std::is_function(3)

NAME
std::is_function - std::is_function

Synopsis
   Defined in header <type_traits>
   template< class T > (since C++11)
   struct is_function;
   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.
   The behavior of a program that adds specializations for is_function
   or is_function_v
   (since C++17) is undefined.

Template parameters
   T - a type to check
  Helper variable template
   template< class T > (since C++17)
   inline constexpr bool is_function_v = is_function<T>::value; Inherited from std::integral_constant

Member constants
   value true if T is a function type , false otherwise
   [static] (public static member constant)

Member functions
   operator bool converts the object to bool, returns value
                 (public member function)
   operator() returns value
   (C++14) (public member function)

Member types
   Type Definition
   value_type bool
   type std::integral_constant<bool, value>

Notes
   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:
 template<class T>
 struct is_function : std::integral_constant<
     bool,
     !std::is_const<const T>::value && !std::is_reference<T>::value
 > {};
   The implementation shown below is for pedagogical purposes, since it exhibits the
   myriad kinds of function types.

Possible implementation
   // 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 {};

Example
// Run this code
 #include <iostream>
 #include <type_traits>
 struct A {
     int fun() const&;
 };
 template<typename>
 struct PM_traits {};
 template<class T, class U>
 struct PM_traits<U T::*> {
     using member_type = U;
 };
 int f();
 int main()
 {
     std::cout << std::boolalpha;
     std::cout << "#1 " << std::is_function_v<A> << '\n';
     std::cout << "#2 " << std::is_function_v<int(int)> << '\n';
     std::cout << "#3 " << std::is_function_v<decltype(f)> << '\n';
     std::cout << "#4 " << std::is_function_v<int> << '\n';
     using T = PM_traits<decltype(&A::fun)>::member_type; // T is int() const&
     std::cout << "#5 " << std::is_function_v<T> << '\n';
 }

Output:
 #1 false
 #2 true
 #3 true
 #4 false
 #5 true

See also
   is_invocable
   is_invocable_r checks if a type can be invoked (as if by std::invoke) with
   is_nothrow_invocable the given argument types
   is_nothrow_invocable_r (class template)
   (C++17)
   is_object checks if a type is an object type
   (C++11) (class template)
   is_class checks if a type is a non-union class type
   (C++11) (class template)