c++ - Why is it not possible to use private method in a lambda?

Question

Having a class like this:

class A {
public:
    bool hasGrandChild() const;

private:
    bool hasChild() const;
    vector<A> children_;
};

Why is it not possible to use a private method hasChild() in a lambda expression defined in the method hasGrandChild() like this?

bool A::hasGrandChild() const {
    return any_of(children_.begin(), children_.end(), [](A const &a) {
        return a.hasChild();
    });
}

Compiler issues an error that the method hasChild() is private within the context. Is there any workaround?

Edit: It seems that the code as I posted it originally works. I thought that it is equivalent, but the code that does not work on GCC is more like this:

#include <vector>
#include <algorithm>

class Foo;

class BaseA {
protected:
    bool hasChild() const { return !children_.empty(); }
    std::vector<Foo> children_;
};

class BaseB {
protected:
    bool hasChild() const { return false; }
};

class Foo : public BaseA, public BaseB {
public:
  bool hasGrandChild() const {
    return std::any_of(children_.begin(), children_.end(), [](Foo const &foo) {
        return foo.BaseA::hasChild();
      });
  }  
};

int main()
{
  Foo foo;
  foo.hasGrandChild();
  return 0;
}

Seems that there is a problem with fully qualified names as this does not work, but this works.

Answer 1

It seems to be just a GCC bug in a special case when the lambda tries to access a protected member from parent class using fully qualified name. This does not work:

class Base {
protected:
    bool hasChild() const { return !childs_.empty(); }
    std::vector<Foo> childs_;
};

class Foo : public Base {
public:
  bool hasGrandChild() const {
    return std::any_of(childs_.begin(), childs_.end(), [](Foo const &foo) {
      return foo.Base::hasChild();
    });
  }  
};

, but this works:

class Foo : public Base {
public:
  bool hasGrandChild() const {
    return std::any_of(childs_.begin(), childs_.end(), [](Foo const &foo) {
      return foo.hasChild();
    });
  }  
};

According to C++11, 5.1.2/3:

The type of the lambda-expression (which is also the type of the closure object) is a unique, unnamed non-union class type — called the closure type — whose properties are described below. This class type is not an aggregate (8.5.1). The closure type is declared in the smallest block scope, class scope, or namespace scope that contains the corresponding lambda-expression.

And then C++11, 11.7/1:

A nested class is a member and as such has the same access rights as any other member.

So the mentioned function-local lambda should have the same access rights as any other member of the class. Therefore it should be able to call a protected method from a parent class.