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std::is_function - cppreference.com

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.

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. 

// 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 {};