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<meta name="author" content="David Abrahams, Jeremy Siek, Thomas Witt" />
<meta name="organization" content="Boost Consulting, Indiana University Open Systems Lab, Zephyr Associates, Inc." />
<meta name="date" content="2006-09-11" />
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<div class="document" id="new-iterator-concepts">
<h1 class="title">New Iterator Concepts</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;styleadvisor.com">witt&#64;styleadvisor.com</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>, <a class="last reference external" href="http://www.styleadvisor.com">Zephyr Associates, Inc.</a></td></tr>
<tr><th class="docinfo-name">Date:</th>
<td>2006-09-11</td></tr>
<tr class="field"><th class="docinfo-name">Number:</th><td class="field-body">This is a revised version of <a class="reference external" href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003/n1550.htm">n1550</a>=03-0133, which was
accepted for Technical Report 1 by the C++ standard
committee's library working group. This proposal is a
revision of paper <a class="reference external" href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2001/n1297.html">n1297</a>, <a class="reference external" href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003/n1477.html">n1477</a>, and <a class="reference external" href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003/n1531.html">n1531</a>.</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) -->
<!-- Version 1.25 of this ReStructuredText document is the same as
n1550_, the paper accepted by the LWG. -->
<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">We propose a new system of iterator concepts that treat
access and positioning independently. This allows the
concepts to more closely match the requirements
of algorithms and provides better categorizations
of iterators that are used in practice.</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="#motivation" id="id1">Motivation</a></li>
<li><a class="reference internal" href="#impact-on-the-standard" id="id2">Impact on the Standard</a><ul>
<li><a class="reference internal" href="#possible-but-not-proposed-changes-to-the-working-paper" id="id3">Possible (but not proposed) Changes to the Working Paper</a><ul>
<li><a class="reference internal" href="#changes-to-algorithm-requirements" id="id4">Changes to Algorithm Requirements</a></li>
<li><a class="reference internal" href="#deprecations" id="id5">Deprecations</a></li>
<li><a class="reference internal" href="#vector-bool" id="id6"><tt class="docutils literal"><span class="pre">vector&lt;bool&gt;</span></tt></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#design" id="id7">Design</a></li>
<li><a class="reference internal" href="#proposed-text" id="id8">Proposed Text</a><ul>
<li><a class="reference internal" href="#addition-to-lib-iterator-requirements" id="id9">Addition to [lib.iterator.requirements]</a><ul>
<li><a class="reference internal" href="#iterator-value-access-concepts-lib-iterator-value-access" id="id10">Iterator Value Access Concepts [lib.iterator.value.access]</a><ul>
<li><a class="reference internal" href="#readable-iterators-lib-readable-iterators" id="id11">Readable Iterators [lib.readable.iterators]</a></li>
<li><a class="reference internal" href="#writable-iterators-lib-writable-iterators" id="id12">Writable Iterators [lib.writable.iterators]</a></li>
<li><a class="reference internal" href="#swappable-iterators-lib-swappable-iterators" id="id13">Swappable Iterators [lib.swappable.iterators]</a></li>
<li><a class="reference internal" href="#lvalue-iterators-lib-lvalue-iterators" id="id14">Lvalue Iterators [lib.lvalue.iterators]</a></li>
</ul>
</li>
<li><a class="reference internal" href="#iterator-traversal-concepts-lib-iterator-traversal" id="id15">Iterator Traversal Concepts [lib.iterator.traversal]</a><ul>
<li><a class="reference internal" href="#incrementable-iterators-lib-incrementable-iterators" id="id16">Incrementable Iterators [lib.incrementable.iterators]</a></li>
<li><a class="reference internal" href="#single-pass-iterators-lib-single-pass-iterators" id="id17">Single Pass Iterators [lib.single.pass.iterators]</a></li>
<li><a class="reference internal" href="#forward-traversal-iterators-lib-forward-traversal-iterators" id="id18">Forward Traversal Iterators [lib.forward.traversal.iterators]</a></li>
<li><a class="reference internal" href="#bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators" id="id19">Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]</a></li>
<li><a class="reference internal" href="#random-access-traversal-iterators-lib-random-access-traversal-iterators" id="id20">Random Access Traversal Iterators [lib.random.access.traversal.iterators]</a></li>
<li><a class="reference internal" href="#interoperable-iterators-lib-interoperable-iterators" id="id21">Interoperable Iterators [lib.interoperable.iterators]</a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#addition-to-lib-iterator-synopsis" id="id22">Addition to [lib.iterator.synopsis]</a></li>
<li><a class="reference internal" href="#addition-to-lib-iterator-traits" id="id23">Addition to [lib.iterator.traits]</a></li>
</ul>
</li>
<li><a class="reference internal" href="#footnotes" id="id24">Footnotes</a></li>
</ul>
</div>
<div class="section" id="motivation">
<h1><a class="toc-backref" href="#id1">Motivation</a></h1>
<p>The standard iterator categories and requirements are flawed because
they use a single hierarchy of concepts to address two orthogonal
issues: <em>iterator traversal</em> and <em>value access</em>. As a result, many
algorithms with requirements expressed in terms of the iterator
categories are too strict. Also, many real-world iterators can not be
accurately categorized.  A proxy-based iterator with random-access
traversal, for example, may only legally have a category of &quot;input
iterator&quot;, so generic algorithms are unable to take advantage of its
random-access capabilities.  The current iterator concept hierarchy is
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="1" class="docutils">
<colgroup>
<col width="31%" />
<col width="69%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="2">Value Access Requirements in Existing Iterator Categories</th>
</tr>
</thead>
<tbody valign="top">
<tr><td>Output Iterator</td>
<td><tt class="docutils literal"><span class="pre">*i</span> <span class="pre">=</span> <span class="pre">a</span></tt></td>
</tr>
<tr><td>Input Iterator</td>
<td><tt class="docutils literal"><span class="pre">*i</span></tt> is convertible to <tt class="docutils literal"><span class="pre">T</span></tt></td>
</tr>
<tr><td>Forward Iterator</td>
<td><tt class="docutils literal"><span class="pre">*i</span></tt> is <tt class="docutils literal"><span class="pre">T&amp;</span></tt> (or <tt class="docutils literal"><span class="pre">const</span> <span class="pre">T&amp;</span></tt> once <a class="reference external" href="http://www.open-std.org/JTC1/SC22/WG21/docs/lwg-active.html#200">issue 200</a>
is resolved)</td>
</tr>
<tr><td>Random Access Iterator</td>
<td><tt class="docutils literal"><span class="pre">i[n]</span></tt> is convertible to <tt class="docutils literal"><span class="pre">T</span></tt> (also <tt class="docutils literal"><span class="pre">i[n]</span> <span class="pre">=</span> <span class="pre">t</span></tt>
is required for mutable iterators once <a class="reference external" href="http://www.open-std.org/JTC1/SC22/WG21/docs/lwg-active.html#299">issue 299</a>
is resolved)</td>
</tr>
</tbody>
</table>
<p>Because iterator traversal and value access are mixed together in a
single hierarchy, many useful iterators can not be appropriately
categorized. For example, <tt class="docutils literal"><span class="pre">vector&lt;bool&gt;::iterator</span></tt> is almost a
random access iterator, but the return type is not <tt class="docutils literal"><span class="pre">bool&amp;</span></tt> (see
<a class="reference external" href="http://www.open-std.org/JTC1/SC22/WG21/docs/lwg-active.html#96">issue 96</a> and Herb Sutter's paper J16/99-0008 = WG21
N1185). Therefore, the iterators of <tt class="docutils literal"><span class="pre">vector&lt;bool&gt;</span></tt> only meet the
requirements of input iterator and output iterator.  This is so
nonintuitive that the C++ standard contradicts itself on this point.
In paragraph 23.2.4/1 it says that a <tt class="docutils literal"><span class="pre">vector</span></tt> is a sequence that
supports random access iterators.</p>
<p>Another difficult-to-categorize iterator is the transform iterator, an
adaptor which applies a unary function object to the dereferenced
value of the some underlying iterator (see <a class="reference external" href="http://www.boost.org/libs/utility/transform_iterator.htm">transform_iterator</a>).
For unary functions such as <tt class="docutils literal"><span class="pre">times</span></tt>, the return type of
<tt class="docutils literal"><span class="pre">operator*</span></tt> clearly needs to be the <tt class="docutils literal"><span class="pre">result_type</span></tt> of the function
object, which is typically not a reference.  Because random access
iterators are required to return lvalues from <tt class="docutils literal"><span class="pre">operator*</span></tt>, if you
wrap <tt class="docutils literal"><span class="pre">int*</span></tt> with a transform iterator, you do not get a random
access iterator as might be expected, but an input iterator.</p>
<p>A third example is found in the vertex and edge iterators of the
<a class="reference external" href="http://www.boost.org/libs/graph/doc/table_of_contents.html">Boost Graph Library</a>. These iterators return vertex and edge
descriptors, which are lightweight handles created on-the-fly. They
must be returned by-value. As a result, their current standard
iterator category is <tt class="docutils literal"><span class="pre">input_iterator_tag</span></tt>, which means that,
strictly speaking, you could not use these iterators with algorithms
like <tt class="docutils literal"><span class="pre">min_element()</span></tt>. As a temporary solution, the concept
<a class="reference external" href="http://www.boost.org/libs/utility/MultiPassInputIterator.html">Multi-Pass Input Iterator</a> was introduced to describe the vertex and
edge descriptors, but as the design notes for the concept suggest, a
better solution is needed.</p>
<p>In short, there are many useful iterators that do not fit into the
current standard iterator categories. As a result, the following bad
things happen:</p>
<ul class="simple">
<li>Iterators are often mis-categorized.</li>
<li>Algorithm requirements are more strict than necessary, because they
cannot separate the need for random access or bidirectional
traversal from the need for a true reference return type.</li>
</ul>
</div>
<div class="section" id="impact-on-the-standard">
<h1><a class="toc-backref" href="#id2">Impact on the Standard</a></h1>
<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 -->
<!-- Hmm, not sure I understand. Are you talking about whether a
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 -->
<div class="section" id="possible-but-not-proposed-changes-to-the-working-paper">
<h2><a class="toc-backref" href="#id3">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="#id4">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 textual substitutions, listing the
algorithms to which each textual substitution applies.</p>
<p>Forward Iterator -&gt; Forward Traversal Iterator and Readable Iterator</p>
<blockquote>
<tt class="docutils literal"><span class="pre">find_end,</span> <span class="pre">adjacent_find,</span> <span class="pre">search,</span> <span class="pre">search_n,</span> <span class="pre">rotate_copy,</span>
<span class="pre">lower_bound,</span> <span class="pre">upper_bound,</span> <span class="pre">equal_range,</span> <span class="pre">binary_search,</span>
<span class="pre">min_element,</span> <span class="pre">max_element</span></tt></blockquote>
<p>Forward Iterator (1) -&gt; Single Pass Iterator and Readable Iterator,
Forward Iterator (2) -&gt; Forward Traversal Iterator and Readable Iterator</p>
<blockquote>
<tt class="docutils literal"><span class="pre">find_first_of</span></tt></blockquote>
<p>Forward Iterator -&gt; Readable Iterator and Writable Iterator</p>
<blockquote>
<tt class="docutils literal"><span class="pre">iter_swap</span></tt></blockquote>
<p>Forward Iterator -&gt; Single Pass Iterator and Writable Iterator</p>
<blockquote>
<tt class="docutils literal"><span class="pre">fill,</span> <span class="pre">generate</span></tt></blockquote>
<p>Forward Iterator -&gt; Forward Traversal Iterator and Swappable Iterator</p>
<blockquote>
<tt class="docutils literal"><span class="pre">rotate</span></tt></blockquote>
<p>Forward Iterator (1) -&gt; Swappable Iterator and Single Pass Iterator,
Forward Iterator (2) -&gt; Swappable Iterator and  Incrementable Iterator</p>
<blockquote>
<tt class="docutils literal"><span class="pre">swap_ranges</span></tt></blockquote>
<dl class="docutils">
<dt>Forward Iterator -&gt; Forward Traversal Iterator and Readable Iterator and Writable Iterator</dt>
<dd><tt class="docutils literal"><span class="pre">remove,</span> <span class="pre">remove_if,</span> <span class="pre">unique</span></tt></dd>
</dl>
<p>Forward Iterator -&gt; Single Pass Iterator and Readable Iterator and Writable Iterator</p>
<blockquote>
<tt class="docutils literal"><span class="pre">replace,</span> <span class="pre">replace_if</span></tt></blockquote>
<dl class="docutils">
<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Swappable Iterator</dt>
<dd><tt class="docutils literal"><span class="pre">reverse</span></tt></dd>
<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Readable and Swappable Iterator</dt>
<dd><tt class="docutils literal"><span class="pre">partition</span></tt></dd>
</dl>
<p>Bidirectional Iterator (1) -&gt; Bidirectional Traversal Iterator and Readable Iterator,
Bidirectional Iterator (2) -&gt; Bidirectional Traversal Iterator and Writable Iterator</p>
<blockquote>
<tt class="docutils literal"><span class="pre">copy_backwards</span></tt></blockquote>
<dl class="docutils">
<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Swappable Iterator and Readable Iterator</dt>
<dd><tt class="docutils literal"><span class="pre">next_permutation,</span> <span class="pre">prev_permutation</span></tt></dd>
<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Readable Iterator and Writable Iterator</dt>
<dd><tt class="docutils literal"><span class="pre">stable_partition,</span> <span class="pre">inplace_merge</span></tt></dd>
<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Readable Iterator</dt>
<dd><tt class="docutils literal"><span class="pre">reverse_copy</span></tt></dd>
<dt>Random Access Iterator -&gt; Random Access Traversal Iterator and Readable and Writable Iterator</dt>
<dd><tt class="docutils literal"><span class="pre">random_shuffle,</span> <span class="pre">sort,</span> <span class="pre">stable_sort,</span> <span class="pre">partial_sort,</span> <span class="pre">nth_element,</span> <span class="pre">push_heap,</span> <span class="pre">pop_heap</span>
<span class="pre">make_heap,</span> <span class="pre">sort_heap</span></tt></dd>
<dt>Input Iterator (2) -&gt; Incrementable Iterator and Readable Iterator</dt>
<dd><tt class="docutils literal"><span class="pre">equal,</span> <span class="pre">mismatch</span></tt></dd>
<dt>Input Iterator (2) -&gt; Incrementable Iterator and Readable Iterator</dt>
<dd><tt class="docutils literal"><span class="pre">transform</span></tt></dd>
</dl>
</div>
<div class="section" id="deprecations">
<h3><a class="toc-backref" href="#id5">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="#id6"><tt class="docutils 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="docutils literal"><span class="pre">vector&lt;bool&gt;::iterator</span></tt> as a Random
Access Traversal Iterator and Readable Iterator and Writable
Iterator.</p>
</div>
</div>
</div>
<div class="section" id="design">
<h1><a class="toc-backref" href="#id7">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">
<li>Readable Iterator</li>
<li>Writable Iterator</li>
<li>Swappable Iterator</li>
<li>Lvalue Iterator</li>
</ul>
<p>The access concepts describe requirements related to <tt class="docutils literal"><span class="pre">operator*</span></tt> and
<tt class="docutils literal"><span class="pre">operator-&gt;</span></tt>, including the <tt class="docutils literal"><span class="pre">value_type</span></tt>, <tt class="docutils literal"><span class="pre">reference</span></tt>, and
<tt class="docutils literal"><span class="pre">pointer</span></tt> associated types.</p>
<p>The other set of concepts handles traversal:</p>
<ul class="simple">
<li>Incrementable Iterator</li>
<li>Single Pass Iterator</li>
<li>Forward Traversal Iterator</li>
<li>Bidirectional Traversal Iterator</li>
<li>Random Access Traversal Iterator</li>
</ul>
<p>The refinement relationships for the traversal concepts are in the
following diagram.</p>
<img alt="traversal.png" src="traversal.png" />
<p>In addition to the iterator movement operators, such as
<tt class="docutils literal"><span class="pre">operator++</span></tt>, the traversal concepts also include requirements on
position comparison such as <tt class="docutils literal"><span class="pre">operator==</span></tt> and <tt class="docutils literal"><span class="pre">operator&lt;</span></tt>.  The
reason for the fine grain slicing of the concepts into the
Incrementable and Single Pass is to provide concepts that are exact
matches with the original input and output iterator requirements.</p>
<p>This proposal also includes a concept for specifying when an iterator
is interoperable with another iterator, in the sense that <tt class="docutils literal"><span class="pre">int*</span></tt> is
interoperable with <tt class="docutils literal"><span class="pre">int</span> <span class="pre">const*</span></tt>.</p>
<ul class="simple">
<li>Interoperable Iterators</li>
</ul>
<p>The relationship between the new iterator concepts and the old are
given in the following diagram.</p>
<img alt="oldeqnew.png" src="oldeqnew.png" />
<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.</p>
<p>Our design reuses <tt class="docutils literal"><span class="pre">iterator_traits&lt;Iter&gt;::iterator_category</span></tt> to
indicate an iterator's traversal capability.  To specify
capabilities not captured by any old-style iterator category, an
iterator designer can use an <tt class="docutils literal"><span class="pre">iterator_category</span></tt> type that is
convertible to both the the most-derived old iterator category tag
which fits, and the appropriate new iterator traversal tag.</p>
<!-- dwa2003/1/2: Note that we are not *requiring* convertibility to
a new-style traversal tag in order to meet new concepts.
Old-style iterators still fit, after all. -->
<p>We do not provide tags for the purposes of dispatching based on the
access concepts, in part because we could not find a way to
automatically infer the right access tags for old-style iterators.
An iterator's writability may be dependent on the assignability of
its <tt class="docutils literal"><span class="pre">value_type</span></tt> and there's no known way to detect whether an
arbitrary type is assignable.  Fortunately, the need for
dispatching based on access capability is not as great as the need
for dispatching based on traversal capability.</p>
<p>A difficult design decision concerned the <tt class="docutils literal"><span class="pre">operator[]</span></tt>. The direct
approach for specifying <tt class="docutils literal"><span class="pre">operator[]</span></tt> would have a return type of
<tt class="docutils literal"><span class="pre">reference</span></tt>; the same as <tt class="docutils 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
matches the preferred resolution of <a class="reference external" href="http://www.open-std.org/JTC1/SC22/WG21/docs/lwg-active.html#299">issue 299</a>: <tt class="docutils literal"><span class="pre">operator[]</span></tt> is
only required to return something convertible to the <tt class="docutils literal"><span class="pre">value_type</span></tt>
(for a Readable Iterator), and is required to support assignment
<tt class="docutils 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="#id8">Proposed Text</a></h1>
<div class="section" id="addition-to-lib-iterator-requirements">
<h2><a class="toc-backref" href="#id9">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="#id10">Iterator Value Access Concepts [lib.iterator.value.access]</a></h3>
<p>In the tables below, <tt class="docutils literal"><span class="pre">X</span></tt> is an iterator type, <tt class="docutils literal"><span class="pre">a</span></tt> is a constant
object of type <tt class="docutils literal"><span class="pre">X</span></tt>, <tt class="docutils literal"><span class="pre">R</span></tt> is
<tt class="docutils literal"><span class="pre">std::iterator_traits&lt;X&gt;::reference</span></tt>, <tt class="docutils literal"><span class="pre">T</span></tt> is
<tt class="docutils literal"><span class="pre">std::iterator_traits&lt;X&gt;::value_type</span></tt>, and <tt class="docutils literal"><span class="pre">v</span></tt> is a constant
object of type <tt class="docutils literal"><span class="pre">T</span></tt>.</p>
<div class="section" id="readable-iterators-lib-readable-iterators">
<span id="readable-iterator"></span><h4><a class="toc-backref" href="#id11">Readable Iterators [lib.readable.iterators]</a></h4>
<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Readable Iterator</em> concept
for value type <tt class="docutils literal"><span class="pre">T</span></tt> if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> being Assignable and
Copy Constructible, the following expressions are valid and respect
the stated semantics. <tt class="docutils literal"><span class="pre">U</span></tt> is the type of any specified member of
type <tt class="docutils literal"><span class="pre">T</span></tt>.</p>
<table border="1" class="docutils">
<colgroup>
<col width="28%" />
<col width="20%" />
<col width="52%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="3">Readable Iterator Requirements (in addition to Assignable and Copy Constructible)</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Note/Precondition</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">iterator_traits&lt;X&gt;::value_type</span></tt></td>
<td><tt class="docutils literal"><span class="pre">T</span></tt></td>
<td>Any non-reference,
non-cv-qualified type</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">*a</span></tt></td>
<td>Convertible to <tt class="docutils literal"><span class="pre">T</span></tt></td>
<td><dl class="first last docutils">
<dt>pre: <tt class="docutils literal"><span class="pre">a</span></tt> is dereferenceable. If <tt class="docutils literal"><span class="pre">a</span> <span class="pre">==</span> <span class="pre">b</span></tt> then <tt class="docutils literal"><span class="pre">*a</span></tt></dt>
<dd>is equivalent to <tt class="docutils literal"><span class="pre">*b</span></tt>.</dd>
</dl>
</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a-&gt;m</span></tt></td>
<td><tt class="docutils literal"><span class="pre">U&amp;</span></tt></td>
<td>pre: <tt class="docutils literal"><span class="pre">pre:</span> <span class="pre">(*a).m</span></tt> is well-defined. Equivalent to <tt class="docutils literal"><span class="pre">(*a).m</span></tt>.</td>
</tr>
</tbody>
</table>
<!-- We won't say anything about iterator_traits<X>::reference until the DR is resolved. -JGS -->
</div>
<div class="section" id="writable-iterators-lib-writable-iterators">
<span id="writable-iterator"></span><h4><a class="toc-backref" href="#id12">Writable Iterators [lib.writable.iterators]</a></h4>
<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Writable Iterator</em> concept
if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> being Copy Constructible, the following
expressions are valid and respect the stated semantics.  Writable
Iterators have an associated <em>set of value types</em>.</p>
<table border="1" class="docutils">
<colgroup>
<col width="37%" />
<col width="21%" />
<col width="42%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="3">Writable Iterator Requirements (in addition to Copy Constructible)</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Precondition</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">*a</span> <span class="pre">=</span> <span class="pre">o</span></tt></td>
<td>&nbsp;</td>
<td>pre: The type of <tt class="docutils literal"><span class="pre">o</span></tt>
is in the set of
value types of <tt class="docutils literal"><span class="pre">X</span></tt></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="swappable-iterators-lib-swappable-iterators">
<h4><a class="toc-backref" href="#id13">Swappable Iterators [lib.swappable.iterators]</a></h4>
<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Swappable Iterator</em> concept
if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> being Copy Constructible, the following
expressions are valid and respect the stated semantics.</p>
<table border="1" class="docutils">
<colgroup>
<col width="37%" />
<col width="19%" />
<col width="43%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="3">Swappable Iterator Requirements (in addition to Copy Constructible)</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Postcondition</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">iter_swap(a,</span> <span class="pre">b)</span></tt></td>
<td><tt class="docutils literal"><span class="pre">void</span></tt></td>
<td>the pointed to values are
exchanged</td>
</tr>
</tbody>
</table>
<p>[<em>Note:</em> An iterator that is a model of the <a class="reference internal" href="#readable-iterator">Readable Iterator</a> and
<a class="reference internal" href="#writable-iterator">Writable Iterator</a> concepts is also a model of <em>Swappable
Iterator</em>.  <em>--end note</em>]</p>
</div>
<div class="section" id="lvalue-iterators-lib-lvalue-iterators">
<h4><a class="toc-backref" href="#id14">Lvalue Iterators [lib.lvalue.iterators]</a></h4>
<p>The <em>Lvalue Iterator</em> concept adds the requirement that the return
type of <tt class="docutils literal"><span class="pre">operator*</span></tt> type be a reference to the value type of the
iterator.</p>
<table border="1" class="docutils">
<colgroup>
<col width="22%" />
<col width="19%" />
<col width="59%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="3">Lvalue Iterator Requirements</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Note/Assertion</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">*a</span></tt></td>
<td><tt class="docutils literal"><span class="pre">T&amp;</span></tt></td>
<td><tt class="docutils literal"><span class="pre">T</span></tt> is <em>cv</em>
<tt class="docutils literal"><span class="pre">iterator_traits&lt;X&gt;::value_type</span></tt>
where <em>cv</em> is an optional
cv-qualification.  pre: <tt class="docutils literal"><span class="pre">a</span></tt> is
dereferenceable.</td>
</tr>
</tbody>
</table>
<p>If <tt class="docutils literal"><span class="pre">X</span></tt> is a <a class="reference internal" href="#writable-iterator">Writable Iterator</a> then <tt class="docutils literal"><span class="pre">a</span> <span class="pre">==</span> <span class="pre">b</span></tt> if and only if
<tt class="docutils literal"><span class="pre">*a</span></tt> is the same object as <tt class="docutils literal"><span class="pre">*b</span></tt>.  If <tt class="docutils literal"><span class="pre">X</span></tt> is a <a class="reference internal" href="#readable-iterator">Readable
Iterator</a> then <tt class="docutils literal"><span class="pre">a</span> <span class="pre">==</span> <span class="pre">b</span></tt> implies <tt class="docutils literal"><span class="pre">*a</span></tt> is the same object as
<tt class="docutils literal"><span class="pre">*b</span></tt>.</p>
</div>
</div>
<div class="section" id="iterator-traversal-concepts-lib-iterator-traversal">
<h3><a class="toc-backref" href="#id15">Iterator Traversal Concepts [lib.iterator.traversal]</a></h3>
<p>In the tables below, <tt class="docutils literal"><span class="pre">X</span></tt> is an iterator type, <tt class="docutils literal"><span class="pre">a</span></tt> and <tt class="docutils literal"><span class="pre">b</span></tt> are
constant objects of type <tt class="docutils literal"><span class="pre">X</span></tt>, <tt class="docutils literal"><span class="pre">r</span></tt> and <tt class="docutils literal"><span class="pre">s</span></tt> are mutable objects of
type <tt class="docutils literal"><span class="pre">X</span></tt>, <tt class="docutils literal"><span class="pre">T</span></tt> is <tt class="docutils literal"><span class="pre">std::iterator_traits&lt;X&gt;::value_type</span></tt>, and
<tt class="docutils literal"><span class="pre">v</span></tt> is a constant object of type <tt class="docutils literal"><span class="pre">T</span></tt>.</p>
<div class="section" id="incrementable-iterators-lib-incrementable-iterators">
<h4><a class="toc-backref" href="#id16">Incrementable Iterators [lib.incrementable.iterators]</a></h4>
<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Incrementable Iterator</em>
concept if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> being Assignable and Copy
Constructible, the following expressions are valid and respect the
stated semantics.</p>
<table border="1" class="docutils">
<colgroup>
<col width="39%" />
<col width="38%" />
<col width="23%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="3">Incrementable Iterator Requirements (in addition to Assignable, Copy Constructible)</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Assertion</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">++r</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
<td><tt class="docutils literal"><span class="pre">&amp;r</span> <span class="pre">==</span> <span class="pre">&amp;++r</span></tt></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">r++</span></tt></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">*r++</span></tt></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
<td>Convertible to
<tt class="docutils literal"><span class="pre">incrementable_traversal_tag</span></tt></td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<p>If <tt class="docutils literal"><span class="pre">X</span></tt> is a <a class="reference internal" href="#writable-iterator">Writable Iterator</a> then <tt class="docutils literal"><span class="pre">X</span> <span class="pre">a(r++);</span></tt> is equivalent
to <tt class="docutils literal"><span class="pre">X</span> <span class="pre">a(r);</span> <span class="pre">++r;</span></tt> and <tt class="docutils literal"><span class="pre">*r++</span> <span class="pre">=</span> <span class="pre">o</span></tt> is equivalent
to  <tt class="docutils literal"><span class="pre">*r</span> <span class="pre">=</span> <span class="pre">o;</span> <span class="pre">++r</span></tt>.
If <tt class="docutils literal"><span class="pre">X</span></tt> is a <a class="reference internal" href="#readable-iterator">Readable Iterator</a> then <tt class="docutils literal"><span class="pre">T</span> <span class="pre">z(*r++);</span></tt> is equivalent
to <tt class="docutils literal"><span class="pre">T</span> <span class="pre">z(*r);</span> <span class="pre">++r;</span></tt>.</p>
<!-- TR1: incrementable_iterator_tag changed to
incrementable_traversal_tag for consistency. -->
</div>
<div class="section" id="single-pass-iterators-lib-single-pass-iterators">
<h4><a class="toc-backref" href="#id17">Single Pass Iterators [lib.single.pass.iterators]</a></h4>
<p>A class or built-in type <tt class="docutils 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="1" class="docutils">
<colgroup>
<col width="37%" />
<col width="27%" />
<col width="12%" />
<col width="25%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="4">Single Pass Iterator Requirements (in addition to Incrementable Iterator and Equality
Comparable)</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Operational
Semantics</th>
<th class="head">Assertion/
Pre-/Post-condition</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">++r</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
<td>&nbsp;</td>
<td>pre: <tt class="docutils literal"><span class="pre">r</span></tt> is
dereferenceable; post:
<tt class="docutils literal"><span class="pre">r</span></tt> is dereferenceable or
<tt class="docutils literal"><span class="pre">r</span></tt> is past-the-end</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">==</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td>&nbsp;</td>
<td><tt class="docutils literal"><span class="pre">==</span></tt> is an equivalence
relation over its domain</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">!=</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre">==</span> <span class="pre">b)</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">iterator_traits&lt;X&gt;::difference_type</span></tt></td>
<td>A signed integral type
representing the distance
between iterators</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
<td>Convertible to
<tt class="docutils literal"><span class="pre">single_pass_traversal_tag</span></tt></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<!-- TR1: single_pass_iterator_tag changed to
single_pass_traversal_tag for consistency -->
</div>
<div class="section" id="forward-traversal-iterators-lib-forward-traversal-iterators">
<h4><a class="toc-backref" href="#id18">Forward Traversal Iterators [lib.forward.traversal.iterators]</a></h4>
<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Forward Traversal Iterator</em>
concept if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> meeting the requirements of Default
Constructible and Single Pass Iterator, the following expressions are
valid and respect the stated semantics.</p>
<table border="1" class="docutils">
<colgroup>
<col width="38%" />
<col width="34%" />
<col width="27%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="3">Forward Traversal Iterator Requirements (in addition to Default Constructible and Single Pass Iterator)</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Assertion/Note</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">X</span> <span class="pre">u;</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
<td>note: <tt class="docutils literal"><span class="pre">u</span></tt> may have a
singular value.</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">++r</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
<td><tt class="docutils literal"><span class="pre">r</span> <span class="pre">==</span> <span class="pre">s</span></tt> and <tt class="docutils literal"><span class="pre">r</span></tt> is
dereferenceable implies
<tt class="docutils literal"><span class="pre">++r</span> <span class="pre">==</span> <span class="pre">++s.</span></tt></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
<td>Convertible to
<tt class="docutils literal"><span class="pre">forward_traversal_tag</span></tt></td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<!-- TR1: forward_traversal_iterator_tag changed to
forward_traversal_tag for consistency -->
</div>
<div class="section" id="bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators">
<h4><a class="toc-backref" href="#id19">Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]</a></h4>
<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Bidirectional Traversal
Iterator</em> concept if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> meeting the requirements of
Forward Traversal Iterator, the following expressions are valid and
respect the stated semantics.</p>
<table border="1" class="docutils">
<colgroup>
<col width="33%" />
<col width="32%" />
<col width="14%" />
<col width="21%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="4">Bidirectional Traversal Iterator Requirements (in addition to Forward Traversal
Iterator)</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Operational
Semantics</th>
<th class="head">Assertion/
Pre-/Post-condition</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">--r</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
<td>&nbsp;</td>
<td><p class="first">pre: there exists
<tt class="docutils literal"><span class="pre">s</span></tt> such that <tt class="docutils literal"><span class="pre">r</span>
<span class="pre">==</span> <span class="pre">++s</span></tt>.  post:
<tt class="docutils literal"><span class="pre">s</span></tt> is
dereferenceable.</p>
<p class="last"><tt class="docutils literal"><span class="pre">++(--r)</span> <span class="pre">==</span> <span class="pre">r</span></tt>.
<tt class="docutils literal"><span class="pre">--r</span> <span class="pre">==</span> <span class="pre">--s</span></tt>
implies <tt class="docutils literal"><span class="pre">r</span> <span class="pre">==</span>
<span class="pre">s</span></tt>. <tt class="docutils literal"><span class="pre">&amp;r</span> <span class="pre">==</span> <span class="pre">&amp;--r</span></tt>.</p>
</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">r--</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">const</span> <span class="pre">X&amp;</span></tt></td>
<td><pre class="first last literal-block">
{
  X tmp = r;
  --r;
  return tmp;
}
</pre>
</td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
<td>Convertible to
<tt class="docutils literal"><span class="pre">bidirectional_traversal_tag</span></tt></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<!-- TR1: bidirectional_traversal_iterator_tag changed to
bidirectional_traversal_tag for consistency -->
</div>
<div class="section" id="random-access-traversal-iterators-lib-random-access-traversal-iterators">
<h4><a class="toc-backref" href="#id20">Random Access Traversal Iterators [lib.random.access.traversal.iterators]</a></h4>
<p>A class or built-in type <tt class="docutils 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="docutils literal"><span class="pre">Distance</span></tt> is
<tt class="docutils literal"><span class="pre">iterator_traits&lt;X&gt;::difference_type</span></tt> and <tt class="docutils literal"><span class="pre">n</span></tt> represents a
constant object of type <tt class="docutils literal"><span class="pre">Distance</span></tt>.</p>
<table border="1" class="docutils">
<colgroup>
<col width="28%" />
<col width="30%" />
<col width="23%" />
<col width="20%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="4">Random Access Traversal Iterator Requirements (in addition to Bidirectional Traversal Iterator)</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Operational Semantics</th>
<th class="head">Assertion/
Precondition</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">r</span> <span class="pre">+=</span> <span class="pre">n</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
<td><pre class="first last literal-block">
{
  Distance m = n;
  if (m &gt;= 0)
    while (m--)
      ++r;
  else
    while (m++)
      --r;
  return r;
}
</pre>
</td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">+</span> <span class="pre">n</span></tt>, <tt class="docutils literal"><span class="pre">n</span> <span class="pre">+</span> <span class="pre">a</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X</span></tt></td>
<td><tt class="docutils literal"><span class="pre">{</span> <span class="pre">X</span> <span class="pre">tmp</span> <span class="pre">=</span> <span class="pre">a;</span> <span class="pre">return</span> <span class="pre">tmp</span>
<span class="pre">+=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">r</span> <span class="pre">-=</span> <span class="pre">n</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
<td><tt class="docutils literal"><span class="pre">return</span> <span class="pre">r</span> <span class="pre">+=</span> <span class="pre">-n</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">-</span> <span class="pre">n</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X</span></tt></td>
<td><tt class="docutils literal"><span class="pre">{</span> <span class="pre">X</span> <span class="pre">tmp</span> <span class="pre">=</span> <span class="pre">a;</span> <span class="pre">return</span> <span class="pre">tmp</span>
<span class="pre">-=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">b</span> <span class="pre">-</span> <span class="pre">a</span></tt></td>
<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td>
<td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&lt;</span> <span class="pre">b</span> <span class="pre">?</span>&nbsp; <span class="pre">distance(a,b)</span>
<span class="pre">:</span> <span class="pre">-distance(b,a)</span></tt></td>
<td>pre: there exists a
value <tt class="docutils literal"><span class="pre">n</span></tt> of
<tt class="docutils literal"><span class="pre">Distance</span></tt> such that
<tt class="docutils literal"><span class="pre">a</span> <span class="pre">+</span> <span class="pre">n</span> <span class="pre">==</span> <span class="pre">b</span></tt>.  <tt class="docutils literal"><span class="pre">b</span>
<span class="pre">==</span> <span class="pre">a</span> <span class="pre">+</span> <span class="pre">(b</span> <span class="pre">-</span> <span class="pre">a)</span></tt>.</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a[n]</span></tt></td>
<td>convertible to T</td>
<td><tt class="docutils literal"><span class="pre">*(a</span> <span class="pre">+</span> <span class="pre">n)</span></tt></td>
<td>pre: a is a <a class="reference internal" href="#readable-iterator">Readable
Iterator</a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a[n]</span> <span class="pre">=</span> <span class="pre">v</span></tt></td>
<td>convertible to T</td>
<td><tt class="docutils literal"><span class="pre">*(a</span> <span class="pre">+</span> <span class="pre">n)</span> <span class="pre">=</span> <span class="pre">v</span></tt></td>
<td>pre: a is a <a class="reference internal" href="#writable-iterator">Writable
Iterator</a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&lt;</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">b</span> <span class="pre">-</span> <span class="pre">a</span> <span class="pre">&gt;</span> <span class="pre">0</span></tt></td>
<td><tt class="docutils literal"><span class="pre">&lt;</span></tt> is a total
ordering relation</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&gt;</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">b</span> <span class="pre">&lt;</span> <span class="pre">a</span></tt></td>
<td><tt class="docutils literal"><span class="pre">&gt;</span></tt> is a total
ordering relation</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&gt;=</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre">&lt;</span> <span class="pre">b)</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&lt;=</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre">&gt;</span> <span class="pre">b)</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
<td>Convertible to
<tt class="docutils literal"><span class="pre">random_access_traversal_tag</span></tt></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<!-- TR1: random_access_traversal_iterator_tag changed to
random_access_traversal_tag for consistency -->
</div>
<div class="section" id="interoperable-iterators-lib-interoperable-iterators">
<h4><a class="toc-backref" href="#id21">Interoperable Iterators [lib.interoperable.iterators]</a></h4>
<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> that models Single Pass Iterator is
<em>interoperable with</em> a class or built-in type <tt class="docutils literal"><span class="pre">Y</span></tt> that also models
Single Pass Iterator if the following expressions are valid and
respect the stated semantics. In the tables below, <tt class="docutils literal"><span class="pre">x</span></tt> is an object
of type <tt class="docutils literal"><span class="pre">X</span></tt>, <tt class="docutils literal"><span class="pre">y</span></tt> is an object of type <tt class="docutils literal"><span class="pre">Y</span></tt>, <tt class="docutils literal"><span class="pre">Distance</span></tt> is
<tt class="docutils literal"><span class="pre">iterator_traits&lt;Y&gt;::difference_type</span></tt>, and <tt class="docutils literal"><span class="pre">n</span></tt> represents a
constant object of type <tt class="docutils literal"><span class="pre">Distance</span></tt>.</p>
<table border="1" class="docutils">
<colgroup>
<col width="13%" />
<col width="27%" />
<col width="60%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Assertion/Precondition/Postcondition</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">=</span> <span class="pre">x</span></tt></td>
<td><tt class="docutils literal"><span class="pre">Y</span></tt></td>
<td>post: <tt class="docutils literal"><span class="pre">y</span> <span class="pre">==</span> <span class="pre">x</span></tt></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">Y(x)</span></tt></td>
<td><tt class="docutils literal"><span class="pre">Y</span></tt></td>
<td>post: <tt class="docutils literal"><span class="pre">Y(x)</span> <span class="pre">==</span> <span class="pre">x</span></tt></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">y</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">==</span></tt> is an equivalence relation over its domain.</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">==</span> <span class="pre">x</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">==</span></tt> is an equivalence relation over its domain.</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">!=</span> <span class="pre">y</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">bool(a==b)</span> <span class="pre">!=</span> <span class="pre">bool(a!=b)</span></tt> over its domain.</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">!=</span> <span class="pre">x</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">bool(a==b)</span> <span class="pre">!=</span> <span class="pre">bool(a!=b)</span></tt> over its domain.</td>
</tr>
</tbody>
</table>
<p>If <tt class="docutils literal"><span class="pre">X</span></tt> and <tt class="docutils literal"><span class="pre">Y</span></tt> both model Random Access Traversal Iterator then
the following additional requirements must be met.</p>
<table border="1" class="docutils">
<colgroup>
<col width="12%" />
<col width="25%" />
<col width="23%" />
<col width="41%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Operational Semantics</th>
<th class="head">Assertion/ Precondition</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&lt;</span> <span class="pre">y</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">-</span> <span class="pre">x</span> <span class="pre">&gt;</span> <span class="pre">0</span></tt></td>
<td><tt class="docutils literal"><span class="pre">&lt;</span></tt> is a total ordering relation</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&lt;</span> <span class="pre">x</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">-</span> <span class="pre">y</span> <span class="pre">&gt;</span> <span class="pre">0</span></tt></td>
<td><tt class="docutils literal"><span class="pre">&lt;</span></tt> is a total ordering relation</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&gt;</span> <span class="pre">y</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&lt;</span> <span class="pre">x</span></tt></td>
<td><tt class="docutils literal"><span class="pre">&gt;</span></tt> is a total ordering relation</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&gt;</span> <span class="pre">x</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&lt;</span> <span class="pre">y</span></tt></td>
<td><tt class="docutils literal"><span class="pre">&gt;</span></tt> is a total ordering relation</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&gt;=</span> <span class="pre">y</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">!(x</span> <span class="pre">&lt;</span> <span class="pre">y)</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&gt;=</span> <span class="pre">x</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">!(y</span> <span class="pre">&lt;</span> <span class="pre">x)</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&lt;=</span> <span class="pre">y</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">!(x</span> <span class="pre">&gt;</span> <span class="pre">y)</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&lt;=</span> <span class="pre">x</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">!(y</span> <span class="pre">&gt;</span> <span class="pre">x)</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">-</span> <span class="pre">x</span></tt></td>
<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td>
<td><tt class="docutils literal"><span class="pre">distance(Y(x),y)</span></tt></td>
<td>pre: there exists a value <tt class="docutils literal"><span class="pre">n</span></tt> of
<tt class="docutils literal"><span class="pre">Distance</span></tt> such that <tt class="docutils literal"><span class="pre">x</span> <span class="pre">+</span> <span class="pre">n</span> <span class="pre">==</span> <span class="pre">y</span></tt>.
<tt class="docutils literal"><span class="pre">y</span> <span class="pre">==</span> <span class="pre">x</span> <span class="pre">+</span> <span class="pre">(y</span> <span class="pre">-</span> <span class="pre">x)</span></tt>.</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">-</span> <span class="pre">y</span></tt></td>
<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td>
<td><tt class="docutils literal"><span class="pre">distance(y,Y(x))</span></tt></td>
<td>pre: there exists a value <tt class="docutils literal"><span class="pre">n</span></tt> of
<tt class="docutils literal"><span class="pre">Distance</span></tt> such that <tt class="docutils literal"><span class="pre">y</span> <span class="pre">+</span> <span class="pre">n</span> <span class="pre">==</span> <span class="pre">x</span></tt>.
<tt class="docutils literal"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">y</span> <span class="pre">+</span> <span class="pre">(x</span> <span class="pre">-</span> <span class="pre">y)</span></tt>.</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="section" id="addition-to-lib-iterator-synopsis">
<h2><a class="toc-backref" href="#id22">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;
template &lt;class Iterator&gt; struct iterator_traversal;

struct incrementable_traversal_tag { };
struct single_pass_traversal_tag : incrementable_traversal_tag { };
struct forward_traversal_tag : single_pass_traversal_tag { };
struct bidirectional_traversal_tag : forward_traversal_tag { };
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">Addition to [lib.iterator.traits]</a></h2>
<p>The <tt class="docutils literal"><span class="pre">is_readable_iterator</span></tt> class
template satisfies the <a class="reference external" href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003/n1519.htm">UnaryTypeTrait</a> requirements.</p>
<p>Given an iterator type <tt class="docutils literal"><span class="pre">X</span></tt>, <tt class="docutils literal"><span class="pre">is_readable_iterator&lt;X&gt;::value</span></tt>
yields <tt class="docutils literal"><span class="pre">true</span></tt> if, for an object <tt class="docutils literal"><span class="pre">a</span></tt> of type <tt class="docutils literal"><span class="pre">X</span></tt>, <tt class="docutils literal"><span class="pre">*a</span></tt> is
convertible to <tt class="docutils literal"><span class="pre">iterator_traits&lt;X&gt;::value_type</span></tt>, and <tt class="docutils literal"><span class="pre">false</span></tt>
otherwise.</p>
<p><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt> is</p>
<pre class="literal-block">
<em>category-to-traversal</em>(iterator_traits&lt;X&gt;::iterator_category)
</pre>
<p>where <em>category-to-traversal</em> is defined as follows</p>
<pre class="literal-block" id="category-to-traversal">
<em>category-to-traversal</em>(C) =
    if (C is convertible to incrementable_traversal_tag)
        return C;
    else if (C is convertible to random_access_iterator_tag)
        return random_access_traversal_tag;
    else if (C is convertible to bidirectional_iterator_tag)
        return bidirectional_traversal_tag;
    else if (C is convertible to forward_iterator_tag)
        return forward_traversal_tag;
    else if (C is convertible to input_iterator_tag)
        return single_pass_traversal_tag;
    else if (C is convertible to output_iterator_tag)
        return incrementable_traversal_tag;
    else
        <em>the program is ill-formed</em>
</pre>
</div>
</div>
<div class="section" id="footnotes">
<h1><a class="toc-backref" href="#id24">Footnotes</a></h1>
<p>The UnaryTypeTrait concept is defined in <a class="reference external" href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003/n1519.htm">n1519</a>; the LWG is
considering adding the requirement that specializations are derived
from their nested <tt class="docutils literal"><span class="pre">::type</span></tt>.</p>
<!-- LocalWords:  Abrahams Siek Witt const bool Sutter's WG int UL LI href Lvalue
LocalWords:  ReadableIterator WritableIterator SwappableIterator cv pre iter
LocalWords:  ConstantLvalueIterator MutableLvalueIterator CopyConstructible TR
LocalWords:  ForwardTraversalIterator BidirectionalTraversalIterator lvalue
LocalWords:  RandomAccessTraversalIterator dereferenceable Incrementable tmp
LocalWords:  incrementable xxx min prev inplace png oldeqnew AccessTag struct
LocalWords:  TraversalTag typename lvalues DWA Hmm JGS mis enum -->
</div>
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