25 Iterators library [iterators]

25.1 General [iterators.general]

This Clause describes components that C++ programs may use to perform iterations over containers ([containers]), streams ([iostream.format]), stream buffers ([stream.buffers]), and other ranges ([ranges]).
The following subclauses describe iterator requirements, and components for iterator primitives, predefined iterators, and stream iterators, as summarized in Table 84.
Table 84: Iterators library summary [tab:iterators.summary]
Subclause
Header
Iterator requirements
<iterator>
Iterator primitives
Iterator adaptors
Stream iterators
Range access

25.2 Header <iterator> synopsis [iterator.synopsis]

#include <compare> // see [compare.syn] #include <concepts> // see [concepts.syn] namespace std { template<class T> using with-reference = T&; // exposition only template<class T> concept can-reference // exposition only = requires { typename with-reference<T>; }; template<class T> concept dereferenceable // exposition only = requires(T& t) { { *t } -> can-reference; // not required to be equality-preserving }; // [iterator.assoc.types], associated types // [incrementable.traits], incrementable traits template<class> struct incrementable_traits; // freestanding template<class T> using iter_difference_t = see below; // freestanding // [readable.traits], indirectly readable traits template<class> struct indirectly_readable_traits; // freestanding template<class T> using iter_value_t = see below; // freestanding // [iterator.traits], iterator traits template<class I> struct iterator_traits; // freestanding template<class T> requires is_object_v<T> struct iterator_traits<T*>; // freestanding template<dereferenceable T> using iter_reference_t = decltype(*declval<T&>()); // freestanding namespace ranges { // [iterator.cust], customization point objects inline namespace unspecified { // [iterator.cust.move], ranges​::​iter_move inline constexpr unspecified iter_move = unspecified; // freestanding // [iterator.cust.swap], ranges​::​iter_swap inline constexpr unspecified iter_swap = unspecified; // freestanding } } template<dereferenceable T> requires requires(T& t) { { ranges::iter_move(t) } -> can-reference; } using iter_rvalue_reference_t // freestanding = decltype(ranges::iter_move(declval<T&>())); // [iterator.concepts], iterator concepts // [iterator.concept.readable], concept indirectly_readable template<class In> concept indirectly_readable = see below; // freestanding template<indirectly_readable T> using indirect-value-t = see below; // exposition only template<indirectly_readable T> using iter_common_reference_t = // freestanding common_reference_t<iter_reference_t<T>, indirect-value-t<T>>; // [iterator.concept.writable], concept indirectly_writable template<class Out, class T> concept indirectly_writable = see below; // freestanding // [iterator.concept.winc], concept weakly_incrementable template<class I> concept weakly_incrementable = see below; // freestanding // [iterator.concept.inc], concept incrementable template<class I> concept incrementable = see below; // freestanding // [iterator.concept.iterator], concept input_or_output_iterator template<class I> concept input_or_output_iterator = see below; // freestanding // [iterator.concept.sentinel], concept sentinel_for template<class S, class I> concept sentinel_for = see below; // freestanding // [iterator.concept.sizedsentinel], concept sized_sentinel_for template<class S, class I> constexpr bool disable_sized_sentinel_for = false; // freestanding template<class S, class I> concept sized_sentinel_for = see below; // freestanding // [iterator.concept.input], concept input_iterator template<class I> concept input_iterator = see below; // freestanding // [iterator.concept.output], concept output_iterator template<class I, class T> concept output_iterator = see below; // freestanding // [iterator.concept.forward], concept forward_iterator template<class I> concept forward_iterator = see below; // freestanding // [iterator.concept.bidir], concept bidirectional_iterator template<class I> concept bidirectional_iterator = see below; // freestanding // [iterator.concept.random.access], concept random_access_iterator template<class I> concept random_access_iterator = see below; // freestanding // [iterator.concept.contiguous], concept contiguous_iterator template<class I> concept contiguous_iterator = see below; // freestanding // [indirectcallable], indirect callable requirements // [indirectcallable.indirectinvocable], indirect callables template<class F, class I> concept indirectly_unary_invocable = see below; // freestanding template<class F, class I> concept indirectly_regular_unary_invocable = see below; // freestanding template<class F, class I> concept indirect_unary_predicate = see below; // freestanding template<class F, class I1, class I2> concept indirect_binary_predicate = see below; // freestanding template<class F, class I1, class I2 = I1> concept indirect_equivalence_relation = see below; // freestanding template<class F, class I1, class I2 = I1> concept indirect_strict_weak_order = see below; // freestanding template<class F, class... Is> requires (indirectly_readable<Is> && ...) && invocable<F, iter_reference_t<Is>...> using indirect_result_t = invoke_result_t<F, iter_reference_t<Is>...>; // freestanding // [projected], projected template<indirectly_readable I, indirectly_regular_unary_invocable<I> Proj> struct projected; // freestanding template<weakly_incrementable I, class Proj> struct incrementable_traits<projected<I, Proj>>; // freestanding // [alg.req], common algorithm requirements // [alg.req.ind.move], concept indirectly_movable template<class In, class Out> concept indirectly_movable = see below; // freestanding template<class In, class Out> concept indirectly_movable_storable = see below; // freestanding // [alg.req.ind.copy], concept indirectly_copyable template<class In, class Out> concept indirectly_copyable = see below; // freestanding template<class In, class Out> concept indirectly_copyable_storable = see below; // freestanding // [alg.req.ind.swap], concept indirectly_swappable template<class I1, class I2 = I1> concept indirectly_swappable = see below; // freestanding // [alg.req.ind.cmp], concept indirectly_comparable template<class I1, class I2, class R, class P1 = identity, class P2 = identity> concept indirectly_comparable = see below; // freestanding // [alg.req.permutable], concept permutable template<class I> concept permutable = see below; // freestanding // [alg.req.mergeable], concept mergeable template<class I1, class I2, class Out, class R = ranges::less, class P1 = identity, class P2 = identity> concept mergeable = see below; // freestanding // [alg.req.sortable], concept sortable template<class I, class R = ranges::less, class P = identity> concept sortable = see below; // freestanding // [iterator.primitives], primitives // [std.iterator.tags], iterator tags struct input_iterator_tag { }; // freestanding struct output_iterator_tag { }; // freestanding struct forward_iterator_tag: public input_iterator_tag { }; // freestanding struct bidirectional_iterator_tag: public forward_iterator_tag { }; // freestanding struct random_access_iterator_tag: public bidirectional_iterator_tag { }; // freestanding struct contiguous_iterator_tag: public random_access_iterator_tag { }; // freestanding // [iterator.operations], iterator operations template<class InputIterator, class Distance> constexpr void advance(InputIterator& i, Distance n); // freestanding template<class InputIterator> constexpr typename iterator_traits<InputIterator>::difference_type distance(InputIterator first, InputIterator last); // freestanding template<class InputIterator> constexpr InputIterator next(InputIterator x, // freestanding typename iterator_traits<InputIterator>::difference_type n = 1); template<class BidirectionalIterator> constexpr BidirectionalIterator prev(BidirectionalIterator x, // freestanding typename iterator_traits<BidirectionalIterator>::difference_type n = 1); // [range.iter.ops], range iterator operations namespace ranges { // [range.iter.op.advance], ranges​::​advance template<input_or_output_iterator I> constexpr void advance(I& i, iter_difference_t<I> n); // freestanding template<input_or_output_iterator I, sentinel_for<I> S> constexpr void advance(I& i, S bound); // freestanding template<input_or_output_iterator I, sentinel_for<I> S> constexpr iter_difference_t<I> advance(I& i, iter_difference_t<I> n, // freestanding S bound); // [range.iter.op.distance], ranges​::​distance template<class I, sentinel_for<I> S> requires (!sized_sentinel_for<S, I>) constexpr iter_difference_t<I> distance(I first, S last); // freestanding template<class I, sized_sentinel_for<decay_t<I>> S> constexpr iter_difference_t<decay_t<I>> distance(I&& first, S last); // freestanding template<range R> constexpr range_difference_t<R> distance(R&& r); // freestanding // [range.iter.op.next], ranges​::​next template<input_or_output_iterator I> constexpr I next(I x); // freestanding template<input_or_output_iterator I> constexpr I next(I x, iter_difference_t<I> n); // freestanding template<input_or_output_iterator I, sentinel_for<I> S> constexpr I next(I x, S bound); // freestanding template<input_or_output_iterator I, sentinel_for<I> S> constexpr I next(I x, iter_difference_t<I> n, S bound); // freestanding // [range.iter.op.prev], ranges​::​prev template<bidirectional_iterator I> constexpr I prev(I x); // freestanding template<bidirectional_iterator I> constexpr I prev(I x, iter_difference_t<I> n); // freestanding template<bidirectional_iterator I> constexpr I prev(I x, iter_difference_t<I> n, I bound); // freestanding } // [predef.iterators], predefined iterators and sentinels // [reverse.iterators], reverse iterators template<class Iterator> class reverse_iterator; // freestanding template<class Iterator1, class Iterator2> constexpr bool operator==( // freestanding const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr bool operator!=( // freestanding const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr bool operator<( // freestanding const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr bool operator>( // freestanding const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr bool operator<=( // freestanding const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr bool operator>=( // freestanding const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y); template<class Iterator1, three_way_comparable_with<Iterator1> Iterator2> constexpr compare_three_way_result_t<Iterator1, Iterator2> operator<=>(const reverse_iterator<Iterator1>& x, // freestanding const reverse_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr auto operator-( // freestanding const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y) -> decltype(y.base() - x.base()); template<class Iterator> constexpr reverse_iterator<Iterator> operator+( // freestanding iter_difference_t<Iterator> n, const reverse_iterator<Iterator>& x); template<class Iterator> constexpr reverse_iterator<Iterator> make_reverse_iterator(Iterator i); // freestanding template<class Iterator1, class Iterator2> requires (!sized_sentinel_for<Iterator1, Iterator2>) constexpr bool disable_sized_sentinel_for<reverse_iterator<Iterator1>, // freestanding reverse_iterator<Iterator2>> = true; // [insert.iterators], insert iterators template<class Container> class back_insert_iterator; // freestanding template<class Container> constexpr back_insert_iterator<Container> back_inserter(Container& x); // freestanding template<class Container> class front_insert_iterator; // freestanding template<class Container> constexpr front_insert_iterator<Container> front_inserter(Container& x); // freestanding template<class Container> class insert_iterator; // freestanding template<class Container> constexpr insert_iterator<Container> inserter(Container& x, ranges::iterator_t<Container> i); // freestanding // [const.iterators], constant iterators and sentinels // [const.iterators.alias], alias templates template<indirectly_readable I> using iter_const_reference_t = see below; // freestanding template<class Iterator> concept constant-iterator = see below; // exposition only template<input_iterator I> using const_iterator = see below; // freestanding template<semiregular S> using const_sentinel = see below; // freestanding // [const.iterators.iterator], class template basic_const_iterator template<input_iterator Iterator> class basic_const_iterator; // freestanding template<class T, common_with<T> U> requires input_iterator<common_type_t<T, U>> struct common_type<basic_const_iterator<T>, U> { // freestanding using type = basic_const_iterator<common_type_t<T, U>>; }; template<class T, common_with<T> U> requires input_iterator<common_type_t<T, U>> struct common_type<U, basic_const_iterator<T>> { // freestanding using type = basic_const_iterator<common_type_t<T, U>>; }; template<class T, common_with<T> U> requires input_iterator<common_type_t<T, U>> struct common_type<basic_const_iterator<T>, basic_const_iterator<U>> { // freestanding using type = basic_const_iterator<common_type_t<T, U>>; }; template<input_iterator I> constexpr const_iterator<I> make_const_iterator(I it) { return it; } // freestanding template<semiregular S> constexpr const_sentinel<S> make_const_sentinel(S s) { return s; } // freestanding // [move.iterators], move iterators and sentinels template<class Iterator> class move_iterator; // freestanding template<class Iterator1, class Iterator2> constexpr bool operator==( // freestanding const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr bool operator<( // freestanding const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr bool operator>( // freestanding const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr bool operator<=( // freestanding const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr bool operator>=( // freestanding const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y); template<class Iterator1, three_way_comparable_with<Iterator1> Iterator2> constexpr compare_three_way_result_t<Iterator1, Iterator2> operator<=>(const move_iterator<Iterator1>& x, // freestanding const move_iterator<Iterator2>& y); template<class Iterator1, class Iterator2> constexpr auto operator-( // freestanding const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y) -> decltype(x.base() - y.base()); template<class Iterator> constexpr move_iterator<Iterator> operator+(iter_difference_t<Iterator> n, const move_iterator<Iterator>& x); // freestanding template<class Iterator> constexpr move_iterator<Iterator> make_move_iterator(Iterator i); // freestanding template<class Iterator1, class Iterator2> requires (!sized_sentinel_for<Iterator1, Iterator2>) constexpr bool disable_sized_sentinel_for<move_iterator<Iterator1>, // freestanding move_iterator<Iterator2>> = true; template<semiregular S> class move_sentinel; // freestanding // [iterators.common], common iterators template<input_or_output_iterator I, sentinel_for<I> S> requires (!same_as<I, S> && copyable<I>) class common_iterator; // freestanding template<class I, class S> struct incrementable_traits<common_iterator<I, S>>; // freestanding template<input_iterator I, class S> struct iterator_traits<common_iterator<I, S>>; // freestanding // [default.sentinel], default sentinel struct default_sentinel_t; // freestanding inline constexpr default_sentinel_t default_sentinel{}; // freestanding // [iterators.counted], counted iterators template<input_or_output_iterator I> class counted_iterator; // freestanding template<input_iterator I> requires see below struct iterator_traits<counted_iterator<I>>; // freestanding // [unreachable.sentinel], unreachable sentinel struct unreachable_sentinel_t; // freestanding inline constexpr unreachable_sentinel_t unreachable_sentinel{}; // freestanding // [stream.iterators], stream iterators template<class T, class charT = char, class traits = char_traits<charT>, class Distance = ptrdiff_t> class istream_iterator; template<class T, class charT, class traits, class Distance> bool operator==(const istream_iterator<T,charT,traits,Distance>& x, const istream_iterator<T,charT,traits,Distance>& y); template<class T, class charT = char, class traits = char_traits<charT>> class ostream_iterator; template<class charT, class traits = char_traits<charT>> class istreambuf_iterator; template<class charT, class traits> bool operator==(const istreambuf_iterator<charT,traits>& a, const istreambuf_iterator<charT,traits>& b); template<class charT, class traits = char_traits<charT>> class ostreambuf_iterator; // [iterator.range], range access template<class C> constexpr auto begin(C& c) -> decltype(c.begin()); // freestanding template<class C> constexpr auto begin(const C& c) -> decltype(c.begin()); // freestanding template<class C> constexpr auto end(C& c) -> decltype(c.end()); // freestanding template<class C> constexpr auto end(const C& c) -> decltype(c.end()); // freestanding template<class T, size_t N> constexpr T* begin(T (&array)[N]) noexcept; // freestanding template<class T, size_t N> constexpr T* end(T (&array)[N]) noexcept; // freestanding template<class C> constexpr auto cbegin(const C& c) // freestanding noexcept(noexcept(std::begin(c))) -> decltype(std::begin(c)); template<class C> constexpr auto cend(const C& c) // freestanding noexcept(noexcept(std::end(c))) -> decltype(std::end(c)); template<class C> constexpr auto rbegin(C& c) -> decltype(c.rbegin()); // freestanding template<class C> constexpr auto rbegin(const C& c) -> decltype(c.rbegin()); // freestanding template<class C> constexpr auto rend(C& c) -> decltype(c.rend()); // freestanding template<class C> constexpr auto rend(const C& c) -> decltype(c.rend()); // freestanding template<class T, size_t N> constexpr reverse_iterator<T*> rbegin(T (&array)[N]) // freestanding template<class T, size_t N> constexpr reverse_iterator<T*> rend(T (&array)[N]); // freestanding template<class E> constexpr reverse_iterator<const E*> rbegin(initializer_list<E> il); // freestanding template<class E> constexpr reverse_iterator<const E*> rend(initializer_list<E> il); // freestanding template<class C> constexpr auto crbegin(const C& c) -> decltype(std::rbegin(c)); // freestanding template<class C> constexpr auto crend(const C& c) -> decltype(std::rend(c)); // freestanding template<class C> constexpr auto size(const C& c) -> decltype(c.size()); // freestanding template<class T, size_t N> constexpr size_t size(const T (&array)[N]) noexcept; // freestanding template<class C> constexpr auto ssize(const C& c) -> common_type_t<ptrdiff_t, make_signed_t<decltype(c.size())>>; // freestanding template<class T, ptrdiff_t N> constexpr ptrdiff_t ssize(const T (&array)[N]) noexcept; // freestanding template<class C> [[nodiscard]] constexpr auto empty(const C& c) -> decltype(c.empty()); // freestanding template<class T, size_t N> [[nodiscard]] constexpr bool empty(const T (&array)[N]) noexcept; // freestanding template<class E> [[nodiscard]] constexpr bool empty(initializer_list<E> il) noexcept; // freestanding template<class C> constexpr auto data(C& c) -> decltype(c.data()); // freestanding template<class C> constexpr auto data(const C& c) -> decltype(c.data()); // freestanding template<class T, size_t N> constexpr T* data(T (&array)[N]) noexcept; // freestanding template<class E> constexpr const E* data(initializer_list<E> il) noexcept; // freestanding }

25.3 Iterator requirements [iterator.requirements]

25.3.1 In general [iterator.requirements.general]

Iterators are a generalization of pointers that allow a C++ program to work with different data structures (for example, containers and ranges) in a uniform manner.
To be able to construct template algorithms that work correctly and efficiently on different types of data structures, the library formalizes not just the interfaces but also the semantics and complexity assumptions of iterators.
An input iterator i supports the expression *i, resulting in a value of some object type T, called the value type of the iterator.
An output iterator i has a non-empty set of types that are indirectly_writable to the iterator; for each such type T, the expression *i = o is valid where o is a value of type T.
For every iterator type X, there is a corresponding signed integer-like type ([iterator.concept.winc]) called the difference type of the iterator.
Since iterators are an abstraction of pointers, their semantics are a generalization of most of the semantics of pointers in C++.
This ensures that every function template that takes iterators works as well with regular pointers.
This document defines six categories of iterators, according to the operations defined on them: input iterators, output iterators, forward iterators, bidirectional iterators, random access iterators, and contiguous iterators, as shown in Table 85.
Table 85: Relations among iterator categories [tab:iterators.relations]
Contiguous
β†’ Random Access
β†’ Bidirectional
β†’ Forward
β†’ Input
β†’ Output
Forward iterators meet all the requirements of input iterators and can be used whenever an input iterator is specified; Bidirectional iterators also meet all the requirements of forward iterators and can be used whenever a forward iterator is specified; Random access iterators also meet all the requirements of bidirectional iterators and can be used whenever a bidirectional iterator is specified; Contiguous iterators also meet all the requirements of random access iterators and can be used whenever a random access iterator is specified.
Iterators that further meet the requirements of output iterators are called mutable iterators.
Nonmutable iterators are referred to as constant iterators.
In addition to the requirements in this subclause, the nested typedef-names specified in [iterator.traits] shall be provided for the iterator type.
[Note 1: 
Either the iterator type must provide the typedef-names directly (in which case iterator_traits pick them up automatically), or an iterator_traits specialization must provide them.
β€” end note]
Just as a regular pointer to an array guarantees that there is a pointer value pointing past the last element of the array, so for any iterator type there is an iterator value that points past the last element of a corresponding sequence.
Such a value is called a past-the-end value.
Values of an iterator i for which the expression *i is defined are called dereferenceable.
The library never assumes that past-the-end values are dereferenceable.
Iterators can also have singular values that are not associated with any sequence.
Results of most expressions are undefined for singular values; the only exceptions are destroying an iterator that holds a singular value, the assignment of a non-singular value to an iterator that holds a singular value, and, for iterators that meet the Cpp17DefaultConstructible requirements, using a value-initialized iterator as the source of a copy or move operation.
[Note 2: 
This guarantee is not offered for default-initialization, although the distinction only matters for types with trivial default constructors such as pointers or aggregates holding pointers.
β€” end note]
In these cases the singular value is overwritten the same way as any other value.
Dereferenceable values are always non-singular.
Most of the library's algorithmic templates that operate on data structures have interfaces that use ranges.
A range is an iterator and a sentinel that designate the beginning and end of the computation, or an iterator and a count that designate the beginning and the number of elements to which the computation is to be applied.212
An iterator and a sentinel denoting a range are comparable.
A range [i, s) is empty if i == s; otherwise, [i, s) refers to the elements in the data structure starting with the element pointed to by i and up to but not including the element, if any, pointed to by the first iterator j such that j == s.
A sentinel s is called reachable from an iterator i if and only if there is a finite sequence of applications of the expression ++i that makes i == s.
If s is reachable from i, [i, s) denotes a valid range.
A counted range is empty if n == 0; otherwise, refers to the n elements in the data structure starting with the element pointed to by i and up to but not including the element, if any, pointed to by the result of n applications of ++i.
A counted range is valid if and only if n == 0; or n is positive, i is dereferenceable, and is valid.
The result of the application of library functions to invalid ranges is undefined.
All the categories of iterators require only those functions that are realizable for a given category in constant time (amortized).
Therefore, requirement tables and concept definitions for the iterators do not specify complexity.
Destruction of a non-forward iterator may invalidate pointers and references previously obtained from that iterator.
An invalid iterator is an iterator that may be singular.213
Iterators are called constexpr iterators if all operations provided to meet iterator category requirements are constexpr functions.
[Note 3: 
For example, the types β€œpointer to int” and reverse_iterator<int*> are constexpr iterators.
β€” end note]
212)212)
The sentinel denoting the end of a range can have the same type as the iterator denoting the beginning of the range, or a different type.
213)213)
This definition applies to pointers, since pointers are iterators.
The effect of dereferencing an iterator that has been invalidated is undefined.

25.3.2 Associated types [iterator.assoc.types]

25.3.2.1 Incrementable traits [incrementable.traits]

To implement algorithms only in terms of incrementable types, it is often necessary to determine the difference type that corresponds to a particular incrementable type.
Accordingly, it is required that if WI is the name of a type that models the weakly_incrementable concept ([iterator.concept.winc]), the type iter_difference_t<WI> be defined as the incrementable type's difference type.
namespace std { template<class> struct incrementable_traits { }; template<class T> requires is_object_v<T> struct incrementable_traits<T*> { using difference_type = ptrdiff_t; }; template<class I> struct incrementable_traits<const I> : incrementable_traits<I> { }; template<class T> requires requires { typename T::difference_type; } struct incrementable_traits<T> { using difference_type = typename T::difference_type; }; template<class T> requires (!requires { typename T::difference_type; } && requires(const T& a, const T& b) { { a - b } -> integral; }) struct incrementable_traits<T> { using difference_type = make_signed_t<decltype(declval<T>() - declval<T>())>; }; template<class T> using iter_difference_t = see below; }
Let be remove_cvref_t<I>.
The type iter_difference_t<I> denotes
  • incrementable_traits<>​::​difference_type if iterator_traits<> names a specialization generated from the primary template, and
  • iterator_traits<>​::​difference_type otherwise.
Users may specialize incrementable_traits on program-defined types.

25.3.2.2 Indirectly readable traits [readable.traits]

To implement algorithms only in terms of indirectly readable types, it is often necessary to determine the value type that corresponds to a particular indirectly readable type.
Accordingly, it is required that if R is the name of a type that models the indirectly_readable concept ([iterator.concept.readable]), the type iter_value_t<R> be defined as the indirectly readable type's value type.
template<class> struct cond-value-type { }; // exposition only template<class T> requires is_object_v<T> struct cond-value-type<T> { using value_type = remove_cv_t<T>; }; template<class T> concept has-member-value-type = requires { typename T::value_type; }; // exposition only template<class T> concept has-member-element-type = requires { typename T::element_type; }; // exposition only template<class> struct indirectly_readable_traits { }; template<class T> struct indirectly_readable_traits<T*> : cond-value-type<T> { }; template<class I> requires is_array_v<I> struct indirectly_readable_traits<I> { using value_type = remove_cv_t<remove_extent_t<I>>; }; template<class I> struct indirectly_readable_traits<const I> : indirectly_readable_traits<I> { }; template<has-member-value-type T> struct indirectly_readable_traits<T> : cond-value-type<typename T::value_type> { }; template<has-member-element-type T> struct indirectly_readable_traits<T> : cond-value-type<typename T::element_type> { }; template<has-member-value-type T> requires has-member-element-type<T> struct indirectly_readable_traits<T> { }; template<has-member-value-type T> requires has-member-element-type<T> && same_as<remove_cv_t<typename T::element_type>, remove_cv_t<typename T::value_type>> struct indirectly_readable_traits<T> : cond-value-type<typename T::value_type> { }; template<class T> using iter_value_t = see below;
Let be remove_cvref_t<I>.
The type iter_value_t<I> denotes
  • indirectly_readable_traits<>​::​value_type if iterator_traits<> names a specialization generated from the primary template, and
  • iterator_traits<>​::​value_type otherwise.
Class template indirectly_readable_traits may be specialized on program-defined types.
[Note 1: 
Some legacy output iterators define a nested type named value_type that is an alias for void.
These types are not indirectly_readable and have no associated value types.
β€” end note]
[Note 2: 
Smart pointers like shared_ptr<int> are indirectly_readable and have an associated value type, but a smart pointer like shared_ptr<void> is not indirectly_readable and has no associated value type.
β€” end note]

25.3.2.3 Iterator traits [iterator.traits]

To implement algorithms only in terms of iterators, it is sometimes necessary to determine the iterator category that corresponds to a particular iterator type.
Accordingly, it is required that if I is the type of an iterator, the type iterator_traits<I>::iterator_category be defined as the iterator's iterator category.
In addition, the types iterator_traits<I>::pointer iterator_traits<I>::reference shall be defined as the iterator's pointer and reference types; that is, for an iterator object a of class type, the same type as decltype(a.operator->()) and decltype(*a), respectively.
The type iterator_traits<I>​::​pointer shall be void for an iterator of class type I that does not support operator->.
Additionally, in the case of an output iterator, the types iterator_traits<I>::value_type iterator_traits<I>::difference_type iterator_traits<I>::reference may be defined as void.
The definitions in this subclause make use of the following exposition-only concepts: template<class I> concept cpp17-iterator = requires(I i) { { *i } -> can-reference; { ++i } -> same_as<I&>; { *i++ } -> can-reference; } && copyable<I>; template<class I> concept cpp17-input-iterator = cpp17-iterator<I> && equality_comparable<I> && requires(I i) { typename incrementable_traits<I>::difference_type; typename indirectly_readable_traits<I>::value_type; typename common_reference_t<iter_reference_t<I>&&, typename indirectly_readable_traits<I>::value_type&>; typename common_reference_t<decltype(*i++)&&, typename indirectly_readable_traits<I>::value_type&>; requires signed_integral<typename incrementable_traits<I>::difference_type>; }; template<class I> concept cpp17-forward-iterator = cpp17-input-iterator<I> && constructible_from<I> && is_reference_v<iter_reference_t<I>> && same_as<remove_cvref_t<iter_reference_t<I>>, typename indirectly_readable_traits<I>::value_type> && requires(I i) { { i++ } -> convertible_to<const I&>; { *i++ } -> same_as<iter_reference_t<I>>; }; template<class I> concept cpp17-bidirectional-iterator = cpp17-forward-iterator<I> && requires(I i) { { --i } -> same_as<I&>; { i-- } -> convertible_to<const I&>; { *i-- } -> same_as<iter_reference_t<I>>; }; template<class I> concept cpp17-random-access-iterator = cpp17-bidirectional-iterator<I> && totally_ordered<I> && requires(I i, typename incrementable_traits<I>::difference_type n) { { i += n } -> same_as<I&>; { i -= n } -> same_as<I&>; { i + n } -> same_as<I>; { n + i } -> same_as<I>; { i - n } -> same_as<I>; { i - i } -> same_as<decltype(n)>; { i[n] } -> convertible_to<iter_reference_t<I>>; };
The members of a specialization iterator_traits<I> generated from the iterator_traits primary template are computed as follows:
  • If I has valid ([temp.deduct]) member types difference_type, value_type, reference, and iterator_category, then iterator_traits<I> has the following publicly accessible members: using iterator_category = typename I::iterator_category; using value_type = typename I::value_type; using difference_type = typename I::difference_type; using pointer = see below; using reference = typename I::reference;
    If the qualified-id I​::​pointer is valid and denotes a type, then iterator_traits<I>​::​pointer names that type; otherwise, it names void.
  • Otherwise, if I satisfies the exposition-only concept cpp17-input-iterator, iterator_traits<I> has the following publicly accessible members: using iterator_category = see below; using value_type = typename indirectly_readable_traits<I>::value_type; using difference_type = typename incrementable_traits<I>::difference_type; using pointer = see below; using reference = see below;
  • Otherwise, if I satisfies the exposition-only concept cpp17-iterator, then iterator_traits<I> has the following publicly accessible members: using iterator_category = output_iterator_tag; using value_type = void; using difference_type = see below; using pointer = void; using reference = void;
    If the qualified-id incrementable_traits<I>​::​difference_type is valid and denotes a type, then difference_type names that type; otherwise, it names void.
  • Otherwise, iterator_traits<I> has no members by any of the above names.
Explicit or partial specializations of iterator_traits may have a member type iterator_concept that is used to indicate conformance to the iterator concepts ([iterator.concepts]).
[Example 1: 
To indicate conformance to the input_iterator concept but a lack of conformance to the Cpp17InputIterator requirements ([input.iterators]), an iterator_traits specialization might have iterator_concept denote input_iterator_tag but not define iterator_category.
β€” end example]
iterator_traits is specialized for pointers as namespace std { template<class T> requires is_object_v<T> struct iterator_traits<T*> { using iterator_concept = contiguous_iterator_tag; using iterator_category = random_access_iterator_tag; using value_type = remove_cv_t<T>; using difference_type = ptrdiff_t; using pointer = T*; using reference = T&; }; }
[Example 2: 
To implement a generic reverse function, a C++ program can do the following: template<class BI> void reverse(BI first, BI last) { typename iterator_traits<BI>::difference_type n = distance(first, last); --n; while(n > 0) { typename iterator_traits<BI>::value_type tmp = *first; *first++ = *--last; *last = tmp; n -= 2; } }
β€” end example]

25.3.3 Customization point objects [iterator.cust]

25.3.3.1 ranges​::​iter_move [iterator.cust.move]

The name ranges​::​iter_move denotes a customization point object ([customization.point.object]).
The expression ranges​::​iter_move(E) for a subexpression E is expression-equivalent to:
  • iter_move(E), if E has class or enumeration type and iter_move(E) is a well-formed expression when treated as an unevaluated operand, where the meaning of iter_move is established as-if by performing argument-dependent lookup only ([basic.lookup.argdep]).
  • Otherwise, if the expression *E is well-formed:
  • Otherwise, ranges​::​iter_move(E) is ill-formed.
    [Note 1: 
    This case can result in substitution failure when ranges​::​iter_move(E) appears in the immediate context of a template instantiation.
    β€” end note]
If ranges​::​iter_move(E) is not equal to *E, the program is ill-formed, no diagnostic required.

25.3.3.2 ranges​::​iter_swap [iterator.cust.swap]

The name ranges​::​iter_swap denotes a customization point object ([customization.point.object]) that exchanges the values ([concept.swappable]) denoted by its arguments.
Let iter-exchange-move be the exposition-only function template:
template<class X, class Y> constexpr iter_value_t<X> iter-exchange-move(X&& x, Y&& y) noexcept(noexcept(iter_value_t<X>(iter_move(x))) && noexcept(*x = iter_move(y)));
Effects: Equivalent to: iter_value_t<X> old_value(iter_move(x)); *x = iter_move(y); return old_value;
The expression ranges​::​iter_swap(E1, E2) for subexpressions E1 and E2 is expression-equivalent to:
  • (void)iter_swap(E1, E2), if either E1 or E2 has class or enumeration type and iter_swap(E1, E2) is a well-formed expression with overload resolution performed in a context that includes the declaration template<class I1, class I2> void iter_swap(I1, I2) = delete; and does not include a declaration of ranges​::​iter_swap.
    If the function selected by overload resolution does not exchange the values denoted by E1 and E2, the program is ill-formed, no diagnostic required.
    [Note 1: 
    This precludes calling unconstrained std​::​iter_swap.
    When the deleted overload is viable, program-defined overloads need to be more specialized ([temp.func.order]) to be selected.
    β€” end note]
  • Otherwise, if the types of E1 and E2 each model indirectly_readable, and if the reference types of E1 and E2 model swappable_with ([concept.swappable]), then ranges​::​swap(*E1, *E2).
  • Otherwise, if the types T1 and T2 of E1 and E2 model indirectly_movable_storable<T1, T2> and indirectly_movable_storable<T2, T1>, then (void)(*E1 = iter-exchange-move(E2, E1)), except that E1 is evaluated only once.
  • Otherwise, ranges​::​iter_swap(E1, E2) is ill-formed.
    [Note 2: 
    This case can result in substitution failure when ranges​::​iter_swap(E1, E2) appears in the immediate context of a template instantiation.
    β€” end note]

25.3.4 Iterator concepts [iterator.concepts]

25.3.4.1 General [iterator.concepts.general]

For a type I, let ITER_TRAITS(I) denote the type I if iterator_traits<I> names a specialization generated from the primary template.
Otherwise, ITER_TRAITS(I) denotes iterator_traits<I>.
  • If the qualified-id ITER_TRAITS(I)​::​iterator_concept is valid and names a type, then ITER_CONCEPT(I) denotes that type.
  • Otherwise, if the qualified-id ITER_TRAITS(I)​::​iterator_category is valid and names a type, then ITER_CONCEPT(I) denotes that type.
  • Otherwise, if iterator_traits<I> names a specialization generated from the primary template, then ITER_CONCEPT(I) denotes random_access_iterator_tag.
  • Otherwise, ITER_CONCEPT(I) does not denote a type.
[Note 1: 
ITER_TRAITS enables independent syntactic determination of an iterator's category and concept.
β€” end note]
[Example 1: 
struct I { using value_type = int; using difference_type = int; int operator*() const; I& operator++(); I operator++(int); I& operator--(); I operator--(int); bool operator==(I) const; }; iterator_traits<I>​::​iterator_category denotes input_iterator_tag, and ITER_CONCEPT(I) denotes random_access_iterator_tag.
β€” end example]

25.3.4.2 Concept indirectly_readable [iterator.concept.readable]

Types that are indirectly readable by applying operator* model the indirectly_readable concept, including pointers, smart pointers, and iterators.
template<class In> concept indirectly-readable-impl = // exposition only requires(const In in) { typename iter_value_t<In>; typename iter_reference_t<In>; typename iter_rvalue_reference_t<In>; { *in } -> same_as<iter_reference_t<In>>; { ranges::iter_move(in) } -> same_as<iter_rvalue_reference_t<In>>; } && common_reference_with<iter_reference_t<In>&&, iter_value_t<In>&> && common_reference_with<iter_reference_t<In>&&, iter_rvalue_reference_t<In>&&> && common_reference_with<iter_rvalue_reference_t<In>&&, const iter_value_t<In>&>;
template<class In> concept indirectly_readable = indirectly-readable-impl<remove_cvref_t<In>>;
Given a value i of type I, I models indirectly_readable only if the expression *i is equality-preserving.

25.3.4.3 Concept indirectly_writable [iterator.concept.writable]

The indirectly_writable concept specifies the requirements for writing a value into an iterator's referenced object.
template<class Out, class T> concept indirectly_writable = requires(Out&& o, T&& t) { *o = std::forward<T>(t); // not required to be equality-preserving *std::forward<Out>(o) = std::forward<T>(t); // not required to be equality-preserving const_cast<const iter_reference_t<Out>&&>(*o) = std::forward<T>(t); // not required to be equality-preserving const_cast<const iter_reference_t<Out>&&>(*std::forward<Out>(o)) = std::forward<T>(t); // not required to be equality-preserving };
Let E be an expression such that decltype((E)) is T, and let o be a dereferenceable object of type Out.
Out and T model indirectly_writable<Out, T> only if
  • If Out and T model indirectly_readable<Out> && same_as<iter_value_t<Out>, decay_t<T>>, then *o after any above assignment is equal to the value of E before the assignment.
After evaluating any above assignment expression, o is not required to be dereferenceable.
If E is an xvalue ([basic.lval]), the resulting state of the object it denotes is valid but unspecified ([lib.types.movedfrom]).
[Note 1: 
The only valid use of an operator* is on the left side of the assignment statement.
Assignment through the same value of the indirectly writable type happens only once.
β€” end note]
[Note 2: 
indirectly_writable has the awkward const_cast expressions to reject iterators with prvalue non-proxy reference types that permit rvalue assignment but do not also permit const rvalue assignment.
Consequently, an iterator type I that returns std​::​string by value does not model indirectly_writable<I, std​::​string>.
β€” end note]

25.3.4.4 Concept weakly_incrementable [iterator.concept.winc]

The weakly_incrementable concept specifies the requirements on types that can be incremented with the pre- and post-increment operators.
The increment operations are not required to be equality-preserving, nor is the type required to be equality_comparable.
template<class T> constexpr bool is-integer-like = see below; // exposition only template<class T> constexpr bool is-signed-integer-like = see below; // exposition only template<class I> concept weakly_incrementable = movable<I> && requires(I i) { typename iter_difference_t<I>; requires is-signed-integer-like<iter_difference_t<I>>; { ++i } -> same_as<I&>; // not required to be equality-preserving i++; // not required to be equality-preserving };
A type I is an integer-class type if it is in a set of implementation-defined types that behave as integer types do, as defined below.
[Note 1: 
An integer-class type is not necessarily a class type.
β€” end note]
The range of representable values of an integer-class type is the continuous set of values over which it is defined.
For any integer-class type, its range of representable values is either to (inclusive) for some integer N, in which case it is a signed-integer-class type, or 0 to (inclusive) for some integer N, in which case it is an unsigned-integer-class type.
In both cases, N is called the width of the integer-class type.
The width of an integer-class type is greater than that of every integral type of the same signedness.
A type I other than cv bool is integer-like if it models integral<I> or if it is an integer-class type.
An integer-like type I is signed-integer-like if it models signed_integral<I> or if it is a signed-integer-class type.
An integer-like type I is unsigned-integer-like if it models unsigned_integral<I> or if it is an unsigned-integer-class type.
For every integer-class type I, let B(I) be a unique hypothetical extended integer type of the same signedness with the same width ([basic.fundamental]) as I.
[Note 2: 
The corresponding hypothetical specialization numeric_limits<B(I)> meets the requirements on numeric_limits specializations for integral types ([numeric.limits]).
β€” end note]
For every integral type J, let B(J) be the same type as J.
Expressions of integer-class type are explicitly convertible to any integer-like type, and implicitly convertible to any integer-class type of equal or greater width and the same signedness.
Expressions of integral type are both implicitly and explicitly convertible to any integer-class type.
Conversions between integral and integer-class types and between two integer-class types do not exit via an exception.
The result of such a conversion is the unique value of the destination type that is congruent to the source modulo , where N is the width of the destination type.
Let a be an object of integer-class type I, let b be an object of integer-like type I2 such that the expression b is implicitly convertible to I, let x and y be, respectively, objects of type B(I) and B(I2) as described above that represent the same values as a and b, and let c be an lvalue of any integral type.
  • The expressions a++ and a-- shall be prvalues of type I whose values are equal to that of a prior to the evaluation of the expressions.
    The expression a++ shall modify the value of a by adding 1 to it.
    The expression a-- shall modify the value of a by subtracting 1 from it.
  • The expressions ++a, --a, and &a shall be expression-equivalent to a += 1, a -= 1, and addressof(a), respectively.
  • For every unary-operator @ other than & for which the expression @x is well-formed, @a shall also be well-formed and have the same value, effects, and value category as @x.
    If @x has type bool, so too does @a; if @x has type B(I), then @a has type I.
  • For every assignment operator @= for which c @= x is well-formed, c @= a shall also be well-formed and shall have the same value and effects as c @= x.
    The expression c @= a shall be an lvalue referring to c.
  • For every assignment operator @= for which x @= y is well-formed, a @= b shall also be well-formed and shall have the same effects as x @= y, except that the value that would be stored into x is stored into a.
    The expression a @= b shall be an lvalue referring to a.
  • For every non-assignment binary operator @ for which x @ y and y @ x are well-formed, a @ b and b @ a shall also be well-formed and shall have the same value, effects, and value category as x @ y and y @ x, respectively.
    If x @ y or y @ x has type B(I), then a @ b or b @ a, respectively, has type I; if x @ y or y @ x has type B(I2), then a @ b or b @ a, respectively, has type I2; if x @ y or y @ x has any other type, then a @ b or b @ a, respectively, has that type.
An expression E of integer-class type I is contextually convertible to bool as if by bool(E != I(0)).
All integer-class types model regular ([concepts.object]) and three_way_comparable<strong_ordering> ([cmp.concept]).
A value-initialized object of integer-class type has value 0.
For every (possibly cv-qualified) integer-class type I, numeric_limits<I> is specialized such that each static data member m has the same value as numeric_limits<B(I)>​::​m, and each static member function f returns I(numeric_limits<B(I)>​::​f()).
For any two integer-like types I1 and I2, at least one of which is an integer-class type, common_type_t<I1, I2> denotes an integer-class type whose width is not less than that of I1 or I2.
If both I1 and I2 are signed-integer-like types, then common_type_t<I1, I2> is also a signed-integer-like type.
is-integer-like<I> is true if and only if I is an integer-like type.
is-signed-integer-like<I> is true if and only if I is a signed-integer-like type.
Let i be an object of type I.
When i is in the domain of both pre- and post-increment, i is said to be incrementable.
I models weakly_incrementable<I> only if
  • The expressions ++i and i++ have the same domain.
  • If i is incrementable, then both ++i and i++ advance i to the next element.
  • If i is incrementable, then addressof(++i) is equal to addressof(i).
Recommended practice: The implementaton of an algorithm on a weakly incrementable type should never attempt to pass through the same incrementable value twice; such an algorithm should be a single-pass algorithm.
[Note 3: 
For weakly_incrementable types, a equals b does not imply that ++a equals ++b.
(Equality does not guarantee the substitution property or referential transparency.)
Such algorithms can be used with istreams as the source of the input data through the istream_iterator class template.
β€” end note]

25.3.4.5 Concept incrementable [iterator.concept.inc]

The incrementable concept specifies requirements on types that can be incremented with the pre- and post-increment operators.
The increment operations are required to be equality-preserving, and the type is required to be equality_comparable.
[Note 1: 
This supersedes the annotations on the increment expressions in the definition of weakly_incrementable.
β€” end note]
template<class I> concept incrementable = regular<I> && weakly_incrementable<I> && requires(I i) { { i++ } -> same_as<I>; };
Let a and b be incrementable objects of type I.
I models incrementable only if
  • If bool(a == b) then bool(a++ == b).
  • If bool(a == b) then bool(((void)a++, a) == ++b).
[Note 2: 
The requirement that a equals b implies ++a equals ++b (which is not true for weakly incrementable types) allows the use of multi-pass one-directional algorithms with types that model incrementable.
β€” end note]

25.3.4.6 Concept input_or_output_iterator [iterator.concept.iterator]

The input_or_output_iterator concept forms the basis of the iterator concept taxonomy; every iterator models input_or_output_iterator.
This concept specifies operations for dereferencing and incrementing an iterator.
Most algorithms will require additional operations to compare iterators with sentinels ([iterator.concept.sentinel]), to read ([iterator.concept.input]) or write ([iterator.concept.output]) values, or to provide a richer set of iterator movements ([iterator.concept.forward], [iterator.concept.bidir], [iterator.concept.random.access]).
template<class I> concept input_or_output_iterator = requires(I i) { { *i } -> can-reference; } && weakly_incrementable<I>;
[Note 1: 
Unlike the Cpp17Iterator requirements, the input_or_output_iterator concept does not require copyability.
β€” end note]

25.3.4.7 Concept sentinel_for [iterator.concept.sentinel]

The sentinel_for concept specifies the relationship between an input_or_output_iterator type and a semiregular type whose values denote a range.
Let s and i be values of type S and I such that [i, s) denotes a range.
Types S and I model sentinel_for<S, I> only if
  • i == s is well-defined.
  • If bool(i != s) then i is dereferenceable and [++i, s) denotes a range.
  • assignable_from<I&, S> is either modeled or not satisfied.
The domain of == is not static.
Given an iterator i and sentinel s such that [i, s) denotes a range and i != s, i and s are not required to continue to denote a range after incrementing any other iterator equal to i.
Consequently, i == s is no longer required to be well-defined.

25.3.4.8 Concept sized_sentinel_for [iterator.concept.sizedsentinel]

The sized_sentinel_for concept specifies requirements on an input_or_output_iterator type I and a corresponding sentinel_for<I> that allow the use of the - operator to compute the distance between them in constant time.
template<class S, class I> concept sized_sentinel_for = sentinel_for<S, I> && !disable_sized_sentinel_for<remove_cv_t<S>, remove_cv_t<I>> && requires(const I& i, const S& s) { { s - i } -> same_as<iter_difference_t<I>>; { i - s } -> same_as<iter_difference_t<I>>; };
Let i be an iterator of type I, and s a sentinel of type S such that [i, s) denotes a range.
Let N be the smallest number of applications of ++i necessary to make bool(i == s) be true.
S and I model sized_sentinel_for<S, I> only if
  • If N is representable by iter_difference_t<I>, then s - i is well-defined and equals N.
  • If is representable by iter_difference_t<I>, then i - s is well-defined and equals .
template<class S, class I> constexpr bool disable_sized_sentinel_for = false;
Remarks: Pursuant to [namespace.std], users may specialize disable_sized_sentinel_for for cv-unqualified non-array object types S and I if S and/or I is a program-defined type.
Such specializations shall be usable in constant expressions ([expr.const]) and have type const bool.
[Note 1: 
disable_sized_sentinel_for allows use of sentinels and iterators with the library that satisfy but do not in fact model sized_sentinel_for.
β€” end note]
[Example 1: 
The sized_sentinel_for concept is modeled by pairs of random_access_iterators ([iterator.concept.random.access]) and by counted iterators and their sentinels ([counted.iterator]).
β€” end example]

25.3.4.9 Concept input_iterator [iterator.concept.input]

The input_iterator concept defines requirements for a type whose referenced values can be read (from the requirement for indirectly_readable ([iterator.concept.readable])) and which can be both pre- and post-incremented.
[Note 1: 
Unlike the Cpp17InputIterator requirements ([input.iterators]), the input_iterator concept does not need equality comparison since iterators are typically compared to sentinels.
β€” end note]
template<class I> concept input_iterator = input_or_output_iterator<I> && indirectly_readable<I> && requires { typename ITER_CONCEPT(I); } && derived_from<ITER_CONCEPT(I), input_iterator_tag>;

25.3.4.10 Concept output_iterator [iterator.concept.output]

The output_iterator concept defines requirements for a type that can be used to write values (from the requirement for indirectly_writable ([iterator.concept.writable])) and which can be both pre- and post-incremented.
[Note 1: 
Output iterators are not required to model equality_comparable.
β€” end note]
template<class I, class T> concept output_iterator = input_or_output_iterator<I> && indirectly_writable<I, T> && requires(I i, T&& t) { *i++ = std::forward<T>(t); // not required to be equality-preserving };
Let E be an expression such that decltype((E)) is T, and let i be a dereferenceable object of type I.
I and T model output_iterator<I, T> only if *i++ = E; has effects equivalent to: *i = E; ++i;
Recommended practice: The implementation of an algorithm on output iterators should never attempt to pass through the same iterator twice; such an algorithm should be a single-pass algorithm.

25.3.4.11 Concept forward_iterator [iterator.concept.forward]

The forward_iterator concept adds copyability, equality comparison, and the multi-pass guarantee, specified below.
template<class I> concept forward_iterator = input_iterator<I> && derived_from<ITER_CONCEPT(I), forward_iterator_tag> && incrementable<I> && sentinel_for<I, I>;
The domain of == for forward iterators is that of iterators over the same underlying sequence.
However, value-initialized iterators of the same type may be compared and shall compare equal to other value-initialized iterators of the same type.
[Note 1: 
Value-initialized iterators behave as if they refer past the end of the same empty sequence.
β€” end note]
Pointers and references obtained from a forward iterator into a range [i, s) shall remain valid while [i, s) continues to denote a range.
Two dereferenceable iterators a and b of type X offer the multi-pass guarantee if:
  • a == b implies ++a == ++b and
  • the expression ((void)[](X x){++x;}(a), *a) is equivalent to the expression *a.
[Note 2: 
The requirement that a == b implies ++a == ++b and the removal of the restrictions on the number of assignments through a mutable iterator (which applies to output iterators) allow the use of multi-pass one-directional algorithms with forward iterators.
β€” end note]

25.3.4.12 Concept bidirectional_iterator [iterator.concept.bidir]

The bidirectional_iterator concept adds the ability to move an iterator backward as well as forward.
template<class I> concept bidirectional_iterator = forward_iterator<I> && derived_from<ITER_CONCEPT(I), bidirectional_iterator_tag> && requires(I i) { { --i } -> same_as<I&>; { i-- } -> same_as<I>; };
A bidirectional iterator r is decrementable if and only if there exists some q such that ++q == r.
Decrementable iterators r shall be in the domain of the expressions --r and r--.
Let a and b be equal objects of type I.
I models bidirectional_iterator only if:
  • If a and b are decrementable, then all of the following are true:
    • addressof(--a) == addressof(a)
    • bool(a-- == b)
    • after evaluating both a-- and --b, bool(a == b) is still true
    • bool(++(--a) == b)
  • If a and b are incrementable, then bool(--(++a) == b).

25.3.4.13 Concept random_access_iterator [iterator.concept.random.access]

The random_access_iterator concept adds support for constant-time advancement with +=, +, -=, and -, as well as the computation of distance in constant time with -.
Random access iterators also support array notation via subscripting.
template<class I> concept random_access_iterator = bidirectional_iterator<I> && derived_from<ITER_CONCEPT(I), random_access_iterator_tag> && totally_ordered<I> && sized_sentinel_for<I, I> && requires(I i, const I j, const iter_difference_t<I> n) { { i += n } -> same_as<I&>; { j + n } -> same_as<I>; { n + j } -> same_as<I>; { i -= n } -> same_as<I&>; { j - n } -> same_as<I>; { j[n] } -> same_as<iter_reference_t<I>>; };
Let a and b be valid iterators of type I such that b is reachable from a after n applications of ++a, let D be iter_difference_t<I>, and let n denote a value of type D.
I models random_access_iterator only if
  • (a += n) is equal to b.
  • addressof(a += n) is equal to addressof(a).
  • (a + n) is equal to (a += n).
  • For any two positive values x and y of type D, if (a + D(x + y)) is valid, then (a + D(x + y)) is equal to ((a + x) + y).
  • (a + D(0)) is equal to a.
  • If (a + D(n - 1)) is valid, then (a + n) is equal to [](I c){ return ++c; }(a + D(n - 1)).
  • (b += D(-n)) is equal to a.
  • (b -= n) is equal to a.
  • addressof(b -= n) is equal to addressof(b).
  • (b - n) is equal to (b -= n).
  • If b is dereferenceable, then a[n] is valid and is equal to *b.
  • bool(a <= b) is true.

25.3.4.14 Concept contiguous_iterator [iterator.concept.contiguous]

The contiguous_iterator concept provides a guarantee that the denoted elements are stored contiguously in memory.
template<class I> concept contiguous_iterator = random_access_iterator<I> && derived_from<ITER_CONCEPT(I), contiguous_iterator_tag> && is_lvalue_reference_v<iter_reference_t<I>> && same_as<iter_value_t<I>, remove_cvref_t<iter_reference_t<I>>> && requires(const I& i) { { to_address(i) } -> same_as<add_pointer_t<iter_reference_t<I>>>; };
Let a and b be dereferenceable iterators and c be a non-dereferenceable iterator of type I such that b is reachable from a and c is reachable from b, and let D be iter_difference_t<I>.
The type I models contiguous_iterator only if
  • to_address(a) == addressof(*a),
  • to_address(b) == to_address(a) + D(b - a),
  • to_address(c) == to_address(a) + D(c - a),
  • ranges​::​iter_move(a) has the same type, value category, and effects as std​::​move(*a), and
  • if ranges​::​iter_swap(a, b) is well-formed, it has effects equivalent to ranges​::​swap(*a, *b).

25.3.5 C++17 iterator requirements [iterator.cpp17]

25.3.5.1 General [iterator.cpp17.general]

In the following sections, a and b denote values of type X or const X, difference_type and reference refer to the types iterator_traits<X>​::​difference_type and iterator_traits<X>​::​reference, respectively, n denotes a value of difference_type, u, tmp, and m denote identifiers, r denotes a value of X&, t denotes a value of value type T, o denotes a value of some type that is writable to the output iterator.
[Note 1: 
For an iterator type X there must be an instantiation of iterator_traits<X> ([iterator.traits]).
β€” end note]

25.3.5.2 Cpp17Iterator [iterator.iterators]

The Cpp17Iterator requirements form the basis of the iterator taxonomy; every iterator meets the Cpp17Iterator requirements.
This set of requirements specifies operations for dereferencing and incrementing an iterator.
Most algorithms will require additional operations to read ([input.iterators]) or write ([output.iterators]) values, or to provide a richer set of iterator movements ([forward.iterators], [bidirectional.iterators], [random.access.iterators]).
A type X meets the Cpp17Iterator requirements if:
Table 86: Cpp17Iterator requirements [tab:iterator]
Expression
Return type
Operational
Assertion/note
semantics
pre-/post-condition
*r
unspecified
Preconditions: r is dereferenceable.
++r
X&

25.3.5.3 Input iterators [input.iterators]

A class or pointer type X meets the requirements of an input iterator for the value type T if X meets the Cpp17Iterator ([iterator.iterators]) and Cpp17EqualityComparable (Table 28) requirements and the expressions in Table 87 are valid and have the indicated semantics.
In Table 87, the term the domain of == is used in the ordinary mathematical sense to denote the set of values over which == is (required to be) defined.
This set can change over time.
Each algorithm places additional requirements on the domain of == for the iterator values it uses.
These requirements can be inferred from the uses that algorithm makes of == and !=.
[Example 1: 
The call find(a,b,x) is defined only if the value of a has the property p defined as follows: b has property p and a value i has property p if (*i==x) or if (*i!=x and ++i has property p).
β€” end example]
Table 87: Cpp17InputIterator requirements (in addition to Cpp17Iterator) [tab:inputiterator]
Expression
Return type
Operational
Assertion/note
semantics
pre-/post-condition
a != b
decltype(a != b) models boolean-testable
!(a == b)
Preconditions: (a, b) is in the domain of ==.
*a
reference, convertible to T
Preconditions: a is dereferenceable.

The expression
(void)*a, *a is equivalent to *a.

If a == b and (a, b) is in the domain of == then *a is equivalent to *b.
a->m
(*a).m
Preconditions: a is dereferenceable.
++r
X&
Preconditions: r is dereferenceable.

Postconditions: r is dereferenceable or r is past-the-end;
any copies of the previous value of r are no longer required to be dereferenceable nor to be in the domain of ==.
(void)r++
equivalent to (void)++r
*r++
convertible to T
{ T tmp = *r;
++r;
return tmp; }
Recommended practice: The implementation of an algorithm on input iterators should never attempt to pass through the same iterator twice; such an algorithm should be a single pass algorithm.
[Note 1: 
For input iterators, a == b does not imply ++a == ++b.
(Equality does not guarantee the substitution property or referential transparency.)
Value type T is not required to be a Cpp17CopyAssignable type (Table 34).
Such an algorithm can be used with istreams as the source of the input data through the istream_iterator class template.
β€” end note]

25.3.5.4 Output iterators [output.iterators]

A class or pointer type X meets the requirements of an output iterator if X meets the Cpp17Iterator requirements ([iterator.iterators]) and the expressions in Table 88 are valid and have the indicated semantics.
Table 88: Cpp17OutputIterator requirements (in addition to Cpp17Iterator) [tab:outputiterator]
Expression
Return type
Operational
Assertion/note
semantics
pre-/post-condition
*r = o
result is not used
Remarks: After this operation r is not required to be dereferenceable.

Postconditions: r is incrementable.
++r
X&
addressof(r) == addressof(++r).

Remarks: After this operation r is not required to be dereferenceable.

Postconditions: r is incrementable.
r++
convertible to const X&
{ X tmp = r;
++r;
return tmp; }
Remarks: After this operation r is not required to be dereferenceable.

Postconditions: r is incrementable.
*r++ = o
result is not used
Remarks: After this operation r is not required to be dereferenceable.

Postconditions: r is incrementable.
Recommended practice: The implementation of an algorithm on output iterators should never attempt to pass through the same iterator twice; such an algorithm should be a single-pass algorithm.
[Note 1: 
The only valid use of an operator* is on the left side of the assignment statement.
Assignment through the same value of the iterator happens only once.
Equality and inequality are not necessarily defined.
β€” end note]

25.3.5.5 Forward iterators [forward.iterators]

A class or pointer type X meets the requirements of a forward iterator if
  • X meets the Cpp17InputIterator requirements ([input.iterators]),
  • X meets the Cpp17DefaultConstructible requirements ([utility.arg.requirements]),
  • if X is a mutable iterator, reference is a reference to T; if X is a constant iterator, reference is a reference to const T,
  • the expressions in Table 89 are valid and have the indicated semantics, and
  • objects of type X offer the multi-pass guarantee, described below.
The domain of == for forward iterators is that of iterators over the same underlying sequence.
However, value-initialized iterators may be compared and shall compare equal to other value-initialized iterators of the same type.
[Note 1: 
Value-initialized iterators behave as if they refer past the end of the same empty sequence.
β€” end note]
Two dereferenceable iterators a and b of type X offer the multi-pass guarantee if:
  • a == b implies ++a == ++b and
  • X is a pointer type or the expression (void)++X(a), *a is equivalent to the expression *a.
[Note 2: 
The requirement that a == b implies ++a == ++b (which is not true for input and output iterators) and the removal of the restrictions on the number of the assignments through a mutable iterator (which applies to output iterators) allows the use of multi-pass one-directional algorithms with forward iterators.
β€” end note]
Table 89: Cpp17ForwardIterator requirements (in addition to Cpp17InputIterator) [tab:forwarditerator]
Expression
Return type
Operational
Assertion/note
semantics
pre-/post-condition
r++
convertible to const X&
{ X tmp = r;
++r;
return tmp; }
*r++
reference
If a and b are equal, then either a and b are both dereferenceable or else neither is dereferenceable.
If a and b are both dereferenceable, then a == b if and only if *a and *b are bound to the same object.

25.3.5.6 Bidirectional iterators [bidirectional.iterators]

A class or pointer type X meets the requirements of a bidirectional iterator if, in addition to meeting the Cpp17ForwardIterator requirements, the following expressions are valid as shown in Table 90.
Table 90: Cpp17BidirectionalIterator requirements (in addition to Cpp17ForwardIterator) [tab:bidirectionaliterator]
Expression
Return type
Operational
Assertion/note
semantics
pre-/post-condition
--r
X&
Preconditions: there exists s such that r == ++s.

Postconditions: r is dereferenceable.

--(++r) == r.

--r == --s implies r == s.

addressof(r) == addressof(--r).
r--
convertible to const X&
{ X tmp = r;
--r;
return tmp; }
*r--
reference
[Note 1: 
Bidirectional iterators allow algorithms to move iterators backward as well as forward.
β€” end note]

25.3.5.7 Random access iterators [random.access.iterators]

A class or pointer type X meets the requirements of a random access iterator if, in addition to meeting the Cpp17BidirectionalIterator requirements, the following expressions are valid as shown in Table 91.
Table 91: Cpp17RandomAccessIterator requirements (in addition to Cpp17BidirectionalIterator) [tab:randomaccessiterator]
Expression
Return type
Operational
Assertion/note
semantics
pre-/post-condition
r += n
X&
{ difference_type m = n;
if (m >= 0)
while (m--)
++r;
else
while (m++)
--r;
return r; }
a + n
n + a
X
{ X tmp = a;
return tmp += n; }
a + n == n + a.
r -= n
X&
return r += -n;
Preconditions: the absolute value of n is in the range of representable values of difference_type.
a - n
X
{ X tmp = a;
return tmp -= n; }
b - a
difference_type
return n;
Preconditions: there exists a value n of type difference_type such that a + n == b.

b == a + (b - a).
a[n]
convertible to reference
*(a + n)
a < b
decltype(a < b) models boolean-testable
Effects: Equivalent to: return b - a > 0;
< is a total ordering relation
a > b
decltype(a > b) models boolean-testable
b < a
> is a total ordering relation opposite to <.
a >= b
decltype(a >= b) models boolean-testable
!(a < b)
a <= b
decltype(a <= b) models boolean-testable
!(a > b)

25.3.6 Indirect callable requirements [indirectcallable]

25.3.6.1 General [indirectcallable.general]

There are several concepts that group requirements of algorithms that take callable objects ([func.def]) as arguments.

25.3.6.2 Indirect callable traits [indirectcallable.traits]

To implement algorithms taking projections, it is necessary to determine the projected type of an iterator's value type.
For the exposition-only alias template indirect-value-t, indirect-value-t<T> denotes
  • invoke_result_t<Proj&, indirect-value-t<I>> if T names projected<I, Proj>, and
  • iter_value_t<T>& otherwise.

25.3.6.3 Indirect callables [indirectcallable.indirectinvocable]

The indirect callable concepts are used to constrain those algorithms that accept callable objects ([func.def]) as arguments.
namespace std { template<class F, class I> concept indirectly_unary_invocable = indirectly_readable<I> && copy_constructible<F> && invocable<F&, indirect-value-t<I>> && invocable<F&, iter_reference_t<I>> && invocable<F&, iter_common_reference_t<I>> && common_reference_with< invoke_result_t<F&, indirect-value-t<I>>, invoke_result_t<F&, iter_reference_t<I>>>; template<class F, class I> concept indirectly_regular_unary_invocable = indirectly_readable<I> && copy_constructible<F> && regular_invocable<F&, indirect-value-t<I>> && regular_invocable<F&, iter_reference_t<I>> && regular_invocable<F&, iter_common_reference_t<I>> && common_reference_with< invoke_result_t<F&, indirect-value-t<I>>, invoke_result_t<F&, iter_reference_t<I>>>; template<class F, class I> concept indirect_unary_predicate = indirectly_readable<I> && copy_constructible<F> && predicate<F&, indirect-value-t<I>> && predicate<F&, iter_reference_t<I>> && predicate<F&, iter_common_reference_t<I>>; template<class F, class I1, class I2> concept indirect_binary_predicate = indirectly_readable<I1> && indirectly_readable<I2> && copy_constructible<F> && predicate<F&, indirect-value-t<I1>, indirect-value-t<I2>> && predicate<F&, indirect-value-t<I1>, iter_reference_t<I2>> && predicate<F&, iter_reference_t<I1>, indirect-value-t<I2>> && predicate<F&, iter_reference_t<I1>, iter_reference_t<I2>> && predicate<F&, iter_common_reference_t<I1>, iter_common_reference_t<I2>>; template<class F, class I1, class I2 = I1> concept indirect_equivalence_relation = indirectly_readable<I1> && indirectly_readable<I2> && copy_constructible<F> && equivalence_relation<F&, indirect-value-t<I1>, indirect-value-t<I2>> && equivalence_relation<F&, indirect-value-t<I1>, iter_reference_t<I2>> && equivalence_relation<F&, iter_reference_t<I1>, indirect-value-t<I2>> && equivalence_relation<F&, iter_reference_t<I1>, iter_reference_t<I2>> && equivalence_relation<F&, iter_common_reference_t<I1>, iter_common_reference_t<I2>>; template<class F, class I1, class I2 = I1> concept indirect_strict_weak_order = indirectly_readable<I1> && indirectly_readable<I2> && copy_constructible<F> && strict_weak_order<F&, indirect-value-t<I1>, indirect-value-t<I2>> && strict_weak_order<F&, indirect-value-t<I1>, iter_reference_t<I2>> && strict_weak_order<F&, iter_reference_t<I1>, indirect-value-t<I2>> && strict_weak_order<F&, iter_reference_t<I1>, iter_reference_t<I2>> && strict_weak_order<F&, iter_common_reference_t<I1>, iter_common_reference_t<I2>>; }

25.3.6.4 Class template projected [projected]

Class template projected is used to constrain algorithms that accept callable objects and projections ([defns.projection]).
It combines an indirectly_readable type I and a callable object type Proj into a new indirectly_readable type whose reference type is the result of applying Proj to the iter_reference_t of I.
namespace std { template<class I, class Proj> struct projected-impl { // exposition only struct type { // exposition only using value_type = remove_cvref_t<indirect_result_t<Proj&, I>>; using difference_type = iter_difference_t<I>; // present only if I // models weakly_incrementable indirect_result_t<Proj&, I> operator*() const; // not defined }; }; template<indirectly_readable I, indirectly_regular_unary_invocable<I> Proj> using projected = projected-impl<I, Proj>::type; }

25.3.7 Common algorithm requirements [alg.req]

25.3.7.1 General [alg.req.general]

There are several additional iterator concepts that are commonly applied to families of algorithms.
These group together iterator requirements of algorithm families.
There are three relational concepts that specify how element values are transferred between indirectly_readable and indirectly_writable types: indirectly_movable, indirectly_copyable, and indirectly_swappable.
There are three relational concepts for rearrangements: permutable, mergeable, and sortable.
There is one relational concept for comparing values from different sequences: indirectly_comparable.
[Note 1: 
The ranges​::​less function object type used in the concepts below imposes constraints on the concepts' arguments in addition to those that appear in the concepts' bodies ([range.cmp]).
β€” end note]

25.3.7.2 Concept indirectly_movable [alg.req.ind.move]

The indirectly_movable concept specifies the relationship between an indirectly_readable type and an indirectly_writable type between which values may be moved.
template<class In, class Out> concept indirectly_movable = indirectly_readable<In> && indirectly_writable<Out, iter_rvalue_reference_t<In>>;
The indirectly_movable_storable concept augments indirectly_movable with additional requirements enabling the transfer to be performed through an intermediate object of the indirectly_readable type's value type.
template<class In, class Out> concept indirectly_movable_storable = indirectly_movable<In, Out> && indirectly_writable<Out, iter_value_t<In>> && movable<iter_value_t<In>> && constructible_from<iter_value_t<In>, iter_rvalue_reference_t<In>> && assignable_from<iter_value_t<In>&, iter_rvalue_reference_t<In>>;
Let i be a dereferenceable value of type In.
In and Out model indirectly_movable_storable<In, Out> only if after the initialization of the object obj in iter_value_t<In> obj(ranges::iter_move(i)); obj is equal to the value previously denoted by *i.
If iter_rvalue_reference_t<In> is an rvalue reference type, the resulting state of the value denoted by *i is valid but unspecified ([lib.types.movedfrom]).

25.3.7.3 Concept indirectly_copyable [alg.req.ind.copy]

The indirectly_copyable concept specifies the relationship between an indirectly_readable type and an indirectly_writable type between which values may be copied.
template<class In, class Out> concept indirectly_copyable = indirectly_readable<In> && indirectly_writable<Out, iter_reference_t<In>>;
The indirectly_copyable_storable concept augments indirectly_copyable with additional requirements enabling the transfer to be performed through an intermediate object of the indirectly_readable type's value type.
It also requires the capability to make copies of values.
template<class In, class Out> concept indirectly_copyable_storable = indirectly_copyable<In, Out> && indirectly_writable<Out, iter_value_t<In>&> && indirectly_writable<Out, const iter_value_t<In>&> && indirectly_writable<Out, iter_value_t<In>&&> && indirectly_writable<Out, const iter_value_t<In>&&> && copyable<iter_value_t<In>> && constructible_from<iter_value_t<In>, iter_reference_t<In>> && assignable_from<iter_value_t<In>&, iter_reference_t<In>>;
Let i be a dereferenceable value of type In.
In and Out model indirectly_copyable_storable<In, Out> only if after the initialization of the object obj in iter_value_t<In> obj(*i); obj is equal to the value previously denoted by *i.
If iter_reference_t<In> is an rvalue reference type, the resulting state of the value denoted by *i is valid but unspecified ([lib.types.movedfrom]).

25.3.7.4 Concept indirectly_swappable [alg.req.ind.swap]

The indirectly_swappable concept specifies a swappable relationship between the values referenced by two indirectly_readable types.
template<class I1, class I2 = I1> concept indirectly_swappable = indirectly_readable<I1> && indirectly_readable<I2> && requires(const I1 i1, const I2 i2) { ranges::iter_swap(i1, i1); ranges::iter_swap(i2, i2); ranges::iter_swap(i1, i2); ranges::iter_swap(i2, i1); };

25.3.7.5 Concept indirectly_comparable [alg.req.ind.cmp]

The indirectly_comparable concept specifies the common requirements of algorithms that compare values from two different sequences.
template<class I1, class I2, class R, class P1 = identity, class P2 = identity> concept indirectly_comparable = indirect_binary_predicate<R, projected<I1, P1>, projected<I2, P2>>;

25.3.7.6 Concept permutable [alg.req.permutable]

The permutable concept specifies the common requirements of algorithms that reorder elements in place by moving or swapping them.
template<class I> concept permutable = forward_iterator<I> && indirectly_movable_storable<I, I> && indirectly_swappable<I, I>;

25.3.7.7 Concept mergeable [alg.req.mergeable]

The mergeable concept specifies the requirements of algorithms that merge sorted sequences into an output sequence by copying elements.
template<class I1, class I2, class Out, class R = ranges::less, class P1 = identity, class P2 = identity> concept mergeable = input_iterator<I1> && input_iterator<I2> && weakly_incrementable<Out> && indirectly_copyable<I1, Out> && indirectly_copyable<I2, Out> && indirect_strict_weak_order<R, projected<I1, P1>, projected<I2, P2>>;

25.3.7.8 Concept sortable [alg.req.sortable]

The sortable concept specifies the common requirements of algorithms that permute sequences into ordered sequences (e.g., sort).
template<class I, class R = ranges::less, class P = identity> concept sortable = permutable<I> && indirect_strict_weak_order<R, projected<I, P>>;

25.4 Iterator primitives [iterator.primitives]

25.4.1 General [iterator.primitives.general]

To simplify the use of iterators, the library provides several classes and functions.

25.4.2 Standard iterator tags [std.iterator.tags]

It is often desirable for a function template specialization to find out what is the most specific category of its iterator argument, so that the function can select the most efficient algorithm at compile time.
To facilitate this, the library introduces category tag classes which are used as compile time tags for algorithm selection.
They are: output_iterator_tag, input_iterator_tag, forward_iterator_tag, bidirectional_iterator_tag, random_access_iterator_tag, and contiguous_iterator_tag.
For every iterator of type I, iterator_traits<I>​::​iterator_category shall be defined to be a category tag that describes the iterator's behavior.
Additionally, iterator_traits<I>​::​iterator_concept may be used to indicate conformance to the iterator concepts ([iterator.concepts]).
namespace std { struct output_iterator_tag { }; struct input_iterator_tag { }; struct forward_iterator_tag: public input_iterator_tag { }; struct bidirectional_iterator_tag: public forward_iterator_tag { }; struct random_access_iterator_tag: public bidirectional_iterator_tag { }; struct contiguous_iterator_tag: public random_access_iterator_tag { }; }
[Example 1: 
A program-defined iterator BinaryTreeIterator can be included into the bidirectional iterator category by specializing the iterator_traits template: template<class T> struct iterator_traits<BinaryTreeIterator<T>> { using iterator_category = bidirectional_iterator_tag; using difference_type = ptrdiff_t; using value_type = T; using pointer = T*; using reference = T&; };
β€” end example]
[Example 2: 
If evolve() is well-defined for bidirectional iterators, but can be implemented more efficiently for random access iterators, then the implementation is as follows: template<class BidirectionalIterator> inline void evolve(BidirectionalIterator first, BidirectionalIterator last) { evolve(first, last, typename iterator_traits<BidirectionalIterator>::iterator_category()); } template<class BidirectionalIterator> void evolve(BidirectionalIterator first, BidirectionalIterator last, bidirectional_iterator_tag) { // more generic, but less efficient algorithm } template<class RandomAccessIterator> void evolve(RandomAccessIterator first, RandomAccessIterator last, random_access_iterator_tag) { // more efficient, but less generic algorithm }
β€” end example]

25.4.3 Iterator operations [iterator.operations]

Since only random access iterators provide + and - operators, the library provides two function templates advance and distance.
These function templates use + and - for random access iterators (and are, therefore, constant time for them); for input, forward and bidirectional iterators they use ++ to provide linear time implementations.
template<class InputIterator, class Distance> constexpr void advance(InputIterator& i, Distance n);
Preconditions: n is negative only for bidirectional iterators.
Effects: Increments i by n if n is non-negative, and decrements i by -n otherwise.
template<class InputIterator> constexpr typename iterator_traits<InputIterator>::difference_type distance(InputIterator first, InputIterator last);
Preconditions: last is reachable from first, or InputIterator meets the Cpp17RandomAccessIterator requirements and first is reachable from last.
Effects: If InputIterator meets the Cpp17RandomAccessIterator requirements, returns (last - first); otherwise, increments first until last is reached and returns the number of increments.
template<class InputIterator> constexpr InputIterator next(InputIterator x, typename iterator_traits<InputIterator>::difference_type n = 1);
Effects: Equivalent to: advance(x, n); return x;
template<class BidirectionalIterator> constexpr BidirectionalIterator prev(BidirectionalIterator x, typename iterator_traits<BidirectionalIterator>::difference_type n = 1);
Effects: Equivalent to: advance(x, -n); return x;

25.4.4 Range iterator operations [range.iter.ops]

25.4.4.1 General [range.iter.ops.general]

The library includes the function templates ranges​::​advance, ranges​::​distance, ranges​::​next, and ranges​::​prev to manipulate iterators.
These operations adapt to the set of operators provided by each iterator category to provide the most efficient implementation possible for a concrete iterator type.
[Example 1: 
ranges​::​advance uses the + operator to move a random_access_iterator forward n steps in constant time.
For an iterator type that does not model random_access_iterator, ranges​::​advance instead performs n individual increments with the ++ operator.
β€” end example]
The function templates defined in [range.iter.ops] are not found by argument-dependent name lookup ([basic.lookup.argdep]).
When found by unqualified ([basic.lookup.unqual]) name lookup for the postfix-expression in a function call ([expr.call]), they inhibit argument-dependent name lookup.
[Example 2: void foo() { using namespace std::ranges; std::vector<int> vec{1,2,3}; distance(begin(vec), end(vec)); // #1 }
The function call expression at #1 invokes std​::​ranges​::​distance, not std​::​distance, despite that (a) the iterator type returned from begin(vec) and end(vec) may be associated with namespace std and (b) std​::​distance is more specialized ([temp.func.order]) than std​::​ranges​::​distance since the former requires its first two parameters to have the same type.
β€” end example]
The number and order of deducible template parameters for the function templates defined in [range.iter.ops] is unspecified, except where explicitly stated otherwise.

25.4.4.2 ranges​::​advance [range.iter.op.advance]

template<input_or_output_iterator I> constexpr void ranges::advance(I& i, iter_difference_t<I> n);
Preconditions: If I does not model bidirectional_iterator, n is not negative.
Effects:
template<input_or_output_iterator I, sentinel_for<I> S> constexpr void ranges::advance(I& i, S bound);
Preconditions: Either assignable_from<I&, S> || sized_sentinel_for<S, I> is modeled, or [i, bound) denotes a range.
Effects:
  • If I and S model assignable_from<I&, S>, equivalent to i = std​::​move(bound).
  • Otherwise, if S and I model sized_sentinel_for<S, I>, equivalent to ranges​::​advance(i, bound - i).
  • Otherwise, while bool(i != bound) is true, increments i.
template<input_or_output_iterator I, sentinel_for<I> S> constexpr iter_difference_t<I> ranges::advance(I& i, iter_difference_t<I> n, S bound);
Preconditions: If n > 0, [i, bound) denotes a range.
If n == 0, [i, bound) or [bound, i) denotes a range.
If n < 0, [bound, i) denotes a range, I models bidirectional_iterator, and I and S model same_as<I, S>.
Effects:
  • If S and I model sized_sentinel_for<S, I>:
    • If ​|n|  β‰₯ |bound - i|, equivalent to ranges​::​advance(i, bound).
    • Otherwise, equivalent to ranges​::​advance(i, n).
  • Otherwise,
    • if n is non-negative, while bool(i != bound) is true, increments i but at most n times.
    • Otherwise, while bool(i != bound) is true, decrements i but at most -n times.
Returns: n - M, where M is the difference between the ending and starting positions of i.

25.4.4.3 ranges​::​distance [range.iter.op.distance]

template<class I, sentinel_for<I> S> requires (!sized_sentinel_for<S, I>) constexpr iter_difference_t<I> ranges::distance(I first, S last);
Preconditions: [first, last) denotes a range.
Effects: Increments first until last is reached and returns the number of increments.
template<class I, sized_sentinel_for<decay_t<I>> S> constexpr iter_difference_t<decay_t<I>> ranges::distance(I&& first, S last);
Effects: Equivalent to: return last - static_cast<const decay_t<I>&>(first);
template<range R> constexpr range_difference_t<R> ranges::distance(R&& r);
Effects: If R models sized_range, equivalent to: return static_cast<range_difference_t<R>>(ranges::size(r)); // [range.prim.size]
Otherwise, equivalent to: return ranges::distance(ranges::begin(r), ranges::end(r)); // [range.access]

25.4.4.4 ranges​::​next [range.iter.op.next]

template<input_or_output_iterator I> constexpr I ranges::next(I x);
Effects: Equivalent to: ++x; return x;
template<input_or_output_iterator I> constexpr I ranges::next(I x, iter_difference_t<I> n);
Effects: Equivalent to: ranges​::​advance(x, n); return x;
template<input_or_output_iterator I, sentinel_for<I> S> constexpr I ranges::next(I x, S bound);
Effects: Equivalent to: ranges​::​advance(x, bound); return x;
template<input_or_output_iterator I, sentinel_for<I> S> constexpr I ranges::next(I x, iter_difference_t<I> n, S bound);
Effects: Equivalent to: ranges​::​advance(x, n, bound); return x;

25.4.4.5 ranges​::​prev [range.iter.op.prev]

template<bidirectional_iterator I> constexpr I ranges::prev(I x);
Effects: Equivalent to: --x; return x;
template<bidirectional_iterator I> constexpr I ranges::prev(I x, iter_difference_t<I> n);
Effects: Equivalent to: ranges​::​advance(x, -n); return x;
template<bidirectional_iterator I> constexpr I ranges::prev(I x, iter_difference_t<I> n, I bound);
Effects: Equivalent to: ranges​::​advance(x, -n, bound); return x;

25.5 Iterator adaptors [predef.iterators]

25.5.1 Reverse iterators [reverse.iterators]

25.5.1.1 General [reverse.iterators.general]

Class template reverse_iterator is an iterator adaptor that iterates from the end of the sequence defined by its underlying iterator to the beginning of that sequence.

25.5.1.2 Class template reverse_iterator [reverse.iterator]

namespace std { template<class Iterator> class reverse_iterator { public: using iterator_type = Iterator; using iterator_concept = see below; using iterator_category = see below; using value_type = iter_value_t<Iterator>; using difference_type = iter_difference_t<Iterator>; using pointer = typename iterator_traits<Iterator>::pointer; using reference = iter_reference_t<Iterator>; constexpr reverse_iterator(); constexpr explicit reverse_iterator(Iterator x); template<class U> constexpr reverse_iterator(const reverse_iterator<U>& u); template<class U> constexpr reverse_iterator& operator=(const reverse_iterator<U>& u); constexpr Iterator base() const; constexpr reference operator*() const; constexpr pointer operator->() const requires see below; constexpr reverse_iterator& operator++(); constexpr reverse_iterator operator++(int); constexpr reverse_iterator& operator--(); constexpr reverse_iterator operator--(int); constexpr reverse_iterator operator+ (difference_type n) const; constexpr reverse_iterator& operator+=(difference_type n); constexpr reverse_iterator operator- (difference_type n) const; constexpr reverse_iterator& operator-=(difference_type n); constexpr unspecified operator[](difference_type n) const; friend constexpr iter_rvalue_reference_t<Iterator> iter_move(const reverse_iterator& i) noexcept(see below); template<indirectly_swappable<Iterator> Iterator2> friend constexpr void iter_swap(const reverse_iterator& x, const reverse_iterator<Iterator2>& y) noexcept(see below); protected: Iterator current; }; }
The member typedef-name iterator_concept denotes
The member typedef-name iterator_category denotes
  • random_access_iterator_tag if the type iterator_traits<​Iterator>​::​iterator_category models derived_from<random_access_iterator_tag>, and
  • iterator_traits<​Iterator>​::​iterator_category otherwise.

25.5.1.3 Requirements [reverse.iter.requirements]

The template parameter Iterator shall either meet the requirements of a Cpp17BidirectionalIterator ([bidirectional.iterators]) or model bidirectional_iterator ([iterator.concept.bidir]).
Additionally, Iterator shall either meet the requirements of a Cpp17RandomAccessIterator ([random.access.iterators]) or model random_access_iterator ([iterator.concept.random.access]) if the definitions of any of the members or the non-member operators ([reverse.iter.cmp]) are instantiated ([temp.inst]).

25.5.1.4 Construction and assignment [reverse.iter.cons]

constexpr reverse_iterator();
Effects: Value-initializes current.
Iterator operations applied to the resulting iterator have defined behavior if and only if the corresponding operations are defined on a value-initialized iterator of type Iterator.
constexpr explicit reverse_iterator(Iterator x);
Effects: Initializes current with x.
template<class U> constexpr reverse_iterator(const reverse_iterator<U>& u);
Constraints: is_same_v<U, Iterator> is false and const U& models convertible_to<Iterator>.
Effects: Initializes current with u.current.
template<class U> constexpr reverse_iterator& operator=(const reverse_iterator<U>& u);
Constraints: is_same_v<U, Iterator> is false, const U& models convertible_to<Iterator>, and assignable_from<Iterator&, const U&> is modeled.
Effects: Assigns u.current to current.
Returns: *this.

25.5.1.5 Conversion [reverse.iter.conv]

constexpr Iterator base() const;
Returns: current.

25.5.1.6 Element access [reverse.iter.elem]

constexpr reference operator*() const;
Effects: As if by: Iterator tmp = current; return *--tmp;
constexpr pointer operator->() const requires (is_pointer_v<Iterator> || requires(const Iterator i) { i.operator->(); });
Effects:
  • If Iterator is a pointer type, equivalent to: return prev(current);
  • Otherwise, equivalent to: return prev(current).operator->();
constexpr unspecified operator[](difference_type n) const;
Returns: current[-n-1].

25.5.1.7 Navigation [reverse.iter.nav]

constexpr reverse_iterator operator+(difference_type n) const;
Returns: reverse_iterator(current-n).
constexpr reverse_iterator operator-(difference_type n) const;
Returns: reverse_iterator(current+n).
constexpr reverse_iterator& operator++();
Effects: As if by: --current;
Returns: *this.
constexpr reverse_iterator operator++(int);
Effects: As if by: reverse_iterator tmp = *this; --current; return tmp;
constexpr reverse_iterator& operator--();
Effects: As if by ++current.
Returns: *this.
constexpr reverse_iterator operator--(int);
Effects: As if by: reverse_iterator tmp = *this; ++current; return tmp;
constexpr reverse_iterator& operator+=(difference_type n);
Effects: As if by: current -= n;
Returns: *this.
constexpr reverse_iterator& operator-=(difference_type n);
Effects: As if by: current += n;
Returns: *this.

25.5.1.8 Comparisons [reverse.iter.cmp]

template<class Iterator1, class Iterator2> constexpr bool operator==( const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y);
Constraints: x.base() == y.base() is well-formed and convertible to bool.
Returns: x.base() == y.base().
template<class Iterator1, class Iterator2> constexpr bool operator!=( const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y);
Constraints: x.base() != y.base() is well-formed and convertible to bool.
Returns: x.base() != y.base().
template<class Iterator1, class Iterator2> constexpr bool operator<( const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y);
Constraints: x.base() > y.base() is well-formed and convertible to bool.
Returns: x.base() > y.base().
template<class Iterator1, class Iterator2> constexpr bool operator>( const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y);
Constraints: x.base() < y.base() is well-formed and convertible to bool.
Returns: x.base() < y.base().
template<class Iterator1, class Iterator2> constexpr bool operator<=( const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y);
Constraints: x.base() >= y.base() is well-formed and convertible to bool.
Returns: x.base() >= y.base().
template<class Iterator1, class Iterator2> constexpr bool operator>=( const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y);
Constraints: x.base() <= y.base() is well-formed and convertible to bool.
Returns: x.base() <= y.base().
template<class Iterator1, three_way_comparable_with<Iterator1> Iterator2> constexpr compare_three_way_result_t<Iterator1, Iterator2> operator<=>(const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y);
Returns: y.base() <=> x.base().
[Note 1: 
The argument order in the Returns: element is reversed because this is a reverse iterator.
β€” end note]

25.5.1.9 Non-member functions [reverse.iter.nonmember]

template<class Iterator1, class Iterator2> constexpr auto operator-( const reverse_iterator<Iterator1>& x, const reverse_iterator<Iterator2>& y) -> decltype(y.base() - x.base());
Returns: y.base() - x.base().
template<class Iterator> constexpr reverse_iterator<Iterator> operator+( iter_difference_t<Iterator> n, const reverse_iterator<Iterator>& x);
Returns: reverse_iterator<Iterator>(x.base() - n).
friend constexpr iter_rvalue_reference_t<Iterator> iter_move(const reverse_iterator& i) noexcept(see below);
Effects: Equivalent to: auto tmp = i.base(); return ranges::iter_move(--tmp);
Remarks: The exception specification is equivalent to: is_nothrow_copy_constructible_v<Iterator> && noexcept(ranges::iter_move(--declval<Iterator&>()))
template<indirectly_swappable<Iterator> Iterator2> friend constexpr void iter_swap(const reverse_iterator& x, const reverse_iterator<Iterator2>& y) noexcept(see below);
Effects: Equivalent to: auto xtmp = x.base(); auto ytmp = y.base(); ranges::iter_swap(--xtmp, --ytmp);
Remarks: The exception specification is equivalent to: is_nothrow_copy_constructible_v<Iterator> && is_nothrow_copy_constructible_v<Iterator2> && noexcept(ranges::iter_swap(--declval<Iterator&>(), --declval<Iterator2&>()))
template<class Iterator> constexpr reverse_iterator<Iterator> make_reverse_iterator(Iterator i);
Returns: reverse_iterator<Iterator>(i).

25.5.2 Insert iterators [insert.iterators]

25.5.2.1 General [insert.iterators.general]

To make it possible to deal with insertion in the same way as writing into an array, a special kind of iterator adaptors, called insert iterators, are provided in the library.
With regular iterator classes, while (first != last) *result++ = *first++; causes a range [first, last) to be copied into a range starting with result.
The same code with result being an insert iterator will insert corresponding elements into the container.
This device allows all of the copying algorithms in the library to work in the insert mode instead of the regular overwrite mode.
An insert iterator is constructed from a container and possibly one of its iterators pointing to where insertion takes place if it is neither at the beginning nor at the end of the container.
Insert iterators meet the requirements of output iterators.
operator* returns the insert iterator itself.
The assignment operator=(const T& x) is defined on insert iterators to allow writing into them, it inserts x right before where the insert iterator is pointing.
In other words, an insert iterator is like a cursor pointing into the container where the insertion takes place.
back_insert_iterator inserts elements at the end of a container, front_insert_iterator inserts elements at the beginning of a container, and insert_iterator inserts elements where the iterator points to in a container.
back_inserter, front_inserter, and inserter are three functions making the insert iterators out of a container.

25.5.2.2 Class template back_insert_iterator [back.insert.iterator]

namespace std { template<class Container> class back_insert_iterator { protected: Container* container; public: using iterator_category = output_iterator_tag; using value_type = void; using difference_type = ptrdiff_t; using pointer = void; using reference = void; using container_type = Container; constexpr explicit back_insert_iterator(Container& x); constexpr back_insert_iterator& operator=(const typename Container::value_type& value); constexpr back_insert_iterator& operator=(typename Container::value_type&& value); constexpr back_insert_iterator& operator*(); constexpr back_insert_iterator& operator++(); constexpr back_insert_iterator operator++(int); }; }

25.5.2.2.1 Operations [back.insert.iter.ops]

constexpr explicit back_insert_iterator(Container& x);
Effects: Initializes container with addressof(x).
constexpr back_insert_iterator& operator=(const typename Container::value_type& value);
Effects: As if by: container->push_back(value);
Returns: *this.
constexpr back_insert_iterator& operator=(typename Container::value_type&& value);
Effects: As if by: container->push_back(std​::​move(value));
Returns: *this.
constexpr back_insert_iterator& operator*();
Returns: *this.
constexpr back_insert_iterator& operator++(); constexpr back_insert_iterator operator++(int);
Returns: *this.

25.5.2.2.2 back_inserter [back.inserter]

template<class Container> constexpr back_insert_iterator<Container> back_inserter(Container& x);
Returns: back_insert_iterator<Container>(x).

25.5.2.3 Class template front_insert_iterator [front.insert.iterator]

namespace std { template<class Container> class front_insert_iterator { protected: Container* container; public: using iterator_category = output_iterator_tag; using value_type = void; using difference_type = ptrdiff_t; using pointer = void; using reference = void; using container_type = Container; constexpr explicit front_insert_iterator(Container& x); constexpr front_insert_iterator& operator=(const typename Container::value_type& value); constexpr front_insert_iterator& operator=(typename Container::value_type&& value); constexpr front_insert_iterator& operator*(); constexpr front_insert_iterator& operator++(); constexpr front_insert_iterator operator++(int); }; }

25.5.2.3.1 Operations [front.insert.iter.ops]

constexpr explicit front_insert_iterator(Container& x);
Effects: Initializes container with addressof(x).
constexpr front_insert_iterator& operator=(const typename Container::value_type& value);
Effects: As if by: container->push_front(value);
Returns: *this.
constexpr front_insert_iterator& operator=(typename Container::value_type&& value);
Effects: As if by: container->push_front(std​::​move(value));
Returns: *this.
constexpr front_insert_iterator& operator*();
Returns: *this.
constexpr front_insert_iterator& operator++(); constexpr front_insert_iterator operator++(int);
Returns: *this.

25.5.2.3.2 front_inserter [front.inserter]

template<class Container> constexpr front_insert_iterator<Container> front_inserter(Container& x);
Returns: front_insert_iterator<Container>(x).

25.5.2.4 Class template insert_iterator [insert.iterator]

namespace std { template<class Container> class insert_iterator { protected: Container* container; ranges::iterator_t<Container> iter; public: using iterator_category = output_iterator_tag; using value_type = void; using difference_type = ptrdiff_t; using pointer = void; using reference = void; using container_type = Container; constexpr insert_iterator(Container& x, ranges::iterator_t<Container> i); constexpr insert_iterator& operator=(const typename Container::value_type& value); constexpr insert_iterator& operator=(typename Container::value_type&& value); constexpr insert_iterator& operator*(); constexpr insert_iterator& operator++(); constexpr insert_iterator& operator++(int); }; }

25.5.2.4.1 Operations [insert.iter.ops]

constexpr insert_iterator(Container& x, ranges::iterator_t<Container> i);
Effects: Initializes container with addressof(x) and iter with i.
constexpr insert_iterator& operator=(const typename Container::value_type& value);
Effects: As if by: iter = container->insert(iter, value); ++iter;
Returns: *this.
constexpr insert_iterator& operator=(typename Container::value_type&& value);
Effects: As if by: iter = container->insert(iter, std::move(value)); ++iter;
Returns: *this.
constexpr insert_iterator& operator*();
Returns: *this.
constexpr insert_iterator& operator++(); constexpr insert_iterator& operator++(int);
Returns: *this.

25.5.2.4.2 inserter [inserter]

template<class Container> constexpr insert_iterator<Container> inserter(Container& x, ranges::iterator_t<Container> i);
Returns: insert_iterator<Container>(x, i).

25.5.3 Constant iterators and sentinels [const.iterators]

25.5.3.1 General [const.iterators.general]

Class template basic_const_iterator is an iterator adaptor with the same behavior as the underlying iterator except that its indirection operator implicitly converts the value returned by the underlying iterator's indirection operator to a type such that the adapted iterator is a constant iterator ([iterator.requirements]).
Some generic algorithms can be called with constant iterators to avoid mutation.
Specializations of basic_const_iterator are constant iterators.

25.5.3.2 Alias templates [const.iterators.alias]

template<indirectly_readable It> using iter_const_reference_t = common_reference_t<const iter_value_t<It>&&, iter_reference_t<It>>; template<class It> concept constant-iterator = // exposition only input_iterator<It> && same_as<iter_const_reference_t<It>, iter_reference_t<It>>; template<input_iterator I> using const_iterator = see below;
Result: If I models constant-iterator, I.
Otherwise, basic_const_iterator<I>.
template<semiregular S> using const_sentinel = see below;
Result: If S models input_iterator, const_iterator<S>.
Otherwise, S.

25.5.3.3 Class template basic_const_iterator [const.iterators.iterator]

namespace std { template<class I> concept not-a-const-iterator = see below; // exposition only template<indirectly_readable I> using iter-const-rvalue-reference-t = // exposition only common_reference_t<const iter_value_t<I>&&, iter_rvalue_reference_t<I>>; template<input_iterator Iterator> class basic_const_iterator { Iterator current_ = Iterator(); // exposition only using reference = iter_const_reference_t<Iterator>; // exposition only using rvalue-reference = // exposition only iter-const-rvalue-reference-t<Iterator>; public: using iterator_concept = see below; using iterator_category = see below; // not always present using value_type = iter_value_t<Iterator>; using difference_type = iter_difference_t<Iterator>; basic_const_iterator() requires default_initializable<Iterator> = default; constexpr basic_const_iterator(Iterator current); template<convertible_to<Iterator> U> constexpr basic_const_iterator(basic_const_iterator<U> current); template<different-from<basic_const_iterator> T> requires convertible_to<T, Iterator> constexpr basic_const_iterator(T&& current); constexpr const Iterator& base() const & noexcept; constexpr Iterator base() &&; constexpr reference operator*() const; constexpr const auto* operator->() const requires is_lvalue_reference_v<iter_reference_t<Iterator>> && same_as<remove_cvref_t<iter_reference_t<Iterator>>, value_type>; constexpr basic_const_iterator& operator++(); constexpr void operator++(int); constexpr basic_const_iterator operator++(int) requires forward_iterator<Iterator>; constexpr basic_const_iterator& operator--() requires bidirectional_iterator<Iterator>; constexpr basic_const_iterator operator--(int) requires bidirectional_iterator<Iterator>; constexpr basic_const_iterator& operator+=(difference_type n) requires random_access_iterator<Iterator>; constexpr basic_const_iterator& operator-=(difference_type n) requires random_access_iterator<Iterator>; constexpr reference operator[](difference_type n) const requires random_access_iterator<Iterator>; template<sentinel_for<Iterator> S> constexpr bool operator==(const S& s) const; constexpr bool operator<(const basic_const_iterator& y) const requires random_access_iterator<Iterator>; constexpr bool operator>(const basic_const_iterator& y) const requires random_access_iterator<Iterator>; constexpr bool operator<=(const basic_const_iterator& y) const requires random_access_iterator<Iterator>; constexpr bool operator>=(const basic_const_iterator& y) const requires random_access_iterator<Iterator>; constexpr auto operator<=>(const basic_const_iterator& y) const requires random_access_iterator<Iterator> && three_way_comparable<Iterator>; template<different-from<basic_const_iterator> I> constexpr bool operator<(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<different-from<basic_const_iterator> I> constexpr bool operator>(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<different-from<basic_const_iterator> I> constexpr bool operator<=(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<different-from<basic_const_iterator> I> constexpr bool operator>=(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<different-from<basic_const_iterator> I> constexpr auto operator<=>(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I> && three_way_comparable_with<Iterator, I>; template<not-a-const-iterator I> friend constexpr bool operator<(const I& x, const basic_const_iterator& y) requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<not-a-const-iterator I> friend constexpr bool operator>(const I& x, const basic_const_iterator& y) requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<not-a-const-iterator I> friend constexpr bool operator<=(const I& x, const basic_const_iterator& y) requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<not-a-const-iterator I> friend constexpr bool operator>=(const I& x, const basic_const_iterator& y) requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; friend constexpr basic_const_iterator operator+(const basic_const_iterator& i, difference_type n) requires random_access_iterator<Iterator>; friend constexpr basic_const_iterator operator+(difference_type n, const basic_const_iterator& i) requires random_access_iterator<Iterator>; friend constexpr basic_const_iterator operator-(const basic_const_iterator& i, difference_type n) requires random_access_iterator<Iterator>; template<sized_sentinel_for<Iterator> S> constexpr difference_type operator-(const S& y) const; template<not-a-const-iterator S> requires sized_sentinel_for<S, Iterator> friend constexpr difference_type operator-(const S& x, const basic_const_iterator& y); friend constexpr rvalue-reference iter_move(const basic_const_iterator& i) noexcept(noexcept(static_cast<rvalue-reference>(ranges::iter_move(i.current_)))) { return static_cast<rvalue-reference>(ranges::iter_move(i.current_)); } }; }
Given some type I, the concept not-a-const-iterator is defined as false if I is a specialization of basic_const_iterator and true otherwise.

25.5.3.4 Member types [const.iterators.types]

basic_const_iterator<Iterator>​::​iterator_concept is defined as follows:
The member typedef-name iterator_category is defined if and only if Iterator models forward_iterator.
In that case, basic_const_iterator<Iterator>​::​iterator_category denotes the type iterator_traits<​Iterator>​::​iterator_category.

25.5.3.5 Operations [const.iterators.ops]

constexpr basic_const_iterator(Iterator current);
Effects: Initializes current_ with std​::​move(current).
template<convertible_to<Iterator> U> constexpr basic_const_iterator(basic_const_iterator<U> current);
Effects: Initializes current_ with std​::​move(current.current_).
template<different-from<basic_const_iterator> T> requires convertible_to<T, Iterator> constexpr basic_const_iterator(T&& current);
Effects: Initializes current_ with std​::​forward<T>(current).
constexpr const Iterator& base() const & noexcept;
Effects: Equivalent to: return current_;
constexpr Iterator base() &&;
Effects: Equivalent to: return std​::​move(current_);
constexpr reference operator*() const;
Effects: Equivalent to: return static_cast<reference>(*current_);
constexpr const auto* operator->() const requires is_lvalue_reference_v<iter_reference_t<Iterator>> && same_as<remove_cvref_t<iter_reference_t<Iterator>>, value_type>;
Returns: If Iterator models contiguous_iterator, to_address(current_); otherwise, addressof(*current_).
constexpr basic_const_iterator& operator++();
Effects: Equivalent to: ++current_; return *this;
constexpr void operator++(int);
Effects: Equivalent to: ++current_;
constexpr basic_const_iterator operator++(int) requires forward_iterator<Iterator>;
Effects: Equivalent to: auto tmp = *this; ++*this; return tmp;
constexpr basic_const_iterator& operator--() requires bidirectional_iterator<Iterator>;
Effects: Equivalent to: --current_; return *this;
constexpr basic_const_iterator operator--(int) requires bidirectional_iterator<Iterator>;
Effects: Equivalent to: auto tmp = *this; --*this; return tmp;
constexpr basic_const_iterator& operator+=(difference_type n) requires random_access_iterator<Iterator>; constexpr basic_const_iterator& operator-=(difference_type n) requires random_access_iterator<Iterator>;
Let op be the operator.
Effects: Equivalent to: current_ op n; return *this;
constexpr reference operator[](difference_type n) const requires random_access_iterator<Iterator>
Effects: Equivalent to: return static_cast<reference>(current_[n]);
template<sentinel_for<Iterator> S> constexpr bool operator==(const S& s) const;
Effects: Equivalent to: return current_ == s;
constexpr bool operator<(const basic_const_iterator& y) const requires random_access_iterator<Iterator>; constexpr bool operator>(const basic_const_iterator& y) const requires random_access_iterator<Iterator>; constexpr bool operator<=(const basic_const_iterator& y) const requires random_access_iterator<Iterator>; constexpr bool operator>=(const basic_const_iterator& y) const requires random_access_iterator<Iterator>; constexpr auto operator<=>(const basic_const_iterator& y) const requires random_access_iterator<Iterator> && three_way_comparable<Iterator>;
Let op be the operator.
Effects: Equivalent to: return current_ op y.current_;
template<different-from<basic_const_iterator> I> constexpr bool operator<(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<different-from<basic_const_iterator> I> constexpr bool operator>(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<different-from<basic_const_iterator> I> constexpr bool operator<=(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<different-from<basic_const_iterator> I> constexpr bool operator>=(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<different-from<basic_const_iterator> I> constexpr auto operator<=>(const I& y) const requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I> && three_way_comparable_with<Iterator, I>;
Let op be the operator.
Effects: Equivalent to: return current_ op y;
template<not-a-const-iterator I> friend constexpr bool operator<(const I& x, const basic_const_iterator& y) requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<not-a-const-iterator I> friend constexpr bool operator>(const I& x, const basic_const_iterator& y) requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<not-a-const-iterator I> friend constexpr bool operator<=(const I& x, const basic_const_iterator& y) requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>; template<not-a-const-iterator I> friend constexpr bool operator>=(const I& x, const basic_const_iterator& y) requires random_access_iterator<Iterator> && totally_ordered_with<Iterator, I>;
Let op be the operator.
Returns: Equivalent to: return x op y.current_;
friend constexpr basic_const_iterator operator+(const basic_const_iterator& i, difference_type n) requires random_access_iterator<Iterator>; friend constexpr basic_const_iterator operator+(difference_type n, const basic_const_iterator& i) requires random_access_iterator<Iterator>;
Effects: Equivalent to: return basic_const_iterator(i.current_ + n);
friend constexpr basic_const_iterator operator-(const basic_const_iterator& i, difference_type n) requires random_access_iterator<Iterator>;
Effects: Equivalent to: return basic_const_iterator(i.current_ - n);
template<sized_sentinel_for<Iterator> S> constexpr difference_type operator-(const S& y) const;
Effects: Equivalent to: return current_ - y;
template<not-a-const-iterator S> requires sized_sentinel_for<S, Iterator> friend constexpr difference_type operator-(const S& x, const basic_const_iterator& y);
Effects: Equivalent to: return x - y.current_;

25.5.4 Move iterators and sentinels [move.iterators]

25.5.4.1 General [move.iterators.general]

Class template move_iterator is an iterator adaptor with the same behavior as the underlying iterator except that its indirection operator implicitly converts the value returned by the underlying iterator's indirection operator to an rvalue.
Some generic algorithms can be called with move iterators to replace copying with moving.
[Example 1: list<string> s; // populate the list s vector<string> v1(s.begin(), s.end()); // copies strings into v1 vector<string> v2(make_move_iterator(s.begin()), make_move_iterator(s.end())); // moves strings into v2 β€” end example]

25.5.4.2 Class template move_iterator [move.iterator]

namespace std { template<class Iterator> class move_iterator { public: using iterator_type = Iterator; using iterator_concept = see below; using iterator_category = see below; // not always present using value_type = iter_value_t<Iterator>; using difference_type = iter_difference_t<Iterator>; using pointer = Iterator; using reference = iter_rvalue_reference_t<Iterator>; constexpr move_iterator(); constexpr explicit move_iterator(Iterator i); template<class U> constexpr move_iterator(const move_iterator<U>& u); template<class U> constexpr move_iterator& operator=(const move_iterator<U>& u); constexpr const Iterator& base() const & noexcept; constexpr Iterator base() &&; constexpr reference operator*() const; constexpr move_iterator& operator++(); constexpr auto operator++(int); constexpr move_iterator& operator--(); constexpr move_iterator operator--(int); constexpr move_iterator operator+(difference_type n) const; constexpr move_iterator& operator+=(difference_type n); constexpr move_iterator operator-(difference_type n) const; constexpr move_iterator& operator-=(difference_type n); constexpr reference operator[](difference_type n) const; template<sentinel_for<Iterator> S> friend constexpr bool operator==(const move_iterator& x, const move_sentinel<S>& y); template<sized_sentinel_for<Iterator> S> friend constexpr iter_difference_t<Iterator> operator-(const move_sentinel<S>& x, const move_iterator& y); template<sized_sentinel_for<Iterator> S> friend constexpr iter_difference_t<Iterator> operator-(const move_iterator& x, const move_sentinel<S>& y); friend constexpr iter_rvalue_reference_t<Iterator> iter_move(const move_iterator& i) noexcept(noexcept(ranges::iter_move(i.current))); template<indirectly_swappable<Iterator> Iterator2> friend constexpr void iter_swap(const move_iterator& x, const move_iterator<Iterator2>& y) noexcept(noexcept(ranges::iter_swap(x.current, y.current))); private: Iterator current; // exposition only }; }
The member typedef-name iterator_concept is defined as follows:
The member typedef-name iterator_category is defined if and only if the qualified-id iterator_traits<Iterator>​::​iterator_category is valid and denotes a type.
In that case, iterator_category denotes
  • random_access_iterator_tag if the type iterator_traits<​Iterator>​::​iterator_category models derived_from<random_access_iterator_tag>, and
  • iterator_traits<​Iterator>​::​iterator_category otherwise.

25.5.4.3 Requirements [move.iter.requirements]

The template parameter Iterator shall either meet the Cpp17InputIterator requirements ([input.iterators]) or model input_iterator ([iterator.concept.input]).
Additionally, if any of the bidirectional traversal functions are instantiated, the template parameter shall either meet the Cpp17BidirectionalIterator requirements ([bidirectional.iterators]) or model bidirectional_iterator ([iterator.concept.bidir]).
If any of the random access traversal functions are instantiated, the template parameter shall either meet the Cpp17RandomAccessIterator requirements ([random.access.iterators]) or model random_access_iterator ([iterator.concept.random.access]).

25.5.4.4 Construction and assignment [move.iter.cons]

constexpr move_iterator();
Effects: Value-initializes current.
constexpr explicit move_iterator(Iterator i);
Effects: Initializes current with std​::​move(i).
template<class U> constexpr move_iterator(const move_iterator<U>& u);
Constraints: is_same_v<U, Iterator> is false and const U& models convertible_to<Iterator>.
Effects: Initializes current with u.current.
template<class U> constexpr move_iterator& operator=(const move_iterator<U>& u);
Constraints: is_same_v<U, Iterator> is false, const U& models convertible_to<Iterator>, and assignable_from<Iterator&, const U&> is modeled.
Effects: Assigns u.current to current.
Returns: *this.

25.5.4.5 Conversion [move.iter.op.conv]

constexpr const Iterator& base() const & noexcept;
Returns: current.
constexpr Iterator base() &&;
Returns: std​::​move(current).

25.5.4.6 Element access [move.iter.elem]

constexpr reference operator*() const;
Effects: Equivalent to: return ranges​::​iter_move(current);
constexpr reference operator[](difference_type n) const;
Effects: Equivalent to: return ranges​::​iter_move(current + n);

25.5.4.7 Navigation [move.iter.nav]

constexpr move_iterator& operator++();
Effects: As if by ++current.
Returns: *this.
constexpr auto operator++(int);
Effects: If Iterator models forward_iterator, equivalent to: move_iterator tmp = *this; ++current; return tmp;
Otherwise, equivalent to ++current.
constexpr move_iterator& operator--();
Effects: As if by --current.
Returns: *this.
constexpr move_iterator operator--(int);
Effects: As if by: move_iterator tmp = *this; --current; return tmp;
constexpr move_iterator operator+(difference_type n) const;
Returns: move_iterator(current + n).
constexpr move_iterator& operator+=(difference_type n);
Effects: As if by: current += n;
Returns: *this.
constexpr move_iterator operator-(difference_type n) const;
Returns: move_iterator(current - n).
constexpr move_iterator& operator-=(difference_type n);
Effects: As if by: current -= n;
Returns: *this.

25.5.4.8 Comparisons [move.iter.op.comp]

template<class Iterator1, class Iterator2> constexpr bool operator==(const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y); template<sentinel_for<Iterator> S> friend constexpr bool operator==(const move_iterator& x, const move_sentinel<S>& y);
Constraints: x.base() == y.base() is well-formed and convertible to bool.
Returns: x.base() == y.base().
template<class Iterator1, class Iterator2> constexpr bool operator<(const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y);
Constraints: x.base() < y.base() is well-formed and convertible to bool.
Returns: x.base() < y.base().
template<class Iterator1, class Iterator2> constexpr bool operator>(const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y);
Constraints: y.base() < x.base() is well-formed and convertible to bool.
Returns: y < x.
template<class Iterator1, class Iterator2> constexpr bool operator<=(const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y);
Constraints: y.base() < x.base() is well-formed and convertible to bool.
Returns: !(y < x).
template<class Iterator1, class Iterator2> constexpr bool operator>=(const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y);
Constraints: x.base() < y.base() is well-formed and convertible to bool.
Returns: !(x < y).
template<class Iterator1, three_way_comparable_with<Iterator1> Iterator2> constexpr compare_three_way_result_t<Iterator1, Iterator2> operator<=>(const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y);
Returns: x.base() <=> y.base().

25.5.4.9 Non-member functions [move.iter.nonmember]

template<class Iterator1, class Iterator2> constexpr auto operator-( const move_iterator<Iterator1>& x, const move_iterator<Iterator2>& y) -> decltype(x.base() - y.base()); template<sized_sentinel_for<Iterator> S> friend constexpr iter_difference_t<Iterator> operator-(const move_sentinel<S>& x, const move_iterator& y); template<sized_sentinel_for<Iterator> S> friend constexpr iter_difference_t<Iterator> operator-(const move_iterator& x, const move_sentinel<S>& y);
Returns: x.base() - y.base().
template<class Iterator> constexpr move_iterator<Iterator> operator+(iter_difference_t<Iterator> n, const move_iterator<Iterator>& x);
Constraints: x.base() + n is well-formed and has type Iterator.
Returns: x + n.
friend constexpr iter_rvalue_reference_t<Iterator> iter_move(const move_iterator& i) noexcept(noexcept(ranges::iter_move(i.current)));
Effects: Equivalent to: return ranges​::​iter_move(i.current);
template<indirectly_swappable<Iterator> Iterator2> friend constexpr void iter_swap(const move_iterator& x, const move_iterator<Iterator2>& y) noexcept(noexcept(ranges::iter_swap(x.current, y.current)));
Effects: Equivalent to: ranges​::​iter_swap(x.current, y.current).
template<class Iterator> constexpr move_iterator<Iterator> make_move_iterator(Iterator i);
Returns: move_iterator<Iterator>(std​::​move(i)).

25.5.4.10 Class template move_sentinel [move.sentinel]

Class template move_sentinel is a sentinel adaptor useful for denoting ranges together with move_iterator.
When an input iterator type I and sentinel type S model sentinel_for<S, I>, move_sentinel<S> and move_iterator<I> model sentinel_for<move_sentinel<S>, move_iterator<I>> as well.
[Example 1: 
A move_if algorithm is easily implemented with copy_if using move_iterator and move_sentinel: template<input_iterator I, sentinel_for<I> S, weakly_incrementable O, indirect_unary_predicate<I> Pred> requires indirectly_movable<I, O> void move_if(I first, S last, O out, Pred pred) { ranges::copy_if(move_iterator<I>{std::move(first)}, move_sentinel<S>{last}, std::move(out), pred); }
β€” end example]
namespace std { template<semiregular S> class move_sentinel { public: constexpr move_sentinel(); constexpr explicit move_sentinel(S s); template<class S2> requires convertible_to<const S2&, S> constexpr move_sentinel(const move_sentinel<S2>& s); template<class S2> requires assignable_from<S&, const S2&> constexpr move_sentinel& operator=(const move_sentinel<S2>& s); constexpr S base() const; private: S last; // exposition only }; }

25.5.4.11 Operations [move.sent.ops]

constexpr move_sentinel();
Effects: Value-initializes last.
If is_trivially_default_constructible_v<S> is true, then this constructor is a constexpr constructor.
constexpr explicit move_sentinel(S s);
Effects: Initializes last with std​::​move(s).
template<class S2> requires convertible_to<const S2&, S> constexpr move_sentinel(const move_sentinel<S2>& s);
Effects: Initializes last with s.last.
template<class S2> requires assignable_from<S&, const S2&> constexpr move_sentinel& operator=(const move_sentinel<S2>& s);
Effects: Equivalent to: last = s.last; return *this;
constexpr S base() const;
Returns: last.

25.5.5 Common iterators [iterators.common]

25.5.5.1 Class template common_iterator [common.iterator]

Class template common_iterator is an iterator/sentinel adaptor that is capable of representing a non-common range of elements (where the types of the iterator and sentinel differ) as a common range (where they are the same).
It does this by holding either an iterator or a sentinel, and implementing the equality comparison operators appropriately.
[Note 1: 
The common_iterator type is useful for interfacing with legacy code that expects the begin and end of a range to have the same type.
β€” end note]
[Example 1: template<class ForwardIterator> void fun(ForwardIterator begin, ForwardIterator end); list<int> s; // populate the list s using CI = common_iterator<counted_iterator<list<int>::iterator>, default_sentinel_t>; // call fun on a range of 10 ints fun(CI(counted_iterator(s.begin(), 10)), CI(default_sentinel)); β€” end example]
namespace std { template<input_or_output_iterator I, sentinel_for<I> S> requires (!same_as<I, S> && copyable<I>) class common_iterator { public: constexpr common_iterator() requires default_initializable<I> = default; constexpr common_iterator(I i); constexpr common_iterator(S s); template<class I2, class S2> requires convertible_to<const I2&, I> && convertible_to<const S2&, S> constexpr common_iterator(const common_iterator<I2, S2>& x); template<class I2, class S2> requires convertible_to<const I2&, I> && convertible_to<const S2&, S> && assignable_from<I&, const I2&> && assignable_from<S&, const S2&> constexpr common_iterator& operator=(const common_iterator<I2, S2>& x); constexpr decltype(auto) operator*(); constexpr decltype(auto) operator*() const requires dereferenceable<const I>; constexpr auto operator->() const requires see below; constexpr common_iterator& operator++(); constexpr decltype(auto) operator++(int); template<class I2, sentinel_for<I> S2> requires sentinel_for<S, I2> friend constexpr bool operator==( const common_iterator& x, const common_iterator<I2, S2>& y); template<class I2, sentinel_for<I> S2> requires sentinel_for<S, I2> && equality_comparable_with<I, I2> friend constexpr bool operator==( const common_iterator& x, const common_iterator<I2, S2>& y); template<sized_sentinel_for<I> I2, sized_sentinel_for<I> S2> requires sized_sentinel_for<S, I2> friend constexpr iter_difference_t<I2> operator-( const common_iterator& x, const common_iterator<I2, S2>& y); friend constexpr iter_rvalue_reference_t<I> iter_move(const common_iterator& i) noexcept(noexcept(ranges::iter_move(declval<const I&>()))) requires input_iterator<I>; template<indirectly_swappable<I> I2, class S2> friend constexpr void iter_swap(const common_iterator& x, const common_iterator<I2, S2>& y) noexcept(noexcept(ranges::iter_swap(declval<const I&>(), declval<const I2&>()))); private: variant<I, S> v_; // exposition only }; template<class I, class S> struct incrementable_traits<common_iterator<I, S>> { using difference_type = iter_difference_t<I>; }; template<input_iterator I, class S> struct iterator_traits<common_iterator<I, S>> { using iterator_concept = see below; using iterator_category = see below; using value_type = iter_value_t<I>; using difference_type = iter_difference_t<I>; using pointer = see below; using reference = iter_reference_t<I>; }; }

25.5.5.2 Associated types [common.iter.types]

The nested typedef-names of the specialization of iterator_traits for common_iterator<I, S> are defined as follows.
  • iterator_concept denotes forward_iterator_tag if I models forward_iterator; otherwise it denotes input_iterator_tag.
  • iterator_category denotes forward_iterator_tag if the qualified-id iterator_traits<I>​::​iterator_category is valid and denotes a type that models derived_from<forward_iterator_tag>; otherwise it denotes input_iterator_tag.
  • Let a denote an lvalue of type const common_iterator<I, S>.
    If the expression a.operator->() is well-formed, then pointer denotes decltype(a.operator->()).
    Otherwise, pointer denotes void.

25.5.5.3 Constructors and conversions [common.iter.const]

constexpr common_iterator(I i);
Effects: Initializes v_ as if by v_{in_place_type<I>, std​::​move(i)}.
constexpr common_iterator(S s);
Effects: Initializes v_ as if by v_{in_place_type<S>, std​::​move(s)}.
template<class I2, class S2> requires convertible_to<const I2&, I> && convertible_to<const S2&, S> constexpr common_iterator(const common_iterator<I2, S2>& x);
Preconditions: x.v_.valueless_by_exception() is false.
Effects: Initializes v_ as if by v_{in_place_index<i>, get<i>(x.v_)}, where i is x.v_.index().
template<class I2, class S2> requires convertible_to<const I2&, I> && convertible_to<const S2&, S> && assignable_from<I&, const I2&> && assignable_from<S&, const S2&> constexpr common_iterator& operator=(const common_iterator<I2, S2>& x);
Preconditions: x.v_.valueless_by_exception() is false.
Effects: Equivalent to:
  • If v_.index() == x.v_.index(), then get<i>(v_) = get<i>(x.v_).
  • Otherwise, v_.emplace<i>(get<i>(x.v_)).
where i is x.v_.index().
Returns: *this

25.5.5.4 Accessors [common.iter.access]

constexpr decltype(auto) operator*(); constexpr decltype(auto) operator*() const requires dereferenceable<const I>;
Preconditions: holds_alternative<I>(v_) is true.
Effects: Equivalent to: return *get<I>(v_);
constexpr auto operator->() const requires see below;
The expression in the requires-clause is equivalent to: indirectly_readable<const I> && (requires(const I& i) { i.operator->(); } || is_reference_v<iter_reference_t<I>> || constructible_from<iter_value_t<I>, iter_reference_t<I>>)
Preconditions: holds_alternative<I>(v_) is true.
Effects:
  • If I is a pointer type or if the expression get<I>(v_).operator->() is well-formed, equivalent to: return get<I>(v_);
  • Otherwise, if iter_reference_t<I> is a reference type, equivalent to: auto&& tmp = *get<I>(v_); return addressof(tmp);
  • Otherwise, equivalent to: return proxy(*get<I>(v_)); where proxy is the exposition-only class: class proxy { iter_value_t<I> keep_; constexpr proxy(iter_reference_t<I>&& x) : keep_(std::move(x)) {} public: constexpr const iter_value_t<I>* operator->() const noexcept { return addressof(keep_); } };

25.5.5.5 Navigation [common.iter.nav]

constexpr common_iterator& operator++();
Preconditions: holds_alternative<I>(v_) is true.
Effects: Equivalent to ++get<I>(v_).