#include <iostream>
#include <boost/shared_ptr.hpp>

struct num_ {
  virtual ~num_() {}
  virtual bool is_zero() const = 0;
};
typedef const boost::shared_ptr<const num_> num;

struct zero_ : public num_ {
  bool is_zero() const { return true; }
};

struct inc_ : public num_ {
  num n_;
  inc_(num n) : n_(n) {}
  bool is_zero() const { return false; }
};

num zero() { return num(new zero_); }
num inc(num n) { return num(new inc_(n)); }
num dec(num n) { return boost::dynamic_pointer_cast<const inc_> (n)->n_; }

num operator+ (num n1, num n2) {
  return
    n1->is_zero() ? n2 :
    n2->is_zero() ? n1 :
    inc(n1) + dec(n2);
}

num operator- (num n1, num n2) {
  return
    n1->is_zero() ? n1 :
    n2->is_zero() ? n1 :
    dec(n1) - dec(n2);
}

int to_int(num n) {
  return n->is_zero() ? 0 : to_int(dec(n)) + 1;
}

std::ostream& operator<< (std::ostream &s, num n) {
  return s << to_int(n);
}

int main()
{
  std::cout << inc(inc(inc(zero()))) + inc(inc(zero())) << std::endl;
  return 0;
}

5