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6<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
7<title>New Iterator Concepts</title>
8<meta name="author" content="David Abrahams, Jeremy Siek, Thomas Witt" />
9<meta name="organization" content="Boost Consulting, Indiana University Open Systems Lab, Zephyr Associates, Inc." />
10<meta name="date" content="2006-09-11" />
11<meta name="copyright" content="Copyright David Abrahams, Jeremy Siek, and Thomas Witt 2003." />
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13</head>
14<body>
15<div class="document" id="new-iterator-concepts">
16<h1 class="title">New Iterator Concepts</h1>
17<table class="docinfo" frame="void" rules="none">
18<col class="docinfo-name" />
19<col class="docinfo-content" />
20<tbody valign="top">
21<tr><th class="docinfo-name">Author:</th>
22<td>David Abrahams, Jeremy Siek, Thomas Witt</td></tr>
23<tr><th class="docinfo-name">Contact:</th>
24<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>
25<tr><th class="docinfo-name">Organization:</th>
26<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
27Lab</a>, <a class="last reference external" href="http://www.styleadvisor.com">Zephyr Associates, Inc.</a></td></tr>
28<tr><th class="docinfo-name">Date:</th>
29<td>2006-09-11</td></tr>
30<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://anubis.dkuug.dk/jtc1/sc22/wg21/docs/papers/2003/n1550.html">n1550</a>=03-0133, which was
31accepted for Technical Report 1 by the C++ standard
32committee's library working group. This proposal is a
33revision of paper <a class="reference external" href="http://anubis.dkuug.dk/jtc1/sc22/wg21/docs/papers/2001/n1297.html">n1297</a>, <a class="reference external" href="http://anubis.dkuug.dk/jtc1/sc22/wg21/docs/papers/2003/n1477.html">n1477</a>, and <a class="reference external" href="http://anubis.dkuug.dk/jtc1/sc22/wg21/docs/papers/2003/n1531.html">n1531</a>.</td>
34</tr>
35<tr><th class="docinfo-name">Copyright:</th>
36<td>Copyright David Abrahams, Jeremy Siek, and Thomas Witt
372003.</td></tr>
38</tbody>
39</table>
40<!-- Distributed under the Boost -->
41<!-- Software License, Version 1.0. (See accompanying -->
42<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
43<!-- Version 1.25 of this ReStructuredText document is the same as
44n1550_, the paper accepted by the LWG. -->
45<table class="docutils field-list" frame="void" rules="none">
46<col class="field-name" />
47<col class="field-body" />
48<tbody valign="top">
49<tr class="field"><th class="field-name">Abstract:</th><td class="field-body">We propose a new system of iterator concepts that treat
50access and positioning independently. This allows the
51concepts to more closely match the requirements
52of algorithms and provides better categorizations
53of iterators that are used in practice.</td>
54</tr>
55</tbody>
56</table>
57<div class="contents topic" id="table-of-contents">
58<p class="topic-title first">Table of Contents</p>
59<ul class="simple">
60<li><a class="reference internal" href="#motivation" id="id1">Motivation</a></li>
61<li><a class="reference internal" href="#impact-on-the-standard" id="id2">Impact on the Standard</a><ul>
62<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>
63<li><a class="reference internal" href="#changes-to-algorithm-requirements" id="id4">Changes to Algorithm Requirements</a></li>
64<li><a class="reference internal" href="#deprecations" id="id5">Deprecations</a></li>
65<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>
66</ul>
67</li>
68</ul>
69</li>
70<li><a class="reference internal" href="#design" id="id7">Design</a></li>
71<li><a class="reference internal" href="#proposed-text" id="id8">Proposed Text</a><ul>
72<li><a class="reference internal" href="#addition-to-lib-iterator-requirements" id="id9">Addition to [lib.iterator.requirements]</a><ul>
73<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>
74<li><a class="reference internal" href="#readable-iterators-lib-readable-iterators" id="id11">Readable Iterators [lib.readable.iterators]</a></li>
75<li><a class="reference internal" href="#writable-iterators-lib-writable-iterators" id="id12">Writable Iterators [lib.writable.iterators]</a></li>
76<li><a class="reference internal" href="#swappable-iterators-lib-swappable-iterators" id="id13">Swappable Iterators [lib.swappable.iterators]</a></li>
77<li><a class="reference internal" href="#lvalue-iterators-lib-lvalue-iterators" id="id14">Lvalue Iterators [lib.lvalue.iterators]</a></li>
78</ul>
79</li>
80<li><a class="reference internal" href="#iterator-traversal-concepts-lib-iterator-traversal" id="id15">Iterator Traversal Concepts [lib.iterator.traversal]</a><ul>
81<li><a class="reference internal" href="#incrementable-iterators-lib-incrementable-iterators" id="id16">Incrementable Iterators [lib.incrementable.iterators]</a></li>
82<li><a class="reference internal" href="#single-pass-iterators-lib-single-pass-iterators" id="id17">Single Pass Iterators [lib.single.pass.iterators]</a></li>
83<li><a class="reference internal" href="#forward-traversal-iterators-lib-forward-traversal-iterators" id="id18">Forward Traversal Iterators [lib.forward.traversal.iterators]</a></li>
84<li><a class="reference internal" href="#bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators" id="id19">Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]</a></li>
85<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>
86<li><a class="reference internal" href="#interoperable-iterators-lib-interoperable-iterators" id="id21">Interoperable Iterators [lib.interoperable.iterators]</a></li>
87</ul>
88</li>
89</ul>
90</li>
91<li><a class="reference internal" href="#addition-to-lib-iterator-synopsis" id="id22">Addition to [lib.iterator.synopsis]</a></li>
92<li><a class="reference internal" href="#addition-to-lib-iterator-traits" id="id23">Addition to [lib.iterator.traits]</a></li>
93</ul>
94</li>
95<li><a class="reference internal" href="#footnotes" id="id24">Footnotes</a></li>
96</ul>
97</div>
98<div class="section" id="motivation">
99<h1><a class="toc-backref" href="#id1">Motivation</a></h1>
100<p>The standard iterator categories and requirements are flawed because
101they use a single hierarchy of concepts to address two orthogonal
102issues: <em>iterator traversal</em> and <em>value access</em>. As a result, many
103algorithms with requirements expressed in terms of the iterator
104categories are too strict. Also, many real-world iterators can not be
105accurately categorized.  A proxy-based iterator with random-access
106traversal, for example, may only legally have a category of &quot;input
107iterator&quot;, so generic algorithms are unable to take advantage of its
108random-access capabilities.  The current iterator concept hierarchy is
109geared towards iterator traversal (hence the category names), while
110requirements that address value access sneak in at various places. The
111following table gives a summary of the current value access
112requirements in the iterator categories.</p>
113<table border="1" class="docutils">
114<colgroup>
115<col width="31%" />
116<col width="69%" />
117</colgroup>
118<thead valign="bottom">
119<tr><th class="head" colspan="2">Value Access Requirements in Existing Iterator Categories</th>
120</tr>
121</thead>
122<tbody valign="top">
123<tr><td>Output Iterator</td>
124<td><tt class="docutils literal"><span class="pre">*i</span> <span class="pre">=</span> <span class="pre">a</span></tt></td>
125</tr>
126<tr><td>Input Iterator</td>
127<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>
128</tr>
129<tr><td>Forward Iterator</td>
130<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://anubis.dkuug.dk/JTC1/SC22/WG21/docs/lwg-active.html#200">issue 200</a>
131is resolved)</td>
132</tr>
133<tr><td>Random Access Iterator</td>
134<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>
135is required for mutable iterators once <a class="reference external" href="http://anubis.dkuug.dk/JTC1/SC22/WG21/docs/lwg-active.html#299">issue 299</a>
136is resolved)</td>
137</tr>
138</tbody>
139</table>
140<p>Because iterator traversal and value access are mixed together in a
141single hierarchy, many useful iterators can not be appropriately
142categorized. For example, <tt class="docutils literal"><span class="pre">vector&lt;bool&gt;::iterator</span></tt> is almost a
143random access iterator, but the return type is not <tt class="docutils literal"><span class="pre">bool&amp;</span></tt> (see
144<a class="reference external" href="http://anubis.dkuug.dk/JTC1/SC22/WG21/docs/lwg-active.html#96">issue 96</a> and Herb Sutter's paper J16/99-0008 = WG21
145N1185). Therefore, the iterators of <tt class="docutils literal"><span class="pre">vector&lt;bool&gt;</span></tt> only meet the
146requirements of input iterator and output iterator.  This is so
147nonintuitive that the C++ standard contradicts itself on this point.
148In paragraph 23.2.4/1 it says that a <tt class="docutils literal"><span class="pre">vector</span></tt> is a sequence that
149supports random access iterators.</p>
150<p>Another difficult-to-categorize iterator is the transform iterator, an
151adaptor which applies a unary function object to the dereferenced
152value of the some underlying iterator (see <a class="reference external" href="http://www.boost.org/libs/utility/transform_iterator.htm">transform_iterator</a>).
153For unary functions such as <tt class="docutils literal"><span class="pre">times</span></tt>, the return type of
154<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
155object, which is typically not a reference.  Because random access
156iterators are required to return lvalues from <tt class="docutils literal"><span class="pre">operator*</span></tt>, if you
157wrap <tt class="docutils literal"><span class="pre">int*</span></tt> with a transform iterator, you do not get a random
158access iterator as might be expected, but an input iterator.</p>
159<p>A third example is found in the vertex and edge iterators of the
160<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
161descriptors, which are lightweight handles created on-the-fly. They
162must be returned by-value. As a result, their current standard
163iterator category is <tt class="docutils literal"><span class="pre">input_iterator_tag</span></tt>, which means that,
164strictly speaking, you could not use these iterators with algorithms
165like <tt class="docutils literal"><span class="pre">min_element()</span></tt>. As a temporary solution, the concept
166<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
167edge descriptors, but as the design notes for the concept suggest, a
168better solution is needed.</p>
169<p>In short, there are many useful iterators that do not fit into the
170current standard iterator categories. As a result, the following bad
171things happen:</p>
172<ul class="simple">
173<li>Iterators are often mis-categorized.</li>
174<li>Algorithm requirements are more strict than necessary, because they
175cannot separate the need for random access or bidirectional
176traversal from the need for a true reference return type.</li>
177</ul>
178</div>
179<div class="section" id="impact-on-the-standard">
180<h1><a class="toc-backref" href="#id2">Impact on the Standard</a></h1>
181<p>This proposal for TR1 is a pure extension. Further, the new iterator
182concepts are backward-compatible with the old iterator requirements,
183and old iterators are forward-compatible with the new iterator
184concepts. That is to say, iterators that satisfy the old requirements
185also satisfy appropriate concepts in the new system, and iterators
186modeling the new concepts will automatically satisfy the appropriate
187old requirements.</p>
188<!-- I think we need to say something about the resolution to allow
189convertibility to any of the old-style tags as a TR issue (hope it
190made it). -DWA -->
191<!-- Hmm, not sure I understand. Are you talking about whether a
192standards conforming input iterator is allowed to have
193a tag that is not input_iterator_tag but that
194is convertible to input_iterator_tag? -JGS -->
195<div class="section" id="possible-but-not-proposed-changes-to-the-working-paper">
196<h2><a class="toc-backref" href="#id3">Possible (but not proposed) Changes to the Working Paper</a></h2>
197<p>The extensions in this paper suggest several changes we might make
198to the working paper for the next standard.  These changes are not
199a formal part of this proposal for TR1.</p>
200<div class="section" id="changes-to-algorithm-requirements">
201<h3><a class="toc-backref" href="#id4">Changes to Algorithm Requirements</a></h3>
202<p>The algorithms in the standard library could benefit from the new
203iterator concepts because the new concepts provide a more accurate way
204to express their type requirements. The result is algorithms that are
205usable in more situations and have fewer type requirements.</p>
206<p>For the next working paper (but not for TR1), the committee should
207consider the following changes to the type requirements of algorithms.
208These changes are phrased as textual substitutions, listing the
209algorithms to which each textual substitution applies.</p>
210<p>Forward Iterator -&gt; Forward Traversal Iterator and Readable Iterator</p>
211<blockquote>
212<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>
213<span class="pre">lower_bound,</span> <span class="pre">upper_bound,</span> <span class="pre">equal_range,</span> <span class="pre">binary_search,</span>
214<span class="pre">min_element,</span> <span class="pre">max_element</span></tt></blockquote>
215<p>Forward Iterator (1) -&gt; Single Pass Iterator and Readable Iterator,
216Forward Iterator (2) -&gt; Forward Traversal Iterator and Readable Iterator</p>
217<blockquote>
218<tt class="docutils literal"><span class="pre">find_first_of</span></tt></blockquote>
219<p>Forward Iterator -&gt; Readable Iterator and Writable Iterator</p>
220<blockquote>
221<tt class="docutils literal"><span class="pre">iter_swap</span></tt></blockquote>
222<p>Forward Iterator -&gt; Single Pass Iterator and Writable Iterator</p>
223<blockquote>
224<tt class="docutils literal"><span class="pre">fill,</span> <span class="pre">generate</span></tt></blockquote>
225<p>Forward Iterator -&gt; Forward Traversal Iterator and Swappable Iterator</p>
226<blockquote>
227<tt class="docutils literal"><span class="pre">rotate</span></tt></blockquote>
228<p>Forward Iterator (1) -&gt; Swappable Iterator and Single Pass Iterator,
229Forward Iterator (2) -&gt; Swappable Iterator and  Incrementable Iterator</p>
230<blockquote>
231<tt class="docutils literal"><span class="pre">swap_ranges</span></tt></blockquote>
232<dl class="docutils">
233<dt>Forward Iterator -&gt; Forward Traversal Iterator and Readable Iterator and Writable Iterator</dt>
234<dd><tt class="docutils literal"><span class="pre">remove,</span> <span class="pre">remove_if,</span> <span class="pre">unique</span></tt></dd>
235</dl>
236<p>Forward Iterator -&gt; Single Pass Iterator and Readable Iterator and Writable Iterator</p>
237<blockquote>
238<tt class="docutils literal"><span class="pre">replace,</span> <span class="pre">replace_if</span></tt></blockquote>
239<dl class="docutils">
240<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Swappable Iterator</dt>
241<dd><tt class="docutils literal"><span class="pre">reverse</span></tt></dd>
242<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Readable and Swappable Iterator</dt>
243<dd><tt class="docutils literal"><span class="pre">partition</span></tt></dd>
244</dl>
245<p>Bidirectional Iterator (1) -&gt; Bidirectional Traversal Iterator and Readable Iterator,
246Bidirectional Iterator (2) -&gt; Bidirectional Traversal Iterator and Writable Iterator</p>
247<blockquote>
248<tt class="docutils literal"><span class="pre">copy_backwards</span></tt></blockquote>
249<dl class="docutils">
250<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Swappable Iterator and Readable Iterator</dt>
251<dd><tt class="docutils literal"><span class="pre">next_permutation,</span> <span class="pre">prev_permutation</span></tt></dd>
252<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Readable Iterator and Writable Iterator</dt>
253<dd><tt class="docutils literal"><span class="pre">stable_partition,</span> <span class="pre">inplace_merge</span></tt></dd>
254<dt>Bidirectional Iterator -&gt; Bidirectional Traversal Iterator and Readable Iterator</dt>
255<dd><tt class="docutils literal"><span class="pre">reverse_copy</span></tt></dd>
256<dt>Random Access Iterator -&gt; Random Access Traversal Iterator and Readable and Writable Iterator</dt>
257<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>
258<span class="pre">make_heap,</span> <span class="pre">sort_heap</span></tt></dd>
259<dt>Input Iterator (2) -&gt; Incrementable Iterator and Readable Iterator</dt>
260<dd><tt class="docutils literal"><span class="pre">equal,</span> <span class="pre">mismatch</span></tt></dd>
261<dt>Input Iterator (2) -&gt; Incrementable Iterator and Readable Iterator</dt>
262<dd><tt class="docutils literal"><span class="pre">transform</span></tt></dd>
263</dl>
264</div>
265<div class="section" id="deprecations">
266<h3><a class="toc-backref" href="#id5">Deprecations</a></h3>
267<p>For the next working paper (but not for TR1), the committee should
268consider deprecating the old iterator tags, and
269std::iterator_traits, since it will be superceded by individual
270traits metafunctions.</p>
271</div>
272<div class="section" id="vector-bool">
273<h3><a class="toc-backref" href="#id6"><tt class="docutils literal"><span class="pre">vector&lt;bool&gt;</span></tt></a></h3>
274<p>For the next working paper (but not for TR1), the committee should
275consider reclassifying <tt class="docutils literal"><span class="pre">vector&lt;bool&gt;::iterator</span></tt> as a Random
276Access Traversal Iterator and Readable Iterator and Writable
277Iterator.</p>
278</div>
279</div>
280</div>
281<div class="section" id="design">
282<h1><a class="toc-backref" href="#id7">Design</a></h1>
283<p>The iterator requirements are to be separated into two groups. One set
284of concepts handles the syntax and semantics of value access:</p>
285<ul class="simple">
286<li>Readable Iterator</li>
287<li>Writable Iterator</li>
288<li>Swappable Iterator</li>
289<li>Lvalue Iterator</li>
290</ul>
291<p>The access concepts describe requirements related to <tt class="docutils literal"><span class="pre">operator*</span></tt> and
292<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
293<tt class="docutils literal"><span class="pre">pointer</span></tt> associated types.</p>
294<p>The other set of concepts handles traversal:</p>
295<ul class="simple">
296<li>Incrementable Iterator</li>
297<li>Single Pass Iterator</li>
298<li>Forward Traversal Iterator</li>
299<li>Bidirectional Traversal Iterator</li>
300<li>Random Access Traversal Iterator</li>
301</ul>
302<p>The refinement relationships for the traversal concepts are in the
303following diagram.</p>
304<img alt="traversal.png" src="traversal.png" />
305<p>In addition to the iterator movement operators, such as
306<tt class="docutils literal"><span class="pre">operator++</span></tt>, the traversal concepts also include requirements on
307position 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
308reason for the fine grain slicing of the concepts into the
309Incrementable and Single Pass is to provide concepts that are exact
310matches with the original input and output iterator requirements.</p>
311<p>This proposal also includes a concept for specifying when an iterator
312is interoperable with another iterator, in the sense that <tt class="docutils literal"><span class="pre">int*</span></tt> is
313interoperable with <tt class="docutils literal"><span class="pre">int</span> <span class="pre">const*</span></tt>.</p>
314<ul class="simple">
315<li>Interoperable Iterators</li>
316</ul>
317<p>The relationship between the new iterator concepts and the old are
318given in the following diagram.</p>
319<img alt="oldeqnew.png" src="oldeqnew.png" />
320<p>Like the old iterator requirements, we provide tags for purposes of
321dispatching based on the traversal concepts.  The tags are related via
322inheritance so that a tag is convertible to another tag if the concept
323associated with the first tag is a refinement of the second tag.</p>
324<p>Our design reuses <tt class="docutils literal"><span class="pre">iterator_traits&lt;Iter&gt;::iterator_category</span></tt> to
325indicate an iterator's traversal capability.  To specify
326capabilities not captured by any old-style iterator category, an
327iterator designer can use an <tt class="docutils literal"><span class="pre">iterator_category</span></tt> type that is
328convertible to both the the most-derived old iterator category tag
329which fits, and the appropriate new iterator traversal tag.</p>
330<!-- dwa2003/1/2: Note that we are not *requiring* convertibility to
331a new-style traversal tag in order to meet new concepts.
332Old-style iterators still fit, after all. -->
333<p>We do not provide tags for the purposes of dispatching based on the
334access concepts, in part because we could not find a way to
335automatically infer the right access tags for old-style iterators.
336An iterator's writability may be dependent on the assignability of
337its <tt class="docutils literal"><span class="pre">value_type</span></tt> and there's no known way to detect whether an
338arbitrary type is assignable.  Fortunately, the need for
339dispatching based on access capability is not as great as the need
340for dispatching based on traversal capability.</p>
341<p>A difficult design decision concerned the <tt class="docutils literal"><span class="pre">operator[]</span></tt>. The direct
342approach for specifying <tt class="docutils literal"><span class="pre">operator[]</span></tt> would have a return type of
343<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
344direction would mean that an iterator satisfying the old Random Access
345Iterator requirements would not necessarily be a model of Readable or
346Writable Lvalue Iterator.  Instead we have chosen a design that
347matches the preferred resolution of <a class="reference external" href="http://anubis.dkuug.dk/JTC1/SC22/WG21/docs/lwg-active.html#299">issue 299</a>: <tt class="docutils literal"><span class="pre">operator[]</span></tt> is
348only required to return something convertible to the <tt class="docutils literal"><span class="pre">value_type</span></tt>
349(for a Readable Iterator), and is required to support assignment
350<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>
351</div>
352<div class="section" id="proposed-text">
353<h1><a class="toc-backref" href="#id8">Proposed Text</a></h1>
354<div class="section" id="addition-to-lib-iterator-requirements">
355<h2><a class="toc-backref" href="#id9">Addition to [lib.iterator.requirements]</a></h2>
356<div class="section" id="iterator-value-access-concepts-lib-iterator-value-access">
357<h3><a class="toc-backref" href="#id10">Iterator Value Access Concepts [lib.iterator.value.access]</a></h3>
358<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
359object of type <tt class="docutils literal"><span class="pre">X</span></tt>, <tt class="docutils literal"><span class="pre">R</span></tt> is
360<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
361<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
362object of type <tt class="docutils literal"><span class="pre">T</span></tt>.</p>
363<div class="section" id="readable-iterators-lib-readable-iterators">
364<span id="readable-iterator"></span><h4><a class="toc-backref" href="#id11">Readable Iterators [lib.readable.iterators]</a></h4>
365<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Readable Iterator</em> concept
366for 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
367Copy Constructible, the following expressions are valid and respect
368the stated semantics. <tt class="docutils literal"><span class="pre">U</span></tt> is the type of any specified member of
369type <tt class="docutils literal"><span class="pre">T</span></tt>.</p>
370<table border="1" class="docutils">
371<colgroup>
372<col width="28%" />
373<col width="20%" />
374<col width="52%" />
375</colgroup>
376<thead valign="bottom">
377<tr><th class="head" colspan="3">Readable Iterator Requirements (in addition to Assignable and Copy Constructible)</th>
378</tr>
379<tr><th class="head">Expression</th>
380<th class="head">Return Type</th>
381<th class="head">Note/Precondition</th>
382</tr>
383</thead>
384<tbody valign="top">
385<tr><td><tt class="docutils literal"><span class="pre">iterator_traits&lt;X&gt;::value_type</span></tt></td>
386<td><tt class="docutils literal"><span class="pre">T</span></tt></td>
387<td>Any non-reference,
388non-cv-qualified type</td>
389</tr>
390<tr><td><tt class="docutils literal"><span class="pre">*a</span></tt></td>
391<td>Convertible to <tt class="docutils literal"><span class="pre">T</span></tt></td>
392<td><dl class="first last docutils">
393<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>
394<dd>is equivalent to <tt class="docutils literal"><span class="pre">*b</span></tt>.</dd>
395</dl>
396</td>
397</tr>
398<tr><td><tt class="docutils literal"><span class="pre">a-&gt;m</span></tt></td>
399<td><tt class="docutils literal"><span class="pre">U&amp;</span></tt></td>
400<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>
401</tr>
402</tbody>
403</table>
404<!-- We won't say anything about iterator_traits<X>::reference until the DR is resolved. -JGS -->
405</div>
406<div class="section" id="writable-iterators-lib-writable-iterators">
407<span id="writable-iterator"></span><h4><a class="toc-backref" href="#id12">Writable Iterators [lib.writable.iterators]</a></h4>
408<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Writable Iterator</em> concept
409if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> being Copy Constructible, the following
410expressions are valid and respect the stated semantics.  Writable
411Iterators have an associated <em>set of value types</em>.</p>
412<table border="1" class="docutils">
413<colgroup>
414<col width="37%" />
415<col width="21%" />
416<col width="42%" />
417</colgroup>
418<thead valign="bottom">
419<tr><th class="head" colspan="3">Writable Iterator Requirements (in addition to Copy Constructible)</th>
420</tr>
421<tr><th class="head">Expression</th>
422<th class="head">Return Type</th>
423<th class="head">Precondition</th>
424</tr>
425</thead>
426<tbody valign="top">
427<tr><td><tt class="docutils literal"><span class="pre">*a</span> <span class="pre">=</span> <span class="pre">o</span></tt></td>
428<td>&nbsp;</td>
429<td>pre: The type of <tt class="docutils literal"><span class="pre">o</span></tt>
430is in the set of
431value types of <tt class="docutils literal"><span class="pre">X</span></tt></td>
432</tr>
433</tbody>
434</table>
435</div>
436<div class="section" id="swappable-iterators-lib-swappable-iterators">
437<h4><a class="toc-backref" href="#id13">Swappable Iterators [lib.swappable.iterators]</a></h4>
438<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Swappable Iterator</em> concept
439if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> being Copy Constructible, the following
440expressions are valid and respect the stated semantics.</p>
441<table border="1" class="docutils">
442<colgroup>
443<col width="37%" />
444<col width="19%" />
445<col width="43%" />
446</colgroup>
447<thead valign="bottom">
448<tr><th class="head" colspan="3">Swappable Iterator Requirements (in addition to Copy Constructible)</th>
449</tr>
450<tr><th class="head">Expression</th>
451<th class="head">Return Type</th>
452<th class="head">Postcondition</th>
453</tr>
454</thead>
455<tbody valign="top">
456<tr><td><tt class="docutils literal"><span class="pre">iter_swap(a,</span> <span class="pre">b)</span></tt></td>
457<td><tt class="docutils literal"><span class="pre">void</span></tt></td>
458<td>the pointed to values are
459exchanged</td>
460</tr>
461</tbody>
462</table>
463<p>[<em>Note:</em> An iterator that is a model of the <a class="reference internal" href="#readable-iterator">Readable Iterator</a> and
464<a class="reference internal" href="#writable-iterator">Writable Iterator</a> concepts is also a model of <em>Swappable
465Iterator</em>.  <em>--end note</em>]</p>
466</div>
467<div class="section" id="lvalue-iterators-lib-lvalue-iterators">
468<h4><a class="toc-backref" href="#id14">Lvalue Iterators [lib.lvalue.iterators]</a></h4>
469<p>The <em>Lvalue Iterator</em> concept adds the requirement that the return
470type of <tt class="docutils literal"><span class="pre">operator*</span></tt> type be a reference to the value type of the
471iterator.</p>
472<table border="1" class="docutils">
473<colgroup>
474<col width="22%" />
475<col width="19%" />
476<col width="59%" />
477</colgroup>
478<thead valign="bottom">
479<tr><th class="head" colspan="3">Lvalue Iterator Requirements</th>
480</tr>
481<tr><th class="head">Expression</th>
482<th class="head">Return Type</th>
483<th class="head">Note/Assertion</th>
484</tr>
485</thead>
486<tbody valign="top">
487<tr><td><tt class="docutils literal"><span class="pre">*a</span></tt></td>
488<td><tt class="docutils literal"><span class="pre">T&amp;</span></tt></td>
489<td><tt class="docutils literal"><span class="pre">T</span></tt> is <em>cv</em>
490<tt class="docutils literal"><span class="pre">iterator_traits&lt;X&gt;::value_type</span></tt>
491where <em>cv</em> is an optional
492cv-qualification.  pre: <tt class="docutils literal"><span class="pre">a</span></tt> is
493dereferenceable.</td>
494</tr>
495</tbody>
496</table>
497<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
498<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
499Iterator</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
500<tt class="docutils literal"><span class="pre">*b</span></tt>.</p>
501</div>
502</div>
503<div class="section" id="iterator-traversal-concepts-lib-iterator-traversal">
504<h3><a class="toc-backref" href="#id15">Iterator Traversal Concepts [lib.iterator.traversal]</a></h3>
505<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
506constant 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
507type <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
508<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>
509<div class="section" id="incrementable-iterators-lib-incrementable-iterators">
510<h4><a class="toc-backref" href="#id16">Incrementable Iterators [lib.incrementable.iterators]</a></h4>
511<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Incrementable Iterator</em>
512concept if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> being Assignable and Copy
513Constructible, the following expressions are valid and respect the
514stated semantics.</p>
515<table border="1" class="docutils">
516<colgroup>
517<col width="39%" />
518<col width="38%" />
519<col width="23%" />
520</colgroup>
521<thead valign="bottom">
522<tr><th class="head" colspan="3">Incrementable Iterator Requirements (in addition to Assignable, Copy Constructible)</th>
523</tr>
524<tr><th class="head">Expression</th>
525<th class="head">Return Type</th>
526<th class="head">Assertion</th>
527</tr>
528</thead>
529<tbody valign="top">
530<tr><td><tt class="docutils literal"><span class="pre">++r</span></tt></td>
531<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
532<td><tt class="docutils literal"><span class="pre">&amp;r</span> <span class="pre">==</span> <span class="pre">&amp;++r</span></tt></td>
533</tr>
534<tr><td><tt class="docutils literal"><span class="pre">r++</span></tt></td>
535<td>&nbsp;</td>
536<td>&nbsp;</td>
537</tr>
538<tr><td><tt class="docutils literal"><span class="pre">*r++</span></tt></td>
539<td>&nbsp;</td>
540<td>&nbsp;</td>
541</tr>
542<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
543<td>Convertible to
544<tt class="docutils literal"><span class="pre">incrementable_traversal_tag</span></tt></td>
545<td>&nbsp;</td>
546</tr>
547</tbody>
548</table>
549<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
550to <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
551to  <tt class="docutils literal"><span class="pre">*r</span> <span class="pre">=</span> <span class="pre">o;</span> <span class="pre">++r</span></tt>.
552If <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
553to <tt class="docutils literal"><span class="pre">T</span> <span class="pre">z(*r);</span> <span class="pre">++r;</span></tt>.</p>
554<!-- TR1: incrementable_iterator_tag changed to
555incrementable_traversal_tag for consistency. -->
556</div>
557<div class="section" id="single-pass-iterators-lib-single-pass-iterators">
558<h4><a class="toc-backref" href="#id17">Single Pass Iterators [lib.single.pass.iterators]</a></h4>
559<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Single Pass Iterator</em>
560concept if the following expressions are valid and respect the stated
561semantics.</p>
562<table border="1" class="docutils">
563<colgroup>
564<col width="32%" />
565<col width="29%" />
566<col width="13%" />
567<col width="27%" />
568</colgroup>
569<thead valign="bottom">
570<tr><th class="head" colspan="4">Single Pass Iterator Requirements (in addition to Incrementable Iterator and Equality
571Comparable)</th>
572</tr>
573<tr><th class="head">Expression</th>
574<th class="head">Return Type</th>
575<th class="head">Operational
576Semantics</th>
577<th class="head">Assertion/
578Pre-/Post-condition</th>
579</tr>
580</thead>
581<tbody valign="top">
582<tr><td><tt class="docutils literal"><span class="pre">++r</span></tt></td>
583<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
584<td>&nbsp;</td>
585<td>pre: <tt class="docutils literal"><span class="pre">r</span></tt> is
586dereferenceable; post:
587<tt class="docutils literal"><span class="pre">r</span></tt> is dereferenceable or
588<tt class="docutils literal"><span class="pre">r</span></tt> is past-the-end</td>
589</tr>
590<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">==</span> <span class="pre">b</span></tt></td>
591<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
592<td>&nbsp;</td>
593<td><tt class="docutils literal"><span class="pre">==</span></tt> is an equivalence
594relation over its domain</td>
595</tr>
596<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">!=</span> <span class="pre">b</span></tt></td>
597<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
598<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre">==</span> <span class="pre">b)</span></tt></td>
599<td>&nbsp;</td>
600</tr>
601<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
602<td>Convertible to
603<tt class="docutils literal"><span class="pre">single_pass_traversal_tag</span></tt></td>
604<td>&nbsp;</td>
605<td>&nbsp;</td>
606</tr>
607</tbody>
608</table>
609<!-- TR1: single_pass_iterator_tag changed to
610single_pass_traversal_tag for consistency -->
611</div>
612<div class="section" id="forward-traversal-iterators-lib-forward-traversal-iterators">
613<h4><a class="toc-backref" href="#id18">Forward Traversal Iterators [lib.forward.traversal.iterators]</a></h4>
614<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Forward Traversal Iterator</em>
615concept if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> meeting the requirements of Default
616Constructible and Single Pass Iterator, the following expressions are
617valid and respect the stated semantics.</p>
618<table border="1" class="docutils">
619<colgroup>
620<col width="38%" />
621<col width="34%" />
622<col width="27%" />
623</colgroup>
624<thead valign="bottom">
625<tr><th class="head" colspan="3">Forward Traversal Iterator Requirements (in addition to Default Constructible and Single Pass Iterator)</th>
626</tr>
627<tr><th class="head">Expression</th>
628<th class="head">Return Type</th>
629<th class="head">Assertion/Note</th>
630</tr>
631</thead>
632<tbody valign="top">
633<tr><td><tt class="docutils literal"><span class="pre">X</span> <span class="pre">u;</span></tt></td>
634<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
635<td>note: <tt class="docutils literal"><span class="pre">u</span></tt> may have a
636singular value.</td>
637</tr>
638<tr><td><tt class="docutils literal"><span class="pre">++r</span></tt></td>
639<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
640<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
641dereferenceable implies
642<tt class="docutils literal"><span class="pre">++r</span> <span class="pre">==</span> <span class="pre">++s.</span></tt></td>
643</tr>
644<tr><td><tt class="docutils literal"><span class="pre">iterator_traits&lt;X&gt;::difference_type</span></tt></td>
645<td>A signed integral type representing
646the distance between iterators</td>
647<td>&nbsp;</td>
648</tr>
649<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
650<td>Convertible to
651<tt class="docutils literal"><span class="pre">forward_traversal_tag</span></tt></td>
652<td>&nbsp;</td>
653</tr>
654</tbody>
655</table>
656<!-- TR1: forward_traversal_iterator_tag changed to
657forward_traversal_tag for consistency -->
658</div>
659<div class="section" id="bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators">
660<h4><a class="toc-backref" href="#id19">Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]</a></h4>
661<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Bidirectional Traversal
662Iterator</em> concept if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> meeting the requirements of
663Forward Traversal Iterator, the following expressions are valid and
664respect the stated semantics.</p>
665<table border="1" class="docutils">
666<colgroup>
667<col width="33%" />
668<col width="32%" />
669<col width="14%" />
670<col width="21%" />
671</colgroup>
672<thead valign="bottom">
673<tr><th class="head" colspan="4">Bidirectional Traversal Iterator Requirements (in addition to Forward Traversal
674Iterator)</th>
675</tr>
676<tr><th class="head">Expression</th>
677<th class="head">Return Type</th>
678<th class="head">Operational
679Semantics</th>
680<th class="head">Assertion/
681Pre-/Post-condition</th>
682</tr>
683</thead>
684<tbody valign="top">
685<tr><td><tt class="docutils literal"><span class="pre">--r</span></tt></td>
686<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
687<td>&nbsp;</td>
688<td><p class="first">pre: there exists
689<tt class="docutils literal"><span class="pre">s</span></tt> such that <tt class="docutils literal"><span class="pre">r</span>
690<span class="pre">==</span> <span class="pre">++s</span></tt>.  post:
691<tt class="docutils literal"><span class="pre">s</span></tt> is
692dereferenceable.</p>
693<p class="last"><tt class="docutils literal"><span class="pre">++(--r)</span> <span class="pre">==</span> <span class="pre">r</span></tt>.
694<tt class="docutils literal"><span class="pre">--r</span> <span class="pre">==</span> <span class="pre">--s</span></tt>
695implies <tt class="docutils literal"><span class="pre">r</span> <span class="pre">==</span>
696<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>
697</td>
698</tr>
699<tr><td><tt class="docutils literal"><span class="pre">r--</span></tt></td>
700<td>convertible to <tt class="docutils literal"><span class="pre">const</span> <span class="pre">X&amp;</span></tt></td>
701<td><pre class="first last literal-block">
702{
703  X tmp = r;
704  --r;
705  return tmp;
706}
707</pre>
708</td>
709<td>&nbsp;</td>
710</tr>
711<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
712<td>Convertible to
713<tt class="docutils literal"><span class="pre">bidirectional_traversal_tag</span></tt></td>
714<td>&nbsp;</td>
715<td>&nbsp;</td>
716</tr>
717</tbody>
718</table>
719<!-- TR1: bidirectional_traversal_iterator_tag changed to
720bidirectional_traversal_tag for consistency -->
721</div>
722<div class="section" id="random-access-traversal-iterators-lib-random-access-traversal-iterators">
723<h4><a class="toc-backref" href="#id20">Random Access Traversal Iterators [lib.random.access.traversal.iterators]</a></h4>
724<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Random Access Traversal
725Iterator</em> concept if the following expressions are valid and respect
726the stated semantics.  In the table below, <tt class="docutils literal"><span class="pre">Distance</span></tt> is
727<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
728constant object of type <tt class="docutils literal"><span class="pre">Distance</span></tt>.</p>
729<table border="1" class="docutils">
730<colgroup>
731<col width="28%" />
732<col width="30%" />
733<col width="23%" />
734<col width="20%" />
735</colgroup>
736<thead valign="bottom">
737<tr><th class="head" colspan="4">Random Access Traversal Iterator Requirements (in addition to Bidirectional Traversal Iterator)</th>
738</tr>
739<tr><th class="head">Expression</th>
740<th class="head">Return Type</th>
741<th class="head">Operational Semantics</th>
742<th class="head">Assertion/
743Precondition</th>
744</tr>
745</thead>
746<tbody valign="top">
747<tr><td><tt class="docutils literal"><span class="pre">r</span> <span class="pre">+=</span> <span class="pre">n</span></tt></td>
748<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
749<td><pre class="first last literal-block">
750{
751  Distance m = n;
752  if (m &gt;= 0)
753    while (m--)
754      ++r;
755  else
756    while (m++)
757      --r;
758  return r;
759}
760</pre>
761</td>
762<td>&nbsp;</td>
763</tr>
764<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>
765<td><tt class="docutils literal"><span class="pre">X</span></tt></td>
766<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>
767<span class="pre">+=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td>
768<td>&nbsp;</td>
769</tr>
770<tr><td><tt class="docutils literal"><span class="pre">r</span> <span class="pre">-=</span> <span class="pre">n</span></tt></td>
771<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
772<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>
773<td>&nbsp;</td>
774</tr>
775<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">-</span> <span class="pre">n</span></tt></td>
776<td><tt class="docutils literal"><span class="pre">X</span></tt></td>
777<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>
778<span class="pre">-=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td>
779<td>&nbsp;</td>
780</tr>
781<tr><td><tt class="docutils literal"><span class="pre">b</span> <span class="pre">-</span> <span class="pre">a</span></tt></td>
782<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td>
783<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>
784<span class="pre">:</span> <span class="pre">-distance(b,a)</span></tt></td>
785<td>pre: there exists a
786value <tt class="docutils literal"><span class="pre">n</span></tt> of
787<tt class="docutils literal"><span class="pre">Distance</span></tt> such that
788<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>
789<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>
790</tr>
791<tr><td><tt class="docutils literal"><span class="pre">a[n]</span></tt></td>
792<td>convertible to T</td>
793<td><tt class="docutils literal"><span class="pre">*(a</span> <span class="pre">+</span> <span class="pre">n)</span></tt></td>
794<td>pre: a is a <a class="reference internal" href="#readable-iterator">Readable
795Iterator</a></td>
796</tr>
797<tr><td><tt class="docutils literal"><span class="pre">a[n]</span> <span class="pre">=</span> <span class="pre">v</span></tt></td>
798<td>convertible to T</td>
799<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>
800<td>pre: a is a <a class="reference internal" href="#writable-iterator">Writable
801Iterator</a></td>
802</tr>
803<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&lt;</span> <span class="pre">b</span></tt></td>
804<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
805<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>
806<td><tt class="docutils literal"><span class="pre">&lt;</span></tt> is a total
807ordering relation</td>
808</tr>
809<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&gt;</span> <span class="pre">b</span></tt></td>
810<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
811<td><tt class="docutils literal"><span class="pre">b</span> <span class="pre">&lt;</span> <span class="pre">a</span></tt></td>
812<td><tt class="docutils literal"><span class="pre">&gt;</span></tt> is a total
813ordering relation</td>
814</tr>
815<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&gt;=</span> <span class="pre">b</span></tt></td>
816<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
817<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre">&lt;</span> <span class="pre">b)</span></tt></td>
818<td>&nbsp;</td>
819</tr>
820<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&lt;=</span> <span class="pre">b</span></tt></td>
821<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
822<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre">&gt;</span> <span class="pre">b)</span></tt></td>
823<td>&nbsp;</td>
824</tr>
825<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
826<td>Convertible to
827<tt class="docutils literal"><span class="pre">random_access_traversal_tag</span></tt></td>
828<td>&nbsp;</td>
829<td>&nbsp;</td>
830</tr>
831</tbody>
832</table>
833<!-- TR1: random_access_traversal_iterator_tag changed to
834random_access_traversal_tag for consistency -->
835</div>
836<div class="section" id="interoperable-iterators-lib-interoperable-iterators">
837<h4><a class="toc-backref" href="#id21">Interoperable Iterators [lib.interoperable.iterators]</a></h4>
838<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> that models Single Pass Iterator is
839<em>interoperable with</em> a class or built-in type <tt class="docutils literal"><span class="pre">Y</span></tt> that also models
840Single Pass Iterator if the following expressions are valid and
841respect the stated semantics. In the tables below, <tt class="docutils literal"><span class="pre">x</span></tt> is an object
842of 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
843<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
844constant object of type <tt class="docutils literal"><span class="pre">Distance</span></tt>.</p>
845<table border="1" class="docutils">
846<colgroup>
847<col width="13%" />
848<col width="27%" />
849<col width="60%" />
850</colgroup>
851<thead valign="bottom">
852<tr><th class="head">Expression</th>
853<th class="head">Return Type</th>
854<th class="head">Assertion/Precondition/Postcondition</th>
855</tr>
856</thead>
857<tbody valign="top">
858<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">=</span> <span class="pre">x</span></tt></td>
859<td><tt class="docutils literal"><span class="pre">Y</span></tt></td>
860<td>post: <tt class="docutils literal"><span class="pre">y</span> <span class="pre">==</span> <span class="pre">x</span></tt></td>
861</tr>
862<tr><td><tt class="docutils literal"><span class="pre">Y(x)</span></tt></td>
863<td><tt class="docutils literal"><span class="pre">Y</span></tt></td>
864<td>post: <tt class="docutils literal"><span class="pre">Y(x)</span> <span class="pre">==</span> <span class="pre">x</span></tt></td>
865</tr>
866<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">y</span></tt></td>
867<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
868<td><tt class="docutils literal"><span class="pre">==</span></tt> is an equivalence relation over its domain.</td>
869</tr>
870<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">==</span> <span class="pre">x</span></tt></td>
871<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
872<td><tt class="docutils literal"><span class="pre">==</span></tt> is an equivalence relation over its domain.</td>
873</tr>
874<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">!=</span> <span class="pre">y</span></tt></td>
875<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
876<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>
877</tr>
878<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">!=</span> <span class="pre">x</span></tt></td>
879<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
880<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>
881</tr>
882</tbody>
883</table>
884<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
885the following additional requirements must be met.</p>
886<table border="1" class="docutils">
887<colgroup>
888<col width="12%" />
889<col width="25%" />
890<col width="23%" />
891<col width="41%" />
892</colgroup>
893<thead valign="bottom">
894<tr><th class="head">Expression</th>
895<th class="head">Return Type</th>
896<th class="head">Operational Semantics</th>
897<th class="head">Assertion/ Precondition</th>
898</tr>
899</thead>
900<tbody valign="top">
901<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&lt;</span> <span class="pre">y</span></tt></td>
902<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
903<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>
904<td><tt class="docutils literal"><span class="pre">&lt;</span></tt> is a total ordering relation</td>
905</tr>
906<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&lt;</span> <span class="pre">x</span></tt></td>
907<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
908<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>
909<td><tt class="docutils literal"><span class="pre">&lt;</span></tt> is a total ordering relation</td>
910</tr>
911<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&gt;</span> <span class="pre">y</span></tt></td>
912<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
913<td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&lt;</span> <span class="pre">x</span></tt></td>
914<td><tt class="docutils literal"><span class="pre">&gt;</span></tt> is a total ordering relation</td>
915</tr>
916<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&gt;</span> <span class="pre">x</span></tt></td>
917<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
918<td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&lt;</span> <span class="pre">y</span></tt></td>
919<td><tt class="docutils literal"><span class="pre">&gt;</span></tt> is a total ordering relation</td>
920</tr>
921<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&gt;=</span> <span class="pre">y</span></tt></td>
922<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
923<td><tt class="docutils literal"><span class="pre">!(x</span> <span class="pre">&lt;</span> <span class="pre">y)</span></tt></td>
924<td>&nbsp;</td>
925</tr>
926<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&gt;=</span> <span class="pre">x</span></tt></td>
927<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
928<td><tt class="docutils literal"><span class="pre">!(y</span> <span class="pre">&lt;</span> <span class="pre">x)</span></tt></td>
929<td>&nbsp;</td>
930</tr>
931<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">&lt;=</span> <span class="pre">y</span></tt></td>
932<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
933<td><tt class="docutils literal"><span class="pre">!(x</span> <span class="pre">&gt;</span> <span class="pre">y)</span></tt></td>
934<td>&nbsp;</td>
935</tr>
936<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">&lt;=</span> <span class="pre">x</span></tt></td>
937<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
938<td><tt class="docutils literal"><span class="pre">!(y</span> <span class="pre">&gt;</span> <span class="pre">x)</span></tt></td>
939<td>&nbsp;</td>
940</tr>
941<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">-</span> <span class="pre">x</span></tt></td>
942<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td>
943<td><tt class="docutils literal"><span class="pre">distance(Y(x),y)</span></tt></td>
944<td>pre: there exists a value <tt class="docutils literal"><span class="pre">n</span></tt> of
945<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>.
946<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>
947</tr>
948<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">-</span> <span class="pre">y</span></tt></td>
949<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td>
950<td><tt class="docutils literal"><span class="pre">distance(y,Y(x))</span></tt></td>
951<td>pre: there exists a value <tt class="docutils literal"><span class="pre">n</span></tt> of
952<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>.
953<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>
954</tr>
955</tbody>
956</table>
957</div>
958</div>
959</div>
960<div class="section" id="addition-to-lib-iterator-synopsis">
961<h2><a class="toc-backref" href="#id22">Addition to [lib.iterator.synopsis]</a></h2>
962<pre class="literal-block">
963// lib.iterator.traits, traits and tags
964template &lt;class Iterator&gt; struct is_readable_iterator;
965template &lt;class Iterator&gt; struct iterator_traversal;
966
967struct incrementable_traversal_tag { };
968struct single_pass_traversal_tag : incrementable_traversal_tag { };
969struct forward_traversal_tag : single_pass_traversal_tag { };
970struct bidirectional_traversal_tag : forward_traversal_tag { };
971struct random_access_traversal_tag : bidirectional_traversal_tag { };
972</pre>
973</div>
974<div class="section" id="addition-to-lib-iterator-traits">
975<h2><a class="toc-backref" href="#id23">Addition to [lib.iterator.traits]</a></h2>
976<p>The <tt class="docutils literal"><span class="pre">is_readable_iterator</span></tt> class
977template satisfies the <a class="reference external" href="http://anubis.dkuug.dk/jtc1/sc22/wg21/docs/papers/2003/n1519.htm">UnaryTypeTrait</a> requirements.</p>
978<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>
979yields <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
980convertible 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>
981otherwise.</p>
982<p><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt> is</p>
983<pre class="literal-block">
984<em>category-to-traversal</em>(iterator_traits&lt;X&gt;::iterator_category)
985</pre>
986<p>where <em>category-to-traversal</em> is defined as follows</p>
987<pre class="literal-block" id="category-to-traversal">
988<em>category-to-traversal</em>(C) =
989    if (C is convertible to incrementable_traversal_tag)
990        return C;
991    else if (C is convertible to random_access_iterator_tag)
992        return random_access_traversal_tag;
993    else if (C is convertible to bidirectional_iterator_tag)
994        return bidirectional_traversal_tag;
995    else if (C is convertible to forward_iterator_tag)
996        return forward_traversal_tag;
997    else if (C is convertible to input_iterator_tag)
998        return single_pass_traversal_tag;
999    else if (C is convertible to output_iterator_tag)
1000        return incrementable_traversal_tag;
1001    else
1002        <em>the program is ill-formed</em>
1003</pre>
1004</div>
1005</div>
1006<div class="section" id="footnotes">
1007<h1><a class="toc-backref" href="#id24">Footnotes</a></h1>
1008<p>The UnaryTypeTrait concept is defined in <a class="reference external" href="http://anubis.dkuug.dk/jtc1/sc22/wg21/docs/papers/2003/n1519.htm">n1519</a>; the LWG is
1009considering adding the requirement that specializations are derived
1010from their nested <tt class="docutils literal"><span class="pre">::type</span></tt>.</p>
1011<!-- LocalWords:  Abrahams Siek Witt const bool Sutter's WG int UL LI href Lvalue
1012LocalWords:  ReadableIterator WritableIterator SwappableIterator cv pre iter
1013LocalWords:  ConstantLvalueIterator MutableLvalueIterator CopyConstructible TR
1014LocalWords:  ForwardTraversalIterator BidirectionalTraversalIterator lvalue
1015LocalWords:  RandomAccessTraversalIterator dereferenceable Incrementable tmp
1016LocalWords:  incrementable xxx min prev inplace png oldeqnew AccessTag struct
1017LocalWords:  TraversalTag typename lvalues DWA Hmm JGS mis enum -->
1018</div>
1019</div>
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