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Showing content from https://en.cppreference.com/w/cpp/language/../algorithm/../concepts/../types/add_reference.html below:

std::add_lvalue_reference, std::add_rvalue_reference - cppreference.com

template< class T >
struct add_lvalue_reference;

(1) (since C++11)

template< class T >
struct add_rvalue_reference;

(2) (since C++11)

Creates an lvalue or rvalue reference type of T.

 Type trait  The type referred by the nested type type  T is a referenceable type   T is not a referenceable type  (1) T&[1] T (2) T&&[2]
  1. ↑ This rule reflects the semantics of reference collapsing.
  2. ↑ This rule reflects the semantics of reference collapsing. Note that std::add_rvalue_reference<T&>::type is T&, which is not an rvalue reference type.

If the program adds specializations for any of the templates described on this page, the behavior is undefined.

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

template< class T >
using add_lvalue_reference_t = typename add_lvalue_reference<T>::type;

(since C++14)

template< class T >
using add_rvalue_reference_t = typename add_rvalue_reference<T>::type;

(since C++14) [edit] Notes

The major difference to directly using T& or T&& is that T can be a non-referenceable type. For example, std::add_lvalue_reference<void>::type is void, while void& leads to a compilation error.

[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> // Note that “cv void&” is a substitution failure
    auto try_add_lvalue_reference(int) -> type_identity<T&>;
    template<class T> // Handle T = cv void case
    auto try_add_lvalue_reference(...) -> type_identity<T>;
 
    template<class T>
    auto try_add_rvalue_reference(int) -> type_identity<T&&>;
    template<class T>
    auto try_add_rvalue_reference(...) -> type_identity<T>;
} // namespace detail
 
template<class T>
struct add_lvalue_reference
    : decltype(detail::try_add_lvalue_reference<T>(0)) {};
 
template<class T>
struct add_rvalue_reference
    : decltype(detail::try_add_rvalue_reference<T>(0)) {};
[edit] Example [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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