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<title>New Iterator Concepts</title>
<meta name="author" content="David Abrahams, Jeremy Siek, Thomas Witt" />
<meta name="organization" content="Boost Consulting, Indiana University Open Systems Lab, University of Hanover Institute for Transport Railway Operation and Construction" />
<meta name="date" content="2003-11-22" />
<meta name="date" content="2003-12-01" />
<meta name="copyright" content="Copyright David Abrahams, Jeremy Siek, and Thomas Witt 2003. All rights reserved" />
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<div class="document" id="new-iterator-concepts">
@ -218,7 +27,7 @@ ul.auto-toc {
Systems Lab</a>, University of Hanover <a class="last reference" 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>2003-11-22</td></tr>
<td>2003-12-01</td></tr>
<tr class="field"><th class="docinfo-name">Number:</th><td class="field-body">This is a revised version of <a class="reference" href="http://anubis.dkuug.dk/jtc1/sc22/wg21/docs/papers/2003/n1550.html">n1550</a>=03-0133, which was
accepted for Technical Report 1 by the C++ standard
committee's library working group. This proposal is a
@ -248,40 +57,39 @@ of iterators that are used in practice.</td>
<ul class="simple">
<li><a class="reference" href="#motivation" id="id1" name="id1">Motivation</a></li>
<li><a class="reference" href="#impact-on-the-standard" id="id2" name="id2">Impact on the Standard</a><ul>
<li><a class="reference" href="#proposed-changes-for-tr1" id="id3" name="id3">Proposed Changes for TR1</a></li>
<li><a class="reference" href="#possible-but-not-proposed-changes-to-the-working-paper" id="id4" name="id4">Possible (but not proposed) Changes to the Working Paper</a><ul>
<li><a class="reference" href="#changes-to-algorithm-requirements" id="id5" name="id5">Changes to Algorithm Requirements</a></li>
<li><a class="reference" href="#deprecations" id="id6" name="id6">Deprecations</a></li>
<li><a class="reference" href="#vector-bool" id="id7" name="id7"><tt class="literal"><span class="pre">vector&lt;bool&gt;</span></tt></a></li>
<li><a class="reference" href="#possible-but-not-proposed-changes-to-the-working-paper" id="id3" name="id3">Possible (but not proposed) Changes to the Working Paper</a><ul>
<li><a class="reference" href="#changes-to-algorithm-requirements" id="id4" name="id4">Changes to Algorithm Requirements</a></li>
<li><a class="reference" href="#deprecations" id="id5" name="id5">Deprecations</a></li>
<li><a class="reference" href="#vector-bool" id="id6" name="id6"><tt class="literal"><span class="pre">vector&lt;bool&gt;</span></tt></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference" href="#design" id="id8" name="id8">Design</a></li>
<li><a class="reference" href="#proposed-text" id="id9" name="id9">Proposed Text</a><ul>
<li><a class="reference" href="#addition-to-lib-iterator-requirements" id="id10" name="id10">Addition to [lib.iterator.requirements]</a><ul>
<li><a class="reference" href="#iterator-value-access-concepts-lib-iterator-value-access" id="id11" name="id11">Iterator Value Access Concepts [lib.iterator.value.access]</a><ul>
<li><a class="reference" href="#readable-iterators-lib-readable-iterators" id="id12" name="id12">Readable Iterators [lib.readable.iterators]</a></li>
<li><a class="reference" href="#writable-iterators-lib-writable-iterators" id="id13" name="id13">Writable Iterators [lib.writable.iterators]</a></li>
<li><a class="reference" href="#swappable-iterators-lib-swappable-iterators" id="id14" name="id14">Swappable Iterators [lib.swappable.iterators]</a></li>
<li><a class="reference" href="#lvalue-iterators-lib-lvalue-iterators" id="id15" name="id15">Lvalue Iterators [lib.lvalue.iterators]</a></li>
<li><a class="reference" href="#design" id="id7" name="id7">Design</a></li>
<li><a class="reference" href="#proposed-text" id="id8" name="id8">Proposed Text</a><ul>
<li><a class="reference" href="#addition-to-lib-iterator-requirements" id="id9" name="id9">Addition to [lib.iterator.requirements]</a><ul>
<li><a class="reference" href="#iterator-value-access-concepts-lib-iterator-value-access" id="id10" name="id10">Iterator Value Access Concepts [lib.iterator.value.access]</a><ul>
<li><a class="reference" href="#readable-iterators-lib-readable-iterators" id="id11" name="id11">Readable Iterators [lib.readable.iterators]</a></li>
<li><a class="reference" href="#writable-iterators-lib-writable-iterators" id="id12" name="id12">Writable Iterators [lib.writable.iterators]</a></li>
<li><a class="reference" href="#swappable-iterators-lib-swappable-iterators" id="id13" name="id13">Swappable Iterators [lib.swappable.iterators]</a></li>
<li><a class="reference" href="#lvalue-iterators-lib-lvalue-iterators" id="id14" name="id14">Lvalue Iterators [lib.lvalue.iterators]</a></li>
</ul>
</li>
<li><a class="reference" href="#iterator-traversal-concepts-lib-iterator-traversal" id="id16" name="id16">Iterator Traversal Concepts [lib.iterator.traversal]</a><ul>
<li><a class="reference" href="#incrementable-iterators-lib-incrementable-iterators" id="id17" name="id17">Incrementable Iterators [lib.incrementable.iterators]</a></li>
<li><a class="reference" href="#single-pass-iterators-lib-single-pass-iterators" id="id18" name="id18">Single Pass Iterators [lib.single.pass.iterators]</a></li>
<li><a class="reference" href="#forward-traversal-iterators-lib-forward-traversal-iterators" id="id19" name="id19">Forward Traversal Iterators [lib.forward.traversal.iterators]</a></li>
<li><a class="reference" href="#bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators" id="id20" name="id20">Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]</a></li>
<li><a class="reference" href="#random-access-traversal-iterators-lib-random-access-traversal-iterators" id="id21" name="id21">Random Access Traversal Iterators [lib.random.access.traversal.iterators]</a></li>
<li><a class="reference" href="#iterator-traversal-concepts-lib-iterator-traversal" id="id15" name="id15">Iterator Traversal Concepts [lib.iterator.traversal]</a><ul>
<li><a class="reference" href="#incrementable-iterators-lib-incrementable-iterators" id="id16" name="id16">Incrementable Iterators [lib.incrementable.iterators]</a></li>
<li><a class="reference" href="#single-pass-iterators-lib-single-pass-iterators" id="id17" name="id17">Single Pass Iterators [lib.single.pass.iterators]</a></li>
<li><a class="reference" href="#forward-traversal-iterators-lib-forward-traversal-iterators" id="id18" name="id18">Forward Traversal Iterators [lib.forward.traversal.iterators]</a></li>
<li><a class="reference" href="#bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators" id="id19" name="id19">Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]</a></li>
<li><a class="reference" href="#random-access-traversal-iterators-lib-random-access-traversal-iterators" id="id20" name="id20">Random Access Traversal Iterators [lib.random.access.traversal.iterators]</a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference" href="#addition-to-lib-iterator-synopsis" id="id22" name="id22">Addition to [lib.iterator.synopsis]</a></li>
<li><a class="reference" href="#addition-to-lib-iterator-traits" id="id23" name="id23">Addition to [lib.iterator.traits]</a></li>
<li><a class="reference" href="#addition-to-lib-iterator-synopsis" id="id21" name="id21">Addition to [lib.iterator.synopsis]</a></li>
<li><a class="reference" href="#addition-to-lib-iterator-traits" id="id22" name="id22">Addition to [lib.iterator.traits]</a></li>
</ul>
</li>
<li><a class="reference" href="#footnotes" id="id24" name="id24">Footnotes</a></li>
<li><a class="reference" href="#footnotes" id="id23" name="id23">Footnotes</a></li>
</ul>
</div>
<div class="section" id="motivation">
@ -299,7 +107,7 @@ geared towards iterator traversal (hence the category names), while
requirements that address value access sneak in at various places. The
following table gives a summary of the current value access
requirements in the iterator categories.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="31%" />
<col width="69%" />
@ -367,14 +175,13 @@ traversal from the need for a true reference return type.</li>
</div>
<div class="section" id="impact-on-the-standard">
<h1><a class="toc-backref" href="#id2" name="impact-on-the-standard">Impact on the Standard</a></h1>
<div class="section" id="proposed-changes-for-tr1">
<h2><a class="toc-backref" href="#id3" name="proposed-changes-for-tr1">Proposed Changes for TR1</a></h2>
<p>The new iterator concepts are backward-compatible with the old
iterator requirements, and old iterators are forward-compatible with
the new iterator concepts. That is to say, iterators that satisfy the
old requirements also satisfy appropriate concepts in the new system,
and iterators modeling the new concepts will automatically satisfy the
appropriate old requirements.</p>
<p>This proposal for TR1 is a pure extension. Further, the new iterator
concepts are backward-compatible with the old iterator requirements,
and old iterators are forward-compatible with the new iterator
concepts. That is to say, iterators that satisfy the old requirements
also satisfy appropriate concepts in the new system, and iterators
modeling the new concepts will automatically satisfy the appropriate
old requirements.</p>
<!-- I think we need to say something about the resolution to allow
convertibility to any of the old-style tags as a TR issue (hope it
made it). -DWA -->
@ -382,23 +189,22 @@ made it). -DWA -->
standards conforming input iterator is allowed to have
a tag that is not input_iterator_tag but that
is convertible to input_iterator_tag? -JGS -->
<p>The algorithms in the standard library benefit from the new iterator
concepts because the new concepts provide a more accurate way to
express their type requirements. The result is algorithms that are
usable in more situations and have fewer type requirements.</p>
<p>Note that as currently specified, <tt class="literal"><span class="pre">istreambuf_iterator</span></tt> doesn't
meet the Readable Iterator requirements because its <tt class="literal"><span class="pre">value_type</span></tt>
is not convertible to its <tt class="literal"><span class="pre">reference</span></tt> type. We believe this to
be a defect in the standard; it should be fixed by changing its
<tt class="literal"><span class="pre">reference</span></tt> type from <tt class="literal"><span class="pre">value_type&amp;</span></tt> to <tt class="literal"><span class="pre">value_type</span> <span class="pre">const&amp;</span></tt>.</p>
</div>
<div class="section" id="possible-but-not-proposed-changes-to-the-working-paper">
<h2><a class="toc-backref" href="#id4" name="possible-but-not-proposed-changes-to-the-working-paper">Possible (but not proposed) Changes to the Working Paper</a></h2>
<h2><a class="toc-backref" href="#id3" name="possible-but-not-proposed-changes-to-the-working-paper">Possible (but not proposed) Changes to the Working Paper</a></h2>
<p>The extensions in this paper suggest several changes we might make
to the working paper for the next standard. These changes are not
a formal part of this proposal for TR1.</p>
<div class="section" id="changes-to-algorithm-requirements">
<h3><a class="toc-backref" href="#id5" name="changes-to-algorithm-requirements">Changes to Algorithm Requirements</a></h3>
<h3><a class="toc-backref" href="#id4" name="changes-to-algorithm-requirements">Changes to Algorithm Requirements</a></h3>
<p>The algorithms in the standard library could benefit from the new
iterator concepts because the new concepts provide a more accurate way
to express their type requirements. The result is algorithms that are
usable in more situations and have fewer type requirements.</p>
<p>For the next working paper (but not for TR1), the committee should
consider the following changes to the type requirements of
algorithms. These changes are phrased as phrased as textual
@ -460,14 +266,14 @@ Bidirectional Iterator (2) -&gt; Bidirectional Traversal Iterator and Writable I
</dl>
</div>
<div class="section" id="deprecations">
<h3><a class="toc-backref" href="#id6" name="deprecations">Deprecations</a></h3>
<h3><a class="toc-backref" href="#id5" name="deprecations">Deprecations</a></h3>
<p>For the next working paper (but not for TR1), the committee should
consider deprecating the old iterator tags, and
std::iterator_traits, since it will be superceded by individual
traits metafunctions.</p>
</div>
<div class="section" id="vector-bool">
<h3><a class="toc-backref" href="#id7" name="vector-bool"><tt class="literal"><span class="pre">vector&lt;bool&gt;</span></tt></a></h3>
<h3><a class="toc-backref" href="#id6" name="vector-bool"><tt class="literal"><span class="pre">vector&lt;bool&gt;</span></tt></a></h3>
<p>For the next working paper (but not for TR1), the committee should
consider reclassifying <tt class="literal"><span class="pre">vector&lt;bool&gt;::iterator</span></tt> as a Random
Access Traversal Iterator and Readable Iterator and Writable
@ -476,7 +282,7 @@ Iterator.</p>
</div>
</div>
<div class="section" id="design">
<h1><a class="toc-backref" href="#id8" name="design">Design</a></h1>
<h1><a class="toc-backref" href="#id7" name="design">Design</a></h1>
<p>The iterator requirements are to be separated into two groups. One set
of concepts handles the syntax and semantics of value access:</p>
<ul class="simple">
@ -511,64 +317,19 @@ given in the following diagram.</p>
<p>Like the old iterator requirements, we provide tags for purposes of
dispatching based on the traversal concepts. The tags are related via
inheritance so that a tag is convertible to another tag if the concept
associated with the first tag is a refinement of the second tag.
Since the access concepts are not related via refinement, but instead
cover orthogonal issues, we do not use tags for the access concepts,
but instead use the equivalent of a bit field.</p>
<p>We provide an access mechanism for mapping iterator types to the new
traversal tags and access bit field. Our design reuses
<tt class="literal"><span class="pre">iterator_traits&lt;Iter&gt;::iterator_category</span></tt> as the access
mechanism. To that end, the access and traversal information is
bundled into a single type using the following <cite>iterator_tag</cite> class.</p>
<pre class="literal-block">
enum iterator_access { readable_iterator = 1, writable_iterator = 2,
swappable_iterator = 4, lvalue_iterator = 8 };
template &lt;unsigned int access_bits, class TraversalTag&gt;
struct iterator_tag : /* appropriate old category or categories */ {
static const iterator_access access =
(iterator_access)access_bits &amp;
(readable_iterator | writable_iterator | swappable_iterator);
typedef TraversalTag traversal;
};
</pre>
<p>The <tt class="literal"><span class="pre">access_bits</span></tt> argument is declared to be <tt class="literal"><span class="pre">unsigned</span> <span class="pre">int</span></tt>
instead of the enum <tt class="literal"><span class="pre">iterator_access</span></tt> for convenience of use. For
example, the expression <tt class="literal"><span class="pre">(readable_iterator</span> <span class="pre">|</span> <span class="pre">writable_iterator)</span></tt>
produces an unsigned int, not an <tt class="literal"><span class="pre">iterator_access</span></tt>. The purpose of
the <tt class="literal"><span class="pre">lvalue_iterator</span></tt> part of the <tt class="literal"><span class="pre">iterator_access</span></tt> enum is to
communicate to <tt class="literal"><span class="pre">iterator_tag</span></tt> whether the reference type is an
lvalue so that the appropriate old category can be chosen for the base
class. The <tt class="literal"><span class="pre">lvalue_iterator</span></tt> bit is not recorded in the
<tt class="literal"><span class="pre">iterator_tag::access</span></tt> data member.</p>
<p>The <tt class="literal"><span class="pre">iterator_tag</span></tt> class template is derived from the appropriate
iterator tag or tags from the old requirements based on the access
bits and traversal tag passed as template parameters. The algorithm
for determining the old tag or tags picks the least-refined old
concepts that include all of the requirements of the access and
traversal concepts (that is, the closest fit), if any such category
exists. For example, the category tag for a Readable Single Pass
Iterator will always be derived from <tt class="literal"><span class="pre">input_iterator_tag</span></tt>, while the
category tag for a Single Pass Iterator that is both Readable and
Writable will be derived from both <tt class="literal"><span class="pre">input_iterator_tag</span></tt> and
<tt class="literal"><span class="pre">output_iterator_tag</span></tt>.</p>
<p>We also provide several helper classes that make it convenient to
obtain the access and traversal characteristics of an iterator. These
helper classes work both for iterators whose <tt class="literal"><span class="pre">iterator_category</span></tt> is
<tt class="literal"><span class="pre">iterator_tag</span></tt> and also for iterators using the original iterator
categories.</p>
<pre class="literal-block">
template &lt;class Iterator&gt; struct is_readable { typedef ... type; };
template &lt;class Iterator&gt; struct is_writable { typedef ... type; };
template &lt;class Iterator&gt; struct is_swappable { typedef ... type; };
template &lt;class Iterator&gt; struct traversal_category { typedef ... type; };
</pre>
<p>We do not include a helper class <tt class="literal"><span class="pre">is_lvalue_iterator</span></tt> because that
can easily be deduced by checking whether
<tt class="literal"><span class="pre">iterator_traits&lt;Iterator&gt;::reference</span></tt> is a real reference.</p>
<p>The most difficult design decision concerned the <tt class="literal"><span class="pre">operator[]</span></tt>. The
direct approach for specifying <tt class="literal"><span class="pre">operator[]</span></tt> would have a return type
of <tt class="literal"><span class="pre">reference</span></tt>; the same as <tt class="literal"><span class="pre">operator*</span></tt>. However, going in this
associated with the first tag is a refinement of the second tag. Our
design reuses <tt class="literal"><span class="pre">iterator_traits&lt;Iter&gt;::iterator_category</span></tt> as the
access mechanism for the traversal tag. If an iterator wishes to meet
the requirements of both a new iterator concept and an old iterator
concept, it can use an iterator category type that inherits from both
the the old iterator tag and the new traversal tag.</p>
<p>We do not provide tags for the purposes of dispatching based on the
access concepts. There are two reasons: we could not find a way to
automatically infer the right access tags for old-style iterators and
the need for dispatching based on the access concepts is not as great.</p>
<p>A difficult design decision concerned the <tt class="literal"><span class="pre">operator[]</span></tt>. The direct
approach for specifying <tt class="literal"><span class="pre">operator[]</span></tt> would have a return type of
<tt class="literal"><span class="pre">reference</span></tt>; the same as <tt class="literal"><span class="pre">operator*</span></tt>. However, going in this
direction would mean that an iterator satisfying the old Random Access
Iterator requirements would not necessarily be a model of Readable or
Writable Lvalue Iterator. Instead we have chosen a design that
@ -578,23 +339,23 @@ only required to return something convertible to the <tt class="literal"><span c
<tt class="literal"><span class="pre">i[n]</span> <span class="pre">=</span> <span class="pre">t</span></tt> (for a Writable Iterator).</p>
</div>
<div class="section" id="proposed-text">
<h1><a class="toc-backref" href="#id9" name="proposed-text">Proposed Text</a></h1>
<h1><a class="toc-backref" href="#id8" name="proposed-text">Proposed Text</a></h1>
<div class="section" id="addition-to-lib-iterator-requirements">
<h2><a class="toc-backref" href="#id10" name="addition-to-lib-iterator-requirements">Addition to [lib.iterator.requirements]</a></h2>
<h2><a class="toc-backref" href="#id9" name="addition-to-lib-iterator-requirements">Addition to [lib.iterator.requirements]</a></h2>
<div class="section" id="iterator-value-access-concepts-lib-iterator-value-access">
<h3><a class="toc-backref" href="#id11" name="iterator-value-access-concepts-lib-iterator-value-access">Iterator Value Access Concepts [lib.iterator.value.access]</a></h3>
<h3><a class="toc-backref" href="#id10" name="iterator-value-access-concepts-lib-iterator-value-access">Iterator Value Access Concepts [lib.iterator.value.access]</a></h3>
<p>In the tables below, <tt class="literal"><span class="pre">X</span></tt> is an iterator type, <tt class="literal"><span class="pre">a</span></tt> is a constant
object of type <tt class="literal"><span class="pre">X</span></tt>, <tt class="literal"><span class="pre">R</span></tt> is
<tt class="literal"><span class="pre">std::iterator_traits&lt;X&gt;::reference</span></tt>, <tt class="literal"><span class="pre">T</span></tt> is
<tt class="literal"><span class="pre">std::iterator_traits&lt;X&gt;::value_type</span></tt>, and <tt class="literal"><span class="pre">v</span></tt> is a constant
object of type <tt class="literal"><span class="pre">T</span></tt>.</p>
<a class="target" id="readable-iterator" name="readable-iterator"></a><div class="section" id="readable-iterators-lib-readable-iterators">
<h4><a class="toc-backref" href="#id12" name="readable-iterators-lib-readable-iterators">Readable Iterators [lib.readable.iterators]</a></h4>
<h4><a class="toc-backref" href="#id11" name="readable-iterators-lib-readable-iterators">Readable Iterators [lib.readable.iterators]</a></h4>
<p>A class or built-in type <tt class="literal"><span class="pre">X</span></tt> models the <em>Readable Iterator</em> concept
for the value type <tt class="literal"><span class="pre">T</span></tt> if the following expressions are valid and
respect the stated semantics. <tt class="literal"><span class="pre">U</span></tt> is the type of any specified
member of type <tt class="literal"><span class="pre">T</span></tt>.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="42%" />
<col width="29%" />
@ -643,13 +404,13 @@ to <tt class="literal"><span class="pre">(*a).m</span></tt></td>
</table>
<a class="target" id="writable-iterator" name="writable-iterator"></a></div>
<div class="section" id="writable-iterators-lib-writable-iterators">
<h4><a class="toc-backref" href="#id13" name="writable-iterators-lib-writable-iterators">Writable Iterators [lib.writable.iterators]</a></h4>
<h4><a class="toc-backref" href="#id12" name="writable-iterators-lib-writable-iterators">Writable Iterators [lib.writable.iterators]</a></h4>
<p>A class or built-in type <tt class="literal"><span class="pre">X</span></tt> models the <em>Writable Iterator</em> concept
if the following expressions are valid and respect the stated
semantics. In addition, a model of <em>Writable Iterator</em> must include
in its documentation the <em>set of value types</em> that it allows for
output.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="37%" />
<col width="21%" />
@ -674,11 +435,11 @@ value types of <tt class="literal"><span class="pre">X</span></tt></td>
</table>
</div>
<div class="section" id="swappable-iterators-lib-swappable-iterators">
<h4><a class="toc-backref" href="#id14" name="swappable-iterators-lib-swappable-iterators">Swappable Iterators [lib.swappable.iterators]</a></h4>
<h4><a class="toc-backref" href="#id13" name="swappable-iterators-lib-swappable-iterators">Swappable Iterators [lib.swappable.iterators]</a></h4>
<p>A class or built-in type <tt class="literal"><span class="pre">X</span></tt> models the <em>Swappable Iterator</em> concept
if the following expressions are valid and respect the stated
semantics.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="37%" />
<col width="19%" />
@ -706,10 +467,10 @@ exchanged</td>
</dl>
</div>
<div class="section" id="lvalue-iterators-lib-lvalue-iterators">
<h4><a class="toc-backref" href="#id15" name="lvalue-iterators-lib-lvalue-iterators">Lvalue Iterators [lib.lvalue.iterators]</a></h4>
<h4><a class="toc-backref" href="#id14" name="lvalue-iterators-lib-lvalue-iterators">Lvalue Iterators [lib.lvalue.iterators]</a></h4>
<p>The <em>Lvalue Iterator</em> concept adds the requirement that the
<tt class="literal"><span class="pre">reference</span></tt> type be a reference to the value type of the iterator.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="42%" />
<col width="14%" />
@ -736,17 +497,17 @@ cv-qualification</td>
</div>
</div>
<div class="section" id="iterator-traversal-concepts-lib-iterator-traversal">
<h3><a class="toc-backref" href="#id16" name="iterator-traversal-concepts-lib-iterator-traversal">Iterator Traversal Concepts [lib.iterator.traversal]</a></h3>
<h3><a class="toc-backref" href="#id15" name="iterator-traversal-concepts-lib-iterator-traversal">Iterator Traversal Concepts [lib.iterator.traversal]</a></h3>
<p>In the tables below, <tt class="literal"><span class="pre">X</span></tt> is an iterator type, <tt class="literal"><span class="pre">a</span></tt> and <tt class="literal"><span class="pre">b</span></tt> are
constant objects of type <tt class="literal"><span class="pre">X</span></tt>, <tt class="literal"><span class="pre">r</span></tt> and <tt class="literal"><span class="pre">s</span></tt> are mutable objects of
type <tt class="literal"><span class="pre">X</span></tt>, <tt class="literal"><span class="pre">T</span></tt> is <tt class="literal"><span class="pre">std::iterator_traits&lt;X&gt;::value_type</span></tt>, and
<tt class="literal"><span class="pre">v</span></tt> is a constant object of type <tt class="literal"><span class="pre">T</span></tt>.</p>
<div class="section" id="incrementable-iterators-lib-incrementable-iterators">
<h4><a class="toc-backref" href="#id17" name="incrementable-iterators-lib-incrementable-iterators">Incrementable Iterators [lib.incrementable.iterators]</a></h4>
<h4><a class="toc-backref" href="#id16" name="incrementable-iterators-lib-incrementable-iterators">Incrementable Iterators [lib.incrementable.iterators]</a></h4>
<p>A class or built-in type <tt class="literal"><span class="pre">X</span></tt> models the <em>Incrementable Iterator</em>
concept if the following expressions are valid and respect the stated
semantics.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="39%" />
<col width="37%" />
@ -785,11 +546,11 @@ semantics.</p>
</table>
</div>
<div class="section" id="single-pass-iterators-lib-single-pass-iterators">
<h4><a class="toc-backref" href="#id18" name="single-pass-iterators-lib-single-pass-iterators">Single Pass Iterators [lib.single.pass.iterators]</a></h4>
<h4><a class="toc-backref" href="#id17" name="single-pass-iterators-lib-single-pass-iterators">Single Pass Iterators [lib.single.pass.iterators]</a></h4>
<p>A class or built-in type <tt class="literal"><span class="pre">X</span></tt> models the <em>Single Pass Iterator</em>
concept if the following expressions are valid and respect the stated
semantics.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="36%" />
<col width="33%" />
@ -831,11 +592,11 @@ relation over its domain</td>
</table>
</div>
<div class="section" id="forward-traversal-iterators-lib-forward-traversal-iterators">
<h4><a class="toc-backref" href="#id19" name="forward-traversal-iterators-lib-forward-traversal-iterators">Forward Traversal Iterators [lib.forward.traversal.iterators]</a></h4>
<h4><a class="toc-backref" href="#id18" name="forward-traversal-iterators-lib-forward-traversal-iterators">Forward Traversal Iterators [lib.forward.traversal.iterators]</a></h4>
<p>A class or built-in type <tt class="literal"><span class="pre">X</span></tt> models the <em>Forward Traversal Iterator</em>
concept if the following expressions are valid and respect the stated
semantics.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="44%" />
<col width="39%" />
@ -878,11 +639,11 @@ the distance between iterators</td>
</table>
</div>
<div class="section" id="bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators">
<h4><a class="toc-backref" href="#id20" name="bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators">Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]</a></h4>
<h4><a class="toc-backref" href="#id19" name="bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators">Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]</a></h4>
<p>A class or built-in type <tt class="literal"><span class="pre">X</span></tt> models the <em>Bidirectional Traversal
Iterator</em> concept if the following expressions are valid and respect
the stated semantics.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="35%" />
<col width="44%" />
@ -930,13 +691,13 @@ implies <tt class="literal"><span class="pre">r</span> <span class="pre">==</spa
</table>
</div>
<div class="section" id="random-access-traversal-iterators-lib-random-access-traversal-iterators">
<h4><a class="toc-backref" href="#id21" name="random-access-traversal-iterators-lib-random-access-traversal-iterators">Random Access Traversal Iterators [lib.random.access.traversal.iterators]</a></h4>
<h4><a class="toc-backref" href="#id20" name="random-access-traversal-iterators-lib-random-access-traversal-iterators">Random Access Traversal Iterators [lib.random.access.traversal.iterators]</a></h4>
<p>A class or built-in type <tt class="literal"><span class="pre">X</span></tt> models the <em>Random Access Traversal
Iterator</em> concept if the following expressions are valid and respect
the stated semantics. In the table below, <tt class="literal"><span class="pre">Distance</span></tt> is
<tt class="literal"><span class="pre">iterator_traits&lt;X&gt;::difference_type</span></tt> and <tt class="literal"><span class="pre">n</span></tt> represents a
constant object of type <tt class="literal"><span class="pre">Distance</span></tt>.</p>
<table border class="table">
<table class="table" frame="border" rules="all">
<colgroup>
<col width="31%" />
<col width="35%" />
@ -1044,7 +805,7 @@ ordering relation</td>
</div>
</div>
<div class="section" id="addition-to-lib-iterator-synopsis">
<h2><a class="toc-backref" href="#id22" name="addition-to-lib-iterator-synopsis">Addition to [lib.iterator.synopsis]</a></h2>
<h2><a class="toc-backref" href="#id21" name="addition-to-lib-iterator-synopsis">Addition to [lib.iterator.synopsis]</a></h2>
<pre class="literal-block">
// lib.iterator.traits, traits and tags
template &lt;class Iterator&gt; struct is_readable_iterator;
@ -1058,7 +819,7 @@ struct random_access_traversal_tag : bidirectional_traversal_tag { };
</pre>
</div>
<div class="section" id="addition-to-lib-iterator-traits">
<h2><a class="toc-backref" href="#id23" name="addition-to-lib-iterator-traits">Addition to [lib.iterator.traits]</a></h2>
<h2><a class="toc-backref" href="#id22" name="addition-to-lib-iterator-traits">Addition to [lib.iterator.traits]</a></h2>
<p>The <tt class="literal"><span class="pre">is_readable_iterator</span></tt> and <tt class="literal"><span class="pre">iterator_traversal</span></tt> class
templates satisfy the <a class="reference" href="http://anubis.dkuug.dk/jtc1/sc22/wg21/docs/papers/2003/n1519.htm">UnaryTypeTrait</a> requirements.</p>
<p>Given an iterator type <tt class="literal"><span class="pre">X</span></tt>, <tt class="literal"><span class="pre">is_readable_iterator&lt;X&gt;::value</span></tt>
@ -1087,7 +848,7 @@ traversal-category(X) =
</div>
</div>
<div class="section" id="footnotes">
<h1><a class="toc-backref" href="#id24" name="footnotes">Footnotes</a></h1>
<h1><a class="toc-backref" href="#id23" name="footnotes">Footnotes</a></h1>
<p>The UnaryTypeTrait concept is defined in <a class="reference" href="http://anubis.dkuug.dk/jtc1/sc22/wg21/docs/papers/2003/n1519.htm">n1519</a>; the LWG added the
requirement that specializations are derived from their nested
<tt class="literal"><span class="pre">::type</span></tt>.</p>
@ -1100,11 +861,5 @@ LocalWords: incrementable xxx min prev inplace png oldeqnew AccessTag struct
LocalWords: TraversalTag typename lvalues DWA Hmm JGS mis enum -->
</div>
</div>
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