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<meta name="dcterms.date" content="2019-11-07" />
<title>Remove std::weak_equality and std::strong_equality</title>
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<h1 class="title" style="text-align:center">Remove <code class="sourceCode cpp">std<span class="op">::</span>weak_equality</code> and <code class="sourceCode cpp">std<span class="op">::</span>strong_equality</code></h1>
<table style="border:none;float:right">
<tr>
<td>Document #: </td>
<td>P1959R0</td>
</tr>
<tr>
<td>Date: </td>
<td>2019-11-07</td>
</tr>
<tr>
<td style="vertical-align:top">Project: </td>
<td>Programming Language C++<br>
EWG, LEWG<br>
</td>
</tr>
<tr>
<td style="vertical-align:top">Reply-to: </td>
<td>
Barry Revzin<br><<a href="mailto:barry.revzin@gmail.com" class="email">barry.revzin@gmail.com</a>><br>
</td>
</tr>
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</header>
<div style="clear:both">
<h1 id="introduction" style="border-bottom:1px solid #cccccc"><span class="header-section-number">1</span> Introduction<a href="#introduction" class="self-link"></a></h1>
<p>This paper resolves NB comments <a href="https://github.com/cplusplus/nbballot/issues/168">US 170</a>:</p>
<blockquote>
<p>The <code class="sourceCode cpp">strong_equality</code> and <code class="sourceCode cpp">weak_equality</code> comparison categories don’t make sense now that we split equality from ordering. It doesn’t make sense to declare an <code class="sourceCode cpp"><span class="kw">operator</span><span class="op"><=></span></code> that returns one of these – they just add needless complexity.</p>
</blockquote>
<p>and <a href="https://github.com/cplusplus/nbballot/issues/171">CA 173</a>:</p>
<blockquote>
<p>With the separation of <code class="sourceCode cpp"><span class="op"><=></span></code> and <code class="sourceCode cpp"><span class="op">==</span></code>, <code class="sourceCode cpp">weak_equality</code> has lost its primary use (of being a potential return type of <code class="sourceCode cpp"><span class="op"><=></span></code>). Currently weak_equality serves no useful purpose in the standard (i.e., nothing in std acts on it), and just causes confusion (what’s the difference between weak and strong, when should I use which?) The difference between the two is ill-defined (involving substitutability and “salient” properties, which are also vaguely defined). The best definition of equality for a type is the type’s own <code class="sourceCode cpp"><span class="op">==</span></code> operator. We should not try to sub-divide the concept of equality.</p>
</blockquote>
<p>The first of these comments subsumes the other, and this paper provides the wording for that change.</p>
<h1 id="wording" style="border-bottom:1px solid #cccccc"><span class="header-section-number">2</span> Wording<a href="#wording" class="self-link"></a></h1>
<p>Change 7.6.8 [expr.spaceship], paragraph 7, to remove the ability to call <code class="sourceCode cpp"><span class="op"><=></span></code> on function pointers, pointers to members, and <code class="sourceCode cpp">nullptr_t</code>.</p>
<blockquote>
<p><span class="marginalizedparent"><a class="marginalized">7</a></span> <span class="rm" style="color: #bf0303"><del>If the composite pointer type is a function pointer type, a pointer-to-member type, or <span><code class="sourceCode cpp">std<span class="op">::</span>nullptr_t</code></span>, the result is of type <span><code class="sourceCode cpp">std<span class="op">::</span>strong_equality</code></span>; the result is <span><code class="sourceCode cpp">std<span class="op">::</span>strong_equality<span class="op">::</span>equal</code></span> if the (possibly converted) operands compare equal ([expr.eq]) and <span><code class="sourceCode cpp">std<span class="op">::</span>strong_equality<span class="op">::</span>nonequal</code></span> if they compare unequal, otherwise the result of the operator is unspecified.</del></span></p>
</blockquote>
<p>Change 7.6.8 [expr.spaceship], paragraph 10:</p>
<blockquote>
<p><span class="marginalizedparent"><a class="marginalized">10</a></span> The <span class="rm" style="color: #bf0303"><del>five</del></span> <span class="addu">three</span> comparison category types (the types <code class="sourceCode cpp">std<span class="op">::</span>strong_ordering</code>, <span class="rm" style="color: #bf0303"><del><span><code class="sourceCode cpp">std<span class="op">::</span>strong_equality</code></span>,</del></span> <code class="sourceCode cpp">std<span class="op">::</span>weak_ordering</code>, <span class="rm" style="color: #bf0303"><del><span><code class="sourceCode cpp">std<span class="op">::</span>weak_equality</code></span>,</del></span> and <code class="sourceCode cpp">std<span class="op">::</span>partial_ordering</code>) are not predefined; […]</p>
</blockquote>
<p>Change 11.11.1 [class.compare.default], paragraph 4:</p>
<blockquote>
<p><span class="marginalizedparent"><a class="marginalized">4</a></span> A type <code class="sourceCode cpp">C</code> has <em>strong structural equality</em> if, given a glvalue <code class="sourceCode cpp">x</code> of type <code class="sourceCode cpp"><span class="kw">const</span> C</code>, either:</p>
<ul>
<li><span class="marginalizedparent"><a class="marginalized">(4.1)</a></span> <code class="sourceCode cpp">C</code> is a non-class type and <code class="sourceCode cpp">x <span class="op"><=></span> x</code> is a valid expression of type <code class="sourceCode cpp">std<span class="op">::</span>strong_ordering</code> <span class="rm" style="color: #bf0303"><del>or <span><code class="sourceCode cpp">std<span class="op">::</span>strong_equality</code></span></del></span>, or</li>
<li><span class="marginalizedparent"><a class="marginalized">(4.2)</a></span> <code class="sourceCode cpp">C</code> is a class type where all of the following hold: […]</li>
</ul>
</blockquote>
<p>Remove the <code class="sourceCode cpp">XXX_equality</code> cases from 11.11.3 [class.spaceship], paragraph 1:</p>
<blockquote>
<p><span class="marginalizedparent"><a class="marginalized">1</a></span> The <em>synthesized three-way comparison</em> for comparison category type <code class="sourceCode cpp">R</code> ([cmp.categories]) of glvalues <code class="sourceCode cpp">a</code> and <code class="sourceCode cpp">b</code> of the same type is defined as follows:</p>
<ul>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.1)</a></span> […]</p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.5)</a></span> Otherwise, if <code class="sourceCode cpp">R</code> is <code class="sourceCode cpp">partial_ordering</code>, then</p>
<blockquote>
<div class="sourceCode" id="cb1"><pre class="sourceCode default"><code class="sourceCode default"><span id="cb1-1"><a href="#cb1-1"></a>a == b ? partial_ordering::equivalent : </span>
<span id="cb1-2"><a href="#cb1-2"></a>a < b ? partial_ordering::less :</span>
<span id="cb1-3"><a href="#cb1-3"></a>b < a ? partial_ordering::greater :</span>
<span id="cb1-4"><a href="#cb1-4"></a> partial_ordering::unordered</span></code></pre></div>
</blockquote></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.6)</a></span> <span class="rm" style="color: #bf0303"><del>Otherwise, if <span><code class="sourceCode cpp">R</code></span> is <span><code class="sourceCode cpp">strong_equality</code></span>, then <span><code class="sourceCode cpp">a <span class="op">==</span> b <span class="op">?</span> strong_equality<span class="op">::</span>equal <span class="op">:</span> strong_equality<span class="op">::</span>nonequal</code></span>;</del></span></p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.7)</a></span> <span class="rm" style="color: #bf0303"><del>Otherwise, if <span><code class="sourceCode cpp">R</code></span> is <span><code class="sourceCode cpp">weak_equality</code></span>, then <span><code class="sourceCode cpp">a <span class="op">==</span> b <span class="op">?</span> weak_equality<span class="op">::</span>equivalent <span class="op">:</span> weak_equality<span class="op">::</span>nonequivalent</code></span>;</del></span></p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.8)</a></span> Otherwise, the synthesized three-way comparison is not defined.</p></li>
</ul>
</blockquote>
<p>Remove the <code class="sourceCode cpp">XXX_equality</code> cases from 11.11.3 [class.spaceship], paragraph 3:</p>
<blockquote>
<p>The <em>common comparison type</em> <code class="sourceCode cpp">U</code> of a possibly-empty list of <code class="sourceCode cpp">n</code> types <code class="sourceCode cpp">T0</code>, <code class="sourceCode cpp">T1</code>, …, <code class="sourceCode cpp">Tn−<span class="dv">1</span></code> is defined as follows:</p>
<ul>
<li><span class="marginalizedparent"><a class="marginalized">(4.1)</a></span> If any <code class="sourceCode cpp">Ti</code> is not a comparison category type ([cmp.categories]), <code class="sourceCode cpp">U</code> is void.</li>
<li><span class="marginalizedparent"><a class="marginalized">(4.2)</a></span> <span class="rm" style="color: #bf0303"><del>Otherwise, if at least one <span><code class="sourceCode cpp">Ti</code></span> is <span><code class="sourceCode cpp">std<span class="op">::</span>weak_equality</code></span>, or at least one <span><code class="sourceCode cpp">Ti</code></span> is <span><code class="sourceCode cpp">std<span class="op">::</span>strong_equality</code></span> and at least one <span><code class="sourceCode cpp">Tj</code></span> is <span><code class="sourceCode cpp">std<span class="op">::</span>partial_ordering</code></span> or <span><code class="sourceCode cpp">std<span class="op">::</span>weak_ordering</code></span>, <span><code class="sourceCode cpp">U</code></span> is <span><code class="sourceCode cpp">std<span class="op">::</span>weak_equality</code></span> ([cmp.weakeq]).</del></span></li>
<li><span class="marginalizedparent"><a class="marginalized">(4.3)</a></span> <span class="rm" style="color: #bf0303"><del>Otherwise, if at least one <span><code class="sourceCode cpp">Ti</code></span> is <span><code class="sourceCode cpp">std<span class="op">::</span>strong_equality</code></span>, <span><code class="sourceCode cpp">U</code></span> is <span><code class="sourceCode cpp">std<span class="op">::</span>strong_equality</code></span> ([cmp.strongeq]).</del></span></li>
<li><span class="marginalizedparent"><a class="marginalized">(4.4)</a></span> Otherwise, if at least one <code class="sourceCode cpp">Ti</code> is <code class="sourceCode cpp">std<span class="op">::</span>partial_ordering</code>, <code class="sourceCode cpp">U</code> is <code class="sourceCode cpp">std<span class="op">::</span>partial_ordering</code> ([cmp.partialord]).</li>
<li><span class="marginalizedparent"><a class="marginalized">(4.5)</a></span> Otherwise, if at least one <code class="sourceCode cpp">Ti</code> is <code class="sourceCode cpp">std<span class="op">::</span>weak_ordering</code>, <code class="sourceCode cpp">U</code> is <code class="sourceCode cpp">std<span class="op">::</span>weak_ordering</code> ([cmp.weakord]).</li>
<li><span class="marginalizedparent"><a class="marginalized">(4.6)</a></span> Otherwise, <code class="sourceCode cpp">U</code> is <code class="sourceCode cpp">std<span class="op">::</span>strong_ordering</code> ([cmp.strongord]).</li>
</ul>
</blockquote>
<p>Change the example in 11.11.4 [class.rel], paragraph 3, to use a different type that has no <code class="sourceCode cpp"><span class="op"><</span></code>:</p>
<blockquote>
<div>
<div class="sourceCode" id="cb2"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb2-1"><a href="#cb2-1"></a><span class="va">+ struct HasNoLessThan { };</span></span>
<span id="cb2-2"><a href="#cb2-2"></a></span>
<span id="cb2-3"><a href="#cb2-3"></a> struct C {</span>
<span id="cb2-4"><a href="#cb2-4"></a><span class="st">- friend std::strong_equality operator<=>(const C&, const C&);</span></span>
<span id="cb2-5"><a href="#cb2-5"></a><span class="va">+ friend HasNoLessThan operator<=>(const C&, const C&);</span></span>
<span id="cb2-6"><a href="#cb2-6"></a> bool operator<(const C&) const = default; // OK, function is deleted</span>
<span id="cb2-7"><a href="#cb2-7"></a> };</span></code></pre></div>
</div>
</blockquote>
<p>Remove <code class="sourceCode cpp"><span class="op"><=></span></code> from 12.7 [over.built], paragraph 19:</p>
<blockquote>
<p><span class="marginalizedparent"><a class="marginalized">19</a></span> For every <code class="sourceCode cpp">T</code>, where <code class="sourceCode cpp">T</code> is a pointer-to-member type or <code class="sourceCode cpp">std<span class="op">::</span>nullptr_t</code>, there exist candidate operator functions of the form:</p>
<div>
<div class="sourceCode" id="cb3"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb3-1"><a href="#cb3-1"></a> bool operator==(T, T);</span>
<span id="cb3-2"><a href="#cb3-2"></a> bool operator!=(T, T);</span>
<span id="cb3-3"><a href="#cb3-3"></a><span class="st">- std::strong_equality operator<=>(T, T);</span></span></code></pre></div>
</div>
</blockquote>
<p>Change 13.2 [temp.param]/4 to add back the bullets that <span class="citation" data-cites="P0732R2">[<a href="#ref-P0732R2" role="doc-biblioref">P0732R2</a>]</span> removed, now that these other types no longer have strong structural equality:</p>
<blockquote>
<p><span class="marginalizedparent"><a class="marginalized">4</a></span> A non-type template-parameter shall have one of the following (optionally cv-qualified) types:</p>
<ul>
<li><span class="marginalizedparent"><a class="marginalized">(4.1)</a></span> a literal type that has strong structural equality ([class.compare.default]),</li>
<li><span class="marginalizedparent"><a class="marginalized">(4.2)</a></span> an lvalue reference type,</li>
<li><span class="marginalizedparent"><a class="marginalized">(4.3)</a></span> a type that contains a placeholder type ([dcl.spec.auto]), <span class="rm" style="color: #bf0303"><del>or</del></span></li>
<li><span class="marginalizedparent"><a class="marginalized">(4.4)</a></span> a placeholder for a deduced class type ([dcl.type.class.deduct])<span class="rm" style="color: #bf0303"><del>.</del></span> <span class="addu">,</span></li>
<li><span class="marginalizedparent"><a class="marginalized">(4.5)</a></span> <span class="addu">pointer to object or pointer to function,</span></li>
<li><span class="marginalizedparent"><a class="marginalized">(4.6)</a></span> <span class="addu">pointer to member, or</span></li>
<li><span class="marginalizedparent"><a class="marginalized">(4.7)</a></span> <span class="addu"><code class="sourceCode cpp">std<span class="op">::</span>nullptr_t</code>.</span></li>
</ul>
</blockquote>
<p>Remove the <code class="sourceCode cpp">XXX_equality</code> types from the compare synopsis in 17.11.1 [compare.syn]:</p>
<div>
<div class="sourceCode" id="cb4"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb4-1"><a href="#cb4-1"></a>namespace std {</span>
<span id="cb4-2"><a href="#cb4-2"></a> // [cmp.categories], comparison category types</span>
<span id="cb4-3"><a href="#cb4-3"></a><span class="st">- class weak_equality;</span></span>
<span id="cb4-4"><a href="#cb4-4"></a><span class="st">- class strong_equality;</span></span>
<span id="cb4-5"><a href="#cb4-5"></a> class partial_ordering;</span>
<span id="cb4-6"><a href="#cb4-6"></a> class weak_ordering;</span>
<span id="cb4-7"><a href="#cb4-7"></a> class strong_ordering;</span>
<span id="cb4-8"><a href="#cb4-8"></a></span>
<span id="cb4-9"><a href="#cb4-9"></a> // named comparison functions</span>
<span id="cb4-10"><a href="#cb4-10"></a><span class="st">- constexpr bool is_eq (weak_equality cmp) noexcept { return cmp == 0; }</span></span>
<span id="cb4-11"><a href="#cb4-11"></a><span class="st">- constexpr bool is_neq (weak_equality cmp) noexcept { return cmp != 0; }</span></span>
<span id="cb4-12"><a href="#cb4-12"></a><span class="va">+ constexpr bool is_eq (partial_ordering cmp) noexcept { return cmp == 0; }</span></span>
<span id="cb4-13"><a href="#cb4-13"></a><span class="va">+ constexpr bool is_neq (partial_ordering cmp) noexcept { return cmp != 0; }</span></span>
<span id="cb4-14"><a href="#cb4-14"></a> constexpr bool is_lt (partial_ordering cmp) noexcept { return cmp < 0; }</span>
<span id="cb4-15"><a href="#cb4-15"></a> constexpr bool is_lteq(partial_ordering cmp) noexcept { return cmp <= 0; }</span>
<span id="cb4-16"><a href="#cb4-16"></a> constexpr bool is_gt (partial_ordering cmp) noexcept { return cmp > 0; }</span>
<span id="cb4-17"><a href="#cb4-17"></a> constexpr bool is_gteq(partial_ordering cmp) noexcept { return cmp >= 0; }</span>
<span id="cb4-18"><a href="#cb4-18"></a>}</span></code></pre></div>
</div>
<p>Change 17.11.2.1 [cmp.categories.pre], paragraphs 1-2:</p>
<blockquote>
<p><span class="marginalizedparent"><a class="marginalized">1</a></span> The types <span class="rm" style="color: #bf0303"><del><span><code class="sourceCode cpp">weak_equality</code></span>, <span><code class="sourceCode cpp">strong_equality</code></span>,</del></span> <code class="sourceCode cpp">partial_ordering</code>, <code class="sourceCode cpp">weak_ordering</code>, and <code class="sourceCode cpp">strong_ordering</code> are collectively termed the comparison category types. Each is specified in terms of an exposition-only data member named value whose value typically corresponds to that of an enumerator from one of the following exposition-only enumerations:</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode default"><code class="sourceCode default"><span id="cb5-1"><a href="#cb5-1"></a>enum class eq { equal = 0, equivalent = equal,</span>
<span id="cb5-2"><a href="#cb5-2"></a> nonequal = 1, nonequivalent = nonequal }; // exposition only</span>
<span id="cb5-3"><a href="#cb5-3"></a>enum class ord { less = -1, greater = 1 }; // exposition only</span>
<span id="cb5-4"><a href="#cb5-4"></a>enum class ncmp { unordered = -127 }; // exposition only</span></code></pre></div>
<p><span class="marginalizedparent"><a class="marginalized">2</a></span> [ Note: The type<span class="rm" style="color: #bf0303"><del>s</del></span> <code class="sourceCode cpp">strong_ordering</code> <span class="rm" style="color: #bf0303"><del>and weak_equality</del></span> correspond<span class="addu">s</span><span class="rm" style="color: #bf0303"><del>, respectively,</del></span> to the term<span class="rm" style="color: #bf0303"><del>s</del></span> total ordering <span class="rm" style="color: #bf0303"><del>and equivalence</del></span> in mathematics. — end note ]</p>
</blockquote>
<p>Remove 17.11.2.2 [cmp.weakeq] (the subclause that defines <code class="sourceCode cpp">std<span class="op">::</span>weak_equality</code>).</p>
<p>Remove 17.11.2.3 [cmp.strongeq] (the subclause that defines <code class="sourceCode cpp">std<span class="op">::</span>strong_equality</code>).</p>
<p>Remove the conversion operator to <code class="sourceCode cpp">weak_equality</code> from 17.11.2.4 [cmp.partialord]:</p>
<blockquote>
<div>
<div class="sourceCode" id="cb6"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb6-1"><a href="#cb6-1"></a>namespace std {</span>
<span id="cb6-2"><a href="#cb6-2"></a> class partial_ordering {</span>
<span id="cb6-3"><a href="#cb6-3"></a> [...] </span>
<span id="cb6-4"><a href="#cb6-4"></a> </span>
<span id="cb6-5"><a href="#cb6-5"></a><span class="st">- // conversion</span></span>
<span id="cb6-6"><a href="#cb6-6"></a><span class="st">- constexpr operator weak_equality() const noexcept; </span></span>
<span id="cb6-7"><a href="#cb6-7"></a> </span>
<span id="cb6-8"><a href="#cb6-8"></a> [...]</span>
<span id="cb6-9"><a href="#cb6-9"></a> };</span>
<span id="cb6-10"><a href="#cb6-10"></a>}</span></code></pre></div>
</div>
<div class="rm" style="color: #bf0303">
<p><code class="sourceCode cpp"><span class="kw">constexpr</span> <span class="kw">operator</span> weak_equality<span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span>;</code></p>
<p><span class="marginalizedparent"><a class="marginalized">2</a></span> <em>Returns</em>: <code class="sourceCode cpp">value <span class="op">==</span> <span class="dv">0</span> <span class="op">?</span> weak_equality<span class="op">::</span>equivalent <span class="op">:</span> weak_equality<span class="op">::</span>nonequivalent</code>. [ Note: The result is independent of the <code class="sourceCode cpp">is_ordered</code> member. — end note ]</p>
</div>
</blockquote>
<p>Remove the conversion operator to <code class="sourceCode cpp">weak_equality</code> from 17.11.2.5 [cmp.weakord]:</p>
<blockquote>
<div>
<div class="sourceCode" id="cb7"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb7-1"><a href="#cb7-1"></a>namespace std {</span>
<span id="cb7-2"><a href="#cb7-2"></a> class weak_ordering {</span>
<span id="cb7-3"><a href="#cb7-3"></a> [...] </span>
<span id="cb7-4"><a href="#cb7-4"></a> </span>
<span id="cb7-5"><a href="#cb7-5"></a> // conversion</span>
<span id="cb7-6"><a href="#cb7-6"></a><span class="st">- constexpr operator weak_equality() const noexcept; </span></span>
<span id="cb7-7"><a href="#cb7-7"></a> constexpr operator partial_ordering() const noexcept; </span>
<span id="cb7-8"><a href="#cb7-8"></a> </span>
<span id="cb7-9"><a href="#cb7-9"></a> [...]</span>
<span id="cb7-10"><a href="#cb7-10"></a> };</span>
<span id="cb7-11"><a href="#cb7-11"></a>}</span></code></pre></div>
</div>
<div class="rm" style="color: #bf0303">
<p><code class="sourceCode cpp"><span class="kw">constexpr</span> <span class="kw">operator</span> weak_equality<span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span>;</code></p>
<p><span class="marginalizedparent"><a class="marginalized">2</a></span> <em>Returns</em>: <code class="sourceCode cpp">value <span class="op">==</span> <span class="dv">0</span> <span class="op">?</span> weak_equality<span class="op">::</span>equivalent <span class="op">:</span> weak_equality<span class="op">::</span>nonequivalent</code>.</p>
</div>
</blockquote>
<p>Remove the conversion operators to <code class="sourceCode cpp">XXX_equality</code> from 17.11.2.6 [cmp.strongord]:</p>
<blockquote>
<div>
<div class="sourceCode" id="cb8"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb8-1"><a href="#cb8-1"></a>namespace std {</span>
<span id="cb8-2"><a href="#cb8-2"></a> class strong_ordering {</span>
<span id="cb8-3"><a href="#cb8-3"></a> [...] </span>
<span id="cb8-4"><a href="#cb8-4"></a> </span>
<span id="cb8-5"><a href="#cb8-5"></a> // conversions</span>
<span id="cb8-6"><a href="#cb8-6"></a><span class="st">- constexpr operator weak_equality() const noexcept;</span></span>
<span id="cb8-7"><a href="#cb8-7"></a><span class="st">- constexpr operator strong_equality() const noexcept;</span></span>
<span id="cb8-8"><a href="#cb8-8"></a> constexpr operator partial_ordering() const noexcept;</span>
<span id="cb8-9"><a href="#cb8-9"></a> constexpr operator weak_ordering() const noexcept;</span>
<span id="cb8-10"><a href="#cb8-10"></a> </span>
<span id="cb8-11"><a href="#cb8-11"></a> [...]</span>
<span id="cb8-12"><a href="#cb8-12"></a> };</span>
<span id="cb8-13"><a href="#cb8-13"></a>}</span></code></pre></div>
</div>
<div class="rm" style="color: #bf0303">
<p><code class="sourceCode cpp"><span class="kw">constexpr</span> <span class="kw">operator</span> weak_equality<span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span>;</code></p>
<p><span class="marginalizedparent"><a class="marginalized">2</a></span> <em>Returns</em>: <code class="sourceCode cpp">value <span class="op">==</span> <span class="dv">0</span> <span class="op">?</span> weak_equality<span class="op">::</span>equivalent <span class="op">:</span> weak_equality<span class="op">::</span>nonequivalent</code>.</p>
<p><code class="sourceCode cpp"><span class="kw">constexpr</span> <span class="kw">operator</span> strong_equality<span class="op">()</span> <span class="kw">const</span> <span class="kw">noexcept</span>;</code></p>
<p><span class="marginalizedparent"><a class="marginalized">3</a></span> <em>Returns</em>: <code class="sourceCode cpp">value <span class="op">==</span> <span class="dv">0</span> <span class="op">?</span> strong_equality<span class="op">::</span>equal <span class="op">:</span> strong_equality<span class="op">::</span>nonequal</code>.</p>
</div>
</blockquote>
<p>Simplify the three-way comparable concepts in 17.11.4 [cmp.concept]:</p>
<blockquote>
<div>
<div class="sourceCode" id="cb9"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb9-1"><a href="#cb9-1"></a>template <typename T, typename Cat = partial_ordering></span>
<span id="cb9-2"><a href="#cb9-2"></a> concept three_way_comparable =</span>
<span id="cb9-3"><a href="#cb9-3"></a> <em>weakly-equality-comparable-with</em><T, T> &&</span>
<span id="cb9-4"><a href="#cb9-4"></a><span class="st">- (!convertible_to<Cat, partial_ordering> || <em>partially-ordered-with</em><T, T>) &&</span></span>
<span id="cb9-5"><a href="#cb9-5"></a><span class="va">+ <em>partially-ordered-with</em><T, T> &&</span></span>
<span id="cb9-6"><a href="#cb9-6"></a> requires(const remove_reference_t<T>& a,</span>
<span id="cb9-7"><a href="#cb9-7"></a> const remove_reference_t<T>& b) {</span>
<span id="cb9-8"><a href="#cb9-8"></a> { a <=> b } -> <em>compares-as</em><Cat>;</span>
<span id="cb9-9"><a href="#cb9-9"></a> };</span></code></pre></div>
</div>
<p><span class="marginalizedparent"><a class="marginalized">2</a></span> Let <code class="sourceCode cpp">a</code> and <code class="sourceCode cpp">b</code> be lvalues of type <code class="sourceCode cpp"><span class="kw">const</span> remove_reference_t<span class="op"><</span>T<span class="op">></span></code>. <code class="sourceCode cpp">T</code> and <code class="sourceCode cpp">Cat</code> model <code class="sourceCode cpp">three_way_comparable<span class="op"><</span>T, Cat<span class="op">></span></code> only if:</p>
<ul>
<li><span class="marginalizedparent"><a class="marginalized">(2.1)</a></span> <code class="sourceCode cpp"><span class="op">(</span>a <span class="op"><=></span> b <span class="op">==</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>a <span class="op">==</span> b<span class="op">)</span></code>.</li>
<li><span class="marginalizedparent"><a class="marginalized">(2.2)</a></span> <code class="sourceCode cpp"><span class="op">(</span>a <span class="op"><=></span> b <span class="op">!=</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>a <span class="op">!=</span> b<span class="op">)</span></code>.</li>
<li><span class="marginalizedparent"><a class="marginalized">(2.3)</a></span> <code class="sourceCode cpp"><span class="op">((</span>a <span class="op"><=></span> b<span class="op">)</span> <span class="op"><=></span> <span class="dv">0</span><span class="op">)</span></code> and <code class="sourceCode cpp"><span class="op">(</span><span class="dv">0</span> <span class="op"><=></span> <span class="op">(</span>b <span class="op"><=></span> a<span class="op">))</span></code> are equal.</li>
<li><span class="marginalizedparent"><a class="marginalized">(2.4)</a></span> <span class="rm" style="color: #bf0303"><del>If <span><code class="sourceCode cpp">Cat</code></span> is convertible to <span><code class="sourceCode cpp">strong_equality</code></span>, <span><code class="sourceCode cpp">T</code></span> models <span><code class="sourceCode cpp">equality_comparable_with</code></span> ([concept.equalitycomparable]).</del></span></li>
<li><span class="marginalizedparent"><a class="marginalized">(2.5)</a></span> <span class="rm" style="color: #bf0303"><del>If <span><code class="sourceCode cpp">Cat</code></span> is convertible to <span><code class="sourceCode cpp">partial_ordering</code></span>:</del></span> <span class="ednote" style="color: #0000ff">[ Editor's note: Make the following subbullets into normal bullets ]</span>
<ul>
<li><span class="marginalizedparent"><a class="marginalized">(2.5.1)</a></span> <code class="sourceCode cpp"><span class="op">(</span>a <span class="op"><=></span> b <span class="op"><</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>a <span class="op"><</span> b<span class="op">)</span></code>.</li>
<li><span class="marginalizedparent"><a class="marginalized">(2.5.2)</a></span> <code class="sourceCode cpp"><span class="op">(</span>a <span class="op"><=></span> b <span class="op">></span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>a <span class="op">></span> b<span class="op">)</span></code>.</li>
<li><span class="marginalizedparent"><a class="marginalized">(2.5.3)</a></span> <code class="sourceCode cpp"><span class="op">(</span>a <span class="op"><=></span> b <span class="op"><=</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>a <span class="op"><=</span> b<span class="op">)</span></code>.</li>
<li><span class="marginalizedparent"><a class="marginalized">(2.5.4)</a></span> <code class="sourceCode cpp"><span class="op">(</span>a <span class="op"><=></span> b <span class="op">>=</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>a <span class="op">>=</span> b<span class="op">)</span></code>.</li>
</ul></li>
<li><span class="marginalizedparent"><a class="marginalized">(2.5.5)</a></span> If <code class="sourceCode cpp">Cat</code> is convertible to <code class="sourceCode cpp">strong_ordering</code>, <code class="sourceCode cpp">T</code> models <code class="sourceCode cpp">totally_ordered</code> ([concept.totallyordered]).</li>
</ul>
<div>
<div class="sourceCode" id="cb10"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb10-1"><a href="#cb10-1"></a>template <typename T, typename U,</span>
<span id="cb10-2"><a href="#cb10-2"></a> typename Cat = partial_ordering></span>
<span id="cb10-3"><a href="#cb10-3"></a> concept three_way_comparable_with = </span>
<span id="cb10-4"><a href="#cb10-4"></a> <em>weakly-equality-comparable-with</em><T, U> &&</span>
<span id="cb10-5"><a href="#cb10-5"></a><span class="st">- (!convertible_to<Cat, partial_ordering> || <em>partially-ordered-with</em><T, U>) &&</span></span>
<span id="cb10-6"><a href="#cb10-6"></a><span class="va">+ <em>partially-ordered-with</em><T, U> &&</span></span>
<span id="cb10-7"><a href="#cb10-7"></a> three_way_comparable<T, Cat> &&</span>
<span id="cb10-8"><a href="#cb10-8"></a> three_way_comparable<U, Cat> &&</span>
<span id="cb10-9"><a href="#cb10-9"></a> common_reference_with<const remove_reference_t<T>&, const remove_reference_t<U>&> &&</span>
<span id="cb10-10"><a href="#cb10-10"></a> three_way_comparable<</span>
<span id="cb10-11"><a href="#cb10-11"></a> common_reference_t<const remove_reference_t<T>&, const remove_reference_t<U>&>,</span>
<span id="cb10-12"><a href="#cb10-12"></a> Cat> &&</span>
<span id="cb10-13"><a href="#cb10-13"></a> requires(const remove_reference_t<T>& t,</span>
<span id="cb10-14"><a href="#cb10-14"></a> const remove_reference_t<U>& u) {</span>
<span id="cb10-15"><a href="#cb10-15"></a> { t <=> u } -> <em>compares-as</em><Cat>;</span>
<span id="cb10-16"><a href="#cb10-16"></a> { u <=> t } -> <em>compares-as</em><Cat>;</span>
<span id="cb10-17"><a href="#cb10-17"></a> };</span></code></pre></div>
</div>
<p><span class="marginalizedparent"><a class="marginalized">3</a></span> Let <code class="sourceCode cpp">t</code> and <code class="sourceCode cpp">u</code> be lvalues of types <code class="sourceCode cpp"><span class="kw">const</span> remove_reference_t<span class="op"><</span>T<span class="op">></span></code> and <code class="sourceCode cpp"><span class="kw">const</span> remove_reference_t<span class="op"><</span>U<span class="op">></span></code>, respectively. Let <code class="sourceCode cpp">C</code> be <code class="sourceCode cpp">common_reference_t<span class="op"><</span><span class="kw">const</span> remove_reference_t<span class="op"><</span>T<span class="op">>&</span>, <span class="kw">const</span> remove_reference_t<span class="op"><</span>U<span class="op">>&></span></code>. <code class="sourceCode cpp">T</code>, <code class="sourceCode cpp">U</code>, and <code class="sourceCode cpp">Cat</code> model <code class="sourceCode cpp">ThreeWayComparableWith<span class="op"><</span>T, U, Cat<span class="op">></span></code> only if:</p>
<ul>
<li><span class="marginalizedparent"><a class="marginalized">(3.1)</a></span> <code class="sourceCode cpp">t <span class="op"><=></span> u</code> and <code class="sourceCode cpp">u <span class="op"><=></span> t</code> have the same domain.</li>
<li><span class="marginalizedparent"><a class="marginalized">(3.2)</a></span> <code class="sourceCode cpp"><span class="op">((</span>t <span class="op"><=></span> u<span class="op">)</span> <span class="op"><=></span> <span class="dv">0</span><span class="op">)</span></code> and <code class="sourceCode cpp"><span class="op">(</span><span class="dv">0</span> <span class="op"><=></span> <span class="op">(</span>u <span class="op"><=></span> t<span class="op">))</span></code> are equal.</li>
<li><span class="marginalizedparent"><a class="marginalized">(3.3)</a></span> <code class="sourceCode cpp"><span class="op">(</span>t <span class="op"><=></span> u <span class="op">==</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>t <span class="op">==</span> u<span class="op">)</span></code>.</li>
<li><span class="marginalizedparent"><a class="marginalized">(3.4)</a></span> <code class="sourceCode cpp"><span class="op">(</span>t <span class="op"><=></span> u <span class="op">!=</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>t <span class="op">!=</span> u<span class="op">)</span></code>.</li>
<li><span class="marginalizedparent"><a class="marginalized">(3.5)</a></span> <code class="sourceCode cpp">Cat<span class="op">(</span>t <span class="op"><=></span> u<span class="op">)</span> <span class="op">==</span> Cat<span class="op">(</span>C<span class="op">(</span>t<span class="op">)</span> <span class="op"><=></span> C<span class="op">(</span>u<span class="op">))</span></code>.</li>
<li><span class="marginalizedparent"><a class="marginalized">(3.6)</a></span> <span class="rm" style="color: #bf0303"><del>If <span><code class="sourceCode cpp">Cat</code></span> is convertible to <span><code class="sourceCode cpp">strong_equality</code></span>, <span><code class="sourceCode cpp">T</code></span> and <span><code class="sourceCode cpp">U</code></span> model <span><code class="sourceCode cpp">equality_comparable_with<span class="op"><</span>T, U<span class="op">></span></code></span> ([concepts.equalitycomparable]).</del></span></li>
<li><span class="marginalizedparent"><a class="marginalized">(3.7)</a></span> <span class="rm" style="color: #bf0303"><del>If <span><code class="sourceCode cpp">Cat</code></span> is convertible to <span><code class="sourceCode cpp">partial_ordering</code></span>:</del></span> <span class="ednote" style="color: #0000ff">[ Editor's note: Make the following subbullets into normal bullets ]</span>
<ul>
<li><span class="marginalizedparent"><a class="marginalized">(3.7.1)</a></span> <code class="sourceCode cpp"><span class="op">(</span>t <span class="op"><=></span> u <span class="op"><</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>t <span class="op"><</span> u<span class="op">)</span></code></li>
<li><span class="marginalizedparent"><a class="marginalized">(3.7.2)</a></span> <code class="sourceCode cpp"><span class="op">(</span>t <span class="op"><=></span> u <span class="op">></span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>t <span class="op">></span> u<span class="op">)</span></code></li>
<li><span class="marginalizedparent"><a class="marginalized">(3.7.3)</a></span> <code class="sourceCode cpp"><span class="op">(</span>t <span class="op"><=></span> u <span class="op"><=</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>t <span class="op"><=</span> u<span class="op">)</span></code></li>
<li><span class="marginalizedparent"><a class="marginalized">(3.7.4)</a></span> <code class="sourceCode cpp"><span class="op">(</span>t <span class="op"><=></span> u <span class="op">>=</span> <span class="dv">0</span><span class="op">)</span> <span class="op">==</span> <span class="dt">bool</span><span class="op">(</span>t <span class="op">>=</span> u<span class="op">)</span></code></li>
</ul></li>
<li><span class="marginalizedparent"><a class="marginalized">(3.8)</a></span> If <code class="sourceCode cpp">Cat</code> is convertible to <code class="sourceCode cpp">strong_ordering</code>, <code class="sourceCode cpp">T</code> and <code class="sourceCode cpp">U</code> model <code class="sourceCode cpp">totally_ordered_with<span class="op"><</span>T, U<span class="op">></span></code> ([concepts.totallyordered]).</li>
</ul>
</blockquote>
<p>Change the root comparison category in some of the iterator <code class="sourceCode cpp"><span class="kw">operator</span><span class="op"><=></span></code>s from <code class="sourceCode cpp">weak_equality</code> to <code class="sourceCode cpp">partial_ordering</code> (that is, just remove the provided argument) in 23.2 [iterator.synopsis]:</p>
<blockquote>
<div>
<div class="sourceCode" id="cb11"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb11-1"><a href="#cb11-1"></a>#include <concepts></span>
<span id="cb11-2"><a href="#cb11-2"></a></span>
<span id="cb11-3"><a href="#cb11-3"></a>namespace std {</span>
<span id="cb11-4"><a href="#cb11-4"></a> [...]</span>
<span id="cb11-5"><a href="#cb11-5"></a> </span>
<span id="cb11-6"><a href="#cb11-6"></a><span class="st">- template<class Iterator1, three_way_comparable_with<Iterator1<span class="diffdel">, weak_equality</span>> Iterator2></span></span>
<span id="cb11-7"><a href="#cb11-7"></a><span class="va">+ template<class Iterator1, three_way_comparable_with<Iterator1> Iterator2></span></span>
<span id="cb11-8"><a href="#cb11-8"></a> constexpr compare_three_way_result_t<Iterator1, Iterator2></span>
<span id="cb11-9"><a href="#cb11-9"></a> operator<=>(const reverse_iterator<Iterator1>& x,</span>
<span id="cb11-10"><a href="#cb11-10"></a> const reverse_iterator<Iterator2>& y); </span>
<span id="cb11-11"><a href="#cb11-11"></a> </span>
<span id="cb11-12"><a href="#cb11-12"></a> [...]</span>
<span id="cb11-13"><a href="#cb11-13"></a> </span>
<span id="cb11-14"><a href="#cb11-14"></a><span class="st">- template<class Iterator1, three_way_comparable_with<Iterator1<span class="diffdel">, weak_equality</span>> Iterator2></span></span>
<span id="cb11-15"><a href="#cb11-15"></a><span class="va">+ template<class Iterator1, three_way_comparable_with<Iterator1> Iterator2></span></span>
<span id="cb11-16"><a href="#cb11-16"></a> constexpr compare_three_way_result_t<Iterator1, Iterator2></span>
<span id="cb11-17"><a href="#cb11-17"></a> operator<=>(const move_iterator<Iterator1>& x,</span>
<span id="cb11-18"><a href="#cb11-18"></a> const move_iterator<Iterator2>& y);</span>
<span id="cb11-19"><a href="#cb11-19"></a> </span>
<span id="cb11-20"><a href="#cb11-20"></a> [...]</span>
<span id="cb11-21"><a href="#cb11-21"></a>}</span></code></pre></div>
</div>
</blockquote>
<p>And the same in 23.5.1.7 [reverse.iter.cmp]:</p>
<blockquote>
<div>
<div class="sourceCode" id="cb12"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb12-1"><a href="#cb12-1"></a><span class="st">- template<class Iterator1, three_way_comparable_with<Iterator1<span class="diffdel">, weak_equality</span>> Iterator2></span></span>
<span id="cb12-2"><a href="#cb12-2"></a><span class="va">+ template<class Iterator1, three_way_comparable_with<Iterator1> Iterator2></span></span>
<span id="cb12-3"><a href="#cb12-3"></a> constexpr compare_three_way_result_t<Iterator1, Iterator2></span>
<span id="cb12-4"><a href="#cb12-4"></a> operator<=>(const reverse_iterator<Iterator1>& x,</span>
<span id="cb12-5"><a href="#cb12-5"></a> const reverse_iterator<Iterator2>& y); </span></code></pre></div>
</div>
<p><span class="marginalizedparent"><a class="marginalized">13</a></span> <em>Returns</em>: <code class="sourceCode cpp">y<span class="op">.</span>base<span class="op">()</span> <span class="op"><=></span> x<span class="op">.</span>base<span class="op">()</span></code>.</p>
</blockquote>
<p>And the same in 23.5.3.7 [move.iter.pop.cmp]:</p>
<blockquote>
<div>
<div class="sourceCode" id="cb13"><pre class="sourceCode diff"><code class="sourceCode diff"><span id="cb13-1"><a href="#cb13-1"></a><span class="st">- template<class Iterator1, three_way_comparable_with<Iterator1<span class="diffdel">, weak_equality</span>> Iterator2></span></span>
<span id="cb13-2"><a href="#cb13-2"></a><span class="va">+ template<class Iterator1, three_way_comparable_with<Iterator1> Iterator2></span></span>
<span id="cb13-3"><a href="#cb13-3"></a> constexpr compare_three_way_result_t<Iterator1, Iterator2></span>
<span id="cb13-4"><a href="#cb13-4"></a> operator<=>(const move_iterator<Iterator1>& x,</span>
<span id="cb13-5"><a href="#cb13-5"></a> const move_iterator<Iterator2>& y);</span></code></pre></div>
</div>
<p><span class="marginalizedparent"><a class="marginalized">13</a></span> <em>Returns</em>: <code class="sourceCode cpp">x<span class="op">.</span>base<span class="op">()</span> <span class="op"><=></span> y<span class="op">.</span>base<span class="op">()</span></code>.</p>
</blockquote>
<h1 id="references" style="border-bottom:1px solid #cccccc"><span class="header-section-number">3</span> References<a href="#references" class="self-link"></a></h1>
<div id="refs" role="doc-bibliography">
<div id="ref-P0732R2">
<p>[P0732R2] Jeff Snyder, Louis Dionne. 2018. Class Types in Non-Type Template Parameters. <br />
<a href="https://wg21.link/p0732r2">https://wg21.link/p0732r2</a></p>
</div>
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