c++ using declaration, scope and access control

Question

Typically the 'using' declaration is used to bring into scope some member functions of base classes that would otherwise be hidden. From that point of view it is only a mechanism for making accessible information more convenient to use.
However: the 'using' declaration can also be used to change access constraints (not only for functions but also for attributes). For example:

class C{
public:
  int a;
  void g(){ cout << "C:g()\n"; }
  C() : a(0){}
};

class D : public C{
private:
  using C::a;
  using C::g;
public:
  D() { a = 1; }
};

int main(void){
  D d;
  cout << d.a << endl;  //error: a is inaccessible
  C *cp = &d;
  cout << cp->a << endl; //works
  d.g();  //error: g is inaccessible
  cp->g();  //works
  return 0;
}

I think this limitation of access in the derived class is actually of no use, because you can always access g() and a from a pointer to the base class. So should't there be at least some kind of compiler warning? Or wouldn't it been even better to forbid such limitation of access by a derived class? The using declaration is not the only possibility to add constraints to access. It could also be done via overriding a base class' function an placing it in a section with more access constraints. Are there some reasonable examples where it is indeed nessecary to limit access in such a way? If not I don't see why it should be allowed.

And another thing: at least with g++ the same code compiles well without the word 'using'. That means for the example above: it's possible to write C::a; and C::g; instead of using C::a; using C::g; Is the first only a shortcut for the latter or are there some subtle differences?

//EDIT:
so from the discussion and answers below my conclusion would be:
- it's allowed to limit access constraints in derived classes with public inheritance
- there are useful examples where it could be used
- it's use might cause problem in combination with templates (e.g. a derived class could not be a valid parameter for some template class/function any more although it's base is)
- a cleaner language design should not allow such use
- compiler could at least issue some kind of warning

Answer 1

With regard to your declaration without using: These are called "access declarations", and are deprecated. Here is the text from the Standard, from 11.3/1:

The access of a member of a base class can be changed in the derived class by mentioning its qualified-id in the derived class declaration. Such mention is called an access declaration. The effect of an access declaration qualified-id; is defined to be equivalent to the declaration usingqualified-id; [Footnote: Access declarations are deprecated; member using-declarations (7.3.3) provide a better means of doing the same things. In earlier versions of the C++ language, access declarations were more limited; they were generalized and made equivalent to using-declarations - end footnote]

I would say that most often it's not good to change public members to private or protected members in the derived class, because this will violate the substitution principle: You know a base class has some functions, and if you cast to a derived class then you expect those functions to be callable too, because the derived class is-a base. And like you already mentioned, this invariant is already enforced anyway by the language allowing to convert (which working implicitly!) to a base class reference, or qualifying the function name, and then calling the (then public) function.

If you want to forbid someone calling a set of functions of the base, then i think this hints that containment (or in rare cases, private inheritance) is a better idea.