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<title>Issue 3360: three_way_comparable_with is inconsistent with similar concepts</title>
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<p><em>This page is a snapshot from the LWG issues list, see the <a href="lwg-active.html">Library Active Issues List</a> for more information and the meaning of <a href="lwg-active.html#C++20">C++20</a> status.</em></p>
<h3 id="3360"><a href="lwg-defects.html#3360">3360</a>. <code>three_way_comparable_with</code> is inconsistent with similar concepts</h3>
<p><b>Section:</b> 17.12.4 <a href="https://wg21.link/cmp.concept">[cmp.concept]</a> <b>Status:</b> <a href="lwg-active.html#C++20">C++20</a>
 <b>Submitter:</b> Casey Carter <b>Opened:</b> 2019-12-18 <b>Last modified:</b> 2021-02-25</p>
<p><b>Priority: </b>0
</p>
<p><b>View all other</b> <a href="lwg-index.html#cmp.concept">issues</a> in [cmp.concept].</p>
<p><b>View all issues with</b> <a href="lwg-status.html#C++20">C++20</a> status.</p>
<p><b>Discussion:</b></p>
<p>
The concept <code>three_way_comparable_with</code> is defined in 17.12.4 <a href="https://wg21.link/cmp.concept">[cmp.concept]</a> as:
</p>
<blockquote>
<pre>
template&lt;class T, class U, class Cat = partial_ordering&gt;
  concept three_way_comparable_with =
    <i>weakly-equality-comparable-with</i>&lt;T, U&gt; &amp;&amp;
    <i>partially-ordered-with</i>&lt;T, U&gt; &amp;&amp;
    three_way_comparable&lt;T, Cat&gt; &amp;&amp;
    three_way_comparable&lt;U, Cat&gt; &amp;&amp;
    common_reference_with&lt;const remove_reference_t&lt;T&gt;&amp;, const remove_reference_t&lt;U&gt;&amp;&gt; &amp;&amp;
    three_way_comparable&lt;
      common_reference_t&lt;const remove_reference_t&lt;T&gt;&amp;, const remove_reference_t&lt;U&gt;&amp;&gt;, Cat&gt; &amp;&amp;
    requires(const remove_reference_t&lt;T&gt;&amp; t, const remove_reference_t&lt;U&gt;&amp; u) {
      { t &lt;=&gt; u } -&gt; <i>compares-as</i>&lt;Cat&gt;;
      { u &lt;=&gt; t } -&gt; <i>compares-as</i>&lt;Cat&gt;;
    };
</pre>
</blockquote>
<p>
Which notably doesn't follow the requirement ordering:
</p>
<ol>
<li><p>same-type requirements on <code>T</code></p></li>
<li><p>same-type requirements on <code>U</code></p></li>
<li><p><code>common_reference_with</code> requirement</p></li>
<li><p>same-type requirements on <code>common_reference_t&lt;T, U&gt;</code></p></li>
<li><p>cross-type requirements on <code>T</code> and <code>U</code></p></li>
</ol>
<p>
that the other cross-type comparison concepts (18.5.4 <a href="https://wg21.link/concept.equalitycomparable">[concept.equalitycomparable]</a>, 
18.5.5 <a href="https://wg21.link/concept.totallyordered">[concept.totallyordered]</a>) use. There were some motivating reasons for that ordering:
</p>
<ol>
<li><p>The existence of a common reference type is effectively an opt-in to cross-type concepts. 
Avoiding checking cross-type expressions when no common reference type exists can enable the 
concepts to work even in the presence of poorly-constrained "accidental" cross-type operator 
templates which could otherwise produce compile errors instead of dissatisfied concepts.</p></li>
<li><p>Putting the simpler same-type requirements first can help produce simpler error messages 
when applying the wrong concept to a pair of types, or the right concept to the wrong pair of types. 
"<code>Frobnozzle &lt;=&gt; Frobnozzle</code> is not a valid expression" is more easily deciphered than 
is "<code>std::common_reference&lt;int, FrobNozzle&gt;</code> has no member named type".</p></li>
</ol>
<p>
<code>three_way_comparable_with</code> should be made consistent with <code>equality_comparable_with</code> and 
<code>totally_ordered_with</code> for the above reasons and to make it easier to reason about comparison concepts 
in general.
</p>

<p><i>[2020-01 Status set to Tentatively Ready after five positive votes on the reflector.]</i></p>



<p id="res-3360"><b>Proposed resolution:</b></p>
<p>This wording is relative to <a href="https://wg21.link/n4842">N4842</a>.</p>

<ol>
<li><p>Modify 17.12.4 <a href="https://wg21.link/cmp.concept">[cmp.concept]</a> as indicated:</p>

<blockquote>
<pre>
template&lt;class T, class U, class Cat = partial_ordering&gt;
  concept three_way_comparable_with =
    <del><i>weakly-equality-comparable-with</i>&lt;T, U&gt; &amp;&amp;</del>
    <del><i>partially-ordered-with</i>&lt;T, U&gt; &amp;&amp;</del>
    three_way_comparable&lt;T, Cat&gt; &amp;&amp;
    three_way_comparable&lt;U, Cat&gt; &amp;&amp;
    common_reference_with&lt;const remove_reference_t&lt;T&gt;&amp;, const remove_reference_t&lt;U&gt;&amp;&gt; &amp;&amp;
    three_way_comparable&lt;
      common_reference_t&lt;const remove_reference_t&lt;T&gt;&amp;, const remove_reference_t&lt;U&gt;&amp;&gt;, Cat&gt; &amp;&amp;
    <ins><i>weakly-equality-comparable-with</i>&lt;T, U&gt; &amp;&amp;</ins>
    <ins><i>partially-ordered-with</i>&lt;T, U&gt; &amp;&amp;</ins>
    requires(const remove_reference_t&lt;T&gt;&amp; t, const remove_reference_t&lt;U&gt;&amp; u) {
      { t &lt;=&gt; u } -&gt; <i>compares-as</i>&lt;Cat&gt;;
      { u &lt;=&gt; t } -&gt; <i>compares-as</i>&lt;Cat&gt;;
    };
</pre>
</blockquote>
</li>

</ol>




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