std::bidirectional_iterator(3)

NAME
std::bidirectional_iterator - std::bidirectional_iterator

Synopsis
   Defined in header <iterator>
   template<class I>
   concept bidirectional_iterator =
   std::forward_iterator<I> &&
   std::derived_from</*ITER_CONCEPT*/<I>,
   std::bidirectional_iterator_tag> && (since C++20)
   requires(I i) {
   { --i } -> std::same_as<I&>;
   { i-- } -> std::same_as<I>;
   };
   The concept bidirectional_iterator refines forward_iterator by adding the ability to
   move an iterator backward.
  Iterator concept determination
   Definition of this concept is specified via an exposition-only alias template
   /*ITER_CONCEPT*/.
   In order to determine /*ITER_CONCEPT*/<I>, let ITER_TRAITS<I> denote I if the
   specialization std::iterator_traits<I> is generated from the primary template, or
   std::iterator_traits<I> otherwise:
     * If ITER_TRAITS<I>::iterator_concept is valid and names a type,
       /*ITER_CONCEPT*/<I> denotes the type.
     * Otherwise, if ITER_TRAITS<I>::iterator_category is valid and names a type,
       /*ITER_CONCEPT*/<I> denotes the type.
     * Otherwise, if std::iterator_traits<I> is generated from the primary template,
       /*ITER_CONCEPT*/<I> denotes std::random_access_iterator_tag.
     * Otherwise, /*ITER_CONCEPT*/<I> does not denote a type and results in a
       substitution failure.
  Semantic requirements
   A bidirectional iterator r is said to be decrementable if and only if there exists
   some s such that ++s == r.
   bidirectional_iterator<I> is modeled only if all the concepts it subsumes are
   modeled, and given two objects a and b of type I:
     * If a is decrementable, a is in the domain of the expressions --a and a--.
     * Pre-decrement yields an lvalue that refers to the operand: std::addressof(--a)
       == std::addressof(a);
     * Post-decrement yields the previous value of the operand: if bool(a == b), then
       bool(a-- == b).
     * Post-decrement and pre-decrement perform the same modification on its operand:
       If bool(a == b), then after evaluating both a-- and --b, bool(a == b) still
       holds.
     * Increment and decrement are inverses of each other:
              * If a is incrementable and bool(a == b), then bool(--(++a) == b).
              * If a is decrementable and bool(a == b), then bool(++(--a) == b).
  Equality preservation
   An expression is equality preserving if it results in equal outputs given equal
   inputs.
     * The inputs to an expression consist of its operands.
     * The outputs of an expression consist of its result and all operands modified by
       the expression (if any).
   In specification of standard concepts, operands are defined as the largest
   subexpressions that include only:
     * an id-expression, and
     * invocations of std::move, std::forward, and std::declval.
   The cv-qualification and value category of each operand is determined by assuming
   that each template type parameter denotes a cv-unqualified complete non-array object
   type.
   Every expression required to be equality preserving is further required to be
   stable: two evaluations of such an expression with the same input objects must have
   equal outputs absent any explicit intervening modification of those input objects.
   Unless noted otherwise, every expression used in a requires-expression is required
   to be equality preserving and stable, and the evaluation of the expression may
   modify only its non-constant operands. Operands that are constant must not be
   modified.

Notes
   Unlike the LegacyBidirectionalIterator requirements, the bidirectional_iterator
   concept does not require dereference to return an lvalue.

See also
   forward_iterator specifies that an input_iterator is a forward iterator, supporting
   (C++20) equality comparison and multi-pass
                    (concept)