How do I declare an overloaded operator in an abstract class and override it in a derived non-abstract class?

Question

I'm trying to write an abstract class with some pure virtual binary operators, which should be implemented by the derived class in order to accomplish operator polymorphism. Here's a simplified example:

class Base {
public:
    virtual const Base& operator+ (const Base&) const = 0;
};

class Derived : public Base {
public:
    const Derived& operator+ (const Derived&) const;
};

const Derived& Derived::operator+ (const Derived& rvalue) const {
    return Derived();
}

It doesn't matter right now what the operator does, the important part is what it returns: it returns a temporary Derived object, or a reference to it. Now, if I try to compile, I get this:

test.cpp: In member function ‘virtual const Derived& Derived::operator+(const Derived&) const’:
test.cpp:12:17: error: cannot allocate an object of abstract type ‘Derived’
test.cpp:6:7: note:   because the following virtual functions are pure within ‘Derived’:
test.cpp:3:22: note:    virtual const Base& Base::operator+(const Base&) const

What's wrong? Isn't operator+ (the only pure virtual function in Base) being overriden? Why should Derived be abstract as well?

Answer 1

Although the return type in Derived can be co-variant to the base one, you can't do the same with the argument types. I.e., the overriding function should look like this:

class Derived : public Base 
{ 
public: 
    const Derived& operator+ (const Base&) const; 
}; 

Answer 2

This kind of overloading is not possible with a normal abstract class in a clean way. First: you should declare + as non member Overload operators as member function or non-member (friend) function?.

The best you can get is to inherit from a templated interface if you really need this functionality:

template<typename T>
class AddEnabled {
  public:
    friend T operator+ (T const& left, T const& right) {
      return left+=right;
    }
};

Now you write

class Foo: public AddEnabled<Foo>{
  Foo():mVal(0){
  }

  Foo& operator+=(Foo const& foo){
    mVal+=foo.mVal;
  }

 private:
  int mVal;
}

If you comment out Foo& operator+=(Foo const& foo){ you will get a compiler error saying that the operator is not implemented. If you want to know more about the principles involved lookup http://en.wikipedia.org/wiki/Barton%E2%80%93Nackman_trick and http://en.wikipedia.org/wiki/Curiously_recurring_template_pattern

HTH, Martin