Independently partial interface implementation

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Many people believe that mixing Generic Programming with Polymorphism
is a bad idea, because these concepts are very different, orthogonal.
Many programmers are quite sure these two just do not work together.
However, I think I know at least one case when Generic Programming
extends Polymorphism.
I have created a new pattern allows to implement not full interface,
but by parts. Then, combining the partial implementation you can
easily create specific types you need.

Example:

class AB {
public:
    virtual int a() = 0;
    virtual const char* b() = 0;
}:

template <class TBase> class ImplA1 : public TBase {
public:
    virtual int a() {
              return 1;
     }
};
template <class TBase> class ImplA2 : public TBase {
public:
    virtual int a() {
              return 2;
      }
};
template <class TBase> class ImplB1 : public TBase {
public:
    virtual const char* b() {
              return "10";
      }
};

template <class TBase> class ImplB2 : public TBase {
public:
    virtual const char* b() {
              return "20";
      }
};

Now we can construct new types combining partial implementations of
AB interface:

typedef ImplA1<ImplB1<AB>> A1B1;
typedef ImplA2<ImplB1<AB>> A2B1;
typedef ImplA1<ImplB2<AB>> A1B2;
typedef ImplA2<ImplB2<AB>> A2B2;

Any feedback very appreciated.

Thanks,
Sergey

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