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 <head>
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  <title>P1154R2: Type traits for structural comparison</title>
<style data-fill-with="stylesheet">/******************************************************************************
 *                   Style sheet for the W3C specifications                   *
 *
 * Special classes handled by this style sheet include:
 *
 * Indices
 *   - .toc for the Table of Contents (<ol class="toc">)
 *     + <span class="secno"> for the section numbers
 *   - #toc for the Table of Contents (<nav id="toc">)
 *   - ul.index for Indices (<a href="#ref">term</a><span>, in §N.M</span>)
 *   - table.index for Index Tables (e.g. for properties or elements)
 *
 * Structural Markup
 *   - table.data for general data tables
 *     -> use 'scope' attribute, <colgroup>, <thead>, and <tbody> for best results !
 *     -> use <table class='complex data'> for extra-complex tables
 *     -> use <td class='long'> for paragraph-length cell content
 *     -> use <td class='pre'> when manual line breaks/indentation would help readability
 *   - dl.switch for switch statements
 *   - ol.algorithm for algorithms (helps to visualize nesting)
 *   - .figure and .caption (HTML4) and figure and figcaption (HTML5)
 *     -> .sidefigure for right-floated figures
 *   - ins/del
 *
 * Code
 *   - pre and code
 *
 * Special Sections
 *   - .note       for informative notes             (div, p, span, aside, details)
 *   - .example    for informative examples          (div, p, pre, span)
 *   - .issue      for issues                        (div, p, span)
 *   - .assertion  for assertions                    (div, p, span)
 *   - .advisement for loud normative statements     (div, p, strong)
 *   - .annoying-warning for spec obsoletion notices (div, aside, details)
 *
 * Definition Boxes
 *   - pre.def   for WebIDL definitions
 *   - table.def for tables that define other entities (e.g. CSS properties)
 *   - dl.def    for definition lists that define other entitles (e.g. HTML elements)
 *
 * Numbering
 *   - .secno for section numbers in .toc and headings (<span class='secno'>3.2</span>)
 *   - .marker for source-inserted example/figure/issue numbers (<span class='marker'>Issue 4</span>)
 *   - ::before styled for CSS-generated issue/example/figure numbers:
 *     -> Documents wishing to use this only need to add
 *        figcaption::before,
 *        .caption::before { content: "Figure "  counter(figure) " ";  }
 *        .example::before { content: "Example " counter(example) " "; }
 *        .issue::before   { content: "Issue "   counter(issue) " ";   }
 *
 * Header Stuff (ignore, just don't conflict with these classes)
 *   - .head for the header
 *   - .copyright for the copyright
 *
 * Miscellaneous
 *   - .overlarge for things that should be as wide as possible, even if
 *     that overflows the body text area. This can be used on an item or
 *     on its container, depending on the effect desired.
 *     Note that this styling basically doesn't help at all when printing,
 *     since A4 paper isn't much wider than the max-width here.
 *     It's better to design things to fit into a narrower measure if possible.
 *   - js-added ToC jump links (see fixup.js)
 *
 ******************************************************************************/

/******************************************************************************/
/*                                   Body                                     */
/******************************************************************************/

	body {
		counter-reset: example figure issue;

		/* Layout */
		max-width: 50em;               /* limit line length to 50em for readability   */
		margin: 0 auto;                /* center text within page                     */
		padding: 1.6em 1.5em 2em 50px; /* assume 16px font size for downlevel clients */
		padding: 1.6em 1.5em 2em calc(26px + 1.5em); /* leave space for status flag     */

		/* Typography */
		line-height: 1.5;
		font-family: sans-serif;
		widows: 2;
		orphans: 2;
		word-wrap: break-word;
		overflow-wrap: break-word;
		hyphens: auto;

		/* Colors */
		color: black;
		background: white top left fixed no-repeat;
		background-size: 25px auto;
	}


/******************************************************************************/
/*                         Front Matter & Navigation                          */
/******************************************************************************/

/** Header ********************************************************************/

	div.head { margin-bottom: 1em }
	div.head hr { border-style: solid; }

	div.head h1 {
		font-weight: bold;
		margin: 0 0 .1em;
		font-size: 220%;
	}

	div.head h2 { margin-bottom: 1.5em;}

/** W3C Logo ******************************************************************/

	.head .logo {
		float: right;
		margin: 0.4rem 0 0.2rem .4rem;
	}

	.head img[src*="logos/W3C"] {
		display: block;
		border: solid #1a5e9a;
		border-width: .65rem .7rem .6rem;
		border-radius: .4rem;
		background: #1a5e9a;
		color: white;
		font-weight: bold;
	}

	.head a:hover > img[src*="logos/W3C"],
	.head a:focus > img[src*="logos/W3C"] {
		opacity: .8;
	}

	.head a:active > img[src*="logos/W3C"] {
		background: #c00;
		border-color: #c00;
	}

	/* see also additional rules in Link Styling section */

/** Copyright *****************************************************************/

	p.copyright,
	p.copyright small { font-size: small }

/** Back to Top / ToC Toggle **************************************************/

	@media print {
		#toc-nav {
			display: none;
		}
	}
	@media not print {
		#toc-nav {
			position: fixed;
			z-index: 2;
			bottom: 0; left: 0;
			margin: 0;
			min-width: 1.33em;
			border-top-right-radius: 2rem;
			box-shadow: 0 0 2px;
			font-size: 1.5em;
			color: black;
		}
		#toc-nav > a {
			display: block;
			white-space: nowrap;

			height: 1.33em;
			padding: .1em 0.3em;
			margin: 0;

			background: white;
			box-shadow: 0 0 2px;
			border: none;
			border-top-right-radius: 1.33em;
			background: white;
		}
		#toc-nav > #toc-jump {
			padding-bottom: 2em;
			margin-bottom: -1.9em;
		}

		#toc-nav > a:hover,
		#toc-nav > a:focus {
			background: #f8f8f8;
		}
		#toc-nav > a:not(:hover):not(:focus) {
			color: #707070;
		}

		/* statusbar gets in the way on keyboard focus; remove once browsers fix */
		#toc-nav > a[href="#toc"]:not(:hover):focus:last-child {
			padding-bottom: 1.5rem;
		}

		#toc-nav:not(:hover) > a:not(:focus) > span + span {
			/* Ideally this uses :focus-within on #toc-nav */
			display: none;
		}
		#toc-nav > a > span + span {
			padding-right: 0.2em;
		}

		#toc-toggle-inline {
			vertical-align: 0.05em;
			font-size: 80%;
			color: gray;
			color: hsla(203,20%,40%,.7);
			border-style: none;
			background: transparent;
			position: relative;
		}
		#toc-toggle-inline:hover:not(:active),
		#toc-toggle-inline:focus:not(:active) {
			text-shadow: 1px 1px silver;
			top: -1px;
			left: -1px;
		}

		#toc-nav :active {
			color: #C00;
		}
	}

/** ToC Sidebar ***************************************************************/

	/* Floating sidebar */
	@media screen {
		body.toc-sidebar #toc {
			position: fixed;
			top: 0; bottom: 0;
			left: 0;
			width: 23.5em;
			max-width: 80%;
			max-width: calc(100% - 2em - 26px);
			overflow: auto;
			padding: 0 1em;
			padding-left: 42px;
			padding-left: calc(1em + 26px);
			background: inherit;
			background-color: #f7f8f9;
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) inset;
		}
		body.toc-sidebar #toc h2 {
			margin-top: .8rem;
			font-variant: small-caps;
			font-variant: all-small-caps;
			text-transform: lowercase;
			font-weight: bold;
			color: gray;
			color: hsla(203,20%,40%,.7);
		}
		body.toc-sidebar #toc-jump:not(:focus) {
			width: 0;
			height: 0;
			padding: 0;
			position: absolute;
			overflow: hidden;
		}
	}
	/* Hide main scroller when only the ToC is visible anyway */
	@media screen and (max-width: 28em) {
		body.toc-sidebar {
			overflow: hidden;
		}
	}

	/* Sidebar with its own space */
	@media screen and (min-width: 78em) {
		body:not(.toc-inline) #toc {
			position: fixed;
			top: 0; bottom: 0;
			left: 0;
			width: 23.5em;
			overflow: auto;
			padding: 0 1em;
			padding-left: 42px;
			padding-left: calc(1em + 26px);
			background: inherit;
			background-color: #f7f8f9;
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) inset;
		}
		body:not(.toc-inline) #toc h2 {
			margin-top: .8rem;
			font-variant: small-caps;
			font-variant: all-small-caps;
			text-transform: lowercase;
			font-weight: bold;
			color: gray;
			color: hsla(203,20%,40%,.7);
		}

		body:not(.toc-inline) {
			padding-left: 29em;
		}
		/* See also Overflow section at the bottom */

		body:not(.toc-inline) #toc-jump:not(:focus) {
			width: 0;
			height: 0;
			padding: 0;
			position: absolute;
			overflow: hidden;
		}
	}
	@media screen and (min-width: 90em) {
		body:not(.toc-inline) {
			margin: 0 4em;
		}
	}

/******************************************************************************/
/*                                Sectioning                                  */
/******************************************************************************/

/** Headings ******************************************************************/

	h1, h2, h3, h4, h5, h6, dt {
		page-break-after: avoid;
		page-break-inside: avoid;
		font: 100% sans-serif;   /* Reset all font styling to clear out UA styles */
		font-family: inherit;    /* Inherit the font family. */
		line-height: 1.2;        /* Keep wrapped headings compact */
		hyphens: manual;         /* Hyphenated headings look weird */
	}

	h2, h3, h4, h5, h6 {
		margin-top: 3rem;
	}

	h1, h2, h3 {
		color: #005A9C;
		background: transparent;
	}

	h1 { font-size: 170%; }
	h2 { font-size: 140%; }
	h3 { font-size: 120%; }
	h4 { font-weight: bold; }
	h5 { font-style: italic; }
	h6 { font-variant: small-caps; }
	dt { font-weight: bold; }

/** Subheadings ***************************************************************/

	h1 + h2,
	#subtitle {
		/* #subtitle is a subtitle in an H2 under the H1 */
		margin-top: 0;
	}
	h2 + h3,
	h3 + h4,
	h4 + h5,
	h5 + h6 {
		margin-top: 1.2em; /* = 1 x line-height */
	}

/** Section divider ***********************************************************/

	:not(.head) > hr {
		font-size: 1.5em;
		text-align: center;
		margin: 1em auto;
		height: auto;
		border: transparent solid 0;
		background: transparent;
	}
	:not(.head) > hr::before {
		content: "\2727\2003\2003\2727\2003\2003\2727";
	}

/******************************************************************************/
/*                            Paragraphs and Lists                            */
/******************************************************************************/

	p {
		margin: 1em 0;
	}

	dd > p:first-child,
	li > p:first-child {
		margin-top: 0;
	}

	ul, ol {
		margin-left: 0;
		padding-left: 2em;
	}

	li {
		margin: 0.25em 0 0.5em;
		padding: 0;
	}

	dl dd {
		margin: 0 0 .5em 2em;
	}

	.head dd + dd { /* compact for header */
		margin-top: -.5em;
	}

	/* Style for algorithms */
	ol.algorithm ol:not(.algorithm),
	.algorithm > ol ol:not(.algorithm) {
	 border-left: 0.5em solid #DEF;
	}

	/* Put nice boxes around each algorithm. */
	[data-algorithm]:not(.heading) {
	  padding: .5em;
	  border: thin solid #ddd; border-radius: .5em;
	  margin: .5em calc(-0.5em - 1px);
	}
	[data-algorithm]:not(.heading) > :first-child {
	  margin-top: 0;
	}
	[data-algorithm]:not(.heading) > :last-child {
	  margin-bottom: 0;
	}

	/* Style for switch/case <dl>s */
	dl.switch > dd > ol.only,
	dl.switch > dd > .only > ol {
	 margin-left: 0;
	}
	dl.switch > dd > ol.algorithm,
	dl.switch > dd > .algorithm > ol {
	 margin-left: -2em;
	}
	dl.switch {
	 padding-left: 2em;
	}
	dl.switch > dt {
	 text-indent: -1.5em;
	 margin-top: 1em;
	}
	dl.switch > dt + dt {
	 margin-top: 0;
	}
	dl.switch > dt::before {
	 content: '\21AA';
	 padding: 0 0.5em 0 0;
	 display: inline-block;
	 width: 1em;
	 text-align: right;
	 line-height: 0.5em;
	}

/** Terminology Markup ********************************************************/


/******************************************************************************/
/*                                 Inline Markup                              */
/******************************************************************************/

/** Terminology Markup ********************************************************/
	dfn   { /* Defining instance */
		font-weight: bolder;
	}
	a > i { /* Instance of term */
		font-style: normal;
	}
	dt dfn code, code.idl {
		font-size: medium;
	}
	dfn var {
		font-style: normal;
	}

/** Change Marking ************************************************************/

	del { color: red;  text-decoration: line-through; }
	ins { color: #080; text-decoration: underline;    }

/** Miscellaneous improvements to inline formatting ***************************/

	sup {
		vertical-align: super;
		font-size: 80%
	}

/******************************************************************************/
/*                                    Code                                    */
/******************************************************************************/

/** General monospace/pre rules ***********************************************/

	pre, code, samp {
		font-family: Menlo, Consolas, "DejaVu Sans Mono", Monaco, monospace;
		font-size: .9em;
		page-break-inside: avoid;
		hyphens: none;
		text-transform: none;
	}
	pre code,
	code code {
		font-size: 100%;
	}

	pre {
		margin-top: 1em;
		margin-bottom: 1em;
		overflow: auto;
	}

/** Inline Code fragments *****************************************************/

  /* Do something nice. */

/******************************************************************************/
/*                                    Links                                   */
/******************************************************************************/

/** General Hyperlinks ********************************************************/

	/* We hyperlink a lot, so make it less intrusive */
	a[href] {
		color: #034575;
		text-decoration: none;
		border-bottom: 1px solid #707070;
		/* Need a bit of extending for it to look okay */
		padding: 0 1px 0;
		margin: 0 -1px 0;
	}
	a:visited {
		border-bottom-color: #BBB;
	}

	/* Use distinguishing colors when user is interacting with the link */
	a[href]:focus,
	a[href]:hover {
		background: #f8f8f8;
		background: rgba(75%, 75%, 75%, .25);
		border-bottom-width: 3px;
		margin-bottom: -2px;
	}
	a[href]:active {
		color: #C00;
		border-color: #C00;
	}

	/* Backout above styling for W3C logo */
	.head .logo,
	.head .logo a {
		border: none;
		text-decoration: none;
		background: transparent;
	}

/******************************************************************************/
/*                                    Images                                  */
/******************************************************************************/

	img {
		border-style: none;
	}

	/* For autogen numbers, add
	   .caption::before, figcaption::before { content: "Figure " counter(figure) ". "; }
	*/

	figure, .figure, .sidefigure {
		page-break-inside: avoid;
		text-align: center;
		margin: 2.5em 0;
	}
	.figure img,    .sidefigure img,    figure img,
	.figure object, .sidefigure object, figure object {
		max-width: 100%;
		margin: auto;
	}
	.figure pre, .sidefigure pre, figure pre {
		text-align: left;
		display: table;
		margin: 1em auto;
	}
	.figure table, figure table {
		margin: auto;
	}
	@media screen and (min-width: 20em) {
		.sidefigure {
			float: right;
			width: 50%;
			margin: 0 0 0.5em 0.5em
		}
	}
	.caption, figcaption, caption {
		font-style: italic;
		font-size: 90%;
	}
	.caption::before, figcaption::before, figcaption > .marker {
		font-weight: bold;
	}
	.caption, figcaption {
		counter-increment: figure;
	}

	/* DL list is indented 2em, but figure inside it is not */
	dd > .figure, dd > figure { margin-left: -2em }

/******************************************************************************/
/*                             Colored Boxes                                  */
/******************************************************************************/

	.issue, .note, .example, .assertion, .advisement, blockquote {
		padding: .5em;
		border: .5em;
		border-left-style: solid;
		page-break-inside: avoid;
	}
	span.issue, span.note {
		padding: .1em .5em .15em;
		border-right-style: solid;
	}

	.issue,
	.note,
	.example,
	.advisement,
	.assertion,
	blockquote {
		margin: 1em auto;
	}
	.note  > p:first-child,
	.issue > p:first-child,
	blockquote > :first-child {
		margin-top: 0;
	}
	blockquote > :last-child {
		margin-bottom: 0;
	}

/** Blockquotes ***************************************************************/

	blockquote {
		border-color: silver;
	}

/** Open issue ****************************************************************/

	.issue {
		border-color: #E05252;
		background: #FBE9E9;
		counter-increment: issue;
		overflow: auto;
	}
	.issue::before, .issue > .marker {
		text-transform: uppercase;
		color: #AE1E1E;
		padding-right: 1em;
		text-transform: uppercase;
	}
	/* Add .issue::before { content: "Issue " counter(issue) " "; } for autogen numbers,
	   or use class="marker" to mark up the issue number in source. */

/** Example *******************************************************************/

	.example {
		border-color: #E0CB52;
		background: #FCFAEE;
		counter-increment: example;
		overflow: auto;
		clear: both;
	}
	.example::before, .example > .marker {
		text-transform: uppercase;
		color: #827017;
		min-width: 7.5em;
		display: block;
	}
	/* Add .example::before { content: "Example " counter(example) " "; } for autogen numbers,
	   or use class="marker" to mark up the example number in source. */

/** Non-normative Note ********************************************************/

	.note {
		border-color: #52E052;
		background: #E9FBE9;
		overflow: auto;
	}

	.note::before, .note > .marker,
	details.note > summary::before,
	details.note > summary > .marker {
		text-transform: uppercase;
		display: block;
		color: hsl(120, 70%, 30%);
	}
	/* Add .note::before { content: "Note"; } for autogen label,
	   or use class="marker" to mark up the label in source. */

	details.note > summary {
		display: block;
		color: hsl(120, 70%, 30%);
	}
	details.note[open] > summary {
		border-bottom: 1px silver solid;
	}

/** Assertion Box *************************************************************/
	/*  for assertions in algorithms */

	.assertion {
		border-color: #AAA;
		background: #EEE;
	}

/** Advisement Box ************************************************************/
	/*  for attention-grabbing normative statements */

	.advisement {
		border-color: orange;
		border-style: none solid;
		background: #FFEECC;
	}
	strong.advisement {
		display: block;
		text-align: center;
	}
	.advisement > .marker {
		color: #B35F00;
	}

/** Spec Obsoletion Notice ****************************************************/
	/* obnoxious obsoletion notice for older/abandoned specs. */

	details {
		display: block;
	}
	summary {
		font-weight: bolder;
	}

	.annoying-warning:not(details),
	details.annoying-warning:not([open]) > summary,
	details.annoying-warning[open] {
		background: #fdd;
		color: red;
		font-weight: bold;
		padding: .75em 1em;
		border: thick red;
		border-style: solid;
		border-radius: 1em;
	}
	.annoying-warning :last-child {
		margin-bottom: 0;
	}

@media not print {
	details.annoying-warning[open] {
		position: fixed;
		left: 1em;
		right: 1em;
		bottom: 1em;
		z-index: 1000;
	}
}

	details.annoying-warning:not([open]) > summary {
		text-align: center;
	}

/** Entity Definition Boxes ***************************************************/

	.def {
		padding: .5em 1em;
		background: #DEF;
		margin: 1.2em 0;
		border-left: 0.5em solid #8CCBF2;
	}

/******************************************************************************/
/*                                    Tables                                  */
/******************************************************************************/

	th, td {
		text-align: left;
		text-align: start;
	}

/** Property/Descriptor Definition Tables *************************************/

	table.def {
		/* inherits .def box styling, see above */
		width: 100%;
		border-spacing: 0;
	}

	table.def td,
	table.def th {
		padding: 0.5em;
		vertical-align: baseline;
		border-bottom: 1px solid #bbd7e9;
	}

	table.def > tbody > tr:last-child th,
	table.def > tbody > tr:last-child td {
		border-bottom: 0;
	}

	table.def th {
		font-style: italic;
		font-weight: normal;
		padding-left: 1em;
		width: 3em;
	}

	/* For when values are extra-complex and need formatting for readability */
	table td.pre {
		white-space: pre-wrap;
	}

	/* A footnote at the bottom of a def table */
	table.def           td.footnote {
		padding-top: 0.6em;
	}
	table.def           td.footnote::before {
		content: " ";
		display: block;
		height: 0.6em;
		width: 4em;
		border-top: thin solid;
	}

/** Data tables (and properly marked-up index tables) *************************/
	/*
		 <table class="data"> highlights structural relationships in a table
		 when correct markup is used (e.g. thead/tbody, th vs. td, scope attribute)

		 Use class="complex data" for particularly complicated tables --
		 (This will draw more lines: busier, but clearer.)

		 Use class="long" on table cells with paragraph-like contents
		 (This will adjust text alignment accordingly.)
		 Alternately use class="longlastcol" on tables, to have the last column assume "long".
	*/

	table {
		word-wrap: normal;
		overflow-wrap: normal;
		hyphens: manual;
	}

	table.data,
	table.index {
		margin: 1em auto;
		border-collapse: collapse;
		border: hidden;
		width: 100%;
	}
	table.data caption,
	table.index caption {
		max-width: 50em;
		margin: 0 auto 1em;
	}

	table.data td,  table.data th,
	table.index td, table.index th {
		padding: 0.5em 1em;
		border-width: 1px;
		border-color: silver;
		border-top-style: solid;
	}

	table.data thead td:empty {
		padding: 0;
		border: 0;
	}

	table.data  thead,
	table.index thead,
	table.data  tbody,
	table.index tbody {
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 <body class="h-entry">
  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P1154R2<br>Type traits for structural comparison</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Published Proposal, <time class="dt-updated" datetime="2019-03-10">2019-03-10</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>Authors:
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:arthur.j.odwyer@gmail.com">Arthur O'Dwyer</a>
     <dd>
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:jeff-isocpp@caffeinated.me.uk">Jeff Snyder</a>
     <dt>Audience:
     <dd>LWG
     <dt>Project:
     <dd>ISO/IEC JTC1/SC22/WG21 14882: Programming Language — C++
     <dt>Draft Revision:
     <dd>7
     <dt>Current Source:
     <dd><a href="https://github.com/Quuxplusone/draft/blob/gh-pages/d1154-comparable-traits.bs">github.com/Quuxplusone/draft/blob/gh-pages/d1154-comparable-traits.bs</a>
     <dt>Current:
     <dd><a href="https://rawgit.com/Quuxplusone/draft/gh-pages/d1154-comparable-traits.html">rawgit.com/Quuxplusone/draft/gh-pages/d1154-comparable-traits.html</a>
    </dl>
   </div>
   <div data-fill-with="warning"></div>
   <hr title="Separator for header">
  </div>
  <div class="p-summary" data-fill-with="abstract">
   <h2 class="no-num no-toc no-ref heading settled" id="abstract"><span class="content">Abstract</span></h2>
   <p>Now that <a data-link-type="biblio" href="#biblio-p0732">P0732R2 "Class Types in Non-Type Template Parameters"</a> has been adopted,

  we propose the new type-trait <code class="highlight"><c- n>has_strong_structural_equality</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code>.
  Code is more robust and maintainable when we can <code class="highlight"><c- k>static_assert</c-></code> this property.</p>
  </div>
  <nav data-fill-with="table-of-contents" id="toc">
   <h2 class="no-num no-toc no-ref" id="contents">Table of Contents</h2>
   <ol class="toc" role="directory">
    <li><a href="#changelog"><span class="secno">1</span> <span class="content">Changelog</span></a>
    <li><a href="#structural-equality"><span class="secno">2</span> <span class="content">Strong structural equality should be static-assertable</span></a>
    <li><a href="#compiler-builtin"><span class="secno">3</span> <span class="content">This feature benefits from compiler support</span></a>
    <li><a href="#batteries-included"><span class="secno">4</span> <span class="content">Provide just the one type trait</span></a>
    <li><a href="#wording"><span class="secno">5</span> <span class="content">Proposed wording for C++2a</span></a>
    <li><a href="#polls"><span class="secno">6</span> <span class="content">Straw polls taken of LEWG in Kona (2019-02-18)</span></a>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ol>
   </ol>
  </nav>
  <main>
   <h2 class="heading settled" data-level="1" id="changelog"><span class="secno">1. </span><span class="content">Changelog</span><a class="self-link" href="#changelog"></a></h2>
   <ul>
    <li data-md>
     <p>R2 (post-Kona):</p>
     <ul>
      <li data-md>
       <p>Removed five of the six proposed type-traits at LEWG’s request (see <a href="#polls">§6 Straw polls taken of LEWG in Kona (2019-02-18)</a>).
LEWG voted to forward this version to LWG for C++2a.</p>
     </ul>
   </ul>
   <h2 class="heading settled" data-level="2" id="structural-equality"><span class="secno">2. </span><span class="content">Strong structural equality should be static-assertable</span><a class="self-link" href="#structural-equality"></a></h2>
   <p>The concept of "having strong structural equality" that was introduced by <a data-link-type="biblio" href="#biblio-p0732">[P0732]</a> will become important
to programmers. Take this class type for example:</p>
<pre class="language-c++ highlight"><c- n>template</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- b>size_t</c-> <c- n>N</c-><c- o>></c->
<c- k>struct</c-> <c- n>fixed_string</c->
<c- p>{</c->
    <c- n>constexpr</c-> <c- n>fixed_string</c-><c- p>(</c-><c- k>const</c-> <c- b>char</c-> <c- p>(</c-><c- o>&amp;</c-><c- n>s</c-><c- p>)[</c-><c- n>N</c-><c- o>+</c-><c- mi>1</c-><c- p>])</c->
        <c- p>{</c-> <c- n>std</c-><c- o>::</c-><c- n>copy_n</c-><c- p>(</c-><c- n>s</c-><c- p>,</c-> <c- n>N</c-><c- o>+</c-><c- mi>1</c-><c- p>,</c-> <c- n>m_data</c-><c- p>);</c-> <c- p>}</c->
    <c- k>auto</c-> <c- n>operator</c-><c- o>&lt;=></c-><c- p>(</c-><c- k>const</c-> <c- n>fixed_string</c-> <c- o>&amp;</c-><c- p>)</c-> <c- k>const</c-> <c- o>=</c-> <c- k>default</c-><c- p>;</c->
    <c- b>char</c-> <c- n>m_data</c-><c- p>[</c-><c- n>N</c-><c- o>+</c-><c- mi>1</c-><c- p>];</c->
<c- p>};</c->
</pre>
   <p>This type’s <code class="highlight"><c- k>operator</c-><c- o>&lt;=></c-></code> is a "structural comparison operator"
because it is defaulted, and invokes only other structural comparison operators. Since it yields <code class="highlight"><c- n>strong_ordering</c-></code>, it also has what we might call "strong structural ordering",
although this term is not introduced by P0732.
"Strong structural ordering" is a stricter requirement than P0732’s "strong structural equality,"
which is the prerequisite to use a user-defined type as a non-type template parameter.</p>
   <p>C++ should permit the programmer to test the presence or absence of this property.
Example:</p>
<pre class="language-c++ highlight"><c- n>static_assert</c-><c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>has_strong_structural_equality_v</c-><c- o>&lt;</c-> <c- n>fixed_string</c-><c- o>&lt;</c-><c- mi>5</c-><c- o>></c-> <c- o>></c-><c- p>);</c->
</pre>
   <p>This permits maintainability-minded programmers to express their intention in code.</p>
<pre class="language-c++ highlight"><c- n>template</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- b>size_t</c-> <c- n>N</c-><c- o>></c->
<c- k>struct</c-> <c- n>broken_fixed_string</c->
<c- p>{</c->
    <c- n>constexpr</c-> <c- n>broken_fixed_string</c-><c- p>(</c-><c- k>const</c-> <c- b>char</c-> <c- p>(</c-><c- o>&amp;</c-><c- n>s</c-><c- p>)[</c-><c- n>N</c-><c- o>+</c-><c- mi>1</c-><c- p>])</c->
        <c- p>{</c-> <c- n>std</c-><c- o>::</c-><c- n>copy_n</c-><c- p>(</c-><c- n>s</c-><c- p>,</c-> <c- n>N</c-><c- o>+</c-><c- mi>1</c-><c- p>,</c-> <c- n>m_data</c-><c- p>);</c-> <c- p>}</c->
    <c- k>auto</c-> <c- n>operator</c-><c- o>&lt;=></c-><c- p>(</c-><c- k>const</c-> <c- n>broken_fixed_string</c-> <c- o>&amp;</c-><c- n>rhs</c-><c- p>)</c-> <c- k>const</c->
        <c- p>{</c-> <c- k>return</c-> <c- n>std</c-><c- o>::</c-><c- n>memcmp</c-><c- p>(</c-><c- n>m_data</c-><c- p>,</c-> <c- n>rhs</c-><c- p>.</c-><c- n>m_data</c-><c- p>,</c-> <c- n>N</c-><c- o>+</c-><c- mi>1</c-><c- p>)</c-> <c- o>&lt;=></c-> <c- mi>0</c-><c- p>;</c-> <c- p>}</c->
    <c- b>char</c-> <c- n>m_data</c-><c- p>[</c-><c- n>N</c-><c- o>+</c-><c- mi>1</c-><c- p>];</c->
<c- p>};</c->
<c- n>static_assert</c-><c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>has_strong_structural_equality_v</c-><c- o>&lt;</c-> <c- n>broken_fixed_string</c-><c- o>&lt;</c-><c- mi>5</c-><c- o>></c-> <c- o>></c-><c- p>,</c->
    <c- s>"broken_fixed_string lacks the strong structural equality we expected"</c-><c- p>);</c->

<c- c1>// ... possibly many lines of code here ...</c->
<c- c1>// ... possibly written by a different programmer ...</c->

<c- n>template</c-><c- o>&lt;</c-><c- k>auto</c-> <c- n>V</c-><c- o>></c-> <c- k>struct</c-> <c- n>A</c-> <c- p>{};</c->
<c- n>A</c-><c- o>&lt;</c-><c- n>broken_fixed_string</c-><c- p>(</c-><c- s>"hello"</c-><c- p>)</c-><c- o>></c-> <c- n>a</c-><c- p>;</c->
</pre>
   <p>In the snippet above, we get a nice descriptive <code class="highlight"><c- k>static_assert</c-></code> failure, instead of an
unfriendly spew of diagnostics on the line that tries to instantiate <code class="highlight"><c- n>A</c-></code>.</p>
   <h2 class="heading settled" data-level="3" id="compiler-builtin"><span class="secno">3. </span><span class="content">This feature benefits from compiler support</span><a class="self-link" href="#compiler-builtin"></a></h2>
   <p>P1154R0 claimed that this type-trait could not be implemented without a compiler builtin.
In fact, <code class="highlight"><c- n>has_strong_structural_equality</c-></code> <em>can</em> be implemented according to standard C++17:</p>
<pre class="language-c++ highlight"><c- n>template</c-><c- o>&lt;</c-><c- k>auto</c-><c- o>></c-> <c- k>struct</c-> <c- n>A</c-> <c- p>{};</c->

<c- n>template</c-><c- o>&lt;</c-><c- n>class</c-> <c- n>T</c-><c- p>,</c-> <c- n>template</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-> <c- n>class</c-> <c- o>=</c-> <c- n>A</c-><c- o>></c-> <c- n>using</c-> <c- n>B</c-> <c- o>=</c-> <c- b>void</c-><c- p>;</c->

<c- n>template</c-><c- o>&lt;</c-><c- n>class</c-> <c- n>T</c-><c- p>,</c-> <c- n>class</c-> <c- o>=</c-> <c- b>void</c-><c- o>></c->
<c- k>struct</c-> <c- nl>HasStrongStructuralEquality</c-> <c- p>:</c-> <c- n>std</c-><c- o>::</c-><c- n>false_type</c-> <c- p>{};</c->

<c- n>template</c-><c- o>&lt;</c-><c- n>class</c-> <c- n>T</c-><c- o>></c->
<c- k>struct</c-> <c- n>HasStrongStructuralEquality</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>B</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>></c-> <c- o>:</c-> <c- n>std</c-><c- o>::</c-><c- n>true_type</c-> <c- p>{};</c->

<c- n>static_assert</c-><c- p>(</c-><c- n>HasStrongStructuralEquality</c-><c- o>&lt;</c-> <c- b>int</c-> <c- o>>::</c-><c- n>value</c-><c- p>);</c->
<c- n>static_assert</c-><c- p>(</c-><c- o>!</c-><c- n>HasStrongStructuralEquality</c-><c- o>&lt;</c-> <c- n>std</c-><c- o>::</c-><c- n>string</c-> <c- o>>::</c-><c- n>value</c-><c- p>);</c->
</pre>
   <p>This code relies on subtle and maybe-uncertain rules governing when <code class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>auto</c-><c- o>></c-> <c- k>struct</c-> <c- n>A</c-></code> is a valid argument for a parameter of type <code class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-> <c- k>class</c-></code>.</p>
   <ul>
    <li data-md>
     <p>GCC currently does not support this code — that is,
they fail the second <code class="highlight"><c- k>static_assert</c-></code>.</p>
    <li data-md>
     <p>MSVC flatly rejects it because they don’t support <code class="highlight"><c- k>auto</c-></code> template parameters yet.</p>
    <li data-md>
     <p>Clang accepts this code. The worst that can be said of Clang
is that they give the wrong answer for <code class="highlight"><c- n>HasStrongStructuralEquality</c-><c- o>&lt;</c-><c- b>int</c-><c- o>&amp;&amp;></c-></code>,
but that can easily be worked around on the library side.</p>
   </ul>
   <p>Right now the burden is on the application programmer to know this trivia
and come up with workarounds for GCC and MSVC. We propose to simplify the programmer’s job
by putting this trait into the standard library, where the burden will be on the library
to get it right (probably using a compiler builtin).</p>
   <h2 class="heading settled" data-level="4" id="batteries-included"><span class="secno">4. </span><span class="content">Provide just the one type trait</span><a class="self-link" href="#batteries-included"></a></h2>
   <p>P1154R1 proposed six type-traits, with implementations shown in terms of a
hypothetical compiler builtin <code class="highlight"><c- n>__has_structural_comparison</c-><c- p>(</c-><c- n>T</c-><c- p>)</c-></code>. After the adoption
of <a data-link-type="biblio" href="#biblio-p1185">[P1185]</a>, the general notion of "structural comparison" is no longer meaningful; the
new core-language feature is "strong structural equality" (only).</p>
   <p>Strong structural equality may be provided by a structural (defaulted) <code class="highlight"><c- k>operator</c-><c- o>&lt;=></c-></code> or by a structural (defaulted) <code class="highlight"><c- k>operator</c-><c- o>==</c-></code>. In the latter case, the type might not
support <code class="highlight"><c- k>operator</c-><c- o>&lt;=></c-></code> at all.</p>
   <p>Therefore we propose only the following type-trait, with accompanying <code class="highlight"><c- n>_v</c-></code> variable template.
For exposition purposes only, we provide a sample implementation in terms of
a hypothetical compiler builtin <code class="highlight"><c- n>__has_strong_structural_equality</c-><c- p>(</c-><c- n>T</c-><c- p>)</c-></code>.</p>
   <p><small></small></p>
   <small> <pre class="language-c++ highlight"><c- n>template</c-><c- o>&lt;</c-><c- n>class</c-> <c- n>T</c-><c- o>></c-> <c- k>struct</c-> <c- nl>has_strong_structural_equality</c-> <c- p>:</c->
    <c- n>bool_constant</c-><c- o>&lt;</c-> <c- n>__has_strong_structural_equality</c-><c- p>(</c-><c- n>T</c-><c- p>)</c-> <c- o>></c-> <c- p>{};</c->
</pre></small> 
   <h2 class="heading settled" data-level="5" id="wording"><span class="secno">5. </span><span class="content">Proposed wording for C++2a</span><a class="self-link" href="#wording"></a></h2>
   <p>Add one new entry to Table 47 in <a href="http://eel.is/c++draft/meta.unary.prop">[meta.unary.prop]</a>:</p>
   <p><small></small></p>
   <blockquote>
    <p></p>
    <small> <table> <tbody><tr><th>Template</th><th>Condition</th><th>Preconditions</th></tr> <tr> <td><code class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>T</c-><c- o>></c-> <c- k>struct</c-> <c- n>has_strong_structural_equality</c-><c- p>;</c-></code></td> <td>The type <code class="highlight"><c- n>T</c-></code> has strong structural equality (10.10.1).</td> <td>T shall be a complete type, <i>cv</i> <code class="highlight"><c- b>void</c-></code>, or an array of unknown bound.</td> </tr> </tbody></table> </small>
   </blockquote>
   <h2 class="heading settled" data-level="6" id="polls"><span class="secno">6. </span><span class="content">Straw polls taken of LEWG in Kona (2019-02-18)</span><a class="self-link" href="#polls"></a></h2>
   <table class="def">
    <tbody>
     <tr>
      <th style="width: 70%;">
      <th><strong>SF</strong>
      <th><strong>F</strong>
      <th><strong>N</strong>
      <th><strong>A</strong>
      <th><strong>SA</strong>
     <tr>
      <th><small>We want all of the traits [from P1154R1] (rather than just strong structural equality).</small>
      <th>0
      <th>2
      <th>4
      <th>0
      <th>3
     <tr>
      <th><small>Drop everything but <code class="highlight"><c- n>has_strong_structural_equality</c-><c- p>[</c-><c- n>_v</c-><c- p>]</c-></code>, make sure to coordinate with <a data-link-type="biblio" href="#biblio-p1185">[P1185]</a>, and forward to LWG for C++20.</small>
      <th>3
      <th>5
      <th>1
      <th>0
      <th>0
   </table>
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  <h2 class="no-num no-ref heading settled" id="references"><span class="content">References</span><a class="self-link" href="#references"></a></h2>
  <h3 class="no-num no-ref heading settled" id="informative"><span class="content">Informative References</span><a class="self-link" href="#informative"></a></h3>
  <dl>
   <dt id="biblio-p0732">[P0732]
   <dd>Jeff Snyder; Louis Dionne. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2018/p0732r2.pdf">Class Types in Non-Type Template Parameters</a>. June 2018. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2018/p0732r2.pdf">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2018/p0732r2.pdf</a>
   <dt id="biblio-p1185">[P1185]
   <dd>Barry Revzin. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1185r1.html">&lt;=> != ==</a>. January 2019. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1185r1.html">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1185r1.html</a>
  </dl>