[c++] What is the meaning of "operator bool() const"

When writing my own unique_ptr, I found this case. Given std::unique_ptr's operator==:

template<class T1, class D1, class T2, class D2>
bool operator==(const unique_ptr<T1, D1>& x, const unique_ptr<T2, D2>& y);

template <class T, class D>
bool operator==(const unique_ptr<T, D>& x, nullptr_t) noexcept;

template <class T, class D>
bool operator==(nullptr_t, const unique_ptr<T, D>& x) noexcept;

And this test case from libstdcxx:

  std::unique_ptr<int> ptr;
  if (ptr == 0)
    { }
  if (0 == ptr)
    { }
  if (ptr != 0)
    { }
  if (0 != ptr)
    { }

Note because that ptr has a explicit operator bool() const noexcept;, so operator overload resolution works fine here, e.g., ptr == 0 chooses

 template <class T, class D>
 bool operator==(const unique_ptr<T, D>& x, nullptr_t) noexcept;`.

If it has no explicit keyword here, ptr in ptr == 0 will be converted into bool, then bool will be converted into int, because bool operator==(int, int) is built-in and 0 is int. What is waiting for us is ambiguous overload resolution error.

Here is a Minimal, Complete, and Verifiable example:

#include <cstddef>
struct A
{
    constexpr A(std::nullptr_t) {}
    operator bool() 
    {
        return true;
    }
};

constexpr bool operator ==(A, A) noexcept
{
    return true;
}

constexpr bool operator ==(A, std::nullptr_t) noexcept
{
    return true;
}

constexpr bool operator ==(std::nullptr_t, A) noexcept
{
    return true;
}

int main()
{
    A a1(nullptr);
    A a2(0);
    a1 == 0;
}

gcc:

prog.cc: In function 'int main()':
prog.cc:30:8: error: ambiguous overload for 'operator==' (operand types are 'A' and 'int')
   30 |     a1 == 0;
      |     ~~ ^~ ~
      |     |     |
      |     A     int
prog.cc:30:8: note: candidate: 'operator==(int, int)' <built-in>
   30 |     a1 == 0;
      |     ~~~^~~~
prog.cc:11:16: note: candidate: 'constexpr bool operator==(A, A)'
   11 | constexpr bool operator ==(A, A) noexcept
      |                ^~~~~~~~
prog.cc:16:16: note: candidate: 'constexpr bool operator==(A, std::nullptr_t)'
   16 | constexpr bool operator ==(A, std::nullptr_t) noexcept
      |                ^~~~~~~~

clang:

prog.cc:30:8: error: use of overloaded operator '==' is ambiguous (with operand types 'A' and 'int')
    a1 == 0;
    ~~ ^  ~
prog.cc:16:16: note: candidate function
constexpr bool operator ==(A, std::nullptr_t) noexcept
               ^
prog.cc:11:16: note: candidate function
constexpr bool operator ==(A, A) noexcept
               ^
prog.cc:30:8: note: built-in candidate operator==(int, int)
    a1 == 0;
       ^
prog.cc:30:8: note: built-in candidate operator==(float, int)
prog.cc:30:8: note: built-in candidate operator==(double, int)
prog.cc:30:8: note: built-in candidate operator==(long double, int)
prog.cc:30:8: note: built-in candidate operator==(__float128, int)
prog.cc:30:8: note: built-in candidate operator==(int, float)
prog.cc:30:8: note: built-in candidate operator==(int, double)
prog.cc:30:8: note: built-in candidate operator==(int, long double)
prog.cc:30:8: note: built-in candidate operator==(int, __float128)
prog.cc:30:8: note: built-in candidate operator==(int, long)
prog.cc:30:8: note: built-in candidate operator==(int, long long)
prog.cc:30:8: note: built-in candidate operator==(int, __int128)
prog.cc:30:8: note: built-in candidate operator==(int, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(int, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(int, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(int, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(long, int)
prog.cc:30:8: note: built-in candidate operator==(long long, int)
prog.cc:30:8: note: built-in candidate operator==(__int128, int)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, int)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, int)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, int)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, int)
prog.cc:30:8: note: built-in candidate operator==(float, float)
prog.cc:30:8: note: built-in candidate operator==(float, double)
prog.cc:30:8: note: built-in candidate operator==(float, long double)
prog.cc:30:8: note: built-in candidate operator==(float, __float128)
prog.cc:30:8: note: built-in candidate operator==(float, long)
prog.cc:30:8: note: built-in candidate operator==(float, long long)
prog.cc:30:8: note: built-in candidate operator==(float, __int128)
prog.cc:30:8: note: built-in candidate operator==(float, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(float, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(float, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(float, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(double, float)
prog.cc:30:8: note: built-in candidate operator==(double, double)
prog.cc:30:8: note: built-in candidate operator==(double, long double)
prog.cc:30:8: note: built-in candidate operator==(double, __float128)
prog.cc:30:8: note: built-in candidate operator==(double, long)
prog.cc:30:8: note: built-in candidate operator==(double, long long)
prog.cc:30:8: note: built-in candidate operator==(double, __int128)
prog.cc:30:8: note: built-in candidate operator==(double, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(double, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(double, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(double, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(long double, float)
prog.cc:30:8: note: built-in candidate operator==(long double, double)
prog.cc:30:8: note: built-in candidate operator==(long double, long double)
prog.cc:30:8: note: built-in candidate operator==(long double, __float128)
prog.cc:30:8: note: built-in candidate operator==(long double, long)
prog.cc:30:8: note: built-in candidate operator==(long double, long long)
prog.cc:30:8: note: built-in candidate operator==(long double, __int128)
prog.cc:30:8: note: built-in candidate operator==(long double, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(long double, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(long double, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(long double, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(__float128, float)
prog.cc:30:8: note: built-in candidate operator==(__float128, double)
prog.cc:30:8: note: built-in candidate operator==(__float128, long double)
prog.cc:30:8: note: built-in candidate operator==(__float128, __float128)
prog.cc:30:8: note: built-in candidate operator==(__float128, long)
prog.cc:30:8: note: built-in candidate operator==(__float128, long long)
prog.cc:30:8: note: built-in candidate operator==(__float128, __int128)
prog.cc:30:8: note: built-in candidate operator==(__float128, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(__float128, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(__float128, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(__float128, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(long, float)
prog.cc:30:8: note: built-in candidate operator==(long, double)
prog.cc:30:8: note: built-in candidate operator==(long, long double)
prog.cc:30:8: note: built-in candidate operator==(long, __float128)
prog.cc:30:8: note: built-in candidate operator==(long, long)
prog.cc:30:8: note: built-in candidate operator==(long, long long)
prog.cc:30:8: note: built-in candidate operator==(long, __int128)
prog.cc:30:8: note: built-in candidate operator==(long, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(long, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(long, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(long, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(long long, float)
prog.cc:30:8: note: built-in candidate operator==(long long, double)
prog.cc:30:8: note: built-in candidate operator==(long long, long double)
prog.cc:30:8: note: built-in candidate operator==(long long, __float128)
prog.cc:30:8: note: built-in candidate operator==(long long, long)
prog.cc:30:8: note: built-in candidate operator==(long long, long long)
prog.cc:30:8: note: built-in candidate operator==(long long, __int128)
prog.cc:30:8: note: built-in candidate operator==(long long, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(long long, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(long long, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(long long, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(__int128, float)
prog.cc:30:8: note: built-in candidate operator==(__int128, double)
prog.cc:30:8: note: built-in candidate operator==(__int128, long double)
prog.cc:30:8: note: built-in candidate operator==(__int128, __float128)
prog.cc:30:8: note: built-in candidate operator==(__int128, long)
prog.cc:30:8: note: built-in candidate operator==(__int128, long long)
prog.cc:30:8: note: built-in candidate operator==(__int128, __int128)
prog.cc:30:8: note: built-in candidate operator==(__int128, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(__int128, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(__int128, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(__int128, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, float)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, double)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, long double)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, __float128)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, long)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, long long)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, __int128)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(unsigned int, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, float)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, double)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, long double)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, __float128)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, long)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, long long)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, __int128)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(unsigned long, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, float)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, double)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, long double)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, __float128)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, long)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, long long)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, __int128)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(unsigned long long, unsigned __int128)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, float)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, double)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, long double)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, __float128)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, long)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, long long)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, __int128)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, unsigned int)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, unsigned long)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, unsigned long long)
prog.cc:30:8: note: built-in candidate operator==(unsigned __int128, unsigned __int128)
1 error generated.

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