C++ cannot access protected member function by friend class - c++

Question

The following example is my demo. At first, I create an abstract class named Expr_node. After that I create another class Int_node. In order to access the private and protected member function normally, I set the Expr class as the friend class of Expr_node. However, I still cannot access to the print function by overload the operator<<.
#include <iostream>
#include <string>
#include <utility>
using namespace std;
class Expr_node;
class Int_node;
class Expr {
friend ostream& operator<<(ostream&, const Expr&);
Expr_node* p;
public:
Expr(int);
Expr(const string&, const Expr&);
Expr(const string&, const Expr&, const Expr&);
Expr(const Expr& t);
Expr& operator=(const Expr&);
};
class Expr_node {
friend ostream& operator<< (ostream&, const Expr_node&);
friend class Expr;
int use;
protected:
Expr_node(): use(1) {}
virtual ~Expr_node() = default;
virtual void print(ostream&) const = 0;
};
ostream& operator<< (ostream& o, const Expr_node& e) {
e.print(o);
return o;
}
ostream& operator<< (ostream& o, const Expr& e) {
e.p->print(o);
return o;
}
class Int_node: public Expr_node {
friend class Expr;
int n;
explicit Int_node(int k) : n(k) {}
void print(ostream& o) const override { o << n;}
};

Answer 1

It's the problem of operator<<. It's not class member, but friend function. Implement function inside Expr class, which call print on p. Then call it on Expr parameter.
Something like this:
#include <iostream>
#include <string>
#include <utility>
using namespace std;
class Expr_node;
class Int_node;
class Expr {
friend ostream& operator<<(ostream&, const Expr&);
Expr_node* p;
public:
Expr(int);
Expr(const string&, const Expr&);
Expr(const string&, const Expr&, const Expr&);
Expr(const Expr& t);
Expr& operator=(const Expr&);
void print(ostream& o) const
{
this->p->print(o);
}
};
class Expr_node {
friend ostream& operator<< (ostream&, const Expr_node&);
friend class Expr;
int use;
protected:
Expr_node(): use(1) {}
virtual ~Expr_node() = default;
virtual void print(ostream&) const = 0;
};
ostream& operator<< (ostream& o, const Expr_node& e) {
e.print(o);
return o;
}
ostream& operator<< (ostream& o, const Expr& e) {
e.print(o);
return o;
}