How to use template function for implicit conversion

Question

Very simplified example (nevermind what the class A and operators are doing, it's just for example):

#include <iostream>
using namespace std;

template <bool is_signed>
class A {
public:
    // implicit conversion from int
    A(int a) : a_{is_signed ? -a : a}
    {}

    int a_;
};

bool operator==(A<true> lhs, A<true> rhs) {
    return lhs.a_ == rhs.a_;
}

bool operator==(A<false> lhs, A<false> rhs) {
    return lhs.a_ == rhs.a_;
}

int main() {
    A<true> a1{123};
    A<false> a2{123};

    cout << (a1 == 123) << endl;
    cout << (a2 == 123) << endl;

    return 0;
}

This works.

But if I replace two operator=='s (with same body) with template:

template <bool is_signed>
bool operator==(A<is_signed> lhs, A<is_signed> rhs) {
    return lhs.a_ == rhs.a_;
}

, its compilation produces errors:

prog.cpp: In function ‘int main()’:
prog.cpp:31:14: error: no match for ‘operator==’ (operand types are ‘A<true>’ and ‘int’)
  cout << (a1 == 123) << endl;
           ~~~^~~~~~
prog.cpp:23:6: note: candidate: ‘template<bool is_signed> bool operator==(A<is_signed>, A<is_signed>)’
 bool operator==(A<is_signed> lhs, A<is_signed> rhs) {
      ^~~~~~~~
prog.cpp:23:6: note:   template argument deduction/substitution failed:
prog.cpp:31:17: note:   mismatched types ‘A<is_signed>’ and ‘int’
  cout << (a1 == 123) << endl;
                 ^~~

Is it possible to use template here? Can I use C++17 user-defined template deduction guides somehow? Or anything else?

Answer 1

Implicit conversions are not considered in template argument deduction, which causes the deduction for is_signed fails on the 2nd function argument.

Type deduction does not consider implicit conversions (other than type adjustments listed above): that's the job for overload resolution, which happens later.

If you always use the operator== in the style like a1 == 123, i.e. an A<is_signed> is always used as the 1st operand, you can exclude the 2nd function parameter from the deduction. e.g.

template <bool is_signed>
bool operator==(A<is_signed> lhs, std::type_identity_t<A<is_signed>> rhs) {
    return lhs.a_ == rhs.a_;
}

LIVE

_{PS: std::type_identity is supported since C++20; even it's not hard to implement one.}

Answer 2

Another alternative is friend function, so the function is not template, but use the template argument:

template <bool is_signed>
class A {
public:
    // implicit conversion from int
    A(int a) : a_{is_signed ? -a : a}
    {}

    int a_;

    friend bool operator==(const A& lhs, const A& rhs) {
        return lhs.a_ == rhs.a_;
    }
};

Demo