1<?xml version="1.0" encoding="utf-8" ?> 2<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> 4<head> 5<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> 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." /> 12<link rel="stylesheet" href="../../../rst.css" type="text/css" /> 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@boost-consulting.com">dave@boost-consulting.com</a>, <a class="reference external" href="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</a>, <a class="last reference external" href="mailto:witt@styleadvisor.com">witt@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://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003/n1550.htm">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://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> 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<bool></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 "input 107iterator", 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&</span></tt> (or <tt class="docutils literal"><span class="pre">const</span> <span class="pre">T&</span></tt> once <a class="reference external" href="http://www.open-std.org/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://www.open-std.org/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<bool>::iterator</span></tt> is almost a 143random access iterator, but the return type is not <tt class="docutils literal"><span class="pre">bool&</span></tt> (see 144<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 145N1185). Therefore, the iterators of <tt class="docutils literal"><span class="pre">vector<bool></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 -> 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) -> Single Pass Iterator and Readable Iterator, 216Forward Iterator (2) -> 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 -> 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 -> 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 -> 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) -> Swappable Iterator and Single Pass Iterator, 229Forward Iterator (2) -> 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 -> 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 -> 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 -> Bidirectional Traversal Iterator and Swappable Iterator</dt> 241<dd><tt class="docutils literal"><span class="pre">reverse</span></tt></dd> 242<dt>Bidirectional Iterator -> 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) -> Bidirectional Traversal Iterator and Readable Iterator, 246Bidirectional Iterator (2) -> 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 -> 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 -> 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 -> 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 -> 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) -> 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) -> 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<bool></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<bool>::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-></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<</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<Iter>::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://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 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<X>::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<X>::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<X>::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->m</span></tt></td> 399<td><tt class="docutils literal"><span class="pre">U&</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> </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&</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<X>::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<X>::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&</span></tt></td> 532<td><tt class="docutils literal"><span class="pre">&r</span> <span class="pre">==</span> <span class="pre">&++r</span></tt></td> 533</tr> 534<tr><td><tt class="docutils literal"><span class="pre">r++</span></tt></td> 535<td> </td> 536<td> </td> 537</tr> 538<tr><td><tt class="docutils literal"><span class="pre">*r++</span></tt></td> 539<td> </td> 540<td> </td> 541</tr> 542<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal<X>::type</span></tt></td> 543<td>Convertible to 544<tt class="docutils literal"><span class="pre">incrementable_traversal_tag</span></tt></td> 545<td> </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="37%" /> 565<col width="27%" /> 566<col width="12%" /> 567<col width="25%" /> 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&</span></tt></td> 584<td> </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> </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> </td> 600</tr> 601<tr><td><tt class="docutils literal"><span class="pre">iterator_traits<X>::difference_type</span></tt></td> 602<td>A signed integral type 603representing the distance 604between iterators</td> 605<td> </td> 606<td> </td> 607</tr> 608<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal<X>::type</span></tt></td> 609<td>Convertible to 610<tt class="docutils literal"><span class="pre">single_pass_traversal_tag</span></tt></td> 611<td> </td> 612<td> </td> 613</tr> 614</tbody> 615</table> 616<!-- TR1: single_pass_iterator_tag changed to 617single_pass_traversal_tag for consistency --> 618</div> 619<div class="section" id="forward-traversal-iterators-lib-forward-traversal-iterators"> 620<h4><a class="toc-backref" href="#id18">Forward Traversal Iterators [lib.forward.traversal.iterators]</a></h4> 621<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Forward Traversal Iterator</em> 622concept if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> meeting the requirements of Default 623Constructible and Single Pass Iterator, the following expressions are 624valid and respect the stated semantics.</p> 625<table border="1" class="docutils"> 626<colgroup> 627<col width="38%" /> 628<col width="34%" /> 629<col width="27%" /> 630</colgroup> 631<thead valign="bottom"> 632<tr><th class="head" colspan="3">Forward Traversal Iterator Requirements (in addition to Default Constructible and Single Pass Iterator)</th> 633</tr> 634<tr><th class="head">Expression</th> 635<th class="head">Return Type</th> 636<th class="head">Assertion/Note</th> 637</tr> 638</thead> 639<tbody valign="top"> 640<tr><td><tt class="docutils literal"><span class="pre">X</span> <span class="pre">u;</span></tt></td> 641<td><tt class="docutils literal"><span class="pre">X&</span></tt></td> 642<td>note: <tt class="docutils literal"><span class="pre">u</span></tt> may have a 643singular value.</td> 644</tr> 645<tr><td><tt class="docutils literal"><span class="pre">++r</span></tt></td> 646<td><tt class="docutils literal"><span class="pre">X&</span></tt></td> 647<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 648dereferenceable implies 649<tt class="docutils literal"><span class="pre">++r</span> <span class="pre">==</span> <span class="pre">++s.</span></tt></td> 650</tr> 651<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal<X>::type</span></tt></td> 652<td>Convertible to 653<tt class="docutils literal"><span class="pre">forward_traversal_tag</span></tt></td> 654<td> </td> 655</tr> 656</tbody> 657</table> 658<!-- TR1: forward_traversal_iterator_tag changed to 659forward_traversal_tag for consistency --> 660</div> 661<div class="section" id="bidirectional-traversal-iterators-lib-bidirectional-traversal-iterators"> 662<h4><a class="toc-backref" href="#id19">Bidirectional Traversal Iterators [lib.bidirectional.traversal.iterators]</a></h4> 663<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Bidirectional Traversal 664Iterator</em> concept if, in addition to <tt class="docutils literal"><span class="pre">X</span></tt> meeting the requirements of 665Forward Traversal Iterator, the following expressions are valid and 666respect the stated semantics.</p> 667<table border="1" class="docutils"> 668<colgroup> 669<col width="33%" /> 670<col width="32%" /> 671<col width="14%" /> 672<col width="21%" /> 673</colgroup> 674<thead valign="bottom"> 675<tr><th class="head" colspan="4">Bidirectional Traversal Iterator Requirements (in addition to Forward Traversal 676Iterator)</th> 677</tr> 678<tr><th class="head">Expression</th> 679<th class="head">Return Type</th> 680<th class="head">Operational 681Semantics</th> 682<th class="head">Assertion/ 683Pre-/Post-condition</th> 684</tr> 685</thead> 686<tbody valign="top"> 687<tr><td><tt class="docutils literal"><span class="pre">--r</span></tt></td> 688<td><tt class="docutils literal"><span class="pre">X&</span></tt></td> 689<td> </td> 690<td><p class="first">pre: there exists 691<tt class="docutils literal"><span class="pre">s</span></tt> such that <tt class="docutils literal"><span class="pre">r</span> 692<span class="pre">==</span> <span class="pre">++s</span></tt>. post: 693<tt class="docutils literal"><span class="pre">s</span></tt> is 694dereferenceable.</p> 695<p class="last"><tt class="docutils literal"><span class="pre">++(--r)</span> <span class="pre">==</span> <span class="pre">r</span></tt>. 696<tt class="docutils literal"><span class="pre">--r</span> <span class="pre">==</span> <span class="pre">--s</span></tt> 697implies <tt class="docutils literal"><span class="pre">r</span> <span class="pre">==</span> 698<span class="pre">s</span></tt>. <tt class="docutils literal"><span class="pre">&r</span> <span class="pre">==</span> <span class="pre">&--r</span></tt>.</p> 699</td> 700</tr> 701<tr><td><tt class="docutils literal"><span class="pre">r--</span></tt></td> 702<td>convertible to <tt class="docutils literal"><span class="pre">const</span> <span class="pre">X&</span></tt></td> 703<td><pre class="first last literal-block"> 704{ 705 X tmp = r; 706 --r; 707 return tmp; 708} 709</pre> 710</td> 711<td> </td> 712</tr> 713<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal<X>::type</span></tt></td> 714<td>Convertible to 715<tt class="docutils literal"><span class="pre">bidirectional_traversal_tag</span></tt></td> 716<td> </td> 717<td> </td> 718</tr> 719</tbody> 720</table> 721<!-- TR1: bidirectional_traversal_iterator_tag changed to 722bidirectional_traversal_tag for consistency --> 723</div> 724<div class="section" id="random-access-traversal-iterators-lib-random-access-traversal-iterators"> 725<h4><a class="toc-backref" href="#id20">Random Access Traversal Iterators [lib.random.access.traversal.iterators]</a></h4> 726<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Random Access Traversal 727Iterator</em> concept if the following expressions are valid and respect 728the stated semantics. In the table below, <tt class="docutils literal"><span class="pre">Distance</span></tt> is 729<tt class="docutils literal"><span class="pre">iterator_traits<X>::difference_type</span></tt> and <tt class="docutils literal"><span class="pre">n</span></tt> represents a 730constant object of type <tt class="docutils literal"><span class="pre">Distance</span></tt>.</p> 731<table border="1" class="docutils"> 732<colgroup> 733<col width="28%" /> 734<col width="30%" /> 735<col width="23%" /> 736<col width="20%" /> 737</colgroup> 738<thead valign="bottom"> 739<tr><th class="head" colspan="4">Random Access Traversal Iterator Requirements (in addition to Bidirectional Traversal Iterator)</th> 740</tr> 741<tr><th class="head">Expression</th> 742<th class="head">Return Type</th> 743<th class="head">Operational Semantics</th> 744<th class="head">Assertion/ 745Precondition</th> 746</tr> 747</thead> 748<tbody valign="top"> 749<tr><td><tt class="docutils literal"><span class="pre">r</span> <span class="pre">+=</span> <span class="pre">n</span></tt></td> 750<td><tt class="docutils literal"><span class="pre">X&</span></tt></td> 751<td><pre class="first last literal-block"> 752{ 753 Distance m = n; 754 if (m >= 0) 755 while (m--) 756 ++r; 757 else 758 while (m++) 759 --r; 760 return r; 761} 762</pre> 763</td> 764<td> </td> 765</tr> 766<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> 767<td><tt class="docutils literal"><span class="pre">X</span></tt></td> 768<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> 769<span class="pre">+=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td> 770<td> </td> 771</tr> 772<tr><td><tt class="docutils literal"><span class="pre">r</span> <span class="pre">-=</span> <span class="pre">n</span></tt></td> 773<td><tt class="docutils literal"><span class="pre">X&</span></tt></td> 774<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> 775<td> </td> 776</tr> 777<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">-</span> <span class="pre">n</span></tt></td> 778<td><tt class="docutils literal"><span class="pre">X</span></tt></td> 779<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> 780<span class="pre">-=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td> 781<td> </td> 782</tr> 783<tr><td><tt class="docutils literal"><span class="pre">b</span> <span class="pre">-</span> <span class="pre">a</span></tt></td> 784<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td> 785<td><tt class="docutils literal"><span class="pre">a</span> <span class="pre"><</span> <span class="pre">b</span> <span class="pre">?</span> <span class="pre">distance(a,b)</span> 786<span class="pre">:</span> <span class="pre">-distance(b,a)</span></tt></td> 787<td>pre: there exists a 788value <tt class="docutils literal"><span class="pre">n</span></tt> of 789<tt class="docutils literal"><span class="pre">Distance</span></tt> such that 790<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> 791<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> 792</tr> 793<tr><td><tt class="docutils literal"><span class="pre">a[n]</span></tt></td> 794<td>convertible to T</td> 795<td><tt class="docutils literal"><span class="pre">*(a</span> <span class="pre">+</span> <span class="pre">n)</span></tt></td> 796<td>pre: a is a <a class="reference internal" href="#readable-iterator">Readable 797Iterator</a></td> 798</tr> 799<tr><td><tt class="docutils literal"><span class="pre">a[n]</span> <span class="pre">=</span> <span class="pre">v</span></tt></td> 800<td>convertible to T</td> 801<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> 802<td>pre: a is a <a class="reference internal" href="#writable-iterator">Writable 803Iterator</a></td> 804</tr> 805<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre"><</span> <span class="pre">b</span></tt></td> 806<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 807<td><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">0</span></tt></td> 808<td><tt class="docutils literal"><span class="pre"><</span></tt> is a total 809ordering relation</td> 810</tr> 811<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">></span> <span class="pre">b</span></tt></td> 812<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 813<td><tt class="docutils literal"><span class="pre">b</span> <span class="pre"><</span> <span class="pre">a</span></tt></td> 814<td><tt class="docutils literal"><span class="pre">></span></tt> is a total 815ordering relation</td> 816</tr> 817<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">>=</span> <span class="pre">b</span></tt></td> 818<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 819<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre"><</span> <span class="pre">b)</span></tt></td> 820<td> </td> 821</tr> 822<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre"><=</span> <span class="pre">b</span></tt></td> 823<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 824<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre">></span> <span class="pre">b)</span></tt></td> 825<td> </td> 826</tr> 827<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal<X>::type</span></tt></td> 828<td>Convertible to 829<tt class="docutils literal"><span class="pre">random_access_traversal_tag</span></tt></td> 830<td> </td> 831<td> </td> 832</tr> 833</tbody> 834</table> 835<!-- TR1: random_access_traversal_iterator_tag changed to 836random_access_traversal_tag for consistency --> 837</div> 838<div class="section" id="interoperable-iterators-lib-interoperable-iterators"> 839<h4><a class="toc-backref" href="#id21">Interoperable Iterators [lib.interoperable.iterators]</a></h4> 840<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> that models Single Pass Iterator is 841<em>interoperable with</em> a class or built-in type <tt class="docutils literal"><span class="pre">Y</span></tt> that also models 842Single Pass Iterator if the following expressions are valid and 843respect the stated semantics. In the tables below, <tt class="docutils literal"><span class="pre">x</span></tt> is an object 844of 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 845<tt class="docutils literal"><span class="pre">iterator_traits<Y>::difference_type</span></tt>, and <tt class="docutils literal"><span class="pre">n</span></tt> represents a 846constant object of type <tt class="docutils literal"><span class="pre">Distance</span></tt>.</p> 847<table border="1" class="docutils"> 848<colgroup> 849<col width="13%" /> 850<col width="27%" /> 851<col width="60%" /> 852</colgroup> 853<thead valign="bottom"> 854<tr><th class="head">Expression</th> 855<th class="head">Return Type</th> 856<th class="head">Assertion/Precondition/Postcondition</th> 857</tr> 858</thead> 859<tbody valign="top"> 860<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">=</span> <span class="pre">x</span></tt></td> 861<td><tt class="docutils literal"><span class="pre">Y</span></tt></td> 862<td>post: <tt class="docutils literal"><span class="pre">y</span> <span class="pre">==</span> <span class="pre">x</span></tt></td> 863</tr> 864<tr><td><tt class="docutils literal"><span class="pre">Y(x)</span></tt></td> 865<td><tt class="docutils literal"><span class="pre">Y</span></tt></td> 866<td>post: <tt class="docutils literal"><span class="pre">Y(x)</span> <span class="pre">==</span> <span class="pre">x</span></tt></td> 867</tr> 868<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">y</span></tt></td> 869<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 870<td><tt class="docutils literal"><span class="pre">==</span></tt> is an equivalence relation over its domain.</td> 871</tr> 872<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">==</span> <span class="pre">x</span></tt></td> 873<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 874<td><tt class="docutils literal"><span class="pre">==</span></tt> is an equivalence relation over its domain.</td> 875</tr> 876<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">!=</span> <span class="pre">y</span></tt></td> 877<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 878<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> 879</tr> 880<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">!=</span> <span class="pre">x</span></tt></td> 881<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 882<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> 883</tr> 884</tbody> 885</table> 886<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 887the following additional requirements must be met.</p> 888<table border="1" class="docutils"> 889<colgroup> 890<col width="12%" /> 891<col width="25%" /> 892<col width="23%" /> 893<col width="41%" /> 894</colgroup> 895<thead valign="bottom"> 896<tr><th class="head">Expression</th> 897<th class="head">Return Type</th> 898<th class="head">Operational Semantics</th> 899<th class="head">Assertion/ Precondition</th> 900</tr> 901</thead> 902<tbody valign="top"> 903<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre"><</span> <span class="pre">y</span></tt></td> 904<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 905<td><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">0</span></tt></td> 906<td><tt class="docutils literal"><span class="pre"><</span></tt> is a total ordering relation</td> 907</tr> 908<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre"><</span> <span class="pre">x</span></tt></td> 909<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 910<td><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">0</span></tt></td> 911<td><tt class="docutils literal"><span class="pre"><</span></tt> is a total ordering relation</td> 912</tr> 913<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">></span> <span class="pre">y</span></tt></td> 914<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 915<td><tt class="docutils literal"><span class="pre">y</span> <span class="pre"><</span> <span class="pre">x</span></tt></td> 916<td><tt class="docutils literal"><span class="pre">></span></tt> is a total ordering relation</td> 917</tr> 918<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">></span> <span class="pre">x</span></tt></td> 919<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 920<td><tt class="docutils literal"><span class="pre">x</span> <span class="pre"><</span> <span class="pre">y</span></tt></td> 921<td><tt class="docutils literal"><span class="pre">></span></tt> is a total ordering relation</td> 922</tr> 923<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">>=</span> <span class="pre">y</span></tt></td> 924<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 925<td><tt class="docutils literal"><span class="pre">!(x</span> <span class="pre"><</span> <span class="pre">y)</span></tt></td> 926<td> </td> 927</tr> 928<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">>=</span> <span class="pre">x</span></tt></td> 929<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 930<td><tt class="docutils literal"><span class="pre">!(y</span> <span class="pre"><</span> <span class="pre">x)</span></tt></td> 931<td> </td> 932</tr> 933<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre"><=</span> <span class="pre">y</span></tt></td> 934<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 935<td><tt class="docutils literal"><span class="pre">!(x</span> <span class="pre">></span> <span class="pre">y)</span></tt></td> 936<td> </td> 937</tr> 938<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre"><=</span> <span class="pre">x</span></tt></td> 939<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td> 940<td><tt class="docutils literal"><span class="pre">!(y</span> <span class="pre">></span> <span class="pre">x)</span></tt></td> 941<td> </td> 942</tr> 943<tr><td><tt class="docutils literal"><span class="pre">y</span> <span class="pre">-</span> <span class="pre">x</span></tt></td> 944<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td> 945<td><tt class="docutils literal"><span class="pre">distance(Y(x),y)</span></tt></td> 946<td>pre: there exists a value <tt class="docutils literal"><span class="pre">n</span></tt> of 947<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>. 948<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> 949</tr> 950<tr><td><tt class="docutils literal"><span class="pre">x</span> <span class="pre">-</span> <span class="pre">y</span></tt></td> 951<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td> 952<td><tt class="docutils literal"><span class="pre">distance(y,Y(x))</span></tt></td> 953<td>pre: there exists a value <tt class="docutils literal"><span class="pre">n</span></tt> of 954<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>. 955<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> 956</tr> 957</tbody> 958</table> 959</div> 960</div> 961</div> 962<div class="section" id="addition-to-lib-iterator-synopsis"> 963<h2><a class="toc-backref" href="#id22">Addition to [lib.iterator.synopsis]</a></h2> 964<pre class="literal-block"> 965// lib.iterator.traits, traits and tags 966template <class Iterator> struct is_readable_iterator; 967template <class Iterator> struct iterator_traversal; 968 969struct incrementable_traversal_tag { }; 970struct single_pass_traversal_tag : incrementable_traversal_tag { }; 971struct forward_traversal_tag : single_pass_traversal_tag { }; 972struct bidirectional_traversal_tag : forward_traversal_tag { }; 973struct random_access_traversal_tag : bidirectional_traversal_tag { }; 974</pre> 975</div> 976<div class="section" id="addition-to-lib-iterator-traits"> 977<h2><a class="toc-backref" href="#id23">Addition to [lib.iterator.traits]</a></h2> 978<p>The <tt class="docutils literal"><span class="pre">is_readable_iterator</span></tt> class 979template satisfies the <a class="reference external" href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003/n1519.htm">UnaryTypeTrait</a> requirements.</p> 980<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<X>::value</span></tt> 981yields <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 982convertible to <tt class="docutils literal"><span class="pre">iterator_traits<X>::value_type</span></tt>, and <tt class="docutils literal"><span class="pre">false</span></tt> 983otherwise.</p> 984<p><tt class="docutils literal"><span class="pre">iterator_traversal<X>::type</span></tt> is</p> 985<pre class="literal-block"> 986<em>category-to-traversal</em>(iterator_traits<X>::iterator_category) 987</pre> 988<p>where <em>category-to-traversal</em> is defined as follows</p> 989<pre class="literal-block" id="category-to-traversal"> 990<em>category-to-traversal</em>(C) = 991 if (C is convertible to incrementable_traversal_tag) 992 return C; 993 else if (C is convertible to random_access_iterator_tag) 994 return random_access_traversal_tag; 995 else if (C is convertible to bidirectional_iterator_tag) 996 return bidirectional_traversal_tag; 997 else if (C is convertible to forward_iterator_tag) 998 return forward_traversal_tag; 999 else if (C is convertible to input_iterator_tag) 1000 return single_pass_traversal_tag; 1001 else if (C is convertible to output_iterator_tag) 1002 return incrementable_traversal_tag; 1003 else 1004 <em>the program is ill-formed</em> 1005</pre> 1006</div> 1007</div> 1008<div class="section" id="footnotes"> 1009<h1><a class="toc-backref" href="#id24">Footnotes</a></h1> 1010<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 1011considering adding the requirement that specializations are derived 1012from their nested <tt class="docutils literal"><span class="pre">::type</span></tt>.</p> 1013<!-- LocalWords: Abrahams Siek Witt const bool Sutter's WG int UL LI href Lvalue 1014LocalWords: ReadableIterator WritableIterator SwappableIterator cv pre iter 1015LocalWords: ConstantLvalueIterator MutableLvalueIterator CopyConstructible TR 1016LocalWords: ForwardTraversalIterator BidirectionalTraversalIterator lvalue 1017LocalWords: RandomAccessTraversalIterator dereferenceable Incrementable tmp 1018LocalWords: incrementable xxx min prev inplace png oldeqnew AccessTag struct 1019LocalWords: TraversalTag typename lvalues DWA Hmm JGS mis enum --> 1020</div> 1021</div> 1022<div class="footer"> 1023<hr class="footer" /> 1024<a class="reference external" href="new-iter-concepts.rst">View document source</a>. 1025Generated by <a class="reference external" href="http://docutils.sourceforge.net/">Docutils</a> from <a class="reference external" href="http://docutils.sourceforge.net/rst.html">reStructuredText</a> source. 1026 1027</div> 1028</body> 1029</html> 1030
