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<div class="document" id="iterator-facade">
<h1 class="title">Iterator Facade</h1>
<table class="docinfo" frame="void" rules="none">
<col class="docinfo-name" />
<col class="docinfo-content" />
<tbody valign="top">
<tr><th class="docinfo-name">Author:</th>
<td>David Abrahams, Jeremy Siek, Thomas Witt</td></tr>
<tr><th class="docinfo-name">Contact:</th>
<td><a class="first reference external" href="mailto:dave&#64;boost-consulting.com">dave&#64;boost-consulting.com</a>, <a class="reference external" href="mailto:jsiek&#64;osl.iu.edu">jsiek&#64;osl.iu.edu</a>, <a class="last reference external" href="mailto:witt&#64;ive.uni-hannover.de">witt&#64;ive.uni-hannover.de</a></td></tr>
<tr><th class="docinfo-name">Organization:</th>
<td><a class="first reference external" href="http://www.boost-consulting.com">Boost Consulting</a>, Indiana University <a class="reference external" href="http://www.osl.iu.edu">Open Systems
Lab</a>, University of Hanover <a class="last reference external" href="http://www.ive.uni-hannover.de">Institute for Transport
Railway Operation and Construction</a></td></tr>
<tr><th class="docinfo-name">Date:</th>
<td>2006-09-11</td></tr>
<tr><th class="docinfo-name">Copyright:</th>
<td>Copyright David Abrahams, Jeremy Siek, and Thomas Witt 2003.</td></tr>
</tbody>
</table>
<!-- Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">abstract:</th><td class="field-body"><!-- Copyright David Abrahams 2006. Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<tt class="docutils literal"><span class="pre">iterator_facade</span></tt> 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.</td>
</tr>
</tbody>
</table>
<div class="contents topic" id="table-of-contents">
<p class="topic-title first">Table of Contents</p>
<ul class="simple">
<li><a class="reference internal" href="#overview" id="id23">Overview</a><ul>
<li><a class="reference internal" href="#usage" id="id24">Usage</a></li>
<li><a class="reference internal" href="#iterator-core-access" id="id25">Iterator Core Access</a></li>
<li><a class="reference internal" href="#operator" id="id26"><tt class="docutils literal"><span class="pre">operator[]</span></tt></a></li>
<li><a class="reference internal" href="#id2" id="id27"><tt class="docutils literal"><span class="pre">operator-&gt;</span></tt></a></li>
</ul>
</li>
<li><a class="reference internal" href="#reference" id="id28">Reference</a><ul>
<li><a class="reference internal" href="#iterator-facade-requirements" id="id29"><tt class="docutils literal"><span class="pre">iterator_facade</span></tt> Requirements</a></li>
<li><a class="reference internal" href="#iterator-facade-operations" id="id30"><tt class="docutils literal"><span class="pre">iterator_facade</span></tt> operations</a></li>
</ul>
</li>
<li><a class="reference internal" href="#tutorial-example" id="id31">Tutorial Example</a><ul>
<li><a class="reference internal" href="#the-problem" id="id32">The Problem</a></li>
<li><a class="reference internal" href="#a-basic-iterator-using-iterator-facade" id="id33">A Basic Iterator Using <tt class="docutils literal"><span class="pre">iterator_facade</span></tt></a><ul>
<li><a class="reference internal" href="#template-arguments-for-iterator-facade" id="id34">Template Arguments for <tt class="docutils literal"><span class="pre">iterator_facade</span></tt></a><ul>
<li><a class="reference internal" href="#derived" id="id35"><tt class="docutils literal"><span class="pre">Derived</span></tt></a></li>
<li><a class="reference internal" href="#value" id="id36"><tt class="docutils literal"><span class="pre">Value</span></tt></a></li>
<li><a class="reference internal" href="#categoryortraversal" id="id37"><tt class="docutils literal"><span class="pre">CategoryOrTraversal</span></tt></a></li>
<li><a class="reference internal" href="#id12" id="id38"><tt class="docutils literal"><span class="pre">Reference</span></tt></a></li>
<li><a class="reference internal" href="#difference" id="id39"><tt class="docutils literal"><span class="pre">Difference</span></tt></a></li>
</ul>
</li>
<li><a class="reference internal" href="#constructors-and-data-members" id="id40">Constructors and Data Members</a></li>
<li><a class="reference internal" href="#implementing-the-core-operations" id="id41">Implementing the Core Operations</a></li>
</ul>
</li>
<li><a class="reference internal" href="#a-constant-node-iterator" id="id42">A constant <tt class="docutils literal"><span class="pre">node_iterator</span></tt></a></li>
<li><a class="reference internal" href="#interoperability" id="id43">Interoperability</a></li>
<li><a class="reference internal" href="#telling-the-truth" id="id44">Telling the Truth</a></li>
<li><a class="reference internal" href="#wrap-up" id="id45">Wrap Up</a></li>
</ul>
</li>
</ul>
</div>
<div class="section" id="overview">
<h1><a class="toc-backref" href="#id23">Overview</a></h1>
<!-- Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<!-- Version 1.1 of this ReStructuredText document corresponds to
n1530_, the paper accepted by the LWG for TR1. -->
<!-- Copyright David Abrahams, Jeremy Siek, and Thomas Witt 2003. -->
<p>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:</p>
<ul class="simple">
<li>dereferencing</li>
<li>incrementing</li>
<li>decrementing</li>
<li>equality comparison</li>
<li>random-access motion</li>
<li>distance measurement</li>
</ul>
<p>In addition to the behaviors listed above, the core interface elements
include the associated types exposed through iterator traits:
<tt class="docutils literal"><span class="pre">value_type</span></tt>, <tt class="docutils literal"><span class="pre">reference</span></tt>, <tt class="docutils literal"><span class="pre">difference_type</span></tt>, and
<tt class="docutils literal"><span class="pre">iterator_category</span></tt>.</p>
<p>Iterator facade uses the Curiously Recurring Template
Pattern (CRTP) <a class="citation-reference" href="#cop95" id="id1">[Cop95]</a> so that the user can specify the behavior
of <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> in a derived class.  Former designs used
policy objects to specify the behavior, but that approach was
discarded for several reasons:</p>
<blockquote>
<ol class="arabic simple">
<li>the creation and eventual copying of the policy object may create
overhead that can be avoided with the current approach.</li>
<li>The policy object approach does not allow for custom constructors
on the created iterator types, an essential feature if
<tt class="docutils literal"><span class="pre">iterator_facade</span></tt> should be used in other library
implementations.</li>
<li>Without the use of CRTP, the standard requirement that an
iterator's <tt class="docutils literal"><span class="pre">operator++</span></tt> returns the iterator type itself
would mean that all iterators built with the library would
have to be specializations of <tt class="docutils literal"><span class="pre">iterator_facade&lt;...&gt;</span></tt>, rather
than something more descriptive like
<tt class="docutils literal"><span class="pre">indirect_iterator&lt;T*&gt;</span></tt>.  Cumbersome type generator
metafunctions would be needed to build new parameterized
iterators, and a separate <tt class="docutils literal"><span class="pre">iterator_adaptor</span></tt> layer would be
impossible.</li>
</ol>
</blockquote>
<div class="section" id="usage">
<h2><a class="toc-backref" href="#id24">Usage</a></h2>
<p>The user of <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> derives his iterator class from a
specialization of <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> and passes the derived
iterator class as <tt class="docutils literal"><span class="pre">iterator_facade</span></tt>'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 <tt class="docutils literal"><span class="pre">value_type</span></tt> as
<tt class="docutils literal"><span class="pre">iterator_facade</span></tt>'s <tt class="docutils literal"><span class="pre">Value</span></tt> parameter and omit the
<tt class="docutils literal"><span class="pre">Reference</span></tt> parameter which follows.</p>
<p>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.</p>
<blockquote>
<table border="1" class="docutils">
<colgroup>
<col width="44%" />
<col width="56%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Expression</th>
<th class="head">Effects</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">i.dereference()</span></tt></td>
<td>Access the value referred to</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">i.equal(j)</span></tt></td>
<td>Compare for equality with <tt class="docutils literal"><span class="pre">j</span></tt></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">i.increment()</span></tt></td>
<td>Advance by one position</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">i.decrement()</span></tt></td>
<td>Retreat by one position</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">i.advance(n)</span></tt></td>
<td>Advance by <tt class="docutils literal"><span class="pre">n</span></tt> positions</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">i.distance_to(j)</span></tt></td>
<td>Measure the distance to <tt class="docutils literal"><span class="pre">j</span></tt></td>
</tr>
</tbody>
</table>
</blockquote>
<!-- Should we add a comment that a zero overhead implementation of iterator_facade
is possible with proper inlining? -->
<p>In addition to implementing the core interface functions, an iterator
derived from <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> 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 <tt class="docutils literal"><span class="pre">X</span></tt> is meant to be automatically interoperate with another
iterator type <tt class="docutils literal"><span class="pre">Y</span></tt> (as with constant and mutable iterators) then
there must be an implicit conversion from <tt class="docutils literal"><span class="pre">X</span></tt> to <tt class="docutils literal"><span class="pre">Y</span></tt> or from <tt class="docutils literal"><span class="pre">Y</span></tt>
to <tt class="docutils literal"><span class="pre">X</span></tt> (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.</p>
</div>
<div class="section" id="iterator-core-access">
<h2><a class="toc-backref" href="#id25">Iterator Core Access</a></h2>
<p><tt class="docutils literal"><span class="pre">iterator_facade</span></tt> 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.</p>
<p>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 <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> without fear of
breaking code that was accessing the public core member functions
directly.</p>
<p>In a naive implementation, keeping the derived class' core member
functions private would require it to grant friendship to
<tt class="docutils literal"><span class="pre">iterator_facade</span></tt> and each of the seven operators.  In order to
reduce the burden of limiting access, <tt class="docutils literal"><span class="pre">iterator_core_access</span></tt> 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 <tt class="docutils literal"><span class="pre">iterator_core_access</span></tt> to make his core
member functions available to the library.</p>
<!-- This is no long uptodate -thw -->
<!-- Yes it is; I made sure of it! -DWA -->
<p><tt class="docutils literal"><span class="pre">iterator_core_access</span></tt> 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
<tt class="docutils literal"><span class="pre">iterator_core_access</span></tt> used public member functions it would not
open a safety loophole, as every core member function preserves the
invariants of the iterator.</p>
</div>
<div class="section" id="operator">
<h2><a class="toc-backref" href="#id26"><tt class="docutils literal"><span class="pre">operator[]</span></tt></a></h2>
<p>The indexing operator for a generalized iterator presents special
challenges.  A random access iterator's <tt class="docutils literal"><span class="pre">operator[]</span></tt> is only
required to return something convertible to its <tt class="docutils literal"><span class="pre">value_type</span></tt>.
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. <a class="reference external" href="counting_iterator.html"><tt class="docutils literal"><span class="pre">counting_iterator</span></tt></a>), because <tt class="docutils literal"><span class="pre">*(p+n)</span></tt> is a reference
into the temporary iterator <tt class="docutils literal"><span class="pre">p+n</span></tt>, which is destroyed when
<tt class="docutils literal"><span class="pre">operator[]</span></tt> returns.</p>
<p>Writable iterators built with <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> implement the
semantics required by the preferred resolution to <a class="reference external" href="http://www.open-std.org/jtc1/sc22/wg21/docs/lwg-active.html#299">issue 299</a> and
adopted by proposal <a class="reference external" href="http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2003/n1550.htm">n1550</a>: the result of <tt class="docutils literal"><span class="pre">p[n]</span></tt> is an object
convertible to the iterator's <tt class="docutils literal"><span class="pre">value_type</span></tt>, and <tt class="docutils literal"><span class="pre">p[n]</span> <span class="pre">=</span> <span class="pre">x</span></tt> is
equivalent to <tt class="docutils literal"><span class="pre">*(p</span> <span class="pre">+</span> <span class="pre">n)</span> <span class="pre">=</span> <span class="pre">x</span></tt> (Note: This result object may be
implemented as a proxy containing a copy of <tt class="docutils literal"><span class="pre">p+n</span></tt>).  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
<tt class="docutils literal"><span class="pre">operator[]</span></tt> that returns an lvalue in the derived iterator
class; it will hide the one supplied by <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> from
clients of her iterator.</p>
</div>
<div class="section" id="id2">
<span id="operator-arrow"></span><h2><a class="toc-backref" href="#id27"><tt class="docutils literal"><span class="pre">operator-&gt;</span></tt></a></h2>
<p>The <tt class="docutils literal"><span class="pre">reference</span></tt> 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 <tt class="docutils literal"><span class="pre">value_type</span></tt>.  When the <tt class="docutils literal"><span class="pre">value_type</span></tt>
is a class, however, it must still be possible to access members
through <tt class="docutils literal"><span class="pre">operator-&gt;</span></tt>.  Therefore, an iterator whose <tt class="docutils literal"><span class="pre">reference</span></tt>
type is not in fact a reference must return a proxy containing a copy
of the referenced value from its <tt class="docutils literal"><span class="pre">operator-&gt;</span></tt>.</p>
<p>The return types for <tt class="docutils literal"><span class="pre">iterator_facade</span></tt>'s <tt class="docutils literal"><span class="pre">operator-&gt;</span></tt> and
<tt class="docutils literal"><span class="pre">operator[]</span></tt> are not explicitly specified. Instead, those types
are described in terms of a set of requirements, which must be
satisfied by the <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> implementation.</p>
<table class="docutils citation" frame="void" id="cop95" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[Cop95]</td><td><em>(<a class="fn-backref" href="#id1">1</a>, <a class="fn-backref" href="#id10">2</a>)</em> [Coplien, 1995] Coplien, J., Curiously Recurring Template
Patterns, C++ Report, February 1995, pp. 24-27.</td></tr>
</tbody>
</table>
</div>
</div>
<div class="section" id="reference">
<h1><a class="toc-backref" href="#id28">Reference</a></h1>
<!-- Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<!-- Version 1.3 of this ReStructuredText document corresponds to
n1530_, the paper accepted by the LWG for TR1. -->
<!-- Copyright David Abrahams, Jeremy Siek, and Thomas Witt 2003. -->
<pre class="literal-block">
template &lt;
    class Derived
  , class Value
  , class CategoryOrTraversal
  , class Reference  = Value&amp;
  , class Difference = ptrdiff_t
&gt;
class iterator_facade {
 public:
    typedef remove_const&lt;Value&gt;::type value_type;
    typedef Reference reference;
    typedef Value* pointer;
    typedef Difference difference_type;
    typedef /* see <a class="reference internal" href="#iterator-category">below</a> */ iterator_category;

    reference operator*() const;
    /* see <a class="reference internal" href="#operator-arrow">below</a> */ operator-&gt;() const;
    /* see <a class="reference internal" href="#brackets">below</a> */ operator[](difference_type n) const;
    Derived&amp; operator++();
    Derived operator++(int);
    Derived&amp; operator--();
    Derived operator--(int);
    Derived&amp; operator+=(difference_type n);
    Derived&amp; operator-=(difference_type n);
    Derived operator-(difference_type n) const;
 protected:
    typedef iterator_facade iterator_facade_;
};

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

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

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

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

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

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

// Iterator difference
template &lt;class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2&gt;
/* see <a class="reference internal" href="#minus">below</a> */
operator-(iterator_facade&lt;Dr1,V1,TC1,R1,D1&gt; const&amp; lhs,
          iterator_facade&lt;Dr2,V2,TC2,R2,D2&gt; const&amp; rhs);

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

template &lt;class Dr, class V, class TC, class R, class D&gt;
Derived operator+ (typename Derived::difference_type n,
                   iterator_facade&lt;Dr,V,TC,R,D&gt; const&amp;);
</pre>
<p id="iterator-category">The <tt class="docutils literal"><span class="pre">iterator_category</span></tt> member of <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> is</p>
<pre class="literal-block">
<em>iterator-category</em>(CategoryOrTraversal, value_type, reference)
</pre>
<p>where <em>iterator-category</em> is defined as follows:</p>
<pre class="literal-block" id="id7">
<em>iterator-category</em>(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)
       <em>the program is ill-formed</em>

   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
               &amp;&amp; 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
                   &amp;&amp; R is convertible to V)
                   X1 = input_iterator_tag
               else
                   X1 = C
           }

      2. <a class="reference external" href="new-iter-concepts.html#category-to-traversal"><em>category-to-traversal</em></a>(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.
</pre>
<p>[Note: the intention is to allow <tt class="docutils literal"><span class="pre">iterator_category</span></tt> to be one of
the five original category tags when convertibility to one of the
traversal tags would add no information]</p>
<!-- Copyright David Abrahams 2004. Use, modification and distribution is -->
<!-- subject to the Boost Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<p>The <tt class="docutils literal"><span class="pre">enable_if_interoperable</span></tt> template used above is for exposition
purposes.  The member operators should only be in an overload set
provided the derived types <tt class="docutils literal"><span class="pre">Dr1</span></tt> and <tt class="docutils literal"><span class="pre">Dr2</span></tt> are interoperable,
meaning that at least one of the types is convertible to the other.  The
<tt class="docutils literal"><span class="pre">enable_if_interoperable</span></tt> approach uses SFINAE to take the operators
out of the overload set when the types are not interoperable.
The operators should behave <em>as-if</em> <tt class="docutils literal"><span class="pre">enable_if_interoperable</span></tt>
were defined to be:</p>
<pre class="literal-block">
template &lt;bool, typename&gt; enable_if_interoperable_impl
{};

template &lt;typename T&gt; enable_if_interoperable_impl&lt;true,T&gt;
{ typedef T type; };

template&lt;typename Dr1, typename Dr2, typename T&gt;
struct enable_if_interoperable
  : enable_if_interoperable_impl&lt;
        is_convertible&lt;Dr1,Dr2&gt;::value || is_convertible&lt;Dr2,Dr1&gt;::value
      , T
    &gt;
{};
</pre>
<div class="section" id="iterator-facade-requirements">
<h2><a class="toc-backref" href="#id29"><tt class="docutils literal"><span class="pre">iterator_facade</span></tt> Requirements</a></h2>
<p>The following table describes the typical valid expressions on
<tt class="docutils literal"><span class="pre">iterator_facade</span></tt>'s <tt class="docutils literal"><span class="pre">Derived</span></tt> 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
<tt class="docutils literal"><span class="pre">iterator_core_access</span></tt>.  In addition,
<tt class="docutils literal"><span class="pre">static_cast&lt;Derived*&gt;(iterator_facade*)</span></tt> shall be well-formed.</p>
<p>In the table below, <tt class="docutils literal"><span class="pre">F</span></tt> is <tt class="docutils literal"><span class="pre">iterator_facade&lt;X,V,C,R,D&gt;</span></tt>, <tt class="docutils literal"><span class="pre">a</span></tt> is an
object of type <tt class="docutils literal"><span class="pre">X</span></tt>, <tt class="docutils literal"><span class="pre">b</span></tt> and <tt class="docutils literal"><span class="pre">c</span></tt> are objects of type <tt class="docutils literal"><span class="pre">const</span> <span class="pre">X</span></tt>,
<tt class="docutils literal"><span class="pre">n</span></tt> is an object of <tt class="docutils literal"><span class="pre">F::difference_type</span></tt>, <tt class="docutils literal"><span class="pre">y</span></tt> is a constant
object of a single pass iterator type interoperable with <tt class="docutils literal"><span class="pre">X</span></tt>, and <tt class="docutils literal"><span class="pre">z</span></tt>
is a constant object of a random access traversal iterator type
interoperable with <tt class="docutils literal"><span class="pre">X</span></tt>.</p>
<div class="topic" id="core-operations">
<p class="topic-title first"><tt class="docutils literal"><span class="pre">iterator_facade</span></tt> Core Operations</p>
<table border="1" class="docutils">
<colgroup>
<col width="21%" />
<col width="23%" />
<col width="27%" />
<col width="29%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Assertion/Note</th>
<th class="head">Used to implement Iterator
Concept(s)</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">c.dereference()</span></tt></td>
<td><tt class="docutils literal"><span class="pre">F::reference</span></tt></td>
<td>&nbsp;</td>
<td>Readable Iterator, Writable
Iterator</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">c.equal(y)</span></tt></td>
<td>convertible to bool</td>
<td>true iff <tt class="docutils literal"><span class="pre">c</span></tt> and <tt class="docutils literal"><span class="pre">y</span></tt>
refer to the same
position.</td>
<td>Single Pass Iterator</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a.increment()</span></tt></td>
<td>unused</td>
<td>&nbsp;</td>
<td>Incrementable Iterator</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a.decrement()</span></tt></td>
<td>unused</td>
<td>&nbsp;</td>
<td>Bidirectional Traversal
Iterator</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a.advance(n)</span></tt></td>
<td>unused</td>
<td>&nbsp;</td>
<td>Random Access Traversal
Iterator</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">c.distance_to(z)</span></tt></td>
<td>convertible to
<tt class="docutils literal"><span class="pre">F::difference_type</span></tt></td>
<td>equivalent to
<tt class="docutils literal"><span class="pre">distance(c,</span> <span class="pre">X(z))</span></tt>.</td>
<td>Random Access Traversal
Iterator</td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="section" id="iterator-facade-operations">
<h2><a class="toc-backref" href="#id30"><tt class="docutils literal"><span class="pre">iterator_facade</span></tt> operations</a></h2>
<p>The operations in this section are described in terms of operations on
the core interface of <tt class="docutils literal"><span class="pre">Derived</span></tt> which may be inaccessible
(i.e. private).  The implementation should access these operations
through member functions of class <tt class="docutils literal"><span class="pre">iterator_core_access</span></tt>.</p>
<p><tt class="docutils literal"><span class="pre">reference</span> <span class="pre">operator*()</span> <span class="pre">const;</span></tt></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><tt class="docutils literal"><span class="pre">static_cast&lt;Derived</span> <span class="pre">const*&gt;(this)-&gt;dereference()</span></tt></td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">operator-&gt;()</span> <span class="pre">const;</span></tt> (see <a class="reference internal" href="#operator-arrow">below</a>)</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">If <tt class="docutils literal"><span class="pre">reference</span></tt> is a reference type, an object
of type <tt class="docutils literal"><span class="pre">pointer</span></tt> equal to:</p>
<pre class="literal-block">
&amp;static_cast&lt;Derived const*&gt;(this)-&gt;dereference()
</pre>
<p class="last">Otherwise returns an object of unspecified type such that,
<tt class="docutils literal"><span class="pre">(*static_cast&lt;Derived</span> <span class="pre">const*&gt;(this))-&gt;m</span></tt> is equivalent to <tt class="docutils literal"><span class="pre">(w</span> <span class="pre">=</span> <span class="pre">**static_cast&lt;Derived</span> <span class="pre">const*&gt;(this),</span>
<span class="pre">w.m)</span></tt> for some temporary object <tt class="docutils literal"><span class="pre">w</span></tt> of type <tt class="docutils literal"><span class="pre">value_type</span></tt>.</p>
</td>
</tr>
</tbody>
</table>
<p id="brackets"><em>unspecified</em> <tt class="docutils literal"><span class="pre">operator[](difference_type</span> <span class="pre">n)</span> <span class="pre">const;</span></tt></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Returns:</th><td class="field-body">an object convertible to <tt class="docutils literal"><span class="pre">value_type</span></tt>. For constant
objects <tt class="docutils literal"><span class="pre">v</span></tt> of type <tt class="docutils literal"><span class="pre">value_type</span></tt>, and <tt class="docutils literal"><span class="pre">n</span></tt> of type
<tt class="docutils literal"><span class="pre">difference_type</span></tt>, <tt class="docutils literal"><span class="pre">(*this)[n]</span> <span class="pre">=</span> <span class="pre">v</span></tt> is equivalent to
<tt class="docutils literal"><span class="pre">*(*this</span> <span class="pre">+</span> <span class="pre">n)</span> <span class="pre">=</span> <span class="pre">v</span></tt>, and <tt class="docutils literal"><span class="pre">static_cast&lt;value_type</span>
<span class="pre">const&amp;&gt;((*this)[n])</span></tt> is equivalent to
<tt class="docutils literal"><span class="pre">static_cast&lt;value_type</span> <span class="pre">const&amp;&gt;(*(*this</span> <span class="pre">+</span> <span class="pre">n))</span></tt></td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">Derived&amp;</span> <span class="pre">operator++();</span></tt></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Effects:</th><td class="field-body"><pre class="first last literal-block">
static_cast&lt;Derived*&gt;(this)-&gt;increment();
return *static_cast&lt;Derived*&gt;(this);
</pre>
</td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">Derived</span> <span class="pre">operator++(int);</span></tt></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Effects:</th><td class="field-body"><pre class="first last literal-block">
Derived tmp(static_cast&lt;Derived const*&gt;(this));
++*this;
return tmp;
</pre>
</td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">Derived&amp;</span> <span class="pre">operator--();</span></tt></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Effects:</th><td class="field-body"><pre class="first last literal-block">
static_cast&lt;Derived*&gt;(this)-&gt;decrement();
return *static_cast&lt;Derived*&gt;(this);
</pre>
</td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">Derived</span> <span class="pre">operator--(int);</span></tt></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Effects:</th><td class="field-body"><pre class="first last literal-block">
Derived tmp(static_cast&lt;Derived const*&gt;(this));
--*this;
return tmp;
</pre>
</td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">Derived&amp;</span> <span class="pre">operator+=(difference_type</span> <span class="pre">n);</span></tt></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Effects:</th><td class="field-body"><pre class="first last literal-block">
static_cast&lt;Derived*&gt;(this)-&gt;advance(n);
return *static_cast&lt;Derived*&gt;(this);
</pre>
</td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">Derived&amp;</span> <span class="pre">operator-=(difference_type</span> <span class="pre">n);</span></tt></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Effects:</th><td class="field-body"><pre class="first last literal-block">
static_cast&lt;Derived*&gt;(this)-&gt;advance(-n);
return *static_cast&lt;Derived*&gt;(this);
</pre>
</td>
</tr>
</tbody>
</table>
<p><tt class="docutils literal"><span class="pre">Derived</span> <span class="pre">operator-(difference_type</span> <span class="pre">n)</span> <span class="pre">const;</span></tt></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Effects:</th><td class="field-body"><pre class="first last literal-block">
Derived tmp(static_cast&lt;Derived const*&gt;(this));
return tmp -= n;
</pre>
</td>
</tr>
</tbody>
</table>
<pre class="literal-block">
template &lt;class Dr, class V, class TC, class R, class D&gt;
Derived operator+ (iterator_facade&lt;Dr,V,TC,R,D&gt; const&amp;,
                   typename Derived::difference_type n);

template &lt;class Dr, class V, class TC, class R, class D&gt;
Derived operator+ (typename Derived::difference_type n,
                   iterator_facade&lt;Dr,V,TC,R,D&gt; const&amp;);
</pre>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Effects:</th><td class="field-body"><pre class="first last literal-block">
Derived tmp(static_cast&lt;Derived const*&gt;(this));
return tmp += n;
</pre>
</td>
</tr>
</tbody>
</table>
<pre class="literal-block">
template &lt;class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2&gt;
typename enable_if_interoperable&lt;Dr1,Dr2,bool&gt;::type
operator ==(iterator_facade&lt;Dr1,V1,TC1,R1,D1&gt; const&amp; lhs,
            iterator_facade&lt;Dr2,V2,TC2,R2,D2&gt; const&amp; rhs);
</pre>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">if <tt class="docutils literal"><span class="pre">is_convertible&lt;Dr2,Dr1&gt;::value</span></tt></p>
<dl class="last docutils">
<dt>then</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr1</span> <span class="pre">const&amp;)lhs).equal((Dr2</span> <span class="pre">const&amp;)rhs)</span></tt>.</p>
</dd>
<dt>Otherwise,</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr2</span> <span class="pre">const&amp;)rhs).equal((Dr1</span> <span class="pre">const&amp;)lhs)</span></tt>.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<pre class="literal-block">
template &lt;class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2&gt;
typename enable_if_interoperable&lt;Dr1,Dr2,bool&gt;::type
operator !=(iterator_facade&lt;Dr1,V1,TC1,R1,D1&gt; const&amp; lhs,
            iterator_facade&lt;Dr2,V2,TC2,R2,D2&gt; const&amp; rhs);
</pre>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">if <tt class="docutils literal"><span class="pre">is_convertible&lt;Dr2,Dr1&gt;::value</span></tt></p>
<dl class="last docutils">
<dt>then</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">!((Dr1</span> <span class="pre">const&amp;)lhs).equal((Dr2</span> <span class="pre">const&amp;)rhs)</span></tt>.</p>
</dd>
<dt>Otherwise,</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">!((Dr2</span> <span class="pre">const&amp;)rhs).equal((Dr1</span> <span class="pre">const&amp;)lhs)</span></tt>.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<pre class="literal-block">
template &lt;class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2&gt;
typename enable_if_interoperable&lt;Dr1,Dr2,bool&gt;::type
operator &lt;(iterator_facade&lt;Dr1,V1,TC1,R1,D1&gt; const&amp; lhs,
           iterator_facade&lt;Dr2,V2,TC2,R2,D2&gt; const&amp; rhs);
</pre>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">if <tt class="docutils literal"><span class="pre">is_convertible&lt;Dr2,Dr1&gt;::value</span></tt></p>
<dl class="last docutils">
<dt>then</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr1</span> <span class="pre">const&amp;)lhs).distance_to((Dr2</span> <span class="pre">const&amp;)rhs)</span> <span class="pre">&lt;</span> <span class="pre">0</span></tt>.</p>
</dd>
<dt>Otherwise,</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr2</span> <span class="pre">const&amp;)rhs).distance_to((Dr1</span> <span class="pre">const&amp;)lhs)</span> <span class="pre">&gt;</span> <span class="pre">0</span></tt>.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<pre class="literal-block">
template &lt;class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2&gt;
typename enable_if_interoperable&lt;Dr1,Dr2,bool&gt;::type
operator &lt;=(iterator_facade&lt;Dr1,V1,TC1,R1,D1&gt; const&amp; lhs,
            iterator_facade&lt;Dr2,V2,TC2,R2,D2&gt; const&amp; rhs);
</pre>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">if <tt class="docutils literal"><span class="pre">is_convertible&lt;Dr2,Dr1&gt;::value</span></tt></p>
<dl class="last docutils">
<dt>then</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr1</span> <span class="pre">const&amp;)lhs).distance_to((Dr2</span> <span class="pre">const&amp;)rhs)</span> <span class="pre">&lt;=</span> <span class="pre">0</span></tt>.</p>
</dd>
<dt>Otherwise,</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr2</span> <span class="pre">const&amp;)rhs).distance_to((Dr1</span> <span class="pre">const&amp;)lhs)</span> <span class="pre">&gt;=</span> <span class="pre">0</span></tt>.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<pre class="literal-block">
template &lt;class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2&gt;
typename enable_if_interoperable&lt;Dr1,Dr2,bool&gt;::type
operator &gt;(iterator_facade&lt;Dr1,V1,TC1,R1,D1&gt; const&amp; lhs,
           iterator_facade&lt;Dr2,V2,TC2,R2,D2&gt; const&amp; rhs);
</pre>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">if <tt class="docutils literal"><span class="pre">is_convertible&lt;Dr2,Dr1&gt;::value</span></tt></p>
<dl class="last docutils">
<dt>then</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr1</span> <span class="pre">const&amp;)lhs).distance_to((Dr2</span> <span class="pre">const&amp;)rhs)</span> <span class="pre">&gt;</span> <span class="pre">0</span></tt>.</p>
</dd>
<dt>Otherwise,</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr2</span> <span class="pre">const&amp;)rhs).distance_to((Dr1</span> <span class="pre">const&amp;)lhs)</span> <span class="pre">&lt;</span> <span class="pre">0</span></tt>.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<pre class="literal-block">
template &lt;class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2&gt;
typename enable_if_interoperable&lt;Dr1,Dr2,bool&gt;::type
operator &gt;=(iterator_facade&lt;Dr1,V1,TC1,R1,D1&gt; const&amp; lhs,
            iterator_facade&lt;Dr2,V2,TC2,R2,D2&gt; const&amp; rhs);
</pre>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">if <tt class="docutils literal"><span class="pre">is_convertible&lt;Dr2,Dr1&gt;::value</span></tt></p>
<dl class="last docutils">
<dt>then</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr1</span> <span class="pre">const&amp;)lhs).distance_to((Dr2</span> <span class="pre">const&amp;)rhs)</span> <span class="pre">&gt;=</span> <span class="pre">0</span></tt>.</p>
</dd>
<dt>Otherwise,</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr2</span> <span class="pre">const&amp;)rhs).distance_to((Dr1</span> <span class="pre">const&amp;)lhs)</span> <span class="pre">&lt;=</span> <span class="pre">0</span></tt>.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<pre class="literal-block" id="minus">
template &lt;class Dr1, class V1, class TC1, class R1, class D1,
          class Dr2, class V2, class TC2, class R2, class D2&gt;
typename enable_if_interoperable&lt;Dr1,Dr2,difference&gt;::type
operator -(iterator_facade&lt;Dr1,V1,TC1,R1,D1&gt; const&amp; lhs,
           iterator_facade&lt;Dr2,V2,TC2,R2,D2&gt; const&amp; rhs);
</pre>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Return Type:</th><td class="field-body"><p class="first">if <tt class="docutils literal"><span class="pre">is_convertible&lt;Dr2,Dr1&gt;::value</span></tt></p>
<blockquote>
<dl class="docutils">
<dt>then</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">difference</span></tt> shall be
<tt class="docutils literal"><span class="pre">iterator_traits&lt;Dr1&gt;::difference_type</span></tt>.</p>
</dd>
<dt>Otherwise</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">difference</span></tt> shall be <tt class="docutils literal"><span class="pre">iterator_traits&lt;Dr2&gt;::difference_type</span></tt></p>
</dd>
</dl>
</blockquote>
</td>
</tr>
<tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">if <tt class="docutils literal"><span class="pre">is_convertible&lt;Dr2,Dr1&gt;::value</span></tt></p>
<dl class="last docutils">
<dt>then</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">-((Dr1</span> <span class="pre">const&amp;)lhs).distance_to((Dr2</span> <span class="pre">const&amp;)rhs)</span></tt>.</p>
</dd>
<dt>Otherwise,</dt>
<dd><p class="first last"><tt class="docutils literal"><span class="pre">((Dr2</span> <span class="pre">const&amp;)rhs).distance_to((Dr1</span> <span class="pre">const&amp;)lhs)</span></tt>.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="section" id="tutorial-example">
<h1><a class="toc-backref" href="#id31">Tutorial Example</a></h1>
<!-- Copyright David Abrahams 2004. Use, modification and distribution is -->
<!-- subject to the Boost Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<p>In this section we'll walk through the implementation of a few
iterators using <tt class="docutils literal"><span class="pre">iterator_facade</span></tt>, based around the simple
example of a linked list of polymorphic objects.  This example was
inspired by a <a class="reference external" href="http://thread.gmane.org/gmane.comp.lib.boost.user/5100">posting</a> by Keith Macdonald on the <a class="reference external" href="http://www.boost.org/more/mailing_lists.htm#users">Boost-Users</a>
mailing list.</p>
<div class="section" id="the-problem">
<h2><a class="toc-backref" href="#id32">The Problem</a></h2>
<p>Say we've written a polymorphic linked list node base class:</p>
<pre class="literal-block">
# include &lt;iostream&gt;

struct node_base
{
    node_base() : m_next(0) {}

    // Each node manages all of its tail nodes
    virtual ~node_base() { delete m_next; }

    // Access the rest of the list
    node_base* next() const { return m_next; }

    // print to the stream
    virtual void print(std::ostream&amp; s) const = 0;

    // double the value
    virtual void double_me() = 0;

    void append(node_base* p)
    {
        if (m_next)
            m_next-&gt;append(p);
        else
            m_next = p;
    }

 private:
    node_base* m_next;
};
</pre>
<p>Lists can hold objects of different types by linking together
specializations of the following template:</p>
<pre class="literal-block">
template &lt;class T&gt;
struct node : node_base
{
    node(T x)
      : m_value(x)
    {}

    void print(std::ostream&amp; s) const { s &lt;&lt; this-&gt;m_value; }
    void double_me() { m_value += m_value; }

 private:
    T m_value;
};
</pre>
<p>And we can print any node using the following streaming operator:</p>
<pre class="literal-block">
inline std::ostream&amp; operator&lt;&lt;(std::ostream&amp; s, node_base const&amp; n)
{
    n.print(s);
    return s;
}
</pre>
<p>Our first challenge is to build an appropriate iterator over these
lists.</p>
</div>
<div class="section" id="a-basic-iterator-using-iterator-facade">
<h2><a class="toc-backref" href="#id33">A Basic Iterator Using <tt class="docutils literal"><span class="pre">iterator_facade</span></tt></a></h2>
<p>We will construct a <tt class="docutils literal"><span class="pre">node_iterator</span></tt> class using inheritance from
<tt class="docutils literal"><span class="pre">iterator_facade</span></tt> to implement most of the iterator's operations.</p>
<pre class="literal-block">
# include &quot;node.hpp&quot;
# include &lt;boost/iterator/iterator_facade.hpp&gt;

class node_iterator
  : public boost::iterator_facade&lt;...&gt;
{
   ...
};
</pre>
<div class="section" id="template-arguments-for-iterator-facade">
<h3><a class="toc-backref" href="#id34">Template Arguments for <tt class="docutils literal"><span class="pre">iterator_facade</span></tt></a></h3>
<p><tt class="docutils literal"><span class="pre">iterator_facade</span></tt> has several template parameters, so we must decide
what types to use for the arguments. The parameters are <tt class="docutils literal"><span class="pre">Derived</span></tt>,
<tt class="docutils literal"><span class="pre">Value</span></tt>, <tt class="docutils literal"><span class="pre">CategoryOrTraversal</span></tt>, <tt class="docutils literal"><span class="pre">Reference</span></tt>, and <tt class="docutils literal"><span class="pre">Difference</span></tt>.</p>
<div class="section" id="derived">
<h4><a class="toc-backref" href="#id35"><tt class="docutils literal"><span class="pre">Derived</span></tt></a></h4>
<p>Because <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> is meant to be used with the CRTP
<a class="citation-reference" href="#cop95" id="id10">[Cop95]</a> the first parameter is the iterator class name itself,
<tt class="docutils literal"><span class="pre">node_iterator</span></tt>.</p>
</div>
<div class="section" id="value">
<h4><a class="toc-backref" href="#id36"><tt class="docutils literal"><span class="pre">Value</span></tt></a></h4>
<p>The <tt class="docutils literal"><span class="pre">Value</span></tt> parameter determines the <tt class="docutils literal"><span class="pre">node_iterator</span></tt>'s
<tt class="docutils literal"><span class="pre">value_type</span></tt>.  In this case, we are iterating over <tt class="docutils literal"><span class="pre">node_base</span></tt>
objects, so <tt class="docutils literal"><span class="pre">Value</span></tt> will be <tt class="docutils literal"><span class="pre">node_base</span></tt>.</p>
</div>
<div class="section" id="categoryortraversal">
<h4><a class="toc-backref" href="#id37"><tt class="docutils literal"><span class="pre">CategoryOrTraversal</span></tt></a></h4>
<p>Now we have to determine which <a class="reference external" href="new-iter-concepts.html#iterator-traversal-concepts-lib-iterator-traversal">iterator traversal concept</a> our
<tt class="docutils literal"><span class="pre">node_iterator</span></tt> is going to model.  Singly-linked lists only have
forward links, so our iterator can't can't be a <a class="reference external" href="new-iter-concepts.html#bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators">bidirectional
traversal iterator</a>.  Our iterator should be able to make multiple
passes over the same linked list (unlike, say, an
<tt class="docutils literal"><span class="pre">istream_iterator</span></tt> which consumes the stream it traverses), so it
must be a <a class="reference external" href="new-iter-concepts.html#forward-traversal-iterators-lib-forward-traversal-iterators">forward traversal iterator</a>.  Therefore, we'll pass
<tt class="docutils literal"><span class="pre">boost::forward_traversal_tag</span></tt> in this position<a class="footnote-reference" href="#category" id="id11"><sup>1</sup></a>.</p>
<table class="docutils footnote" frame="void" id="category" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id11">[1]</a></td><td><tt class="docutils literal"><span class="pre">iterator_facade</span></tt> also supports old-style category
tags, so we could have passed <tt class="docutils literal"><span class="pre">std::forward_iterator_tag</span></tt> here;
either way, the resulting iterator's <tt class="docutils literal"><span class="pre">iterator_category</span></tt> will
end up being <tt class="docutils literal"><span class="pre">std::forward_iterator_tag</span></tt>.</td></tr>
</tbody>
</table>
</div>
<div class="section" id="id12">
<h4><a class="toc-backref" href="#id38"><tt class="docutils literal"><span class="pre">Reference</span></tt></a></h4>
<p>The <tt class="docutils literal"><span class="pre">Reference</span></tt> argument becomes the type returned by
<tt class="docutils literal"><span class="pre">node_iterator</span></tt>'s dereference operation, and will also be the
same as <tt class="docutils literal"><span class="pre">std::iterator_traits&lt;node_iterator&gt;::reference</span></tt>.  The
library's default for this parameter is <tt class="docutils literal"><span class="pre">Value&amp;</span></tt>; since
<tt class="docutils literal"><span class="pre">node_base&amp;</span></tt> is a good choice for the iterator's <tt class="docutils literal"><span class="pre">reference</span></tt>
type, we can omit this argument, or pass <tt class="docutils literal"><span class="pre">use_default</span></tt>.</p>
</div>
<div class="section" id="difference">
<h4><a class="toc-backref" href="#id39"><tt class="docutils literal"><span class="pre">Difference</span></tt></a></h4>
<p>The <tt class="docutils literal"><span class="pre">Difference</span></tt> argument determines how the distance between
two <tt class="docutils literal"><span class="pre">node_iterator</span></tt>s will be measured and will also be the
same as <tt class="docutils literal"><span class="pre">std::iterator_traits&lt;node_iterator&gt;::difference_type</span></tt>.
The library's default for <tt class="docutils literal"><span class="pre">Difference</span></tt> is <tt class="docutils literal"><span class="pre">std::ptrdiff_t</span></tt>, an
appropriate type for measuring the distance between any two
addresses in memory, and one that works for almost any iterator,
so we can omit this argument, too.</p>
<p>The declaration of <tt class="docutils literal"><span class="pre">node_iterator</span></tt> will therefore look something
like:</p>
<pre class="literal-block">
# include &quot;node.hpp&quot;
# include &lt;boost/iterator/iterator_facade.hpp&gt;

class node_iterator
  : public boost::iterator_facade&lt;
        node_iterator
      , node_base
      , boost::forward_traversal_tag
    &gt;
{
   ...
};
</pre>
</div>
</div>
<div class="section" id="constructors-and-data-members">
<h3><a class="toc-backref" href="#id40">Constructors and Data Members</a></h3>
<p>Next we need to decide how to represent the iterator's position.
This representation will take the form of data members, so we'll
also need to write constructors to initialize them.  The
<tt class="docutils literal"><span class="pre">node_iterator</span></tt>'s position is quite naturally represented using
a pointer to a <tt class="docutils literal"><span class="pre">node_base</span></tt>.  We'll need a constructor to build an
iterator from a <tt class="docutils literal"><span class="pre">node_base*</span></tt>, and a default constructor to
satisfy the <a class="reference external" href="new-iter-concepts.html#forward-traversal-iterators-lib-forward-traversal-iterators">forward traversal iterator</a> requirements<a class="footnote-reference" href="#default" id="id13"><sup>2</sup></a>.
Our <tt class="docutils literal"><span class="pre">node_iterator</span></tt> then becomes:</p>
<pre class="literal-block">
# include &quot;node.hpp&quot;
# include &lt;boost/iterator/iterator_facade.hpp&gt;

class node_iterator
  : public boost::iterator_facade&lt;
        node_iterator
      , node_base
      , boost::forward_traversal_tag
    &gt;
{
 public:
    node_iterator()
      : m_node(0)
    {}

    explicit node_iterator(node_base* p)
      : m_node(p)
    {}

 private:
    ...
    node_base* m_node;
};
</pre>
<table class="docutils footnote" frame="void" id="default" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id13">[2]</a></td><td>Technically, the C++ standard places almost no
requirements on a default-constructed iterator, so if we were
really concerned with efficiency, we could've written the
default constructor to leave <tt class="docutils literal"><span class="pre">m_node</span></tt> uninitialized.</td></tr>
</tbody>
</table>
</div>
<div class="section" id="implementing-the-core-operations">
<h3><a class="toc-backref" href="#id41">Implementing the Core Operations</a></h3>
<p>The last step is to implement the <a class="reference internal" href="#core-operations">core operations</a> required by
the concepts we want our iterator to model.  Referring to the
<a class="reference internal" href="#core-operations">table</a>, we can see that the first three rows are applicable
because <tt class="docutils literal"><span class="pre">node_iterator</span></tt> needs to satisfy the requirements for
<a class="reference external" href="new-iter-concepts.html#readable-iterators-lib-readable-iterators">readable iterator</a>, <a class="reference external" href="new-iter-concepts.html#single-pass-iterators-lib-single-pass-iterators">single pass iterator</a>, and <a class="reference external" href="new-iter-concepts.html#incrementable-iterators-lib-incrementable-iterators">incrementable
iterator</a>.</p>
<p>We therefore need to supply <tt class="docutils literal"><span class="pre">dereference</span></tt>,
<tt class="docutils literal"><span class="pre">equal</span></tt>, and <tt class="docutils literal"><span class="pre">increment</span></tt> members.  We don't want these members
to become part of <tt class="docutils literal"><span class="pre">node_iterator</span></tt>'s public interface, so we can
make them private and grant friendship to
<tt class="docutils literal"><span class="pre">boost::iterator_core_access</span></tt>, a &quot;back-door&quot; that
<tt class="docutils literal"><span class="pre">iterator_facade</span></tt> uses to get access to the core operations:</p>
<pre class="literal-block">
# include &quot;node.hpp&quot;
# include &lt;boost/iterator/iterator_facade.hpp&gt;

class node_iterator
  : public boost::iterator_facade&lt;
        node_iterator
      , node_base
      , boost::forward_traversal_tag
    &gt;
{
 public:
    node_iterator()
      : m_node(0) {}

    explicit node_iterator(node_base* p)
      : m_node(p) {}

 private:
    friend class boost::iterator_core_access;

    void increment() { m_node = m_node-&gt;next(); }

    bool equal(node_iterator const&amp; other) const
    {
        return this-&gt;m_node == other.m_node;
    }

    node_base&amp; dereference() const { return *m_node; }

    node_base* m_node;
};
</pre>
<p>Voilà; a complete and conforming readable, forward-traversal
iterator!  For a working example of its use, see <a class="reference external" href="../example/node_iterator1.cpp">this program</a>.</p>
</div>
</div>
<div class="section" id="a-constant-node-iterator">
<h2><a class="toc-backref" href="#id42">A constant <tt class="docutils literal"><span class="pre">node_iterator</span></tt></a></h2>
<div class="sidebar">
<p class="first sidebar-title">Constant and Mutable iterators</p>
<p>The term <strong>mutable iterator</strong> means an iterator through which
the object it references (its &quot;referent&quot;) can be modified.  A
<strong>constant iterator</strong> is one which doesn't allow modification of
its referent.</p>
<p>The words <em>constant</em> and <em>mutable</em> don't refer to the ability to
modify the iterator itself.  For example, an <tt class="docutils literal"><span class="pre">int</span> <span class="pre">const*</span></tt> is a
non-<tt class="docutils literal"><span class="pre">const</span></tt> <em>constant iterator</em>, which can be incremented
but doesn't allow modification of its referent, and <tt class="docutils literal"><span class="pre">int*</span>
<span class="pre">const</span></tt> is a <tt class="docutils literal"><span class="pre">const</span></tt> <em>mutable iterator</em>, which cannot be
modified but which allows modification of its referent.</p>
<p class="last">Confusing?  We agree, but those are the standard terms.  It
probably doesn't help much that a container's constant iterator
is called <tt class="docutils literal"><span class="pre">const_iterator</span></tt>.</p>
</div>
<p>Now, our <tt class="docutils literal"><span class="pre">node_iterator</span></tt> gives clients access to both <tt class="docutils literal"><span class="pre">node</span></tt>'s <tt class="docutils literal"><span class="pre">print(std::ostream&amp;)</span> <span class="pre">const</span></tt> member function, but also its
mutating <tt class="docutils literal"><span class="pre">double_me()</span></tt> member.  If we wanted to build a
<em>constant</em> <tt class="docutils literal"><span class="pre">node_iterator</span></tt>, we'd only have to make three
changes:</p>
<pre class="literal-block">
class const_node_iterator
  : public boost::iterator_facade&lt;
        const_node_iterator
      , node_base <strong>const</strong>
      , boost::forward_traversal_tag
    &gt;
{
 public:
    const_node_iterator()
      : m_node(0) {}

    explicit const_node_iterator(node_base* p)
      : m_node(p) {}

 private:
    friend class boost::iterator_core_access;

    void increment() { m_node = m_node-&gt;next(); }

    bool equal(const_node_iterator const&amp; other) const
    {
        return this-&gt;m_node == other.m_node;
    }

    node_base <strong>const</strong>&amp; dereference() const { return *m_node; }

    node_base <strong>const</strong>* m_node;
};
</pre>
<div class="sidebar">
<p class="first sidebar-title"><tt class="docutils literal"><span class="pre">const</span></tt> and an iterator's <tt class="docutils literal"><span class="pre">value_type</span></tt></p>
<p class="last">The C++ standard requires an iterator's <tt class="docutils literal"><span class="pre">value_type</span></tt> <em>not</em> be
<tt class="docutils literal"><span class="pre">const</span></tt>-qualified, so <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> strips the
<tt class="docutils literal"><span class="pre">const</span></tt> from its <tt class="docutils literal"><span class="pre">Value</span></tt> parameter in order to produce the
iterator's <tt class="docutils literal"><span class="pre">value_type</span></tt>.  Making the <tt class="docutils literal"><span class="pre">Value</span></tt> argument
<tt class="docutils literal"><span class="pre">const</span></tt> provides a useful hint to <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> that the
iterator is a <em>constant iterator</em>, and the default <tt class="docutils literal"><span class="pre">Reference</span></tt>
argument will be correct for all lvalue iterators.</p>
</div>
<p>As a matter of fact, <tt class="docutils literal"><span class="pre">node_iterator</span></tt> and <tt class="docutils literal"><span class="pre">const_node_iterator</span></tt>
are so similar that it makes sense to factor the common code out
into a template as follows:</p>
<pre class="literal-block">
template &lt;class Value&gt;
class node_iter
  : public boost::iterator_facade&lt;
        node_iter&lt;Value&gt;
      , Value
      , boost::forward_traversal_tag
    &gt;
{
 public:
    node_iter()
      : m_node(0) {}

    explicit node_iter(Value* p)
      : m_node(p) {}

 private:
    friend class boost::iterator_core_access;

    bool equal(node_iter&lt;Value&gt; const&amp; other) const
    {
        return this-&gt;m_node == other.m_node;
    }

    void increment()
    { m_node = m_node-&gt;next(); }

    Value&amp; dereference() const
    { return *m_node; }

    Value* m_node;
};
typedef node_iter&lt;node_base&gt; node_iterator;
typedef node_iter&lt;node_base const&gt; node_const_iterator;
</pre>
</div>
<div class="section" id="interoperability">
<h2><a class="toc-backref" href="#id43">Interoperability</a></h2>
<p>Our <tt class="docutils literal"><span class="pre">const_node_iterator</span></tt> works perfectly well on its own, but
taken together with <tt class="docutils literal"><span class="pre">node_iterator</span></tt> it doesn't quite meet
expectations.  For example, we'd like to be able to pass a
<tt class="docutils literal"><span class="pre">node_iterator</span></tt> where a <tt class="docutils literal"><span class="pre">node_const_iterator</span></tt> was expected,
just as you can with <tt class="docutils literal"><span class="pre">std::list&lt;int&gt;</span></tt>'s <tt class="docutils literal"><span class="pre">iterator</span></tt> and
<tt class="docutils literal"><span class="pre">const_iterator</span></tt>.  Furthermore, given a <tt class="docutils literal"><span class="pre">node_iterator</span></tt> and a
<tt class="docutils literal"><span class="pre">node_const_iterator</span></tt> into the same list, we should be able to
compare them for equality.</p>
<p>This expected ability to use two different iterator types together
is known as <a class="reference external" href="new-iter-concepts.html#interoperable-iterators-lib-interoperable-iterators"><strong>interoperability</strong></a>.  Achieving interoperability in
our case is as simple as templatizing the <tt class="docutils literal"><span class="pre">equal</span></tt> function and
adding a templatized converting constructor<a class="footnote-reference" href="#broken" id="id16"><sup>3</sup></a><a class="footnote-reference" href="#random" id="id17"><sup>4</sup></a>:</p>
<pre class="literal-block">
template &lt;class Value&gt;
class node_iter
  : public boost::iterator_facade&lt;
        node_iter&lt;Value&gt;
      , Value
      , boost::forward_traversal_tag
    &gt;
{
 public:
    node_iter()
      : m_node(0) {}

    explicit node_iter(Value* p)
      : m_node(p) {}

    template &lt;class OtherValue&gt;
    node_iter(node_iter&lt;OtherValue&gt; const&amp; other)
      : m_node(other.m_node) {}

 private:
    friend class boost::iterator_core_access;
    template &lt;class&gt; friend class node_iter;

    template &lt;class OtherValue&gt;
    bool equal(node_iter&lt;OtherValue&gt; const&amp; other) const
    {
        return this-&gt;m_node == other.m_node;
    }

    void increment()
    { m_node = m_node-&gt;next(); }

    Value&amp; dereference() const
    { return *m_node; }

    Value* m_node;
};
typedef impl::node_iterator&lt;node_base&gt; node_iterator;
typedef impl::node_iterator&lt;node_base const&gt; node_const_iterator;
</pre>
<table class="docutils footnote" frame="void" id="broken" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id16">[3]</a></td><td>If you're using an older compiler and it can't handle
this example, see the <a class="reference external" href="../example/node_iterator2.hpp">example code</a> for workarounds.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="random" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id17">[4]</a></td><td>If <tt class="docutils literal"><span class="pre">node_iterator</span></tt> had been a <a class="reference external" href="new-iter-concepts.html#random-access-traversal-iterators-lib-random-access-traversal-iterators">random access
traversal iterator</a>, we'd have had to templatize its
<tt class="docutils literal"><span class="pre">distance_to</span></tt> function as well.</td></tr>
</tbody>
</table>
<p>You can see an example program which exercises our interoperable
iterators <a class="reference external" href="../example/node_iterator2.cpp">here</a>.</p>
</div>
<div class="section" id="telling-the-truth">
<h2><a class="toc-backref" href="#id44">Telling the Truth</a></h2>
<p>Now <tt class="docutils literal"><span class="pre">node_iterator</span></tt> and <tt class="docutils literal"><span class="pre">node_const_iterator</span></tt> behave exactly as
you'd expect... almost.  We can compare them and we can convert in
one direction: from <tt class="docutils literal"><span class="pre">node_iterator</span></tt> to <tt class="docutils literal"><span class="pre">node_const_iterator</span></tt>.
If we try to convert from <tt class="docutils literal"><span class="pre">node_const_iterator</span></tt> to
<tt class="docutils literal"><span class="pre">node_iterator</span></tt>, we'll get an error when the converting
constructor tries to initialize <tt class="docutils literal"><span class="pre">node_iterator</span></tt>'s <tt class="docutils literal"><span class="pre">m_node</span></tt>, a
<tt class="docutils literal"><span class="pre">node*</span></tt> with a <tt class="docutils literal"><span class="pre">node</span> <span class="pre">const*</span></tt>.  So what's the problem?</p>
<p>The problem is that
<tt class="docutils literal"><span class="pre">boost::</span></tt><a class="reference external" href="../../type_traits/index.html#relationships"><tt class="docutils literal"><span class="pre">is_convertible</span></tt></a><tt class="docutils literal"><span class="pre">&lt;node_const_iterator,node_iterator&gt;::value</span></tt>
will be <tt class="docutils literal"><span class="pre">true</span></tt>, but it should be <tt class="docutils literal"><span class="pre">false</span></tt>.  <a class="reference external" href="../../type_traits/index.html#relationships"><tt class="docutils literal"><span class="pre">is_convertible</span></tt></a>
lies because it can only see as far as the <em>declaration</em> of
<tt class="docutils literal"><span class="pre">node_iter</span></tt>'s converting constructor, but can't look inside at
the <em>definition</em> to make sure it will compile.  A perfect solution
would make <tt class="docutils literal"><span class="pre">node_iter</span></tt>'s converting constructor disappear when
the <tt class="docutils literal"><span class="pre">m_node</span></tt> conversion would fail.</p>
<p>In fact, that sort of magic is possible using
<a class="reference external" href="../../utility/enable_if.html"><tt class="docutils literal"><span class="pre">boost::enable_if</span></tt></a>.  By rewriting the converting constructor as
follows, we can remove it from the overload set when it's not
appropriate:</p>
<pre class="literal-block">
#include &lt;boost/type_traits/is_convertible.hpp&gt;
#include &lt;boost/utility/enable_if.hpp&gt;

  ...

private:
  struct enabler {};

public:
  template &lt;class OtherValue&gt;
  node_iter(
      node_iter&lt;OtherValue&gt; const&amp; other
    , typename boost::enable_if&lt;
          boost::is_convertible&lt;OtherValue*,Value*&gt;
        , enabler
      &gt;::type = enabler()
  )
    : m_node(other.m_node) {}
</pre>
</div>
<div class="section" id="wrap-up">
<h2><a class="toc-backref" href="#id45">Wrap Up</a></h2>
<p>This concludes our <tt class="docutils literal"><span class="pre">iterator_facade</span></tt> tutorial, but before you
stop reading we urge you to take a look at <a class="reference external" href="iterator_adaptor.html"><tt class="docutils literal"><span class="pre">iterator_adaptor</span></tt></a>.
There's another way to approach writing these iterators which might
even be superior.</p>
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