What is the correct (or best) way to subclass the Python set class, adding a new instance variable?

I'm implementing an object that is almost identical to a set, but requires an extra instance variable, so I am subclassing the built-in set object. What is the best way to make sure that the value of this variable is copied when one of my objects is copied?

Using the old sets module, the following code worked perfectly:

import sets
class Fooset(sets.Set):
    def __init__(self, s = []):
        sets.Set.__init__(self, s)
        if isinstance(s, Fooset):
            self.foo = s.foo
        else:
            self.foo = 'default'
f = Fooset([1,2,4])
f.foo = 'bar'
assert( (f | f).foo == 'bar')

but this does not work using the built-in set module.

The only solution that I can see is to override every single method that returns a copied set object... in which case I might as well not bother subclassing the set object. Surely there is a standard way to do this?

(To clarify, the following code does not work (the assertion fails):

class Fooset(set):
    def __init__(self, s = []):
        set.__init__(self, s)
        if isinstance(s, Fooset):
            self.foo = s.foo
        else:
            self.foo = 'default'

f = Fooset([1,2,4])
f.foo = 'bar'
assert( (f | f).foo == 'bar')

)

My favorite way to wrap methods of a built-in collection:

class Fooset(set):
    def __init__(self, s=(), foo=None):
        super(Fooset,self).__init__(s)
        if foo is None and hasattr(s, 'foo'):
            foo = s.foo
        self.foo = foo



    @classmethod
    def _wrap_methods(cls, names):
        def wrap_method_closure(name):
            def inner(self, *args):
                result = getattr(super(cls, self), name)(*args)
                if isinstance(result, set) and not hasattr(result, 'foo'):
                    result = cls(result, foo=self.foo)
                return result
            inner.fn_name = name
            setattr(cls, name, inner)
        for name in names:
            wrap_method_closure(name)

Fooset._wrap_methods(['__ror__', 'difference_update', '__isub__', 
    'symmetric_difference', '__rsub__', '__and__', '__rand__', 'intersection',
    'difference', '__iand__', 'union', '__ixor__', 
    'symmetric_difference_update', '__or__', 'copy', '__rxor__',
    'intersection_update', '__xor__', '__ior__', '__sub__',
])

Essentially the same thing you're doing in your own answer, but with fewer loc. It's also easy to put in a metaclass if you want to do the same thing with lists and dicts as well.