Ошибки при вынесении operator== за структуру

public struct three_values {
public:
    std::string string;
    three_values(std::string new_string) {}
    std::string to_string() {}
    operator std::string() {}
};
bool operator==(const three_values _Left, const three_values _Right) {
    return (_Left.to_string() == _Right.to_string());
}

std::string to_string() const {    }

bool operator==(const three_values &_Left, const three_values &_Right) {
    return (_Left.to_string() == _Right.to_string());
}

std::string a;
const char *b;
if (a == b)

class three_values {
private:
    std::string string;
public:
    three_values(const std::string & new_string) {}
    std::string to_string() { return string; }
    friend bool operator == (const three_values & lhs, const three_values & rhs);
};
 
bool operator == (const three_values & lhs, const three_values & rhs) 
{
    return lhs.string == rhs.string;
}