This subclause contains some basic function and class templates that are used throughout the rest of the library.
The header <utility> defines several types and function templates that are described in this Clause. It also defines the template pair and various function templates that operate on pair objects.
#include <initializer_list>
namespace std {
  // [operators], operators:
  namespace rel_ops {
    template<class T> bool operator!=(const T&, const T&);
    template<class T> bool operator> (const T&, const T&);
    template<class T> bool operator<=(const T&, const T&);
    template<class T> bool operator>=(const T&, const T&);
  }
  // [utility.swap], swap:
  template<class T> void swap(T& a, T& b) noexcept(see below);
  template <class T, size_t N> void swap(T (&a)[N], T (&b)[N]) noexcept(noexcept(swap(*a, *b)));
  // [utility.exchange], exchange:
  template <class T, class U=T> T exchange(T& obj, U&& new_val);
  // [forward], forward/move:
  template <class T> 
    constexpr T&& forward(remove_reference_t<T>& t) noexcept;
  template <class T>
    constexpr T&& forward(remove_reference_t<T>&& t) noexcept;
  template <class T>
    constexpr remove_reference_t<T>&& move(T&&) noexcept;
  template <class T>
    constexpr conditional_t<
    !is_nothrow_move_constructible<T>::value && is_copy_constructible<T>::value,
    const T&, T&&> move_if_noexcept(T& x) noexcept;
  // [declval], declval:
  template <class T>
    add_rvalue_reference_t<T> declval() noexcept;  // as unevaluated operand
  // [pairs], pairs:
  template <class T1, class T2> struct pair;
  // [pairs.spec], pair specialized algorithms:
  template <class T1, class T2>
    constexpr bool operator==(const pair<T1,T2>&, const pair<T1,T2>&);
  template <class T1, class T2>
    constexpr bool operator< (const pair<T1,T2>&, const pair<T1,T2>&);
  template <class T1, class T2>
    constexpr bool operator!=(const pair<T1,T2>&, const pair<T1,T2>&);
  template <class T1, class T2>
    constexpr bool operator> (const pair<T1,T2>&, const pair<T1,T2>&);
  template <class T1, class T2>
    constexpr bool operator>=(const pair<T1,T2>&, const pair<T1,T2>&);
  template <class T1, class T2>
    constexpr bool operator<=(const pair<T1,T2>&, const pair<T1,T2>&);
  template <class T1, class T2>
    void swap(pair<T1,T2>& x, pair<T1,T2>& y) noexcept(noexcept(x.swap(y)));
  template <class T1, class T2>
    constexpr see below make_pair(T1&&, T2&&);
  // [pair.astuple], tuple-like access to pair:
  template <class T> class tuple_size;
  template <size_t I, class T> class tuple_element;
  template <class T1, class T2> struct tuple_size<pair<T1, T2> >;
  template <class T1, class T2> struct tuple_element<0, pair<T1, T2> >;
  template <class T1, class T2> struct tuple_element<1, pair<T1, T2> >;
  template<size_t I, class T1, class T2>
    constexpr tuple_element_t<I, pair<T1, T2>>&
      get(pair<T1, T2>&) noexcept;
  template<size_t I, class T1, class T2>
    constexpr tuple_element_t<I, pair<T1, T2>>&&
      get(pair<T1, T2>&&) noexcept;
  template<size_t I, class T1, class T2>
    constexpr const tuple_element_t<I, pair<T1, T2>>&
      get(const pair<T1, T2>&) noexcept;
  template <class T, class U>
    constexpr T& get(pair<T, U>& p) noexcept;
  template <class T, class U>
    constexpr const T& get(const pair<T, U>& p) noexcept;
  template <class T, class U>
    constexpr T&& get(pair<T, U>&& p) noexcept;
  template <class T, class U>
    constexpr T& get(pair<U, T>& p) noexcept;
  template <class T, class U>
    constexpr const T& get(const pair<U, T>& p) noexcept;
  template <class T, class U>
    constexpr T&& get(pair<U, T>&& p) noexcept;
  // [pair.piecewise], pair piecewise construction
  struct piecewise_construct_t { };
  constexpr piecewise_construct_t piecewise_construct{};
  template <class... Types> class tuple;  // defined in <tuple>
  // [intseq], Compile-time integer sequences
  template<class T, T...> struct integer_sequence;
  template<size_t... I>
    using index_sequence = integer_sequence<size_t, I...>;
  template<class T, T N>
    using make_integer_sequence = integer_sequence<T, see below>;
  template<size_t N>
    using make_index_sequence = make_integer_sequence<size_t, N>;
  template<class... T>
    using index_sequence_for = make_index_sequence<sizeof...(T)>;
}
To avoid redundant definitions of operator!= out of operator== and operators >, <=, and >= out of operator<, the library provides the following:
Requires: Type T is EqualityComparable (Table [equalitycomparable]).
Returns: !(x == y).
template <class T> bool operator>(const T& x, const T& y);
Requires: Type T is LessThanComparable (Table [lessthancomparable]).
Returns: y < x.
template <class T> bool operator<=(const T& x, const T& y);
Requires: Type T is LessThanComparable (Table [lessthancomparable]).
Returns: !(y < x).
template <class T> bool operator>=(const T& x, const T& y);
Requires: Type T is LessThanComparable (Table [lessthancomparable]).
Returns: !(x < y).
In this library, whenever a declaration is provided for an operator!=, operator>, operator>=, or operator<=, and requirements and semantics are not explicitly provided, the requirements and semantics are as specified in this Clause.
template<class T> void swap(T& a, T& b) noexcept(see below);
Remark: The expression inside noexcept is equivalent to:
is_nothrow_move_constructible<T>::value && is_nothrow_move_assignable<T>::value
Requires: Type T shall be MoveConstructible (Table [moveconstructible]) and MoveAssignable (Table [moveassignable]).
Effects: Exchanges values stored in two locations.
template<class T, size_t N>
  void swap(T (&a)[N], T (&b)[N]) noexcept(noexcept(swap(*a, *b)));
Requires: a[i] shall be swappable with ([swappable.requirements]) b[i] for all i in the range [0,N).
Effects: swap_ranges(a, a + N, b)
template <class T, class U=T> T exchange(T& obj, U&& new_val);
Effects: Equivalent to:
T old_val = std::move(obj); obj = std::forward<U>(new_val); return old_val;
The library provides templated helper functions to simplify applying move semantics to an lvalue and to simplify the implementation of forwarding functions.
template <class T> constexpr T&& forward(remove_reference_t<T>& t) noexcept;
template <class T> constexpr T&& forward(remove_reference_t<T>&& t) noexcept;
Returns: static_cast<T&&>(t).
Remark: If the second form is instantiated with an lvalue reference type, the program is ill-formed.
[ Example:
template <class T, class A1, class A2>
shared_ptr<T> factory(A1&& a1, A2&& a2) {
  return shared_ptr<T>(new T(std::forward<A1>(a1), std::forward<A2>(a2)));
}
struct A {
  A(int&, const double&);
};
void g() {
  shared_ptr<A> sp1 = factory<A>(2, 1.414); // error: 2 will not bind to int&
  int i = 2;
  shared_ptr<A> sp2 = factory<A>(i, 1.414); // OK
}
In the first call to factory, A1 is deduced as int, so 2 is forwarded to A's constructor as an rvalue. In the second call to factory, A1 is deduced as int&, so i is forwarded to A's constructor as an lvalue. In both cases, A2 is deduced as double, so 1.414 is forwarded to A's constructor as an rvalue.
— end example ]
template <class T> constexpr remove_reference_t<T>&& move(T&& t) noexcept;
Returns: static_cast<remove_reference_t<T>&&>(t).
[ Example:
template <class T, class A1>
shared_ptr<T> factory(A1&& a1) {
  return shared_ptr<T>(new T(std::forward<A1>(a1)));
}
struct A {
  A();
  A(const A&);  // copies from lvalues
  A(A&&);       // moves from rvalues
};
void g() {
  A a;
  shared_ptr<A> sp1 = factory<A>(a);              // “a” binds to A(const A&)
  shared_ptr<A> sp1 = factory<A>(std::move(a));   // “a” binds to A(A&&)
}
In the first call to factory, A1 is deduced as A&, so a is forwarded as a non-const lvalue. This binds to the constructor A(const A&), which copies the value from a. In the second call to factory, because of the call std::move(a), A1 is deduced as A, so a is forwarded as an rvalue. This binds to the constructor A(A&&), which moves the value from a.
— end example ]
template <class T> constexpr conditional_t<
  !is_nothrow_move_constructible<T>::value && is_copy_constructible<T>::value,
  const T&, T&&> move_if_noexcept(T& x) noexcept;
Returns: std::move(x)
The library provides the function template declval to simplify the definition of expressions which occur as unevaluated operands (Clause [expr]).
template <class T>
  add_rvalue_reference_t<T> declval() noexcept;  // as unevaluated operand
Remarks: If this function is odr-used ([basic.def.odr]), the program is ill-formed.
Remarks: The template parameter T of declval may be an incomplete type.
[ Example:
template <class To, class From> decltype(static_cast<To>(declval<From>())) convert(From&&);
declares a function template convert which only participates in overloading if the type From can be explicitly converted to type To. For another example see class template common_type ([meta.trans.other]). — end example ]