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Showing content from https://en.cppreference.com/w/cpp/language/../keyword/../language/../types/is_function.html below:

std::is_function - cppreference.com

template< class T >
struct is_function;

std::is_function is a UnaryTypeTrait.

Checks whether T is a function type. Types like std::function, lambdas, classes with overloaded operator() and pointers to functions don't count as function types. Provides the member constant value which is equal to true, if T is a function type. Otherwise, value is equal to false.

If the program adds specializations for std::is_function or std::is_function_v, the behavior is undefined.

template< class T >
constexpr bool is_function_v = is_function<T>::value;

std::is_function can be implemented in much simpler ways. Implementations similar to the following one are used by new versions of libc++, libstdc++ and MS STL:

The implementation shown below is for pedagogical purposes, since it exhibits the myriad kinds of function types.

// primary template
template<class>
struct is_function : std::false_type {};
 
// specialization for regular functions
template<class Ret, class... Args>
struct is_function<Ret(Args...)> : std::true_type {};
 
// specialization for variadic functions such as std::printf
template<class Ret, class... Args>
struct is_function<Ret(Args......)> : std::true_type {};
 
// specialization for function types that have cv-qualifiers
template<class Ret, class... Args>
struct is_function<Ret(Args...) const> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) volatile> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const volatile> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) volatile> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const volatile> : std::true_type {};
 
// specialization for function types that have ref-qualifiers
template<class Ret, class... Args>
struct is_function<Ret(Args...) &> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const &> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) volatile &> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const volatile &> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) &> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const &> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) volatile &> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const volatile &> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) &&> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const &&> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) volatile &&> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const volatile &&> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) &&> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const &&> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) volatile &&> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const volatile &&> : std::true_type {};
 
// specializations for noexcept versions of all the above (C++17 and later)
template<class Ret, class... Args>
struct is_function<Ret(Args...) noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) volatile noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const volatile noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) volatile noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const volatile noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) & noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const & noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) volatile & noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const volatile & noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) & noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const & noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) volatile & noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const volatile & noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) && noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const && noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) volatile && noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args...) const volatile && noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) && noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const && noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) volatile && noexcept> : std::true_type {};
template<class Ret, class... Args>
struct is_function<Ret(Args......) const volatile && noexcept> : std::true_type {};

#include <functional>
#include <type_traits>
 
int f();
static_assert(std::is_function_v<decltype(f)>);
 
static_assert(std::is_function_v<int(int)>);
static_assert(!std::is_function_v<int>);
static_assert(!std::is_function_v<decltype([]{})>);
static_assert(!std::is_function_v<std::function<void()>>);
 
struct O { void operator()() {} };
static_assert(std::is_function_v<O()>);
 
struct A
{
    static int foo();
    int fun() const&;
};
static_assert(!std::is_function_v<A>);
static_assert(std::is_function_v<decltype(A::foo)>);
static_assert(!std::is_function_v<decltype(&A::fun)>);
 
template<typename>
struct PM_traits {};
template<class T, class U>
struct PM_traits<U T::*> { using member_type = U; };
 
int main()
{
    using T = PM_traits<decltype(&A::fun)>::member_type; // T is int() const&
    static_assert(std::is_function_v<T>);
}

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