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. All input iterators i support the expression *i, resulting in a value of some object type T, called the value type of the iterator. All output iterators support the expression *i = o where o is a value of some type that is in the set of types that are writable to the particular iterator type of i. All iterators i for which the expression (*i).m is well-defined, support 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 [tab:iterators.relations].
| 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.
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> ([iterator.traits]). — end note ]
This definition applies to pointers, since pointers are iterators. The effect of dereferencing an iterator that has been invalidated is undefined.