23 Iterators library [iterators]

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 =
  copyable<I> && requires(I i) {
    {   *i } -> can-reference;
    {  ++i } -> same_as<I&>;
    { *i++ } -> can-reference;
  };

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_lvalue_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:

• (3.1)
  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.
• (3.2)
  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;
  

  • (3.2.1)
    If the qualified-id I​::​pointer is valid and denotes a type, pointer names that type. Otherwise, if decltype(​declval<I&>().operator->()) is well-formed, then pointer names that type. Otherwise, pointer names void.
  • (3.2.2)
    If the qualified-id I​::​reference is valid and denotes a type, reference names that type. Otherwise, reference names iter_­reference_­t<I>.
  • (3.2.3)
    If the qualified-id I​::​iterator_­category is valid and denotes a type, iterator_­category names that type. Otherwise, iterator_­category names:
    • (3.2.3.1)
      random_­access_­iterator_­tag if I satisfies cpp17-random-access-iterator, or otherwise
    • (3.2.3.2)
      bidirectional_­iterator_­tag if I satisfies cpp17-bidirectional-iterator, or otherwise
    • (3.2.3.3)
      forward_­iterator_­tag if I satisfies cpp17-forward-iterator, or otherwise
    • (3.2.3.4)
      input_­iterator_­tag.
• (3.3)
  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.
• (3.4)
  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]).

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&;
  };
}