Polymorphic abstract base class with operator== or equivalen= t functionality; design considerations

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Here is the scenario:
I am attempting to design a polymorphic abstract base class (i.e. an
interface), which will be extended, and its pure virtual functions
implemented, by a set of concrete classes.
I want all the concrete classes to support equality testing, so I
thought of adding a pure virtual 'operator==' method to the abstract
base class which will be implemented by any concrete class
implementing the interface. But this approach poses some problems as
the signature of base class's 'operator==' method and derived class's
'operator==' method do not match.

E.g.
class IString
{
public:
    virtual ~IString() {}

    virtual unsigned int length() const = 0;
    virtual bool operator==(const IString&) = 0;
    virtual bool operator!=(const IString&) = 0;
};

class CString : public IString
{
public:
    CString :
        strLen(0),
        str(0)
    {}
    ~CString() {}

    virtual unsigned int length() const
    { return strLen; }

    virtual bool operator==(const CString&)
    { return true; } // dummy implementation

    virtual bool operator!=(const CString&)
    { return true; } // dummy implementation

private:
    unsigned int strLen;
    char* str;
};

int main()
{
    CString S;

    return 0;
}

On compiling the above code with gcc 4.5.0, I get the following
(expected) error:
error: cannot declare variable =91S' to be of abstract type =91CString'
because the following virtual functions are pure within =91CString':
virtual bool IString::operator==(const IString&)
virtual bool IString::operator!=(const IString&)

Pardon my na=EFvet=E9, but is what I am try to achieve, sane? Is there
another way to achieve what I am attempting?

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