Why does C++ forbid private inheritance of a final class?

Question

C++11 introduced the final keyword to C++.

It can be used on a virtual method or on a class.

Declaring a class final forbids any kind of inheritance: public, protected and private.

struct A final {
};

class B: private A {
};

 error: base 'A' ^ is marked 'final'

While it can be reasonable to forbid public inheritance (e.g. if my class doesn't have a virtual destructor, or for other reasons), why should I forbid private inheritance?

Might it be that if final forbade only public inheritance, that std::string and its other friends in std would have been final -- as they should -- for not having a virtual destructor?

EDIT:

Howard Hinnant already answered Why the standard containers are not final but still, there is a reason for declaring a class final but allowing private inheritance.

Answer 1

Inheritance is inheritance. Accessibility is orthogonal to it. It only protects from statically treating the derived class as the base, outside the scope of the derived class. It makes no difference at runtime, and if private inheritance was allowed, you could write this:

struct C {
    virtual void foo() {}
};

struct A final : C {
    virtual void foo() {}
};

void baz(A& ref) { ref.foo(); }

class B: private A {
   virtual void foo() {}
   void bar() {
       baz(*this);
   }
};

Private inheritance doesn't stop you from using run-time polymorphism. If final is meant to fully prevent further overriding, then private inheritance must be included in the prohibition.

Answer 2

In addition to what Story Teller said, consider the reason for introducing final: It's supposed to help optimizations.

When a class is final, and you have a pointer to it, the compiler can prove which member function you are calling, even if it's virtual. If the class is not final, the pointer could actually be a pointer to some derived class, which could conceivably override the virtual method, forcing a full dynamic vtable lookup.

Whether the inheritance is private or not, it is always possible to create a base-class pointer. In the case of private inheritance, the creation of this base-class pointer would be restricted to the deriving class, the derived class, and any base of the derived class, which is still more code than the optimizer has available to make its decisions. As such, only forbidding all inheritance allows the virtual call optimizations to be made.