What's the right way to overload operator== for a class hierarchy?

Suppose I have the following class hierarchy:

class A
{
    int foo;
    virtual ~A() = 0;
};

A::~A() {}

class B : public A
{
    int bar;
};

class C : public A
{
    int baz;
};

What's the right way to overload operator== for these classes? If I make them all free functions, then B and C can't leverage A's version without casting. It would also prevent someone from doing a deep comparison having only references to A. If I make them virtual member functions, then a derived version might look like this:

bool B::operator==(const A& rhs) const
{
    const B* ptr = dynamic_cast<const B*>(&rhs);        
    if (ptr != 0) {
        return (bar == ptr->bar) && (A::operator==(*this, rhs));
    }
    else {
        return false;
    }
}

Again, I still have to cast (and it feels wrong). Is there a preferred way to do this?

Update:

There are only two answers so far, but it looks like the right way is analogous to the assignment operator:

Make non-leaf classes abstract
Protected non-virtual in the non-leaf classes
Public non-virtual in the leaf classes

Any user attempt to compare two objects of different types will not compile because the base function is protected, and the leaf classes can leverage the parent's version to compare that part of the data.

Solution

For this sort of hierarchy I would definitely follow the Scott Meyer's Effective C++ advice and avoid having any concrete base classes. You appear to be doing this in any case.

I would implement operator== as a free functions, probably friends, only for the concrete leaf-node class types.

If the base class has to have data members, then I would provide a (probably protected) non-virtual helper function in the base class (isEqual, say) which the derived classes' operator== could use.

E.g.

bool operator==(const B& lhs, const B& rhs)
{
    return lhs.isEqual( rhs ) && lhs.bar == rhs.bar;
}

By avoiding having an operator== that works on abstract base classes and keeping compare functions protected, you don't ever get accidentally fallbacks in client code where only the base part of two differently typed objects are compared.

I'm not sure whether I'd implement a virtual compare function with a dynamic_cast, I would be reluctant to do this but if there was a proven need for it I would probably go with a pure virtual function in the base class (not operator==) which was then overriden in the concrete derived classes as something like this, using the operator== for the derived class.

bool B::pubIsEqual( const A& rhs ) const
{
    const B* b = dynamic_cast< const B* >( &rhs );
    return b != NULL && *this == *b;
}