Private inheritance restricting base class interface

Private inheritance is useful when it is required to restrict the public interface of the class:

class A {
public:
    int move();
    int turn();
};

class B : private A {
public:
    using A::turn; 
};

B b;
b.move();  // compile error
b.turn();  // OK

This approach efficiently prevents an access to the A public methods by casting to the A pointer or reference:

B b; 
A& a = static_cast<A&>(b); // compile error

In the case of public inheritance such casting will provide access to all the A public methods despite on alternative ways to prevent this in derived B, like hiding:

class B : public A {
private:
    int move();  
};

or private using:

class B : public A {
private:
    using A::move;  
};

then for both cases it is possible:

B b;
A& a = static_cast<A&>(b); // OK for public inheritance
a.move(); // OK