Check if a class has a possibly-overloaded function call operator

Question

I am wondering whether it would be possible to implement a trait in C++20 to check if a type T is such that it has a possibly overloaded/possibly templated function call operator: operator().

// Declaration
template <class T>
struct has_function_call_operator;

// Definition
???  

// Variable template
template <class T>
inline constexpr bool has_function_call_operator_v 
= has_function_call_operator<T>::value;

so that a code such as the following would lead to the correct result:

#include <iostream>
#include <type_traits>

struct no_function_call_operator {
};

struct one_function_call_operator {
    constexpr void operator()(int) noexcept;
};

struct overloaded_function_call_operator {
    constexpr void operator()(int) noexcept;
    constexpr void operator()(double) noexcept;
    constexpr void operator()(int, double) noexcept;
};

struct templated_function_call_operator {
    template <class... Args>
    constexpr void operator()(Args&&...) noexcept;
};

struct mixed_function_call_operator
: overloaded_function_call_operator
, templated_function_call_operator {
};

template <class T>
struct has_function_call_operator: std::false_type {};

template <class T>
requires std::is_member_function_pointer_v<decltype(&T::operator())>
struct has_function_call_operator<T>: std::true_type {};

template <class T>
inline constexpr bool has_function_call_operator_v 
= has_function_call_operator<T>::value;

int main(int argc, char* argv[]) {
    std::cout << has_function_call_operator_v<no_function_call_operator>;
    std::cout << has_function_call_operator_v<one_function_call_operator>;
    std::cout << has_function_call_operator_v<overloaded_function_call_operator>;
    std::cout << has_function_call_operator_v<templated_function_call_operator>;
    std::cout << has_function_call_operator_v<mixed_function_call_operator>;
    std::cout << std::endl;
}

Currently it prints 01000 instead of 01111. If it is not doable in the broadest possible sense, it can be assumed that T is inheritable if that helps. The weirdest possible template metaprogramming tricks are welcome as long as they are fully compliant with the C++20 standard.

Answer 1

&T::operator() is ambiguous for the 3 failing cases.

So your traits found is there is an unambiguous operator()

As you allow T to be not final, we might apply your traits to (fake) class with existing inherited operator() and class to test:

template <class T>
struct has_one_function_call_operator: std::false_type {};

template <class T>
requires std::is_member_function_pointer_v<decltype(&T::operator())>
struct has_one_function_call_operator<T>: std::true_type {};

struct WithOp
{
    void operator()() const;  
};

template <typename T>
struct Mixin : T, WithOp {};

// if T has no `operator()`, Mixin<T> has unambiguous `operator()` coming from `WithOp`
// else Mixin<T> has ambiguous `operator()`
template <class T>
using has_function_call_operator =
    std::bool_constant<!has_one_function_call_operator<Mixin<T>>::value>;

template <class T>
inline constexpr bool has_function_call_operator_v 
= has_function_call_operator<T>::value;

Demo