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Showing content from https://en.cppreference.com/w/cpp/language/../error/error_code/../../types/add_pointer.html below:

std::add_pointer - cppreference.com

template< class T >
struct add_pointer;

(since C++11)

If T is a referenceable type or (possibly cv-qualified) void, the member typedef type provided is typename std::remove_reference<T>::type*.

Otherwise, the member typedef type provided is T.

If the program adds specializations for std::add_pointer, the behavior is undefined.

[edit] Nested types Name Definition type determined as above [edit] Helper types

template< class T >
using add_pointer_t = typename add_pointer<T>::type;

(since C++14) [edit] Possible implementation 
namespace detail
{
    template<class T>
    struct type_identity { using type = T; }; // or use std::type_identity (since C++20)
 
    template<class T>
    auto try_add_pointer(int)
      -> type_identity<typename std::remove_reference<T>::type*>; // usual case
 
    template<class T>
    auto try_add_pointer(...)
      -> type_identity<T>; // unusual case (cannot form std::remove_reference<T>::type*)
} // namespace detail
 
template<class T>
struct add_pointer : decltype(detail::try_add_pointer<T>(0)) {};
[edit] Example 
#include <iostream>
#include <type_traits>
 
template<typename F, typename Class>
void ptr_to_member_func_cvref_test(F Class::*)
{
    // F is an “abominable function type”
    using FF = std::add_pointer_t<F>;
    static_assert(std::is_same_v<F, FF>, "FF should be precisely F");
}
 
struct S
{
    void f_ref() & {}
    void f_const() const {}
};
 
int main()
{
    int i = 123;
    int& ri = i;
    typedef std::add_pointer<decltype(i)>::type IntPtr;
    typedef std::add_pointer<decltype(ri)>::type IntPtr2;
    IntPtr pi = &i;
    std::cout << "i = " << i << '\n';
    std::cout << "*pi = " << *pi << '\n';
 
    static_assert(std::is_pointer_v<IntPtr>, "IntPtr should be a pointer");
    static_assert(std::is_same_v<IntPtr, int*>, "IntPtr should be a pointer to int");
    static_assert(std::is_same_v<IntPtr2, IntPtr>, "IntPtr2 should be equal to IntPtr");
 
    typedef std::remove_pointer<IntPtr>::type IntAgain;
    IntAgain j = i;
    std::cout << "j = " << j << '\n';
 
    static_assert(!std::is_pointer_v<IntAgain>, "IntAgain should not be a pointer");
    static_assert(std::is_same_v<IntAgain, int>, "IntAgain should be equal to int");
 
    ptr_to_member_func_cvref_test(&S::f_ref);
    ptr_to_member_func_cvref_test(&S::f_const);
}

Output:

i = 123
*pi = 123
j = 123
[edit] Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR Applied to Behavior as published Correct behavior LWG 2101 C++11 the program was ill-formed if T is a function type with cv or ref the type produced is T in this case [edit] See also

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