Question

I understand C++ can’t define operator== automatically for a class, but why can’t it use !(a == b) for a != b when operator!= isn’t available but operator== is?

I’m aware of std::rel_ops although I hadn’t heard of it before today.

Answer 1

Because operator== does not necessarily mean the opposite of operator!=.

I cannot think of any instance where operator== would not mean !operator!=, but they are separate operators. One of the most liberating and, at times, most frustrating things about C++ is that C++ applies a minimal set of restrictions about how you can write your code. If you have an instance where operator== is not the opposite of operator!=, then you should be able to express that in C++. And, in fact, you can.

You take the good with the bad in C++. You may consider this to be in the set of “the bad”.

Bear in mind that in the vast majority of cases, it is trivial to correctly implement operator!= in terms of operator==.

bool Gizmo::operator!=(const Gizmo& rhs) const
{
  return !operator==(rhs);
}