Templated parameter with default value will throw compile error.

CE.cpp

#include <iostream>
#include <functional>

using namespace std;

template <typename T>
bool compare_by_value(const T& a, const T& b) { return a < b; }

template <typename Comp>
bool alex_compare_int(const int& a, const int &b, Comp comp = compare_by_value) {
  return comp(a, b);
}

template <typename Value, typename Comp = bool(&)(const Value&, const Value&)>
bool alex_compare(const Value& a, const Value& b, Comp comp = compare_by_value) {
  return comp(a, b);
}

int main() {
  // fail
  cout << alex_compare_int(1, 2) << endl;
  // ok
  cout << alex_compare(1, 2) << endl;
  cout << alex_compare(1, 2, function(compare_by_value<int>)) << endl;
  return 0;
}