Pure virtual function with implementation

To be clear, you are misunderstanding what = 0; after a virtual function means.

= 0 means derived classes must provide an implementation, not that the base class can not provide an implementation.

In practice, when you mark a virtual function as pure (=0), there is very little point in providing a definition, because it will never be called unless someone explicitly does so via Base::Function(...) or if the Base class constructor calls the virtual function in question.

A pure virtual function must be implemented in a derived type that will be directly instantiated, however the base type can still define an implementation. A derived class can explicitly call the base class implementation (if access permissions allow it) by using a fully-scoped name (by calling A::f() in your example - if A::f() were public or protected). Something like:

class B : public A {

    virtual void f() {
        // class B doesn't have anything special to do for f()
        //  so we'll call A's

        // note that A's declaration of f() would have to be public 
        //  or protected to avoid a compile time problem

        A::f();
    }

};

The use case I can think of off the top of my head is when there's a more-or-less reasonable default behavior, but the class designer wants that sort-of-default behavior be invoked only explicitly. It can also be the case what you want derived classes to always perform their own work but also be able to call a common set of functionality.

Note that even though it's permitted by the language, it's not something that I see commonly used (and the fact that it can be done seems to surprise most C++ programmers, even experienced ones).