144 lines
25 KiB
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144 lines
25 KiB
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<title>std::totally_ordered, std::totally_ordered_with</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>totally_ordered, <span style="font-size:0.7em; line-height:130%">std::</span>totally_ordered_with</h1>
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</a>‎ | <a href="cpp-concepts.html">concepts</a></span></div>
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<div>定义于头文件 <code><a href="cpp-header-concepts.html"><concepts></a></code></div>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span> <span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span><br /></span>
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<p>concept totally_ordered <span class="sy1">=</span><br /></p>
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std<span class="sy4">::</span><span class="me2">equality_comparable</span><span class="sy1"><</span>T<span class="sy1">></span> <span class="sy3">&&</span> __PartiallyOrderedWith<span class="sy1"><</span>T, T<span class="sy1">></span><span class="sy4">;</span></div>
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<td>(1)</td>
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<td><span class="t-mark-rev t-since-cxx20">(C++20 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span> <span class="sy1"><</span><span class="kw1">class</span> T, <span class="kw1">class</span> U<span class="sy1">></span><br /></span>
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<p>concept totally_ordered_with <span class="sy1">=</span><br />
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std<span class="sy4">::</span><span class="me2">totally_ordered</span><span class="sy1"><</span>T<span class="sy1">></span> <span class="sy3">&&</span><br />
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std<span class="sy4">::</span><span class="me2">totally_ordered</span><span class="sy1"><</span>U<span class="sy1">></span> <span class="sy3">&&</span><br />
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std<span class="sy4">::</span><span class="me2">equality_comparable_with</span><span class="sy1"><</span>T, U<span class="sy1">></span> <span class="sy3">&&</span><br />
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std<span class="sy4">::</span><span class="me2">totally_ordered</span><span class="sy1"><</span><br />
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std<span class="sy4">::</span><span class="me2">common_reference_t</span><span class="sy1"><</span><br />
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<span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>,<br />
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<span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>U<span class="sy1">></span><span class="sy3">&</span><span class="sy1">>></span> <span class="sy3">&&</span><br /></p>
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__PartiallyOrderedWith<span class="sy1"><</span>T, U<span class="sy1">></span><span class="sy4">;</span></div>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-cxx20">(C++20 起)</span></td>
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</tr>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T, <span class="kw1">class</span> U<span class="sy1">></span><br /></span>
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<p>concept __PartiallyOrderedWith <span class="sy1">=</span> <span class="co1">// 仅用于阐释</span><br />
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requires<span class="br0">(</span><span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> t,<br />
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<span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>U<span class="sy1">></span><span class="sy3">&</span> u<span class="br0">)</span> <span class="br0">{</span><br />
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<span class="br0">{</span> t <span class="sy1"><</span> u <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">></span> boolean<span class="sy2">-</span>testable<span class="sy4">;</span><br />
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<span class="br0">{</span> t <span class="sy1">></span> u <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">></span> boolean<span class="sy2">-</span>testable<span class="sy4">;</span><br />
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<span class="br0">{</span> t <span class="sy1"><=</span> u <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">></span> boolean<span class="sy2">-</span>testable<span class="sy4">;</span><br />
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<span class="br0">{</span> t <span class="sy1">>=</span> u <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">></span> boolean<span class="sy2">-</span>testable<span class="sy4">;</span><br />
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<span class="br0">{</span> u <span class="sy1"><</span> t <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">></span> boolean<span class="sy2">-</span>testable<span class="sy4">;</span><br />
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<span class="br0">{</span> u <span class="sy1">></span> t <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">></span> boolean<span class="sy2">-</span>testable<span class="sy4">;</span><br />
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<span class="br0">{</span> u <span class="sy1"><=</span> t <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">></span> boolean<span class="sy2">-</span>testable<span class="sy4">;</span><br />
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<span class="br0">{</span> u <span class="sy1">>=</span> t <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">></span> boolean<span class="sy2">-</span>testable<span class="sy4">;</span><br /></p>
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<span class="br0">}</span><span class="sy4">;</span></div>
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<td>(3)</td>
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<td><span class="t-mark-rev t-since-cxx20">(C++20 起)</span></td>
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<div class="t-li1"><span class="t-li">1)</span> 概念 <code>std::totally_ordered</code> 指定比较运算符 <code>==,!=,<,>,<=,>=</code> 在一个类型上产生的结果与该类型上的<a href="https://en.wikipedia.org/wiki/Total_order#Strict_total_order" class="extiw" title="enwiki:Total order">严格全序</a>一致。</div>
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<div class="t-li1"><span class="t-li">2)</span> 概念 <code>std::totally_ordered_with</code> 指定比较运算符 <code>==,!=,<,>,<=,>=</code> 在（可能混合的） <code>T</code> 和 <code>U</code> 运算数上产生的结果等价于比较转换到其共用类型的运算数的结果。</div>
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<div class="t-li1"><span class="t-li">3)</span> 仅用于阐释的概念 <code><i>__PartiallyOrderedWith</i></code> 指定 <code>T</code> 类型对象与 <code>U</code> 类型对象能（以任何顺序）用 <code><</code> 、 <code>></code> 、 <code><=</code> 及 <code>>=</code> 在一个偏序中彼此比较，且比较结果一致。</div>
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<h3><span class="mw-headline" id=".E8.AF.AD.E4.B9.89.E8.A6.81.E6.B1.82">语义要求</span></h3>
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<p>这些概念仅若其所蕴含的概念均被实现才得到实现。</p>
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<div class="t-li1"><span class="t-li">1)</span> <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">totally_ordered</span><span class="sy1"><</span>T<span class="sy1">></span></span></span> 仅若符合下列条件才得到实现。给定 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>T<span class="sy1">></span></span></span> 类型左值 <code>a</code> 、 <code>b</code> 和 <code>c</code> ：
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<ul>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1"><</span> b<span class="br0">)</span></span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">></span> b<span class="br0">)</span></span></span> 和 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">==</span> b<span class="br0">)</span></span></span> 恰有一者为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw2">true</span></span></span> ；</li>
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<li>若 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1"><</span> b<span class="br0">)</span></span></span> 与 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>b <span class="sy1"><</span> c<span class="br0">)</span></span></span> 均为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw2">true</span></span></span> ，则 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1"><</span> c<span class="br0">)</span></span></span> 为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw2">true</span></span></span> ；</li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">></span> b<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>b <span class="sy1"><</span> a<span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">>=</span> b<span class="br0">)</span> <span class="sy1">==</span> <span class="sy3">!</span><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1"><</span> b<span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1"><=</span> b<span class="br0">)</span> <span class="sy1">==</span> <span class="sy3">!</span><span class="kw4">bool</span><span class="br0">(</span>b <span class="sy1"><</span> a<span class="br0">)</span></span></span></li>
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</ul>
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</div>
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<div class="t-li1"><span class="t-li">2)</span> 正式而言， <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">totally_ordered_with</span><span class="sy1"><</span>T, U<span class="sy1">></span></span></span> 仅若符合下列条件才得到实现。仅若给定
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<ul>
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<li><code>t</code> ， <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>T<span class="sy1">></span></span></span> 类型左值，与</li>
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<li><code>u</code> ， <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>U<span class="sy1">></span></span></span> 类型左值，</li>
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</ul>
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<p>并令 <code>C</code> 为 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">common_reference_t</span><span class="sy1"><</span><span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>U<span class="sy1">></span><span class="sy3">&</span><span class="sy1">></span></span></span> ：</p>
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<ul>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1"><</span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>t<span class="br0">)</span> <span class="sy1"><</span> C<span class="br0">(</span>u<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1">></span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>t<span class="br0">)</span> <span class="sy1">></span> C<span class="br0">(</span>u<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1"><=</span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>t<span class="br0">)</span> <span class="sy1"><=</span> C<span class="br0">(</span>u<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1">>=</span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>t<span class="br0">)</span> <span class="sy1">>=</span> C<span class="br0">(</span>u<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1"><</span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>u<span class="br0">)</span> <span class="sy1"><</span> C<span class="br0">(</span>t<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1">></span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>u<span class="br0">)</span> <span class="sy1">></span> C<span class="br0">(</span>t<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1"><=</span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>u<span class="br0">)</span> <span class="sy1"><=</span> C<span class="br0">(</span>t<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1">>=</span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>u<span class="br0">)</span> <span class="sy1">>=</span> C<span class="br0">(</span>t<span class="br0">)</span><span class="br0">)</span></span></span></li>
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</ul>
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</div>
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<div class="t-li1"><span class="t-li">3)</span> 正式而言， <code>T</code> 与 <code>U</code> 实现 <span class="t-c"><span class="mw-geshi cpp source-cpp">__PartiallyOrderedWith<span class="sy1"><</span>T, U<span class="sy1">></span></span></span> ，仅若给定
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<ul>
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<li><code>t</code> ， <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>T<span class="sy1">></span></span></span> 类型左值，与</li>
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<li><code>u</code> ， <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">const</span> <a href="cpp-types-remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1"><</span>U<span class="sy1">></span></span></span> 类型左值</li>
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</ul>
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<p>下列为真：</p>
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<ul>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp">t <span class="sy1"><</span> u</span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp">t <span class="sy1"><=</span> u</span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp">t <span class="sy1">></span> u</span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp">t <span class="sy1">>=</span> u</span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp">u <span class="sy1"><</span> t</span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp">u <span class="sy1"><=</span> t</span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp">u <span class="sy1">></span> t</span></span> 及 <span class="t-c"><span class="mw-geshi cpp source-cpp">u <span class="sy1">>=</span> t</span></span> 拥有相同定义域；</li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1"><</span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1">></span> t<span class="br0">)</span></span></span> ；</li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1"><</span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1">></span> u<span class="br0">)</span></span></span> ；</li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1"><=</span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1">>=</span> t<span class="br0">)</span></span></span> ；且</li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1"><=</span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1">>=</span> u<span class="br0">)</span></span></span> 。</li>
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</ul>
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</div>
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<h3><span class="mw-headline" id=".E7.9B.B8.E7.AD.89.E6.80.A7.E4.BF.9D.E6.8C.81">相等性保持</span></h3>
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<p>若表达式对给定的相等输入产生相等输出，则它<i>保持相等性</i>。</p>
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<ul>
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<li>表达式的输入由其操作数组成。</li>
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<li>表达式的输出由其结果和表达式所修改的所有操作数（若存在）组成。</li>
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</ul>
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<p>在标准概念的规范中，操作数定义为仅包含下列内容的最大子表达式：</p>
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<ul>
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<li><a href="cpp-language-expressions.html#.E5.88.9D.E7.AD.89.E8.A1.A8.E8.BE.BE.E5.BC.8F">标识表达式</a>，及</li>
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<li>对 <a href="cpp-utility-move.html"><tt>std::move</tt></a> 、 <span class="t-lc"><a href="cpp-utility-forward.html">std::forward</a></span> 与 <span class="t-lc"><a href="cpp-utility-declval.html">std::declval</a></span> 的调用。</li>
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</ul>
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<p>每个操作数的 cv 限定与值类别，是通过假设每个模板类型形参代表一个 cv 无限定的非数组对象类型确定的。</p>
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<p>进一步要求每个要求保持相等性的表达式都<i>稳定</i>：这种表达式带相同输入对象的二次求值必须拥有相等的输出，而无任何对这些输入对象的显式中间修改。</p>
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<p>除非另外提醒，每个用于 <i>requires 表达式</i>中的表达式都要求保持相等性且稳定，而表达式的求值必须只修改其非常操作数。必须不修改常操作数。</p>
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<h3><span class="mw-headline" id=".E9.9A.90.E5.BC.8F.E8.A1.A8.E8.BE.BE.E5.BC.8F.E5.8F.98.E7.A7.8D">隐式表达式变种</span></h3>
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<p>使用不修改某 const 左值运算数的表达式的 <i>requires 表达式</i>亦隐式要求该表达式的额外变种对给定运算数接受非 const 左值或（可为 const 的）右值，除非以有区别的语义显式要求这种表达式变种。这些<i>隐式表达式变种</i>必须符合与声明的表达式的相同的语义。不指定实现以何种程度校验变种的语法。</p>
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