Defined in header <iterator>
template<class I>
  concept bidirectional_iterator =
    std::forward_iterator<I> &&
    std::derived_from</*ITER_CONCEPT*/<I>, std::bidirectional_iterator_tag> &&
    requires(I i) {
      { --i } -> std::same_as<I&>;
      { i-- } -> std::same_as<I>;
(since C++20)

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:

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.


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

See also

specifies that an input_iterator is a forward iterator, supporting equality comparison and multi-pass

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