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Iterator Facade and Adaptor

Author: David Abrahams, Jeremy Siek, Thomas Witt
Contact: dave@boost-consulting.com, jsiek@osl.iu.edu, witt@styleadvisor.com
Organization: Boost Consulting, Indiana University Open Systems Lab, Zephyr Associates, Inc.
Date: 2006-09-11
Number:This is a revised version of N1530=03-0113, which was accepted for Technical Report 1 by the C++ standard committee's library working group.
copyright:Copyright David Abrahams, Jeremy Siek, and Thomas Witt 2003.
abstract:We propose a set of class templates that help programmers build standard-conforming iterators, both from scratch and by adapting other iterators.

Table of Contents

Motivation

Iterators play an important role in modern C++ programming. The iterator is the central abstraction of the algorithms of the Standard Library, allowing algorithms to be re-used in in a wide variety of contexts. The C++ Standard Library contains a wide variety of useful iterators. Every one of the standard containers comes with constant and mutable iterators2, and also reverse versions of those same iterators which traverse the container in the opposite direction. The Standard also supplies istream_iterator and ostream_iterator for reading from and writing to streams, insert_iterator, front_insert_iterator and back_insert_iterator for inserting elements into containers, and raw_storage_iterator for initializing raw memory [7].

Despite the many iterators supplied by the Standard Library, obvious and useful iterators are missing, and creating new iterator types is still a common task for C++ programmers. The literature documents several of these, for example line_iterator [3] and Constant_iterator [9]. The iterator abstraction is so powerful that we expect programmers will always need to invent new iterator types.

Although it is easy to create iterators that almost conform to the standard, the iterator requirements contain subtleties which can make creating an iterator which actually conforms quite difficult. Further, the iterator interface is rich, containing many operators that are technically redundant and tedious to implement. To automate the repetitive work of constructing iterators, we propose iterator_facade, an iterator base class template which provides the rich interface of standard iterators and delegates its implementation to member functions of the derived class. In addition to reducing the amount of code necessary to create an iterator, the iterator_facade also provides compile-time error detection. Iterator implementation mistakes that often go unnoticed are turned into compile-time errors because the derived class implementation must match the expectations of the iterator_facade.

A common pattern of iterator construction is the adaptation of one iterator to form a new one. The functionality of an iterator is composed of four orthogonal aspects: traversal, indirection, equality comparison and distance measurement. Adapting an old iterator to create a new one often saves work because one can reuse one aspect of functionality while redefining the other. For example, the Standard provides reverse_iterator, which adapts any Bidirectional Iterator by inverting its direction of traversal. As with plain iterators, iterator adaptors defined outside the Standard have become commonplace in the literature:

[1]We use the term concept to mean a set of requirements that a type must satisfy to be used with a particular template parameter.
[2]The term mutable iterator refers to iterators over objects that can be changed by assigning to the dereferenced iterator, while constant iterator refers to iterators over objects that cannot be modified.

To fulfill the need for constructing adaptors, we propose the iterator_adaptor class template. Instantiations of iterator_adaptor serve as a base classes for new iterators, providing the default behavior of forwarding all operations to the underlying iterator. The user can selectively replace these features in the derived iterator class. This proposal also includes a number of more specialized adaptors, such as the transform_iterator that applies some user-specified function during the dereference of the iterator.

Impact on the Standard

This proposal is purely an addition to the C++ standard library. However, note that this proposal relies on the proposal for New Iterator Concepts.

Design

Iterator Concepts

This proposal is formulated in terms of the new iterator concepts as proposed in n1550, since user-defined and especially adapted iterators suffer from the well known categorization problems that are inherent to the current iterator categories.

This proposal does not strictly depend on proposal n1550, as there is a direct mapping between new and old categories. This proposal could be reformulated using this mapping if n1550 was not accepted.

Interoperability

The question of iterator interoperability is poorly addressed in the current standard. There are currently two defect reports that are concerned with interoperability issues.

Issue 179 concerns the fact that mutable container iterator types are only required to be convertible to the corresponding constant iterator types, but objects of these types are not required to interoperate in comparison or subtraction expressions. This situation is tedious in practice and out of line with the way built in types work. This proposal implements the proposed resolution to issue 179, as most standard library implementations do nowadays. In other words, if an iterator type A has an implicit or user defined conversion to an iterator type B, the iterator types are interoperable and the usual set of operators are available.

Issue 280 concerns the current lack of interoperability between reverse iterator types. The proposed new reverse_iterator template fixes the issues raised in 280. It provides the desired interoperability without introducing unwanted overloads.

Iterator Facade

While the iterator interface is rich, there is a core subset of the interface that is necessary for all the functionality. We have identified the following core behaviors for iterators:

  • dereferencing
  • incrementing
  • decrementing
  • equality comparison
  • random-access motion
  • distance measurement

In addition to the behaviors listed above, the core interface elements include the associated types exposed through iterator traits: value_type, reference, difference_type, and iterator_category.

Iterator facade uses the Curiously Recurring Template Pattern (CRTP) [Cop95] so that the user can specify the behavior of iterator_facade in a derived class. Former designs used policy objects to specify the behavior, but that approach was discarded for several reasons:

  1. the creation and eventual copying of the policy object may create overhead that can be avoided with the current approach.
  2. The policy object approach does not allow for custom constructors on the created iterator types, an essential feature if iterator_facade should be used in other library implementations.
  3. Without the use of CRTP, the standard requirement that an iterator's operator++ returns the iterator type itself would mean that all iterators built with the library would have to be specializations of iterator_facade<...>, rather than something more descriptive like indirect_iterator<T*>. Cumbersome type generator metafunctions would be needed to build new parameterized iterators, and a separate iterator_adaptor layer would be impossible.

Usage

The user of iterator_facade derives his iterator class from a specialization of iterator_facade and passes the derived iterator class as iterator_facade's first template parameter. The order of the other template parameters have been carefully chosen to take advantage of useful defaults. For example, when defining a constant lvalue iterator, the user can pass a const-qualified version of the iterator's value_type as iterator_facade's Value parameter and omit the Reference parameter which follows.

The derived iterator class must define member functions implementing the iterator's core behaviors. The following table describes expressions which are required to be valid depending on the category of the derived iterator type. These member functions are described briefly below and in more detail in the iterator facade requirements.

Expression Effects
i.dereference() Access the value referred to
i.equal(j) Compare for equality with j
i.increment() Advance by one position
i.decrement() Retreat by one position
i.advance(n) Advance by n positions
i.distance_to(j) Measure the distance to j

In addition to implementing the core interface functions, an iterator derived from iterator_facade typically defines several constructors. To model any of the standard iterator concepts, the iterator must at least have a copy constructor. Also, if the iterator type X is meant to be automatically interoperate with another iterator type Y (as with constant and mutable iterators) then there must be an implicit conversion from X to Y or from Y to X (but not both), typically implemented as a conversion constructor. Finally, if the iterator is to model Forward Traversal Iterator or a more-refined iterator concept, a default constructor is required.

Iterator Core Access

iterator_facade and the operator implementations need to be able to access the core member functions in the derived class. Making the core member functions public would expose an implementation detail to the user. The design used here ensures that implementation details do not appear in the public interface of the derived iterator type.

Preventing direct access to the core member functions has two advantages. First, there is no possibility for the user to accidently use a member function of the iterator when a member of the value_type was intended. This has been an issue with smart pointer implementations in the past. The second and main advantage is that library implementers can freely exchange a hand-rolled iterator implementation for one based on iterator_facade without fear of breaking code that was accessing the public core member functions directly.

In a naive implementation, keeping the derived class' core member functions private would require it to grant friendship to iterator_facade and each of the seven operators. In order to reduce the burden of limiting access, iterator_core_access is provided, a class that acts as a gateway to the core member functions in the derived iterator class. The author of the derived class only needs to grant friendship to iterator_core_access to make his core member functions available to the library.

iterator_core_access will be typically implemented as an empty class containing only private static member functions which invoke the iterator core member functions. There is, however, no need to standardize the gateway protocol. Note that even if iterator_core_access used public member functions it would not open a safety loophole, as every core member function preserves the invariants of the iterator.

operator[]

The indexing operator for a generalized iterator presents special challenges. A random access iterator's operator[] is only required to return something convertible to its value_type. Requiring that it return an lvalue would rule out currently-legal random-access iterators which hold the referenced value in a data member (e.g. counting_iterator), because *(p+n) is a reference into the temporary iterator p+n, which is destroyed when operator[] returns.

Writable iterators built with iterator_facade implement the semantics required by the preferred resolution to issue 299 and adopted by proposal n1550: the result of p[n] is an object convertible to the iterator's value_type, and p[n] = x is equivalent to *(p + n) = x (Note: This result object may be implemented as a proxy containing a copy of p+n). This approach will work properly for any random-access iterator regardless of the other details of its implementation. A user who knows more about the implementation of her iterator is free to implement an operator[] that returns an lvalue in the derived iterator class; it will hide the one supplied by iterator_facade from clients of her iterator.

operator->

The reference type of a readable iterator (and today's input iterator) need not in fact be a reference, so long as it is convertible to the iterator's value_type. When the value_type is a class, however, it must still be possible to access members through operator->. Therefore, an iterator whose reference type is not in fact a reference must return a proxy containing a copy of the referenced value from its operator->.

The return types for iterator_facade's operator-> and operator[] are not explicitly specified. Instead, those types are described in terms of a set of requirements, which must be satisfied by the iterator_facade implementation.

[Cop95][Coplien, 1995] Coplien, J., Curiously Recurring Template Patterns, C++ Report, February 1995, pp. 24-27.

Iterator Adaptor

The iterator_adaptor class template adapts some Base3 type to create a new iterator. Instantiations of iterator_adaptor are derived from a corresponding instantiation of iterator_facade and implement the core behaviors in terms of the Base type. In essence, iterator_adaptor merely forwards all operations to an instance of the Base type, which it stores as a member.

[3]The term "Base" here does not refer to a base class and is not meant to imply the use of derivation. We have followed the lead of the standard library, which provides a base() function to access the underlying iterator object of a reverse_iterator adaptor.

The user of iterator_adaptor creates a class derived from an instantiation of iterator_adaptor and then selectively redefines some of the core member functions described in the iterator_facade core requirements table. The Base type need not meet the full requirements for an iterator; it need only support the operations used by the core interface functions of iterator_adaptor that have not been redefined in the user's derived class.

Several of the template parameters of iterator_adaptor default to use_default. This allows the user to make use of a default parameter even when she wants to specify a parameter later in the parameter list. Also, the defaults for the corresponding associated types are somewhat complicated, so metaprogramming is required to compute them, and use_default can help to simplify the implementation. Finally, the identity of the use_default type is not left unspecified because specification helps to highlight that the Reference template parameter may not always be identical to the iterator's reference type, and will keep users from making mistakes based on that assumption.

Specialized Adaptors

This proposal also contains several examples of specialized adaptors which were easily implemented using iterator_adaptor:

  • indirect_iterator, which iterates over iterators, pointers, or smart pointers and applies an extra level of dereferencing.
  • A new reverse_iterator, which inverts the direction of a Base iterator's motion, while allowing adapted constant and mutable iterators to interact in the expected ways (unlike those in most implementations of C++98).
  • transform_iterator, which applies a user-defined function object to the underlying values when dereferenced.
  • filter_iterator, which provides a view of an iterator range in which some elements of the underlying range are skipped.
  • counting_iterator, which adapts any incrementable type (e.g. integers, iterators) so that incrementing/decrementing the adapted iterator and dereferencing it produces successive values of the Base type.
  • function_output_iterator, which makes it easier to create custom output iterators.

Based on examples in the Boost library, users have generated many new adaptors, among them a permutation adaptor which applies some permutation to a random access iterator, and a strided adaptor, which adapts a random access iterator by multiplying its unit of motion by a constant factor. In addition, the Boost Graph Library (BGL) uses iterator adaptors to adapt other graph libraries, such as LEDA [10] and Stanford GraphBase [8], to the BGL interface (which requires C++ Standard compliant iterators).

Proposed Text

Header <iterator_helper> synopsis [lib.iterator.helper.synopsis]

struct use_default;

struct iterator_core_access { /* implementation detail */ };

template <
    class Derived
  , class Value
  , class CategoryOrTraversal
  , class Reference  = Value&
  , class Difference = ptrdiff_t
>
class iterator_facade;

template <
    class Derived
  , class Base
  , class Value      = use_default
  , class CategoryOrTraversal  = use_default
  , class Reference  = use_default
  , class Difference = use_default
>
class iterator_adaptor;

template <
    class Iterator
  , class Value = use_default
  , class CategoryOrTraversal = use_default
  , class Reference = use_default
  , class Difference = use_default
>
class indirect_iterator;

template <class Dereferenceable>
struct pointee;

template <class Dereferenceable>
struct indirect_reference;

template <class Iterator>
class reverse_iterator;

template <
    class UnaryFunction
  , class Iterator
  , class Reference = use_default
  , class Value = use_default
>
class transform_iterator;

template <class Predicate, class Iterator>
class filter_iterator;

template <
    class Incrementable
  , class CategoryOrTraversal  = use_default
  , class Difference = use_default
>
class counting_iterator;

template <class UnaryFunction>
class function_output_iterator;

Iterator facade [lib.iterator.facade]

iterator_facade is a base class template that implements the interface of standard iterators in terms of a few core functions and associated types, to be supplied by a derived iterator class.

Class template iterator_facade

template <
    class Derived
  , class Value
  , class CategoryOrTraversal
  , class Reference  = Value&
  , class Difference = ptrdiff_t
>
class iterator_facade {
 public:
    typedef remove_const<Value>::type value_type;
    typedef Reference reference;
    typedef Value* pointer;
    typedef Difference difference_type;
    typedef /* see below */ iterator_category;

    reference operator*() const;
    /* see below */ operator->() const;
    /* see below */ operator[](difference_type n) const;
    Derived& operator++();
    Derived operator++(int);
    Derived& operator--();
    Derived operator--(int);
    Derived& operator+=(difference_type n);
    Derived& operator-=(difference_type n);
    Derived operator-(difference_type n) const;
 protected:
    typedef iterator_facade iterator_facade_;
};

// Comparison operators
template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type // exposition
operator ==(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
            iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator !=(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
            iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator <(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
           iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator <=(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
            iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator >(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
           iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator >=(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
            iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);

// Iterator difference
template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
/* see below */
operator-(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
          iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);

// Iterator addition
template <class Dr, class V, class TC, class R, class D>
Derived operator+ (iterator_facade<Dr,V,TC,R,D> const&,
                   typename Derived::difference_type n);

template <class Dr, class V, class TC, class R, class D>
Derived operator+ (typename Derived::difference_type n,
                   iterator_facade<Dr,V,TC,R,D> const&);

The iterator_category member of iterator_facade is

iterator-category(CategoryOrTraversal, value_type, reference)

where iterator-category is defined as follows:

iterator-category(C,R,V) :=
   if (C is convertible to std::input_iterator_tag
       || C is convertible to std::output_iterator_tag
   )
       return C

   else if (C is not convertible to incrementable_traversal_tag)
       the program is ill-formed

   else return a type X satisfying the following two constraints:

      1. X is convertible to X1, and not to any more-derived
         type, where X1 is defined by:

           if (R is a reference type
               && C is convertible to forward_traversal_tag)
           {
               if (C is convertible to random_access_traversal_tag)
                   X1 = random_access_iterator_tag
               else if (C is convertible to bidirectional_traversal_tag)
                   X1 = bidirectional_iterator_tag
               else
                   X1 = forward_iterator_tag
           }
           else
           {
               if (C is convertible to single_pass_traversal_tag
                   && R is convertible to V)
                   X1 = input_iterator_tag
               else
                   X1 = C
           }

      2. category-to-traversal(X) is convertible to the most
         derived traversal tag type to which X is also
         convertible, and not to any more-derived traversal tag
         type.

[Note: the intention is to allow iterator_category to be one of the five original category tags when convertibility to one of the traversal tags would add no information]

The enable_if_interoperable template used above is for exposition purposes. The member operators should only be in an overload set provided the derived types Dr1 and Dr2 are interoperable, meaning that at least one of the types is convertible to the other. The enable_if_interoperable approach uses SFINAE to take the operators out of the overload set when the types are not interoperable. The operators should behave as-if enable_if_interoperable were defined to be:

template <bool, typename> enable_if_interoperable_impl
{};

template <typename T> enable_if_interoperable_impl<true,T>
{ typedef T type; };

template<typename Dr1, typename Dr2, typename T>
struct enable_if_interoperable
  : enable_if_interoperable_impl<
        is_convertible<Dr1,Dr2>::value || is_convertible<Dr2,Dr1>::value
      , T
    >
{};

iterator_facade Requirements

The following table describes the typical valid expressions on iterator_facade's Derived parameter, depending on the iterator concept(s) it will model. The operations in the first column must be made accessible to member functions of class iterator_core_access. In addition, static_cast<Derived*>(iterator_facade*) shall be well-formed.

In the table below, F is iterator_facade<X,V,C,R,D>, a is an object of type X, b and c are objects of type const X, n is an object of F::difference_type, y is a constant object of a single pass iterator type interoperable with X, and z is a constant object of a random access traversal iterator type interoperable with X.

iterator_facade Core Operations

Expression Return Type Assertion/Note Used to implement Iterator Concept(s)
c.dereference() F::reference   Readable Iterator, Writable Iterator
c.equal(y) convertible to bool true iff c and y refer to the same position. Single Pass Iterator
a.increment() unused   Incrementable Iterator
a.decrement() unused   Bidirectional Traversal Iterator
a.advance(n) unused   Random Access Traversal Iterator
c.distance_to(z) convertible to F::difference_type equivalent to distance(c, X(z)). Random Access Traversal Iterator

iterator_facade operations

The operations in this section are described in terms of operations on the core interface of Derived which may be inaccessible (i.e. private). The implementation should access these operations through member functions of class iterator_core_access.

reference operator*() const;

Returns:static_cast<Derived const*>(this)->dereference()

operator->() const; (see below)

Returns:

If reference is a reference type, an object of type pointer equal to:

&static_cast<Derived const*>(this)->dereference()

Otherwise returns an object of unspecified type such that, (*static_cast<Derived const*>(this))->m is equivalent to (w = **static_cast<Derived const*>(this), w.m) for some temporary object w of type value_type.

unspecified operator[](difference_type n) const;

Returns:an object convertible to value_type. For constant objects v of type value_type, and n of type difference_type, (*this)[n] = v is equivalent to *(*this + n) = v, and static_cast<value_type const&>((*this)[n]) is equivalent to static_cast<value_type const&>(*(*this + n))

Derived& operator++();

Effects:
static_cast<Derived*>(this)->increment();
return *static_cast<Derived*>(this);

Derived operator++(int);

Effects:
Derived tmp(static_cast<Derived const*>(this));
++*this;
return tmp;

Derived& operator--();

Effects:
static_cast<Derived*>(this)->decrement();
return *static_cast<Derived*>(this);

Derived operator--(int);

Effects:
Derived tmp(static_cast<Derived const*>(this));
--*this;
return tmp;

Derived& operator+=(difference_type n);

Effects:
static_cast<Derived*>(this)->advance(n);
return *static_cast<Derived*>(this);

Derived& operator-=(difference_type n);

Effects:
static_cast<Derived*>(this)->advance(-n);
return *static_cast<Derived*>(this);

Derived operator-(difference_type n) const;

Effects:
Derived tmp(static_cast<Derived const*>(this));
return tmp -= n;
template <class Dr, class V, class TC, class R, class D>
Derived operator+ (iterator_facade<Dr,V,TC,R,D> const&,
                   typename Derived::difference_type n);

template <class Dr, class V, class TC, class R, class D>
Derived operator+ (typename Derived::difference_type n,
                   iterator_facade<Dr,V,TC,R,D> const&);
Effects:
Derived tmp(static_cast<Derived const*>(this));
return tmp += n;
template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator ==(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
            iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);
Returns:

if is_convertible<Dr2,Dr1>::value

then

((Dr1 const&)lhs).equal((Dr2 const&)rhs).

Otherwise,

((Dr2 const&)rhs).equal((Dr1 const&)lhs).

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator !=(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
            iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);
Returns:

if is_convertible<Dr2,Dr1>::value

then

!((Dr1 const&)lhs).equal((Dr2 const&)rhs).

Otherwise,

!((Dr2 const&)rhs).equal((Dr1 const&)lhs).

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator <(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
           iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);
Returns:

if is_convertible<Dr2,Dr1>::value

then

((Dr1 const&)lhs).distance_to((Dr2 const&)rhs) < 0.

Otherwise,

((Dr2 const&)rhs).distance_to((Dr1 const&)lhs) > 0.

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator <=(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
            iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);
Returns:

if is_convertible<Dr2,Dr1>::value

then

((Dr1 const&)lhs).distance_to((Dr2 const&)rhs) <= 0.

Otherwise,

((Dr2 const&)rhs).distance_to((Dr1 const&)lhs) >= 0.

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator >(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
           iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);
Returns:

if is_convertible<Dr2,Dr1>::value

then

((Dr1 const&)lhs).distance_to((Dr2 const&)rhs) > 0.

Otherwise,

((Dr2 const&)rhs).distance_to((Dr1 const&)lhs) < 0.

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,bool>::type
operator >=(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
            iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);
Returns:

if is_convertible<Dr2,Dr1>::value

then

((Dr1 const&)lhs).distance_to((Dr2 const&)rhs) >= 0.

Otherwise,

((Dr2 const&)rhs).distance_to((Dr1 const&)lhs) <= 0.

template <class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2>
typename enable_if_interoperable<Dr1,Dr2,difference>::type
operator -(iterator_facade<Dr1,V1,TC1,R1,D1> const& lhs,
           iterator_facade<Dr2,V2,TC2,R2,D2> const& rhs);
Return Type:

if is_convertible<Dr2,Dr1>::value

then

difference shall be iterator_traits<Dr1>::difference_type.

Otherwise

difference shall be iterator_traits<Dr2>::difference_type

Returns:

if is_convertible<Dr2,Dr1>::value

then

-((Dr1 const&)lhs).distance_to((Dr2 const&)rhs).

Otherwise,

((Dr2 const&)rhs).distance_to((Dr1 const&)lhs).

Iterator adaptor [lib.iterator.adaptor]

Each specialization of the iterator_adaptor class template is derived from a specialization of iterator_facade. The core interface functions expected by iterator_facade are implemented in terms of the iterator_adaptor's Base template parameter. A class derived from iterator_adaptor typically redefines some of the core interface functions to adapt the behavior of the Base type. Whether the derived class models any of the standard iterator concepts depends on the operations supported by the Base type and which core interface functions of iterator_facade are redefined in the Derived class.

Class template iterator_adaptor

template <
    class Derived
  , class Base
  , class Value               = use_default
  , class CategoryOrTraversal = use_default
  , class Reference           = use_default
  , class Difference = use_default
>
class iterator_adaptor
  : public iterator_facade<Derived, V', C', R', D'> // see details
{
    friend class iterator_core_access;
 public:
    iterator_adaptor();
    explicit iterator_adaptor(Base const& iter);
    typedef Base base_type;
    Base const& base() const;
 protected:
    typedef iterator_adaptor iterator_adaptor_;
    Base const& base_reference() const;
    Base& base_reference();
 private: // Core iterator interface for iterator_facade.
    typename iterator_adaptor::reference dereference() const;

    template <
    class OtherDerived, class OtherIterator, class V, class C, class R, class D
    >
    bool equal(iterator_adaptor<OtherDerived, OtherIterator, V, C, R, D> const& x) const;

    void advance(typename iterator_adaptor::difference_type n);
    void increment();
    void decrement();

    template <
        class OtherDerived, class OtherIterator, class V, class C, class R, class D
    >
    typename iterator_adaptor::difference_type distance_to(
        iterator_adaptor<OtherDerived, OtherIterator, V, C, R, D> const& y) const;

 private:
    Base m_iterator; // exposition only
};

iterator_adaptor requirements

static_cast<Derived*>(iterator_adaptor*) shall be well-formed. The Base argument shall be Assignable and Copy Constructible.

iterator_adaptor base class parameters

The V', C', R', and D' parameters of the iterator_facade used as a base class in the summary of iterator_adaptor above are defined as follows:

V' = if (Value is use_default)
          return iterator_traits<Base>::value_type
      else
          return Value

C' = if (CategoryOrTraversal is use_default)
          return iterator_traversal<Base>::type
      else
          return CategoryOrTraversal

R' = if (Reference is use_default)
          if (Value is use_default)
              return iterator_traits<Base>::reference
          else
              return Value&
      else
          return Reference

D' = if (Difference is use_default)
          return iterator_traits<Base>::difference_type
      else
          return Difference

iterator_adaptor public operations

iterator_adaptor();

Requires:The Base type must be Default Constructible.
Returns:An instance of iterator_adaptor with m_iterator default constructed.

explicit iterator_adaptor(Base const& iter);

Returns:An instance of iterator_adaptor with m_iterator copy constructed from iter.

Base const& base() const;

Returns:m_iterator

iterator_adaptor protected member functions

Base const& base_reference() const;

Returns:A const reference to m_iterator.

Base& base_reference();

Returns:A non-const reference to m_iterator.

iterator_adaptor private member functions

typename iterator_adaptor::reference dereference() const;

Returns:*m_iterator
template <
class OtherDerived, class OtherIterator, class V, class C, class R, class D
>
bool equal(iterator_adaptor<OtherDerived, OtherIterator, V, C, R, D> const& x) const;
Returns:m_iterator == x.base()

void advance(typename iterator_adaptor::difference_type n);

Effects:m_iterator += n;

void increment();

Effects:++m_iterator;

void decrement();

Effects:--m_iterator;
template <
    class OtherDerived, class OtherIterator, class V, class C, class R, class D
>
typename iterator_adaptor::difference_type distance_to(
    iterator_adaptor<OtherDerived, OtherIterator, V, C, R, D> const& y) const;
Returns:y.base() - m_iterator

Specialized adaptors [lib.iterator.special.adaptors]

The enable_if_convertible<X,Y>::type expression used in this section is for exposition purposes. The converting constructors for specialized adaptors should be only be in an overload set provided that an object of type X is implicitly convertible to an object of type Y. The signatures involving enable_if_convertible should behave as-if enable_if_convertible were defined to be:

template <bool> enable_if_convertible_impl
{};

template <> enable_if_convertible_impl<true>
{ struct type; };

template<typename From, typename To>
struct enable_if_convertible
  : enable_if_convertible_impl<is_convertible<From,To>::value>
{};

If an expression other than the default argument is used to supply the value of a function parameter whose type is written in terms of enable_if_convertible, the program is ill-formed, no diagnostic required.

[Note: The enable_if_convertible approach uses SFINAE to take the constructor out of the overload set when the types are not implicitly convertible. ]

Indirect iterator

indirect_iterator adapts an iterator by applying an extra dereference inside of operator*(). For example, this iterator adaptor makes it possible to view a container of pointers (e.g. list<foo*>) as if it were a container of the pointed-to type (e.g. list<foo>). indirect_iterator depends on two auxiliary traits, pointee and indirect_reference, to provide support for underlying iterators whose value_type is not an iterator.

Class template pointee

template <class Dereferenceable>
struct pointee
{
    typedef /* see below */ type;
};
Requires:For an object x of type Dereferenceable, *x is well-formed. If ++x is ill-formed it shall neither be ambiguous nor shall it violate access control, and Dereferenceable::element_type shall be an accessible type. Otherwise iterator_traits<Dereferenceable>::value_type shall be well formed. [Note: These requirements need not apply to explicit or partial specializations of pointee]

type is determined according to the following algorithm, where x is an object of type Dereferenceable:

if ( ++x is ill-formed )
{
    return ``Dereferenceable::element_type``
}
else if (``*x`` is a mutable reference to
         std::iterator_traits<Dereferenceable>::value_type)
{
    return iterator_traits<Dereferenceable>::value_type
}
else
{
    return iterator_traits<Dereferenceable>::value_type const
}

Class template indirect_reference

template <class Dereferenceable>
struct indirect_reference
{
    typedef /* see below */ type;
};
Requires:For an object x of type Dereferenceable, *x is well-formed. If ++x is ill-formed it shall neither be ambiguous nor shall it violate access control, and pointee<Dereferenceable>::type& shall be well-formed. Otherwise iterator_traits<Dereferenceable>::reference shall be well formed. [Note: These requirements need not apply to explicit or partial specializations of indirect_reference]

type is determined according to the following algorithm, where x is an object of type Dereferenceable:

if ( ++x is ill-formed )
    return ``pointee<Dereferenceable>::type&``
else
    std::iterator_traits<Dereferenceable>::reference

Class template indirect_iterator

template <
    class Iterator
  , class Value = use_default
  , class CategoryOrTraversal = use_default
  , class Reference = use_default
  , class Difference = use_default
>
class indirect_iterator
{
 public:
    typedef /* see below */ value_type;
    typedef /* see below */ reference;
    typedef /* see below */ pointer;
    typedef /* see below */ difference_type;
    typedef /* see below */ iterator_category;

    indirect_iterator();
    indirect_iterator(Iterator x);

    template <
        class Iterator2, class Value2, class Category2
      , class Reference2, class Difference2
    >
    indirect_iterator(
        indirect_iterator<
             Iterator2, Value2, Category2, Reference2, Difference2
        > const& y
      , typename enable_if_convertible<Iterator2, Iterator>::type* = 0 // exposition
    );

    Iterator const& base() const;
    reference operator*() const;
    indirect_iterator& operator++();
    indirect_iterator& operator--();
private:
   Iterator m_iterator; // exposition
};

The member types of indirect_iterator are defined according to the following pseudo-code, where V is iterator_traits<Iterator>::value_type

if (Value is use_default) then
    typedef remove_const<pointee<V>::type>::type value_type;
else
    typedef remove_const<Value>::type value_type;

if (Reference is use_default) then
    if (Value is use_default) then
        typedef indirect_reference<V>::type reference;
    else
        typedef Value& reference;
else
    typedef Reference reference;

if (Value is use_default) then
    typedef pointee<V>::type* pointer;
else
    typedef Value* pointer;

if (Difference is use_default)
    typedef iterator_traits<Iterator>::difference_type difference_type;
else
    typedef Difference difference_type;

if (CategoryOrTraversal is use_default)
    typedef iterator-category (
        iterator_traversal<Iterator>::type,``reference``,``value_type``
    ) iterator_category;
else
    typedef iterator-category (
        CategoryOrTraversal,``reference``,``value_type``
    ) iterator_category;

indirect_iterator requirements

The expression *v, where v is an object of iterator_traits<Iterator>::value_type, shall be valid expression and convertible to reference. Iterator shall model the traversal concept indicated by iterator_category. Value, Reference, and Difference shall be chosen so that value_type, reference, and difference_type meet the requirements indicated by iterator_category.

[Note: there are further requirements on the iterator_traits<Iterator>::value_type if the Value parameter is not use_default, as implied by the algorithm for deducing the default for the value_type member.]

indirect_iterator models

In addition to the concepts indicated by iterator_category and by iterator_traversal<indirect_iterator>::type, a specialization of indirect_iterator models the following concepts, Where v is an object of iterator_traits<Iterator>::value_type:

  • Readable Iterator if reference(*v) is convertible to value_type.
  • Writable Iterator if reference(*v) = t is a valid expression (where t is an object of type indirect_iterator::value_type)
  • Lvalue Iterator if reference is a reference type.

indirect_iterator<X,V1,C1,R1,D1> is interoperable with indirect_iterator<Y,V2,C2,R2,D2> if and only if X is interoperable with Y.

indirect_iterator operations

In addition to the operations required by the concepts described above, specializations of indirect_iterator provide the following operations.

indirect_iterator();

Requires:Iterator must be Default Constructible.
Effects:Constructs an instance of indirect_iterator with a default-constructed m_iterator.

indirect_iterator(Iterator x);

Effects:Constructs an instance of indirect_iterator with m_iterator copy constructed from x.
template <
    class Iterator2, class Value2, unsigned Access, class Traversal
  , class Reference2, class Difference2
>
indirect_iterator(
    indirect_iterator<
         Iterator2, Value2, Access, Traversal, Reference2, Difference2
    > const& y
  , typename enable_if_convertible<Iterator2, Iterator>::type* = 0 // exposition
);
Requires:Iterator2 is implicitly convertible to Iterator.
Effects:Constructs an instance of indirect_iterator whose m_iterator subobject is constructed from y.base().

Iterator const& base() const;

Returns:m_iterator

reference operator*() const;

Returns:**m_iterator

indirect_iterator& operator++();

Effects:++m_iterator
Returns:*this

indirect_iterator& operator--();

Effects:--m_iterator
Returns:*this

Reverse iterator

The reverse iterator adaptor iterates through the adapted iterator range in the opposite direction.

Class template reverse_iterator

template <class Iterator>
class reverse_iterator
{
public:
  typedef iterator_traits<Iterator>::value_type value_type;
  typedef iterator_traits<Iterator>::reference reference;
  typedef iterator_traits<Iterator>::pointer pointer;
  typedef iterator_traits<Iterator>::difference_type difference_type;
  typedef /* see below */ iterator_category;

  reverse_iterator() {}
  explicit reverse_iterator(Iterator x) ;

  template<class OtherIterator>
  reverse_iterator(
      reverse_iterator<OtherIterator> const& r
    , typename enable_if_convertible<OtherIterator, Iterator>::type* = 0 // exposition
  );
  Iterator const& base() const;
  reference operator*() const;
  reverse_iterator& operator++();
  reverse_iterator& operator--();
private:
  Iterator m_iterator; // exposition
};

If Iterator models Random Access Traversal Iterator and Readable Lvalue Iterator, then iterator_category is convertible to random_access_iterator_tag. Otherwise, if Iterator models Bidirectional Traversal Iterator and Readable Lvalue Iterator, then iterator_category is convertible to bidirectional_iterator_tag. Otherwise, iterator_category is convertible to input_iterator_tag.

reverse_iterator requirements

Iterator must be a model of Bidirectional Traversal Iterator. The type iterator_traits<Iterator>::reference must be the type of *i, where i is an object of type Iterator.

reverse_iterator models

A specialization of reverse_iterator models the same iterator traversal and iterator access concepts modeled by its Iterator argument. In addition, it may model old iterator concepts specified in the following table:

If I models then reverse_iterator<I> models
Readable Lvalue Iterator, Bidirectional Traversal Iterator Bidirectional Iterator
Writable Lvalue Iterator, Bidirectional Traversal Iterator Mutable Bidirectional Iterator
Readable Lvalue Iterator, Random Access Traversal Iterator Random Access Iterator
Writable Lvalue Iterator, Random Access Traversal Iterator Mutable Random Access Iterator

reverse_iterator<X> is interoperable with reverse_iterator<Y> if and only if X is interoperable with Y.

reverse_iterator operations

In addition to the operations required by the concepts modeled by reverse_iterator, reverse_iterator provides the following operations.

reverse_iterator();

Requires:Iterator must be Default Constructible.
Effects:Constructs an instance of reverse_iterator with m_iterator default constructed.

explicit reverse_iterator(Iterator x);

Effects:Constructs an instance of reverse_iterator with m_iterator copy constructed from x.
template<class OtherIterator>
reverse_iterator(
    reverse_iterator<OtherIterator> const& r
  , typename enable_if_convertible<OtherIterator, Iterator>::type* = 0 // exposition
);
Requires:OtherIterator is implicitly convertible to Iterator.
Effects:Constructs instance of reverse_iterator whose m_iterator subobject is constructed from y.base().

Iterator const& base() const;

Returns:m_iterator

reference operator*() const;

Effects:
Iterator tmp = m_iterator;
return *--tmp;

reverse_iterator& operator++();

Effects:--m_iterator
Returns:*this

reverse_iterator& operator--();

Effects:++m_iterator
Returns:*this

Transform iterator

The transform iterator adapts an iterator by modifying the operator* to apply a function object to the result of dereferencing the iterator and returning the result.

Class template transform_iterator

template <class UnaryFunction,
          class Iterator,
          class Reference = use_default,
          class Value = use_default>
class transform_iterator
{
public:
  typedef /* see below */ value_type;
  typedef /* see below */ reference;
  typedef /* see below */ pointer;
  typedef iterator_traits<Iterator>::difference_type difference_type;
  typedef /* see below */ iterator_category;

  transform_iterator();
  transform_iterator(Iterator const& x, UnaryFunction f);

  template<class F2, class I2, class R2, class V2>
  transform_iterator(
        transform_iterator<F2, I2, R2, V2> const& t
      , typename enable_if_convertible<I2, Iterator>::type* = 0      // exposition only
      , typename enable_if_convertible<F2, UnaryFunction>::type* = 0 // exposition only
  );
  UnaryFunction functor() const;
  Iterator const& base() const;
  reference operator*() const;
  transform_iterator& operator++();
  transform_iterator& operator--();
private:
  Iterator m_iterator; // exposition only
  UnaryFunction m_f;   // exposition only
};

If Reference is use_default then the reference member of transform_iterator is result_of<UnaryFunction(iterator_traits<Iterator>::reference)>::type. Otherwise, reference is Reference.

If Value is use_default then the value_type member is remove_cv<remove_reference<reference> >::type. Otherwise, value_type is Value.

If Iterator models Readable Lvalue Iterator and if Iterator models Random Access Traversal Iterator, then iterator_category is convertible to random_access_iterator_tag. Otherwise, if Iterator models Bidirectional Traversal Iterator, then iterator_category is convertible to bidirectional_iterator_tag. Otherwise iterator_category is convertible to forward_iterator_tag. If Iterator does not model Readable Lvalue Iterator then iterator_category is convertible to input_iterator_tag.

transform_iterator requirements

The type UnaryFunction must be Assignable, Copy Constructible, and the expression f(*i) must be valid where f is an object of type UnaryFunction, i is an object of type Iterator, and where the type of f(*i) must be result_of<UnaryFunction(iterator_traits<Iterator>::reference)>::type.

The argument Iterator shall model Readable Iterator.

transform_iterator models

The resulting transform_iterator models the most refined of the following that is also modeled by Iterator.

  • Writable Lvalue Iterator if transform_iterator::reference is a non-const reference.
  • Readable Lvalue Iterator if transform_iterator::reference is a const reference.
  • Readable Iterator otherwise.

The transform_iterator models the most refined standard traversal concept that is modeled by the Iterator argument.

If transform_iterator is a model of Readable Lvalue Iterator then it models the following original iterator concepts depending on what the Iterator argument models.

If Iterator models then transform_iterator models
Single Pass Iterator Input Iterator
Forward Traversal Iterator Forward Iterator
Bidirectional Traversal Iterator Bidirectional Iterator
Random Access Traversal Iterator Random Access Iterator

If transform_iterator models Writable Lvalue Iterator then it is a mutable iterator (as defined in the old iterator requirements).

transform_iterator<F1, X, R1, V1> is interoperable with transform_iterator<F2, Y, R2, V2> if and only if X is interoperable with Y.

transform_iterator operations

In addition to the operations required by the concepts modeled by transform_iterator, transform_iterator provides the following operations.

transform_iterator();

Returns:An instance of transform_iterator with m_f and m_iterator default constructed.

transform_iterator(Iterator const& x, UnaryFunction f);

Returns:An instance of transform_iterator with m_f initialized to f and m_iterator initialized to x.
template<class F2, class I2, class R2, class V2>
transform_iterator(
      transform_iterator<F2, I2, R2, V2> const& t
    , typename enable_if_convertible<I2, Iterator>::type* = 0      // exposition only
    , typename enable_if_convertible<F2, UnaryFunction>::type* = 0 // exposition only
);
Returns:An instance of transform_iterator with m_f initialized to t.functor() and m_iterator initialized to t.base().
Requires:OtherIterator is implicitly convertible to Iterator.

UnaryFunction functor() const;

Returns:m_f

Iterator const& base() const;

Returns:m_iterator

reference operator*() const;

Returns:m_f(*m_iterator)

transform_iterator& operator++();

Effects:++m_iterator
Returns:*this

transform_iterator& operator--();

Effects:--m_iterator
Returns:*this

Filter iterator

The filter iterator adaptor creates a view of an iterator range in which some elements of the range are skipped. A predicate function object controls which elements are skipped. When the predicate is applied to an element, if it returns true then the element is retained and if it returns false then the element is skipped over. When skipping over elements, it is necessary for the filter adaptor to know when to stop so as to avoid going past the end of the underlying range. A filter iterator is therefore constructed with pair of iterators indicating the range of elements in the unfiltered sequence to be traversed.

Class template filter_iterator

template <class Predicate, class Iterator>
class filter_iterator
{
 public:
    typedef iterator_traits<Iterator>::value_type value_type;
    typedef iterator_traits<Iterator>::reference reference;
    typedef iterator_traits<Iterator>::pointer pointer;
    typedef iterator_traits<Iterator>::difference_type difference_type;
    typedef /* see below */ iterator_category;

    filter_iterator();
    filter_iterator(Predicate f, Iterator x, Iterator end = Iterator());
    filter_iterator(Iterator x, Iterator end = Iterator());
    template<class OtherIterator>
    filter_iterator(
        filter_iterator<Predicate, OtherIterator> const& t
        , typename enable_if_convertible<OtherIterator, Iterator>::type* = 0 // exposition
        );
    Predicate predicate() const;
    Iterator end() const;
    Iterator const& base() const;
    reference operator*() const;
    filter_iterator& operator++();
private:
    Predicate m_pred; // exposition only
    Iterator m_iter;  // exposition only
    Iterator m_end;   // exposition only
};

If Iterator models Readable Lvalue Iterator and Bidirectional Traversal Iterator then iterator_category is convertible to std::bidirectional_iterator_tag. Otherwise, if Iterator models Readable Lvalue Iterator and Forward Traversal Iterator then iterator_category is convertible to std::forward_iterator_tag. Otherwise iterator_category is convertible to std::input_iterator_tag.

filter_iterator requirements

The Iterator argument shall meet the requirements of Readable Iterator and Single Pass Iterator or it shall meet the requirements of Input Iterator.

The Predicate argument must be Assignable, Copy Constructible, and the expression p(x) must be valid where p is an object of type Predicate, x is an object of type iterator_traits<Iterator>::value_type, and where the type of p(x) must be convertible to bool.

filter_iterator models

The concepts that filter_iterator models are dependent on which concepts the Iterator argument models, as specified in the following tables.

If Iterator models then filter_iterator models
Single Pass Iterator Single Pass Iterator
Forward Traversal Iterator Forward Traversal Iterator
Bidirectional Traversal Iterator Bidirectional Traversal Iterator
If Iterator models then filter_iterator models
Readable Iterator Readable Iterator
Writable Iterator Writable Iterator
Lvalue Iterator Lvalue Iterator
If Iterator models then filter_iterator models
Readable Iterator, Single Pass Iterator Input Iterator
Readable Lvalue Iterator, Forward Traversal Iterator Forward Iterator
Writable Lvalue Iterator, Forward Traversal Iterator Mutable Forward Iterator
Writable Lvalue Iterator, Bidirectional Iterator Mutable Bidirectional Iterator

filter_iterator<P1, X> is interoperable with filter_iterator<P2, Y> if and only if X is interoperable with Y.

filter_iterator operations

In addition to those operations required by the concepts that filter_iterator models, filter_iterator provides the following operations.

filter_iterator();

Requires:Predicate and Iterator must be Default Constructible.
Effects:Constructs a filter_iterator whose``m_pred``, m_iter, and m_end members are a default constructed.

filter_iterator(Predicate f, Iterator x, Iterator end = Iterator());

Effects:Constructs a filter_iterator where m_iter is either the first position in the range [x,end) such that f(*m_iter) == true or else``m_iter == end``. The member m_pred is constructed from f and m_end from end.

filter_iterator(Iterator x, Iterator end = Iterator());

Requires:Predicate must be Default Constructible and Predicate is a class type (not a function pointer).
Effects:Constructs a filter_iterator where m_iter is either the first position in the range [x,end) such that m_pred(*m_iter) == true or else``m_iter == end``. The member m_pred is default constructed.
template <class OtherIterator>
filter_iterator(
    filter_iterator<Predicate, OtherIterator> const& t
    , typename enable_if_convertible<OtherIterator, Iterator>::type* = 0 // exposition
    );``
Requires:OtherIterator is implicitly convertible to Iterator.
Effects:Constructs a filter iterator whose members are copied from t.

Predicate predicate() const;

Returns:m_pred

Iterator end() const;

Returns:m_end

Iterator const& base() const;

Returns:m_iterator

reference operator*() const;

Returns:*m_iter

filter_iterator& operator++();

Effects:Increments m_iter and then continues to increment m_iter until either m_iter == m_end or m_pred(*m_iter) == true.
Returns:*this

Counting iterator

counting_iterator adapts an object by adding an operator* that returns the current value of the object. All other iterator operations are forwarded to the adapted object.

Class template counting_iterator

template <
    class Incrementable
  , class CategoryOrTraversal = use_default
  , class Difference = use_default
>
class counting_iterator
{
public:
    typedef Incrementable value_type;
    typedef const Incrementable& reference;
    typedef const Incrementable* pointer;
    typedef /* see below */ difference_type;
    typedef /* see below */ iterator_category;

    counting_iterator();
    counting_iterator(counting_iterator const& rhs);
    explicit counting_iterator(Incrementable x);
    Incrementable const& base() const;
    reference operator*() const;
    counting_iterator& operator++();
    counting_iterator& operator--();
private:
    Incrementable m_inc; // exposition
};

If the Difference argument is use_default then difference_type is an unspecified signed integral type. Otherwise difference_type is Difference.

iterator_category is determined according to the following algorithm:

if (CategoryOrTraversal is not use_default)
    return CategoryOrTraversal
else if (numeric_limits<Incrementable>::is_specialized)
    return iterator-category(
        random_access_traversal_tag, Incrementable, const Incrementable&)
else
    return iterator-category(
         iterator_traversal<Incrementable>::type,
         Incrementable, const Incrementable&)
[Note: implementers are encouraged to provide an implementation of
operator- and a difference_type that avoids overflows in the cases where std::numeric_limits<Incrementable>::is_specialized is true.]

counting_iterator requirements

The Incrementable argument shall be Copy Constructible and Assignable.

If iterator_category is convertible to forward_iterator_tag or forward_traversal_tag, the following must be well-formed:

Incrementable i, j;
++i;         // pre-increment
i == j;      // operator equal

If iterator_category is convertible to bidirectional_iterator_tag or bidirectional_traversal_tag, the following expression must also be well-formed:

--i

If iterator_category is convertible to random_access_iterator_tag or random_access_traversal_tag, the following must must also be valid:

counting_iterator::difference_type n;
i += n;
n = i - j;
i < j;

counting_iterator models

Specializations of counting_iterator model Readable Lvalue Iterator. In addition, they model the concepts corresponding to the iterator tags to which their iterator_category is convertible. Also, if CategoryOrTraversal is not use_default then counting_iterator models the concept corresponding to the iterator tag CategoryOrTraversal. Otherwise, if numeric_limits<Incrementable>::is_specialized, then counting_iterator models Random Access Traversal Iterator. Otherwise, counting_iterator models the same iterator traversal concepts modeled by Incrementable.

counting_iterator<X,C1,D1> is interoperable with counting_iterator<Y,C2,D2> if and only if X is interoperable with Y.

counting_iterator operations

In addition to the operations required by the concepts modeled by counting_iterator, counting_iterator provides the following operations.

counting_iterator();

Requires:Incrementable is Default Constructible.
Effects:Default construct the member m_inc.

counting_iterator(counting_iterator const& rhs);

Effects:Construct member m_inc from rhs.m_inc.

explicit counting_iterator(Incrementable x);

Effects:Construct member m_inc from x.

reference operator*() const;

Returns:m_inc

counting_iterator& operator++();

Effects:++m_inc
Returns:*this

counting_iterator& operator--();

Effects:--m_inc
Returns:*this

Incrementable const& base() const;

Returns:m_inc

Function output iterator

The function output iterator adaptor makes it easier to create custom output iterators. The adaptor takes a unary function and creates a model of Output Iterator. Each item assigned to the output iterator is passed as an argument to the unary function. The motivation for this iterator is that creating a conforming output iterator is non-trivial, particularly because the proper implementation usually requires a proxy object.

function_output_iterator requirements

UnaryFunction must be Assignable and Copy Constructible.

function_output_iterator models

function_output_iterator is a model of the Writable and Incrementable Iterator concepts.

function_output_iterator operations

explicit function_output_iterator(const UnaryFunction& f = UnaryFunction());

Effects:Constructs an instance of function_output_iterator with m_f constructed from f.

operator*();

Returns:An object r of unspecified type such that r = t is equivalent to m_f(t) for all t.

function_output_iterator& operator++();

Returns:*this

function_output_iterator& operator++(int);

Returns:*this