The ForwardIterator concept refines InputIterator ([iterators.input]), adding equality comparison and the multi-pass guarantee, specified below.
template <class I>
concept bool ForwardIterator =
InputIterator<I> &&
DerivedFrom<iterator_category_t<I>, forward_iterator_tag> &&
Incrementable<I> &&
Sentinel<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: Value-initialized iterators behave as if they refer past the end of the same empty sequence. — 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 ([](X x){++x;}(a), *a) is equivalent to the expression *a.
[ Note: The requirement that a == b implies ++a == ++b (which is not true for weaker iterators) 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. — end note ]