c++ operator overloading & polymorphism-Collection of common programming errors

First, polymorphism works with both references and pointers. And operator overloading works with references. So there’s no problem at that level.

There is a potential problem with binary operators. Direct language support for polymorphism on an operator only works on the left hand operand. Where as for something like binary +, one logically would expect double dispatch. While this can be implemented, it is somewhat more complex, especially if the hierarchies are open.

For operators like binary +, which normally return a new object, there is also the question of the return type. Typically, this can’t be a reference, since there is no object with an appropriate type to refer to. Patterns like the letter-envelop idiom have been developed to deal with this, but they aren’t necessarily simple, and they often have very significant run-time overhead. Or the overloaded operator returns a special type, which only saves its arguments, and knows how to calculate the value with the correct type when requested.