Difference between private, public, and protected inheritance

Question

What is the difference between public, private, and protected inheritance in C++?

Answer 1

Public inheritance models an IS-A relationship. With

class B {};
class D : public B {};

every D is a B.

Private inheritance models an IS-IMPLEMENTED-USING relationship (or whatever that's called). With

class B {};
class D : private B {};

a D is not a B, but every D uses its B in its implementation. Private inheritance can always be eliminated by using containment instead:

class B {};
class D {
  private: 
    B b_;
};

This D, too, can be implemented using B, in this case using its b_. Containment is a less tight coupling between types than inheritance, so in general it should be preferred. Sometimes using containment instead of private inheritance is not as convenient as private inheritance. Often that's a lame excuse for being lazy.

I don't think anyone knows what protected inheritance models. At least I haven't seen any convincing explanation yet.