.

One can either contruct these graphs by hand, or use the build_graph function which will construct one of these mappings from a given object and a function which returns the bases of any given object.

The docstrings offer a little more information on this process, and see http://www.python.org/download/releases/2.3/mro/ for more info on the algorithm itself.