Iterators are a generalization of pointers that allow a C++ program to work with different data structures
(containers) 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
*writable* to the iterator;
for each such type T, the expression *i = o
is valid where o is a value of type T.
An iterator
i
for which the expression
(*i).m
is well-defined supports the expression
i->m
with the same semantics as
(*i).m.
For every iterator type
X
for which
equality is defined, there is a corresponding signed integer type called the
*difference type*
of the iterator.

Since iterators are an abstraction of pointers, their semantics is 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 International Standard defines five categories of iterators, according to the operations defined on them: input iterators, output iterators, forward iterators, bidirectional iterators and random access iterators, as shown in Table 93.

Table 93 — Relations among iterator categories

Random Access | → Bidirectional |
→ Forward | → Input |

→ Output |

Forward iterators satisfy all the requirements of input iterators and can be used whenever an input iterator is specified; Bidirectional iterators also satisfy all the requirements of forward iterators and can be used whenever a forward iterator is specified; Random access iterators also satisfy all the requirements of bidirectional iterators and can be used whenever a bidirectional iterator is specified.

Iterators that further satisfy 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-name*s specified in [iterator.traits]
shall be provided for the iterator type.
[ Note: Either the iterator type must provide the *typedef-name*s directly
(in which case iterator_traits pick them up automatically), or
an iterator_traits specialization must provide them. — end note ]

Iterators that further satisfy the requirement that,
for integral values n and
dereferenceable iterator values a and (a + n),
*(a + n) is equivalent to *(addressof(*a) + n),
are called *contiguous iterators*.
[ Note:
For example, the type “pointer to int” is a contiguous iterator,
but reverse_iterator<int *> is not.
For a valid iterator range [a,b) with dereferenceable a,
the corresponding range denoted by pointers is
[addressof(*a),addressof(*a) + (b - a));
b might not be dereferenceable.
— 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.
These values are called
*past-the-end*
values.
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.
[ Example:
After the declaration of an uninitialized pointer
x
(as with
int* x;),
x
must always be assumed to have a singular value of a pointer.
— end example ]
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 satisfy the
DefaultConstructible requirements, using a value-initialized iterator
as the source of a copy or move operation. [ Note: 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.
— end note ]
In these cases the singular
value is overwritten the same way as any other value.
Dereferenceable
values are always non-singular.

An iterator
j
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 == j.
If
j
is reachable from
i,
they refer to elements of the same sequence.

Most of the library's algorithmic templates that operate on data structures have interfaces that use ranges.
A
*range*
is a pair of iterators that designate the beginning and end of the computation.
A range [i, i)
is an empty range;
in general, a range [i, j)
refers to the elements in the data structure starting with the element
pointed to by
i
and up to but not including the element pointed to by
j.
Range [i, j)
is valid if and only if
j
is reachable from
i.
The result of the application of functions in the library 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 for the iterators do not have a complexity column.

Destruction of an iterator may invalidate pointers and references previously obtained from that iterator.

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: For an iterator type X there must be an instantiation of iterator_traits<X>. — end note ]

This definition applies to pointers, since pointers are iterators. The effect of dereferencing an iterator that has been invalidated is undefined.

The Iterator requirements form the basis of the iterator concept taxonomy; every iterator satisfies the Iterator requirements. This set of requirements specifies operations for dereferencing and incrementing an iterator. Most algorithms will require additional operations to read or write values, or to provide a richer set of iterator movements ([forward.iterators], [bidirectional.iterators], [random.access.iterators]).

A type X satisfies the Iterator requirements if:

X satisfies the CopyConstructible, CopyAssignable, and Destructible requirements ([utility.arg.requirements]) and lvalues of type X are swappable, and

the expressions in Table 94 are valid and have the indicated semantics.

Table 94 — Iterator requirements

Expression | Return type | Operational | Assertion/note |

semantics | pre-/post-condition | ||

*r | unspecified | Requires: r is dereferenceable. | |

++r | X& |

A class or pointer type X satisfies the requirements of an input iterator for the value type T if X satisfies the Iterator and EqualityComparable requirements and the expressions in Table 95 are valid and have the indicated semantics.

In Table 95, 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: 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). — end example ]

Table 95 — Input iterator requirements (in addition to Iterator)

Expression | Return type | Operational | Assertion/note |

semantics | pre-/post-condition | ||

a != b | contextually convertible to bool | !(a == b) | Requires: (a, b) is in the domain of ==. |

*a | reference, convertible to T |
Requires: 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 | Requires: a is dereferenceable. | |

++r | X& |
Requires: 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 either to be dereferenceable or to be in the domain of ==. | |

(void)r++ | equivalent to (void)++r | ||

*r++ | convertible to T |
{ T tmp = *r; ++r; return tmp; } |

[ Note: For input iterators, a == b does not imply ++a == ++b. (Equality does not guarantee the substitution property or referential transparency.) Algorithms on input iterators should never attempt to pass through the same iterator twice. They should be single pass algorithms. Value type T is not required to be a CopyAssignable type. These algorithms can be used with istreams as the source of the input data through the istream_iterator class template. — end note ]

A class or pointer type X satisfies the requirements of an output iterator if X satisfies the Iterator requirements and the expressions in Table 96 are valid and have the indicated semantics.

Table 96 — Output iterator requirements (in addition to Iterator)

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& |
&r == &++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. |

[ Note: 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. Algorithms on output iterators should never attempt to pass through the same iterator twice. They should be single pass algorithms. Equality and inequality might not be defined. Algorithms that take output iterators can be used with ostreams as the destination for placing data through the ostream_iterator class as well as with insert iterators and insert pointers. — end note ]

A class or pointer type X satisfies the requirements of a forward iterator if

X satisfies the requirements of an input iterator,

X satisfies the DefaultConstructible 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 97 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: Value-initialized iterators behave as if they refer past the end of the same empty sequence. — 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: 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. — end note ]

Table 97 — Forward iterator requirements (in addition to input iterator)

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.

A class or pointer type X satisfies the requirements of a bidirectional iterator if, in addition to satisfying the requirements for forward iterators, the following expressions are valid as shown in Table 98.

Table 98 — Bidirectional iterator requirements (in addition to forward iterator)

Expression | Return type | Operational | Assertion/note |

semantics | pre-/post-condition | ||

--r | X& |
Requires: there exists s such that r == ++s. Postconditions: r is dereferenceable. --(++r) == r. --r == --s implies r == s. &r == &--r. | |

r-- | convertible to const X& |
{ X tmp = r; --r; return tmp; } | |

*r-- | reference |

A class or pointer type X satisfies the requirements of a random access iterator if, in addition to satisfying the requirements for bidirectional iterators, the following expressions are valid as shown in Table 99.

Table 99 — Random access iterator requirements (in addition to bidirectional iterator)

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; | Requires: 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 |
Requires: 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 | contextually convertible to bool | b - a > 0 | < is a total ordering relation |

a > b | contextually convertible to bool | b < a | > is a total ordering relation opposite to <. |

a >= b | contextually convertible to bool | !(a < b) | |

a <= b | contextually convertible to bool. | !(a > b) |