<!doctype html><html lang="en">
 <head>
  <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
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  <title>P0891R2: Make strong_order a Customization Point!</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">P0891R2<br>Make strong_order a Customization Point!</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="subtitle"><span class="content">Published Proposal, <time class="dt-updated" datetime="2019-01-20">2019-01-20</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="https://github.com/atomgalaxy/a-little-order/strong-ordering.bs">https://github.com/atomgalaxy/a-little-order/strong-ordering.bs</a>
     <dt>Authors:
     <dd>
      <dd class="editor p-author h-card vcard"><span class="p-name fn">Gašper Ažman &lt;gasper.azman@gmail.com></span>
     <dd>
      <dd class="editor p-author h-card vcard"><span class="p-name fn">Jeff Snyder &lt;jeff-isocpp@caffeinated.me.uk></span>
     <dt>Audience:
     <dd>LEWG, LWG
     <dt>Project:
     <dd>ISO/IEC JTC1/SC22/WG21 14882: Programming Language — C++
    </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>The specification of ordering algorithms at the end of <a data-link-type="biblio" href="#biblio-p0768r1">[P0768R1]</a> does not provide the ability to provide a default order for user-defined types (since they are specified in such a way that they are not intended to be customisation points), and yet mixes in such a customisation for IEC559 floating point types. This paper suggests providing the functionality of both in a composable and principled way.</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="#history"><span class="secno">1</span> <span class="content">Revision History</span></a>
     <ol class="toc">
      <li><a href="#rap-feedback"><span class="secno">1.1</span> <span class="content">R1: Incorporated feedback from LEWG meeting in Rappersville.</span></a>
      <li><a href="#sd-feedback"><span class="secno">1.2</span> <span class="content">R2: Incorporated feedback from LEWG meeting in San Diego, merged with <span>[P0863R1]</span></span></a>
     </ol>
    <li><a href="#sup"><span class="secno">2</span> <span class="content">Status of this paper</span></a>
    <li><a href="#problem"><span class="secno">3</span> <span class="content">Problem Description</span></a>
    <li><a href="#principles"><span class="secno">4</span> <span class="content">Principles</span></a>
    <li>
     <a href="#discussion"><span class="secno">5</span> <span class="content">Discussion</span></a>
     <ol class="toc">
      <li>
       <a href="#discussion-customisation"><span class="secno">5.1</span> <span class="content">Discussion of the <span>Customisation</span> principle</span></a>
       <ol class="toc">
        <li><a href="#but-is-it-legal-ill-make-it-legal"><span class="secno">5.1.1</span> <span class="content">Is it useful?</span></a>
        <li><a href="#impl-effort"><span class="secno">5.1.2</span> <span class="content">Given that it is viral, is it worth the implementation effort?</span></a>
        <li>
         <a href="#faq-teaching"><span class="secno">5.1.3</span> <span class="content">How can I teach this?</span></a>
         <ol class="toc">
          <li><a href="#wrinting-new"><span class="secno">5.1.3.1</span> <span class="content">Writing new types:</span></a>
          <li><a href="#using-orderings"><span class="secno">5.1.3.2</span> <span class="content">Using orderings:</span></a>
         </ol>
       </ol>
      <li><a href="#discussion-fallback"><span class="secno">5.2</span> <span class="content">Discussion of the <span>Fallback</span> principle</span></a>
     </ol>
    <li><a href="#lewg-questions"><span class="secno">6</span> <span class="content">Questions for LEWG:</span></a>
    <li>
     <a href="#proposal"><span class="secno">7</span> <span class="content">Proposal</span></a>
     <ol class="toc">
      <li><a href="#proposal-remove-equal"><span class="secno">7.1</span> <span class="content">Remove the <code class="highlight"><c- n>strong_equal</c-></code> and <code class="highlight"><c- n>weak_equal</c-></code> comparison algorithms</span></a>
      <li><a href="#proposal-customisation"><span class="secno">7.2</span> <span class="content">Make <code class="highlight"><c- n>strong_order</c-></code> and friends customisation points</span></a>
      <li><a href="#proposal-iec559"><span class="secno">7.3</span> <span class="content">Replace the IEC559 rule in <code class="highlight"><c- n>strong_order</c-></code> with separate overloads</span></a>
      <li><a href="#proposal-weakening"><span class="secno">7.4</span> <span class="content">Make the weaker customisation points call stronger customizatoin points</span></a>
      <li><a href="#proposal-fallback"><span class="secno">7.5</span> <span class="content">Add fallback functions</span></a>
     </ol>
    <li><a href="#wording"><span class="secno">8</span> <span class="content">Proposed Wording</span></a>
    <li><a href="#ack"><span class="secno">9</span> <span class="content">Acknowledgments</span></a>
    <li><a href="#example-cust-point"><span class="secno"></span> <span class="content">Appendix A: Proof <code class="highlight"><c- n>strong_order</c-></code> is not a valid customisation point</span></a>
    <li>
     <a href="#index"><span class="secno"></span> <span class="content">Index</span></a>
     <ol class="toc">
      <li><a href="#index-defined-here"><span class="secno"></span> <span class="content">Terms defined by this specification</span></a>
     </ol>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#normative"><span class="secno"></span> <span class="content">Normative References</span></a>
      <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="history"><span class="secno">1. </span><span class="content">Revision History</span><a class="self-link" href="#history"></a></h2>
   <h3 class="heading settled" data-level="1.1" id="rap-feedback"><span class="secno">1.1. </span><span class="content">R1: Incorporated feedback from LEWG meeting in Rappersville.</span><a class="self-link" href="#rap-feedback"></a></h3>
   <p>The feedback was:</p>
   <ul>
    <li data-md>
     <p>Remove the floating point exception (bullet 1.1) as R0 recommended, since Unicode strings, etc., are a possible rationale.</p>
    <li data-md>
     <p>Do not propose propose making existing <code class="highlight"><c- o>*</c-><c- n>_order</c-></code> functions "customisation points" (as used in <a data-link-type="biblio" href="#biblio-p0551r3">[P0551R3]</a>).</p>
    <li data-md>
     <p>Add a new <code class="highlight"><c- n>default_order</c-></code> customisation point, along with a bikeshedding section on its actual name, with the behaviour:</p>
     <ul>
      <li data-md>
       <p>It has the IEC 559 behavior from bullet 1.1 of <code class="highlight"><c- n>strong_order</c-></code></p>
      <li data-md>
       <p>It is defined for all (other) floating-point types; it is implementation-defined whether it is consistent with the partial order from the comparison operators. (Implementations should do this.)</p>
      <li data-md>
       <p>It is a customisation point (à la <a data-link-type="biblio" href="#biblio-p0551r3">[P0551R3]</a>).</p>
     </ul>
    <li data-md>
     <p>Investigate the possibility of adding Lawrence’s weak order (from <a data-link-type="biblio" href="#biblio-p0100r2">[P0100R2]</a>) for floating-point numbers (which did not make it in with spaceship).</p>
   </ul>
   <h3 class="heading settled" data-level="1.2" id="sd-feedback"><span class="secno">1.2. </span><span class="content">R2: Incorporated feedback from LEWG meeting in San Diego, merged with <a data-link-type="biblio" href="#biblio-p0863r1">[P0863R1]</a></span><a class="self-link" href="#sd-feedback"></a></h3>
   <p>Feedback in San Diego was:</p>
   <ul>
    <li data-md>
     <p>We want to solve <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>set</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> for not obviously comparable <code class="highlight"><c- n>T</c-></code> (0/6/4/1/1).</p>
    <li data-md>
     <p>We want to solve <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>unordered_set</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> for not obviously hasheable <code class="highlight"><c- n>T</c-></code>. (Out of scope of this paper)</p>
    <li data-md>
     <p>We need to adress the fact that containers need to provide specializations of <code class="highlight"><c- n>strong_order</c-></code> if it is a customisation point.</p>
    <li data-md>
     <p>We want <code class="highlight"><c- n>strong_order</c-></code> to be the customisation point (Herb’s proposed poll) - never taken.</p>
   </ul>
   <h2 class="heading settled" data-level="2" id="sup"><span class="secno">2. </span><span class="content">Status of this paper</span><a class="self-link" href="#sup"></a></h2>
   <p>R2 of this paper is a merge of its R1 and Jeff Snyder’s <a data-link-type="biblio" href="#biblio-p0863r1">[P0863R1]</a>, and is synchronized with Barry Revzin’s <a data-link-type="biblio" href="#biblio-d1186r1">[D1186R1]</a>. It incorporates all feedback for R0 and R1, and presents a coherent design for the library components of <code class="highlight"><c- o>&lt;=></c-></code>.</p>
   <h2 class="heading settled" data-level="3" id="problem"><span class="secno">3. </span><span class="content">Problem Description</span><a class="self-link" href="#problem"></a></h2>
   <p>This paper is a proposal to amend the <em>comparison algorithms</em> that have been voted into the working draft as part of <a data-link-type="biblio" href="#biblio-p0768r1">[P0768R1]</a>.</p>
   <p>As worded, the <code class="highlight"><c- n>strong_order</c-></code> comparison algorithm provides:</p>
   <ul>
    <li data-md>
     <p>a strong ordering for some types that do not have it provided by <code class="highlight"><c- o>&lt;=></c-></code> (IEC559 floating point types),</p>
    <li data-md>
     <p>a way of generating a value of type <code class="highlight"><c- n>strong_ordering</c-></code> by falling back to the <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;</c-></code> operators if <code class="highlight"><c- o>&lt;=></c-></code> is not callable or does not result in a <code class="highlight"><c- n>strong_ordering</c-></code>.</p>
   </ul>
   <p>However, the authors of this paper and the author of <a data-link-type="biblio" href="#biblio-p0515r3">[P0515R3]</a> intended for <code class="highlight"><c- n>strong_order</c-></code> to be a customisation point, and it is not currently usable as such.</p>
   <p>In the standard, we need to provide the ability to customize <code class="highlight"><c- n>strong_order</c-></code> and a way to fall back to <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;</c-></code>. This paper argues that these are fundamentally incompatible, and cannot be served by the same function.</p>
   <p><a data-link-type="biblio" href="#biblio-p0891r0">[P0891R0]</a> and <a data-link-type="biblio" href="#biblio-p0891r1">[P0891R1]</a> of this paper presented the case for having a customisation point for ordering in the language. This paper only summarizes the currently relevant bits of that discussion. For wider context, the reader should refer to the previous revisions, as well as to <a data-link-type="biblio" href="#biblio-p0863r1">[P0863R1]</a>.</p>
   <h2 class="heading settled" data-level="4" id="principles"><span class="secno">4. </span><span class="content">Principles</span><a class="self-link" href="#principles"></a></h2>
   <p>To arrive at the final design of this paper, we used the following principles:</p>
   <ul>
    <li data-md>
     <p><dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="consistency">Consistency</dfn>: <code class="highlight"><c- o>*</c-><c- n>_order</c-></code> algorithms should behave consistently with <code class="highlight"><c- o>&lt;=></c-></code> by default.</p>
    <li data-md>
     <p><dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="weakening">Weakening</dfn>: If a type has a given order, than it also has all weaker orders.</p>
    <li data-md>
     <p><dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="ambiguity-of-legacy">Ambiguity of Legacy</dfn>: The ordering category provided by the legacy comparison operators is ambiguous. The standard currently expects merely that <code class="highlight"><c- o>&lt;</c-></code> provides a weak ordering.</p>
    <li data-md>
     <p><dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="customisation">Customisation</dfn>: As <code class="highlight"><c- o>&lt;=></c-></code> is a customisation point for the natural ordering on a type, so <code class="highlight"><c- n>strong_order</c-></code> is a customisation point for an arbitrary strong order on that type.</p>
    <li data-md>
     <p><dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="fallback">Fallback</dfn>: We need convenient functions to get <code class="highlight"><c- o>*</c-><c- n>_ordering</c-></code> types from legacy comparison operators.</p>
   </ul>
   <p>From these principles, these corollaries follow:</p>
   <ul>
    <li data-md>
     <p><dfn data-dfn-type="dfn" data-noexport id="corollary-1">Corollary 1<a class="self-link" href="#corollary-1"></a></dfn>: from <a data-link-type="dfn" href="#consistency" id="ref-for-consistency">Consistency</a> it follows that, if <code class="highlight"><c- o>&lt;=></c-></code> provides a given order <code class="highlight"><c- n>X</c-></code>, then the default implementation of <code class="highlight"><c- n>X_order</c-></code> should use it.<br> <i>Example</i>: <code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- mi>1</c-><c- p>,</c-> <c- mi>2</c-><c- p>)</c-></code> should be equivalent to <code class="highlight"><c- mi>1</c-> <c- o>&lt;=></c-> <c- mi>2</c-></code>, since <code class="highlight"><c- b>int</c-></code>'s <code class="highlight"><c- k>operator</c-><c- o>&lt;=></c-></code> provides a strong ordering. <code class="highlight"><c- n>weak_order</c-><c- p>(</c-><c- mi>1</c-><c- p>,</c-> <c- mi>2</c-><c- p>)</c-></code> likewise, since <code class="highlight"><c- mi>1</c-> <c- o>&lt;=></c-> <c- mi>2</c-></code> is convertible to <code class="highlight"><c- n>strong_ordering</c-></code>.</p>
    <li data-md>
     <p><dfn data-dfn-type="dfn" data-noexport id="corollary-2">Corollary 2<a class="self-link" href="#corollary-2"></a></dfn>: from <a data-link-type="dfn" href="#consistency" id="ref-for-consistency①">Consistency</a>, <a data-link-type="dfn" href="#weakening" id="ref-for-weakening">Weakening</a> and <a data-link-type="dfn" href="#customisation" id="ref-for-customisation">Customisation</a>, it follows that:</p>
     <ul>
      <li data-md>
       <p>if <code class="highlight"><c- o>&lt;=></c-></code> does not provide a strong enough order, but a stronger ordering function (e.g. <code class="highlight"><c- n>strong_order</c-></code> for <code class="highlight"><c- n>weak_order</c-></code>, <code class="highlight"><c- n>weak_order</c-></code> for <code class="highlight"><c- n>partial_order</c-></code>) is available, then the weaker ordering function must fall back on it (this works recursively, so if <code class="highlight"><c- n>strong_order</c-></code> is defined, so is <code class="highlight"><c- n>partial_order</c-></code>).<br> <i>Example</i>: given <code class="highlight"><c- k>struct</c-> <c- n>C</c-> <c- p>{</c-> <c- n>partial_ordering</c-> <c- k>operator</c-><c- o>&lt;=></c-><c- p>(</c-><c- n>C</c-> <c- k>const</c-><c- o>&amp;</c-><c- p>)</c-> <c- k>const</c-><c- p>;</c-> <c- p>};</c-> <c- n>strong_ordering</c-> <c- nf>strong_order</c-><c- p>(</c-><c- n>C</c-> <c- k>const</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>C</c-> <c- k>const</c-><c- o>&amp;</c-><c- p>);</c-></code>, <code class="highlight"><c- n>weak_order</c-><c- p>(</c-><c- n>c1</c-><c- p>,</c-> <c- n>c2</c-><c- p>)</c-></code> should return <code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- n>c1</c-><c- p>,</c-> <c- n>c2</c-><c- p>)</c-></code>, because <code class="highlight"><c- n>c1</c-> <c- o>&lt;=></c-> <c- n>c2</c-></code> does not provide a sufficiently strong order.</p>
     </ul>
    <li data-md>
     <p><dfn data-dfn-type="dfn" data-noexport id="corollary-3">Corollary 3<a class="self-link" href="#corollary-3"></a></dfn>: from <a data-link-type="dfn" href="#consistency" id="ref-for-consistency②">Consistency</a> and <a data-link-type="dfn" href="#fallback" id="ref-for-fallback">Fallback</a>, it follows that if <code class="highlight"><c- o>&lt;=></c-></code> exists, the fallback function should use it in preference of legacy comparison operators.</p>
    <li data-md>
     <p><dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="corollary-4">Corollary 4</dfn>: From <a data-link-type="dfn" href="#fallback" id="ref-for-fallback①">Fallback</a> and <a data-link-type="dfn" href="#ambiguity-of-legacy" id="ref-for-ambiguity-of-legacy">Ambiguity of Legacy</a>, it follows that by using a fallback function, the user is asserting that <code class="highlight"><c- o>&lt;</c-></code> and <code class="highlight"><c- o>==</c-></code> implement the corresponding ordering.</p>
    <li data-md>
     <p><dfn class="dfn-paneled" data-dfn-type="dfn" data-noexport id="corollary-5">Corollary 5</dfn>: From <a data-link-type="dfn" href="#customisation" id="ref-for-customisation①">Customisation</a> and the definition of <em>customisation point</em>, it follows that <code class="highlight"><c- o>*</c-><c- n>_order</c-></code> functions must be specified as <i>does not participate in overload resolution</i> when they cannot be synthesized according to the above rules.</p>
    <li data-md>
     <p><dfn data-dfn-type="dfn" data-noexport id="corollary-6">Corollary 6<a class="self-link" href="#corollary-6"></a></dfn>: From <a data-link-type="dfn" href="#corollary-4" id="ref-for-corollary-4">Corollary 4</a> and <a data-link-type="dfn" href="#corollary-5" id="ref-for-corollary-5">Corollary 5</a> it follows that the fallbacks and the customisation points cannot be the same functions, as their roles are fundamentally incompatible. To illustrate: the fallback function for synthesizing <code class="highlight"><c- n>strong_ordering</c-></code> must exist whenever <code class="highlight"><c- o>&lt;</c-></code> and <code class="highlight"><c- o>==</c-></code> do, but the <code class="highlight"><c- n>strong_order</c-></code> customisation point must not be synthesized purely from those.</p>
   </ul>
   <p>In addition, we have made the following observations:</p>
   <ul>
    <li data-md>
     <p>Given <a data-link-type="biblio" href="#biblio-d1186r1">[D1186R1]</a> provides a method of generating a <code class="highlight"><c- o>&lt;=></c-></code> operator from <code class="highlight"><c- o>&lt;</c-></code> and <code class="highlight"><c- o>==</c-></code>, we should (due to <a data-link-type="dfn" href="#consistency" id="ref-for-consistency③">Consistency</a>) defer to that method for synthesizing the fallback functions.</p>
    <li data-md>
     <p>If <code class="highlight"><c- n>strong_order</c-></code> is a customisation point for providing a stronger order than <code class="highlight"><c- o>&lt;=></c-></code> does, data structures that recurse to their contents for <code class="highlight"><c- o>&lt;=></c-></code> should also recurse for <code class="highlight"><c- n>strong_order</c-></code>.</p>
    <li data-md>
     <p>Given that the <code class="highlight"><c- o>&lt;=></c-></code> operator is not being provided for any of the types in the standard library C++20, we are deferring proposing this until such time as <code class="highlight"><c- o>&lt;=></c-></code> is proposed for them as well.</p>
   </ul>
   <h2 class="heading settled" data-level="5" id="discussion"><span class="secno">5. </span><span class="content">Discussion</span><a class="self-link" href="#discussion"></a></h2>
   <h3 class="heading settled" data-level="5.1" id="discussion-customisation"><span class="secno">5.1. </span><span class="content">Discussion of the <a data-link-type="dfn" href="#customisation" id="ref-for-customisation②">Customisation</a> principle</span><a class="self-link" href="#discussion-customisation"></a></h3>
   <p>The arguments around whether <code class="highlight"><c- n>strong_order</c-></code> should be a customisation point have centered around the following questions:</p>
   <ul>
    <li data-md>
     <p>Is it even useful?</p>
    <li data-md>
     <p>Given that it is viral, is it worth the implementation effort?</p>
    <li data-md>
     <p>Should all of the comparison algorithms be customisation points?</p>
    <li data-md>
     <p>How can this be taught?</p>
   </ul>
   <h4 class="heading settled" data-level="5.1.1" id="but-is-it-legal-ill-make-it-legal"><span class="secno">5.1.1. </span><span class="content">Is it useful?</span><a class="self-link" href="#but-is-it-legal-ill-make-it-legal"></a></h4>
   <p>There are many algorithms and data strucutres that do not care about ordering
per se, but do require some arbitrary order. Examples of these include <code class="highlight"><c- n>set</c-></code>, <code class="highlight"><c- n>map</c-></code>, and fast implementations of set algorithms (union, intersection,
difference, etc), which are typically based on ordered sequences.</p>
   <p>There also exist types for which there is no natural strong ordering, such as <code class="highlight"><c- b>float</c-></code> and <code class="highlight"><c- n>complex</c-></code>. Even though these types do not have a natural strong
ordering, it is nevertheless very useful to provide an arbitrary strong
ordering for them, e.g. so that they can be used in containers such as <code class="highlight"><c- n>set</c-></code> and <code class="highlight"><c- n>map</c-></code>. Having an arbitrary strong ordering is in fact so useful that <em>Stepanov</em> and <em>Mc Jones</em> included it it in their definition of <em>Regular</em> in <i>Elements of Programming</i>.</p>
   <p>In order to make it possible to use IEC559 floating-point types in <code class="highlight"><c- n>set</c-></code>s and <code class="highlight"><c- n>map</c-></code>s, the existing <code class="highlight"><c- n>strong_order</c-></code> comparison algorithm includes a special rule for IEC559 floating point types. This works well for simple sets of
floating point numbers, but it breaks down quickly when we try more complicated
examples such as <code class="highlight"><c- n>set</c-><c- o>&lt;</c-><c- n>optional</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>></c-></code> or <code class="highlight"><c- n>set</c-><c- o>&lt;</c-><c- n>pair</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-><c- b>int</c-><c- o>>></c-></code>. To make
these examples work, we need to <em>customise</em> <code class="highlight"><c- n>strong_order</c-></code> for <code class="highlight"><c- n>optional</c-></code>, <code class="highlight"><c- n>pair</c-></code> and other container types, and for that to be permitted <code class="highlight"><c- n>strong_order</c-></code> must be a customisation point.</p>
   <p>Having an agreed-upon customisation point for an arbitrary order is long
overdue. It is time to define what that customisation point is, so it can be
provided and used consistently across C++ libraries and applications. That name
should be <code class="highlight"><c- n>strong_order</c-></code>, since <code class="highlight"><c- n>default_order</c-></code> as a distinct customisation
point was rejected by LEWG in San Diego in favor of the design in R0 of this
paper.</p>
   <h4 class="heading settled" data-level="5.1.2" id="impl-effort"><span class="secno">5.1.2. </span><span class="content">Given that it is viral, is it worth the implementation effort?</span><a class="self-link" href="#impl-effort"></a></h4>
   <p>Given that any customisation point we designate has to potentially be overloaded for all the generic wrappers in the standard library, is it worth the effort of defining them?</p>
   <p>This paper does not propose any such wrappers, because the standard library does not even support <code class="highlight"><c- k>operator</c-> <c- o>&lt;=></c-></code> for such wrapper types yet. This paper only proposes that <code class="highlight"><c- n>strong_order</c-></code> be established as a customisation point.</p>
   <h4 class="heading settled" data-level="5.1.3" id="faq-teaching"><span class="secno">5.1.3. </span><span class="content">How can I teach this?</span><a class="self-link" href="#faq-teaching"></a></h4>
   <p>For types that endeavour to be <em>Regular</em> or something like it (as in, have sane value semantics), do the following.</p>
   <h5 class="heading settled" data-level="5.1.3.1" id="wrinting-new"><span class="secno">5.1.3.1. </span><span class="content">Writing new types:</span><a class="self-link" href="#wrinting-new"></a></h5>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- k>operator</c-><c- o>==</c-></code> defines what "strong equality" means. This is because copies must compare equal, and <code class="highlight"><c- o>==</c-></code> should be the finest relation that observes this rule. EOP defines it as "must represent the same value in the domain of the type."</p>
    <li data-md>
     <p>if <code class="highlight"><c- p>(</c-><c- n>x</c-> <c- o>&lt;=></c-> <c- n>y</c-><c- p>)</c-> <c- o>==</c-> <c- mi>0</c-></code> if and only if <code class="highlight"><c- n>x</c-> <c- o>==</c-> <c- n>y</c-></code>, then <code class="highlight"><c- k>operator</c-><c- o>&lt;=></c-></code> should return <code class="highlight"><c- n>strong_ordering</c-></code>, otherwise it should return <code class="highlight"><c- n>weak_ordering</c-></code> (unless it only defines a partial order, and then it must return <code class="highlight"><c- n>partial_ordering</c-></code> anyway).</p>
    <li data-md>
     <p>If your type does not provide an order, you should still provide an overload of <code class="highlight"><c- n>strong_order</c-></code> that defines an arbitrary order consistent with <code class="highlight"><c- o>==</c-></code>.</p>
    <li data-md>
     <p>If you are obeying the rule of zero, writing <code class="highlight"><c- k>auto</c-> <c- k>operator</c-><c- o>&lt;=></c-><c- p>(...)</c-> <c- o>=</c-> <c- k>default</c-></code> will give you the correct <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;=></c-></code> without any additional work. In most cases, this should already be enough, since <code class="highlight"><c- o>&lt;=></c-></code> will result in a <code class="highlight"><c- n>strong_ordering</c-></code>.</p>
    <li data-md>
     <p>If you are writing a generic wrapper, or your constituent types have an overloaded <code class="highlight"><c- n>strong_order</c-></code>, you must then also define <code class="highlight"><c- n>strong_order</c-></code> to be:</p>
   </ul>
<pre class="highlight"><c- n>strong_ordering</c-> <c- nf>strong_order</c-><c- p>(</c-><c- n>T</c-> <c- n>x</c-><c- p>,</c-> <c- n>T</c-> <c- n>y</c-><c- p>)</c-> <c- p>{</c->
  <c- k>if</c-> <c- p>(</c-><c- k>auto</c-> <c- n>ord</c-> <c- o>=</c-> <c- n>strong_order</c-><c- p>(</c-><c- n>x</c-><c- p>.</c-><c- n>a</c-><c- p>,</c-> <c- n>y</c-><c- p>.</c-><c- n>a</c-><c- p>);</c-> <c- n>is_neq</c-><c- p>(</c-><c- n>ord</c-><c- p>))</c-> <c- p>{</c-> <c- k>return</c-> <c- n>ord</c-><c- p>;</c-> <c- p>}</c->
  <c- k>if</c-> <c- p>(</c-><c- k>auto</c-> <c- n>ord</c-> <c- o>=</c-> <c- n>strong_order</c-><c- p>(</c-><c- n>x</c-><c- p>.</c-><c- n>b</c-><c- p>,</c-> <c- n>y</c-><c- p>.</c-><c- n>b</c-><c- p>);</c-> <c- n>is_neq</c-><c- p>(</c-><c- n>ord</c-><c- p>))</c-> <c- p>{</c-> <c- k>return</c-> <c- n>ord</c-><c- p>;</c-> <c- p>}</c->
  <c- c1>// ... for all members</c->
  <c- k>return</c-> <c- n>strong_ordering</c-><c- o>::</c-><c- n>equal</c-><c- p>;</c->
<c- p>}</c->
</pre>
   <h5 class="heading settled" data-level="5.1.3.2" id="using-orderings"><span class="secno">5.1.3.2. </span><span class="content">Using orderings:</span><a class="self-link" href="#using-orderings"></a></h5>
   <p>Generic algorithms should require and call <code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- n>x</c-><c- p>,</c-> <c- n>y</c-><c- p>)</c-></code>, <code class="highlight"><c- n>weak_order</c-><c- p>(</c-><c- n>x</c-><c- p>,</c-> <c- n>y</c-><c- p>)</c-></code> or <code class="highlight"><c- n>partial_order</c-><c- p>(</c-><c- n>x</c-><c- p>,</c-> <c- n>y</c-><c- p>)</c-></code> (depending on the ordering requirements of the algorithm) after a <code class="highlight"><c- k>using</c-> <c- n>namsepace</c-> <c- n>std</c-><c- p>;</c-></code>.
These will find the most appropriate ordering available, or SFINAE away if no suitable ordering is available. For example, if an algorithm calls <code class="highlight"><c- n>weak_order</c-></code> on a type which has <code class="highlight"><c- o>&lt;=></c-></code> returning <code class="highlight"><c- n>partial_order</c-></code>, does not provide an overload of <code class="highlight"><c- n>weak_order</c-></code>, but does overload <code class="highlight"><c- n>strong_order</c-></code>, then <code class="highlight"><c- n>strong_order</c-></code> will end up being called. The intent is that these "always do the right thing".</p>
   <h3 class="heading settled" data-level="5.2" id="discussion-fallback"><span class="secno">5.2. </span><span class="content">Discussion of the <a data-link-type="dfn" href="#fallback" id="ref-for-fallback②">Fallback</a> principle</span><a class="self-link" href="#discussion-fallback"></a></h3>
   <p>The arguments on whether we need to provide the fallback functions for legacy types center around a few questions:</p>
   <ul>
    <li data-md>
     <p>How do we make it easy to define <code class="highlight"><c- o>&lt;=></c-></code> for types which have members which only define <code class="highlight"><c- o>&lt;</c-></code> and <code class="highlight"><c- o>==</c-></code>, but not <code class="highlight"><c- o>&lt;=></c-></code>?</p>
    <li data-md>
     <p>How should generic code work with types that may or may not define <code class="highlight"><c- o>&lt;=></c-></code>, <em>but are assumed to have the requisite preconditions on</em> <code class="highlight"><c- o>&lt;</c-></code> <em>and</em> <code class="highlight"><c- o>==</c-></code>?</p>
    <li data-md>
     <p>In a context where we need to pass an ordering type as a parameter to a function, but we need to obtain it from a legacy type, how do we do that?</p>
   </ul>
   <p><a data-link-type="biblio" href="#biblio-d1186r1">[D1186R1]</a> makes the first of these trivial, and defines the algorithms necessary to make use of the legacy type’s <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;</c-></code> operators. Helpfully, it defines the <code class="highlight"><c- mi>3</c-><c- n>WAY</c-><c- o>&lt;></c-><c- p>(</c-><c- n>X</c-><c- p>,</c-> <c- n>Y</c-><c- p>)</c-></code> specification macro, which contains the core of its fallback logic.</p>
   <p>The second two questions boil down to the same thing: if we have a type that implements <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;</c-></code>, and we know it has a particular ordering, how do we convert that into a value of the appropriate <code class="highlight"><c- n>X_ordering</c-></code> type? We expect this to become a common problem, and therefore the standard should provide convenience functions that call <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;</c-></code> and return an <code class="highlight"><c- n>X_ordering</c-></code> value representing the result.  In specifying these functions, we can re-use the <code class="highlight"><c- mi>3</c-><c- n>WAY</c-><c- o>&lt;></c-><c- p>(</c-><c- n>X</c-><c- p>,</c-> <c- n>Y</c-><c- p>)</c-></code> from <a data-link-type="biblio" href="#biblio-d1186r1">[D1186R1]</a>, both for convenience and consistency.</p>
   <p>However, as C++ applications and libraries are updated to implement <code class="highlight"><c- k>operator</c-> <c- o>&lt;=></c-></code> for their types, the need for these fallback functions should diminish. On the other hand, the customisation points are a feature with permenant utility. Due to customziation points having a longer term utility, they should get the <code class="highlight"><c- n>X_order</c-></code> names, and we should find new names for fallback functions.</p>
   <h2 class="heading settled" data-level="6" id="lewg-questions"><span class="secno">6. </span><span class="content">Questions for LEWG:</span><a class="self-link" href="#lewg-questions"></a></h2>
   <ol>
    <li data-md>
     <p>Is there consensus that the <a data-link-type="dfn" href="#customisation" id="ref-for-customisation③">Customisation</a> premise (as above) is correct and should be adopted?</p>
     <ul>
      <li data-md>
       <p>If not, then should the IEC559 exception bullet in the current working draft be removed?</p>
     </ul>
    <li data-md>
     <p>Is there consensus that the <a data-link-type="dfn" href="#fallback" id="ref-for-fallback③">Fallback</a> premise (as above) is correct and should be adopted?</p>
     <ul>
      <li data-md>
       <p>Rejecting this means that we are rejecting the rationale for their inclusion in the current working draft and that they should be removed.</p>
     </ul>
   </ol>
   <p>(The <a data-link-type="dfn" href="#consistency" id="ref-for-consistency④">Consistency</a>, <a data-link-type="dfn" href="#weakening" id="ref-for-weakening①">Weakening</a> and <a data-link-type="dfn" href="#ambiguity-of-legacy" id="ref-for-ambiguity-of-legacy①">Ambiguity of Legacy</a> are true from a good design, mathematical, and empirical point of view, respectively, so they are not subject to poll).</p>
   <h2 class="heading settled" data-level="7" id="proposal"><span class="secno">7. </span><span class="content">Proposal</span><a class="self-link" href="#proposal"></a></h2>
   <h3 class="heading settled" data-level="7.1" id="proposal-remove-equal"><span class="secno">7.1. </span><span class="content">Remove the <code class="highlight"><c- n>strong_equal</c-></code> and <code class="highlight"><c- n>weak_equal</c-></code> comparison algorithms</span><a class="self-link" href="#proposal-remove-equal"></a></h3>
   <p>If we accept <a data-link-type="biblio" href="#biblio-p1185r0">[P1185R0]</a>'s rationale for not calling <code class="highlight"><c- o>&lt;=></c-></code> when the user only
needs equality (as EWG did in San Diego), we should also avoid doing so in the
library. However, without making assumptions about the behaviour of <code class="highlight"><c- o>==</c-></code>, there
is no way to implement <code class="highlight"><c- n>strong_equal</c-></code> and <code class="highlight"><c- n>weak_equal</c-></code> without calling <code class="highlight"><c- o>&lt;=></c-></code>.</p>
   <p>Therefore, we propose removing the <code class="highlight"><c- n>strong_equal</c-></code> and <code class="highlight"><c- n>weak_equal</c-></code> algorithms.</p>
   <h3 class="heading settled" data-level="7.2" id="proposal-customisation"><span class="secno">7.2. </span><span class="content">Make <code class="highlight"><c- n>strong_order</c-></code> and friends customisation points</span><a class="self-link" href="#proposal-customisation"></a></h3>
   <p>For the functions <code class="highlight"><c- n>strong_order</c-></code>, <code class="highlight"><c- n>weak_order</c-></code> and <code class="highlight"><c- n>partial_order</c-></code> we propose to:</p>
   <ul>
    <li data-md>
     <p>Replace the functions with <a href="http://eel.is/c++draft/customization.point.object">Customsation Point Objects</a>.</p>
    <li data-md>
     <p>Remove the fallbacks to <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;</c-></code></p>
    <li data-md>
     <p>Have the functions not participate in overload resolution (instead of being defined as deleted) if there is no strong order available.</p>
   </ul>
   <h3 class="heading settled" data-level="7.3" id="proposal-iec559"><span class="secno">7.3. </span><span class="content">Replace the IEC559 rule in <code class="highlight"><c- n>strong_order</c-></code> with separate overloads</span><a class="self-link" href="#proposal-iec559"></a></h3>
   <p>Since <code class="highlight"><c- n>strong_order</c-></code> is a customisation point, the strong order for floating
point types should be provided as overloads of <code class="highlight"><c- n>strong_order</c-></code> rather than being
baked into the generic <code class="highlight"><c- n>strong_order</c-></code> function.</p>
   <p>We propose that the bullet point regarding <code class="highlight"><c- n>IEC559</c-></code> be removed from the <code class="highlight"><c- n>strong_order</c-></code> algorithm, and that the following three overloads for <code class="highlight"><c- n>strong_order</c-></code> are added:</p>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- b>float</c-><c- p>,</c-> <c- b>float</c-><c- p>);</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- b>double</c-><c- p>,</c-> <c- b>double</c-><c- p>);</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- b>long</c-> <c- b>double</c-><c- p>,</c-> <c- b>long</c-> <c- b>double</c-><c- p>);</c-></code></p>
   </ul>
   <p>These overloads should implement the <code class="highlight"><c- n>totalOrder</c-></code> operation as specified in
ISO/IEC/IEEE 60559, and should not participate in overload resolution if <code class="highlight"><c- n>numeric_limts</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>::</c-><c- n>is_iec559</c-></code> is <code class="highlight">false</code> for the type of their arguments.</p>
   <h3 class="heading settled" data-level="7.4" id="proposal-weakening"><span class="secno">7.4. </span><span class="content">Make the weaker customisation points call stronger customizatoin points</span><a class="self-link" href="#proposal-weakening"></a></h3>
   <p>To handle cases such as where a type provides a <code class="highlight"><c- n>partial_ordering</c-></code> from <code class="highlight"><c- o>&lt;=></c-></code> and a <code class="highlight"><c- n>strong_order</c-></code> overload, if a customisation point cannot get an
appropriate result from calling <code class="highlight"><c- o>&lt;=></c-></code>, it should try to call a customisation
point for an order stronger than its own. Specifically:</p>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- n>weak_order</c-></code> should fall back to calling <code class="highlight"><c- n>strong_order</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>partial_order</c-></code> should fall back to calling <code class="highlight"><c- n>weak_order</c-></code></p>
   </ul>
   <h3 class="heading settled" data-level="7.5" id="proposal-fallback"><span class="secno">7.5. </span><span class="content">Add fallback functions</span><a class="self-link" href="#proposal-fallback"></a></h3>
   <p>To avoid losing the functionality of the existing comparison algorithms, we
propose to keep them under new names, with the following changes to their
behaviour:</p>
   <ul>
    <li data-md>
     <p>They will, in preference to anything else, return the
result of calling the corresponding customisation point.</p>
    <li data-md>
     <p>They will not attempt to call <code class="highlight"><c- o>&lt;=></c-></code> directly, as this is called by the
customisation point.</p>
    <li data-md>
     <p>They will fall back to <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;</c-></code> using the language mechanism proposed by <a data-link-type="biblio" href="#biblio-d1186r1">[D1186R1]</a> instead of calling <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;</c-></code> directly.</p>
   </ul>
   <p>As per the original comparison algorithms, they will be defined as deleted if
neither the corresponding customisation point nor the <code class="highlight"><c- o>==</c-></code> and <code class="highlight"><c- o>&lt;</c-></code> operators
are available.</p>
   <p>Following the same reasoning as in <a href="#proposal-remove-equal">§7.1 Remove the strong_equal and weak_equal comparison algorithms</a>, there will be no fallback
functions for <code class="highlight"><c- n>strong_equality</c-></code> and <code class="highlight"><c- n>weak_equality</c-></code>.</p>
   <p>We propose naming the fallback functions <code class="highlight"><c- n>assumed_strong_order</c-></code>, <code class="highlight"><c- n>assumed_weak_order</c-></code> and <code class="highlight"><c- n>assumed_partial_order</c-></code>.</p>
   <p>Other options to consider:</p>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- n>assumed_X_order</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>X_order_assume</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>assume_X_order</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>fallback_X_order</c-></code></p>
    <li data-md>
     <p><code class="highlight"><c- n>X_order_fallback</c-></code></p>
   </ul>
   <p>See the <a data-link-type="dfn" href="#fallback" id="ref-for-fallback④">fallback</a> discussion on why the <code class="highlight"><c- n>X_order</c-></code> names should be given to the customisation points.</p>
   <h2 class="heading settled" data-level="8" id="wording"><span class="secno">8. </span><span class="content">Proposed Wording</span><a class="self-link" href="#wording"></a></h2>
   <p>Change the current <code class="highlight"><c- n>strong_order</c-></code> to <code class="highlight"><c- n>assumed_strong_order</c-></code> (but see bikeshedding section):</p>
   <p><code class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>T</c-><c- o>></c-> <c- k>constexpr</c-> <c- n>strong_ordering</c-></code> <span class="ins"><code class="highlight"><c- n>assumed</c-></code></span><code class="highlight"><c- n>_strong_order</c-><c- p>(</c-><c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>a</c-><c- p>,</c-> <c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>b</c-><c- p>);</c-></code></p>
   <ul class="std ins">
    <li># Effects: Compares two values and produces a result of type <code class="highlight"><c- n>strong_ordering</c-></code>:
    <ul>
     <li class="del">(1.1) If <code class="highlight"><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>::</c-><c- n>is_iec559</c-></code> is true, returns a result of type <code class="highlight"><c- n>strong_ordering</c-></code> that is consistent with the totalOrder operation as specified in ISO/IEC/IEEE 60559.
     <li>(#.1) If the expression <code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>)</c-></code> is well-formed and convertible to <code class="highlight"><c- n>strong_ordering</c-></code>, return the result of the expression,
     <li class="del">(1.2) Otherwise, returns <code class="highlight"><c- n>a</c-> <c- o>&lt;=></c-> <c- n>b</c-></code> if that expression is well-formed and convertible to <code class="highlight"><c- n>strong_ordering</c-></code>.
     <li>(#.2) Otherwise, if the expression <code class="highlight"><c- mi>3</c-><c- n>WAY</c-><c- o>&lt;</c-><c- n>strong_ordering</c-><c- o>></c-><c- p>(</c-><c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>)</c-></code> is well-formed, return the result of the expression,
     <li class="del">(1.3) Otherwise, if the expression a &lt;=> b is well-formed, then the function is defined as deleted.
     <li class="del">(1.4) Otherwise, if the expressions a == b and a &lt; b are each well-formed and convertible to bool, then
     <ul>
      <li class="del">(1.4.1) if a == b is true, returns <code class="highlight"><c- n>strong_ordering</c-><c- o>::</c-><c- n>equal</c-></code>;
      <li class="del">(1.4.2) otherwise, if a &lt; b is true, returns <code class="highlight"><c- n>strong_ordering</c-><c- o>::</c-><c- n>less</c-></code>;
      <li class="del">(1.4.3) otherwise, returns <code class="highlight"><c- n>strong_ordering</c-><c- o>::</c-><c- n>greater</c-></code>.
     </ul>
     <li>(#.<span class="del">5</span>3) Otherwise, the function shall be defined as deleted.
    </ul>
   </ul>
   <p>Change the current <code class="highlight"><c- n>weak_order</c-></code> to <code class="highlight"><c- n>assumed_weak_order</c-></code> (but see bikeshedding section):</p>
   <p><code class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>T</c-><c- o>></c-> <c- k>constexpr</c-> <c- n>weak_ordering</c-></code> <span class="ins"><code class="highlight"><c- n>assumed</c-></code></span><code class="highlight"><c- n>_weak_order</c-><c- p>(</c-><c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>a</c-><c- p>,</c-> <c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>b</c-><c- p>);</c-></code></p>
   <ul class="std ins">
    <li># Effects: Compares two values and produces a result of type <code class="highlight"><c- n>weak_ordering</c-></code>:
    <ul>
     <li>(#.1) If the expression <code class="highlight"><c- n>weak_order</c-><c- p>(</c-><c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>)</c-></code> is well-formed and convertible to <code class="highlight"><c- n>weak_ordering</c-></code>, return the result of the expression,
     <li class="del">(2.1) Returns <code class="highlight"><c- n>a</c-> <c- o>&lt;=></c-> <c- n>b</c-></code> if that expression is well-formed and convertible to <code class="highlight"><c- n>weak_ordering</c-></code>.
     <li>(#.2) Otherwise, if the expression <code class="highlight"><c- mi>3</c-><c- n>WAY</c-><c- o>&lt;</c-><c- n>weak_ordering</c-><c- o>></c-><c- p>(</c-><c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>)</c-></code> is well-formed, return the result of the expression,
     <li class="del">(2.2) Otherwise, if the expression a &lt;=> b is well-formed, then the function is defined as deleted.
     <li class="del">(2.3) Otherwise, if the expressions a == b and a &lt; b are each well-formed and convertible to bool, then
     <ul>
      <li class="del">(2.3.1) if a == b is true, returns <code class="highlight"><c- n>weak_ordering</c-><c- o>::</c-><c- n>eqivalen</c-></code>;
      <li class="del">(2.3.2) otherwise, if a &lt; b is true, returns <code class="highlight"><c- n>weak_ordering</c-><c- o>::</c-><c- n>less</c-></code>;
      <li class="del">(2.3.3) otherwise, returns <code class="highlight"><c- n>weak_ordering</c-><c- o>::</c-><c- n>greater</c-></code>.
     </ul>
     <li>(#.<span class="del">4</span>3) Otherwise, the function shall be defined as deleted.
    </ul>
   </ul>
   <p>Change the current <code class="highlight"><c- n>partial_order</c-></code> to <code class="highlight"><c- n>assumed_partial_order</c-></code> (but see bikeshedding section):</p>
   <p><code class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>T</c-><c- o>></c-> <c- k>constexpr</c-> <c- n>partial_ordering</c-></code> <span class="ins"><code class="highlight"><c- n>assumed</c-></code></span><code class="highlight"><c- n>_partial_order</c-><c- p>(</c-><c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>a</c-><c- p>,</c-> <c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>b</c-><c- p>);</c-></code></p>
   <ul class="std ins">
    <li># Effects: Compares two values and produces a result of type <code class="highlight"><c- n>partial_ordering</c-></code>:
    <ul>
     <li>(#.1) If the expression <code class="highlight"><c- n>partial_order</c-><c- p>(</c-><c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>)</c-></code> is well-formed and convertible to <code class="highlight"><c- n>partial_ordering</c-></code>, return the result of the expression,
     <li class="del">(2.1) Returns <code class="highlight"><c- n>a</c-> <c- o>&lt;=></c-> <c- n>b</c-></code> if that expression is well-formed and convertible to <code class="highlight"><c- n>partial_ordering</c-></code>.
     <li>(#.2) Otherwise, if the expression <code class="highlight"><c- mi>3</c-><c- n>WAY</c-><c- o>&lt;</c-><c- n>partial_ordering</c-><c- o>></c-><c- p>(</c-><c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>)</c-></code> is well-formed, return the result of the expression,
     <li class="del">(2.2) Otherwise, if the expression a &lt;=> b is well-formed, then the function is defined as deleted.
     <li class="del">(2.3) Otherwise, if the expressions a == b and a &lt; b are each well-formed and convertible to bool, then
     <ul>
      <li class="del">(2.3.1) if a == b is true, returns <code class="highlight"><c- n>partial_ordering</c-><c- o>::</c-><c- n>eqivalen</c-></code>;
      <li class="del">(2.3.2) otherwise, if a &lt; b is true, returns <code class="highlight"><c- n>partial_ordering</c-><c- o>::</c-><c- n>less</c-></code>;
      <li class="del">(2.3.3) otherwise, returns <code class="highlight"><c- n>partial_ordering</c-><c- o>::</c-><c- n>greater</c-></code>.
     </ul>
     <li>(#.<span class="del">4</span>3) Otherwise, the function shall be defined as deleted.
    </ul>
   </ul>
   <p>From section 24.x.4, Comparison Algorithms [cmp.alg], remove <code class="highlight"><c- n>strong_equal</c-></code> and <code class="highlight"><c- n>weak_equal</c-></code>:</p>
   <div class="del">
     <code class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>T</c-><c- o>></c-> <c- k>constexpr</c-> <c- n>strong_equality</c-> <c- n>strong_equal</c-><c- p>(</c-><c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>a</c-><c- p>,</c-> <c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>b</c-><c- p>);</c-></code> 
    <ul>
     <li>4 <i>Effects</i>: Compares two values and produces a result of type <code class="highlight"><c- n>strong_equality</c-></code>:
     <ul>
      <li>(4.1) Returns a &lt;=> b if that expression is well-formed and convertible to <code class="highlight"><c- n>strong_equality</c-></code>.
      <li>(4.2) Otherwise, if the expression a &lt;=> b is well-formed, then the function is defined as deleted.
      <li>(4.3) Otherwise, if the expression a == b is well-formed and convertible to bool, then
      <ul>
       <li>(4.3.1) if a == b is true, returns <code class="highlight"><c- n>strong_equality</c-><c- o>::</c-><c- n>equal</c-></code>;
       <li>(4.3.2) otherwise, returns <code class="highlight"><c- n>strong_equality</c-><c- o>::</c-><c- n>nonequal</c-></code>.
      </ul>
      <li>(4.4) Otherwise, the function is defined as deleted.
     </ul>
    </ul>
    <p><code class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>T</c-><c- o>></c-> <c- k>constexpr</c-> <c- n>weak_equality</c-> <c- n>weak_equal</c-><c- p>(</c-><c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>a</c-><c- p>,</c-> <c- k>const</c-> <c- n>T</c-><c- o>&amp;</c-> <c- n>b</c-><c- p>);</c-></code></p>
    <li>5 <i>Effects</i>: Compares two values and produces a result of type <code class="highlight"><c- n>weak_equality</c-></code>:
    <ul>
     <li>(5.1) Returns a &lt;=> b if that expression is well-formed and convertible to <code class="highlight"><c- n>weak_equality</c-></code>.
     <li>(5.2) Otherwise, if the expression a &lt;=> b is well-formed, then the function is defined as deleted.
     <li>(5.3) Otherwise, if the expression a == b is well-formed and convertible to bool, then
     <ul>
      <li>(5.3.1) if a == b is true, returns <code class="highlight"><c- n>weak_equality</c-><c- o>::</c-><c- n>equivalent</c-></code>;
      <li>(5.3.2) otherwise, returns <code class="highlight"><c- n>weak_equality</c-><c- o>::</c-><c- n>nonequivalent</c-></code>.
     </ul>
     <li>(5.4) Otherwise, the function is defined as deleted.
    </ul>
   </div>
   <p>Then add the <code class="highlight"><c- n>strong_order</c-></code> customisation point object:</p>
   <div class="ins">
     (#) The name <code class="highlight"><c- n>strong_order</c-></code> denotes a customisation point object. The expression <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>strong_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> for some subexpressions <code class="highlight"><c- n>E</c-></code> and <code class="highlight"><c- n>F</c-></code> with type <code class="highlight"><c- n>T</c-></code> is expression-equivalent to: 
    <ul style="list-style-type: none; padding-left: 0px;">
     <li>(#.1) <code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> if it is a valid expression,
     <li>(#.2) Otherwise, <code class="highlight"><c- n>E</c-> <c- o>&lt;=></c-> <c- n>F</c-></code> if it is a valid expression and its type is convertible to <code class="highlight"><c- n>strong_ordering</c-></code>,
     <li>(#.3) Otherwise, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>strong_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> is ill-formed. [Note: This case can result in substitution failure when <code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> appears in the immediate context of a template instantiation. --end note]
    </ul>
     [Note: Whenever <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>strong_order</c-></code> is a valid expression, its type is convertible to <code class="highlight"><c- n>strong_ordering</c-></code>. --end note] 
   </div>
   <p>Add overloads for IEC559 types:</p>
   <div class="ins"> (#) <code class="highlight"><c- n>strong_order</c-><c- p>(</c-><c- n>T</c-><c- p>,</c-> <c- n>T</c-><c- p>)</c-></code> when <code class="highlight"><c- n>T</c-></code> is a type for which <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>numeric_limits</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>::</c-><c- n>is_iec559</c-></code> is <code class="highlight">true</code> shall be a valid expression, whose value shall be consistent with the totalOrder operation as specified in ISO/IEC/IEEE 60559. </div>
   <p>Add the <code class="highlight"><c- n>weak_order</c-></code> customisation point object:</p>
   <div class="ins">
     (#) The name <code class="highlight"><c- n>weak_order</c-></code> denotes a customisation point object. The expression <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>weak_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> for some subexpressions <code class="highlight"><c- n>E</c-></code> and <code class="highlight"><c- n>F</c-></code> with type <code class="highlight"><c- n>T</c-></code> is expression-equivalent to: 
    <ul style="list-style-type: none;">
     <li>(#.1) <code class="highlight"><c- n>weak_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> if it is a valid expression,
     <li>(#.2) Otherwise, <code class="highlight"><c- n>E</c-> <c- o>&lt;=></c-> <c- n>F</c-></code> if it is a valid expression and its type is convertible to <code class="highlight"><c- n>weak_ordering</c-></code>,
     <li>(#.3) Otherwise, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>strong_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> if it is a valid expression,
     <li>(#.4) Otherwise, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>weak_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> is ill-formed. [Note: This case can result in substitution failure when <code class="highlight"><c- n>weak_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> appears in the immediate context of a template instantiation. --end note]
    </ul>
     [Note: Whenever <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>weak_order</c-></code> is a valid expression, its type is convertible to <code class="highlight"><c- n>weak_ordering</c-></code>. --end note] 
   </div>
   <p>Add the <code class="highlight"><c- n>partial_order</c-></code> customisation point object:</p>
   <div class="ins">
     (#) The name <code class="highlight"><c- n>partial_order</c-></code> denotes a customisation point object. The expression <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>partial_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> for some subexpressions <code class="highlight"><c- n>E</c-></code> and <code class="highlight"><c- n>F</c-></code> with type <code class="highlight"><c- n>T</c-></code> is expression-equivalent to: 
    <ul style="list-style-type: none;">
     <li>(#.1) <code class="highlight"><c- n>partial_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> if it is a valid expression,
     <li>(#.2) Otherwise, <code class="highlight"><c- n>E</c-> <c- o>&lt;=></c-> <c- n>F</c-></code> if it is a valid expression and its type is convertible to <code class="highlight"><c- n>partial_ordering</c-></code>,
     <li>(#.3) Otherwise, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>weak_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> if it is a valid expression,
     <li>(#.4) Otherwise, <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>partial_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> is ill-formed. [Note: This case can result in substitution failure when <code class="highlight"><c- n>partial_order</c-><c- p>(</c-><c- n>E</c-><c- p>,</c-> <c- n>F</c-><c- p>)</c-></code> appears in the immediate context of a template instantiation. --end note]
    </ul>
     [Note: Whenever <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>partial_order</c-></code> is a valid expression, its type is convertible to <code class="highlight"><c- n>partial_ordering</c-></code>. --end note] 
   </div>
   <h2 class="heading settled" data-level="9" id="ack"><span class="secno">9. </span><span class="content">Acknowledgments</span><a class="self-link" href="#ack"></a></h2>
   <p>We would like to thank</p>
   <ul>
    <li data-md>
     <p><strong>Roger Orr</strong> for bringing this to our attention;</p>
    <li data-md>
     <p><strong>Thomas Köppe</strong> for his valuable comments, review, and most of all some extremely clear and laconic wording;</p>
    <li data-md>
     <p><strong>Sam Finch</strong> for <em>thoroughly</em> breaking the original examples, some example code, great substantive comments, and pointing out that the current definition actually breaks types that define a partially-ordered set of comparison operators;</p>
    <li data-md>
     <p><strong>Richard Smith</strong> for further fixing my example in light of Concepts, and example code.</p>
    <li data-md>
     <p><strong>Herb Sutter and Walter Brown</strong> for providing (mutually opposing) guidance on customisation points.</p>
    <li data-md>
     <p><strong>Louis Dionne</strong> for great comments on the structure of the paper and how to bring the focus where it needs to be;</p>
    <li data-md>
     <p><strong>Walter Brown</strong> for representing the paper at a committee meeting when Gašper could not make it in person, and guidance with direction;</p>
    <li data-md>
     <p><strong>Barry Revzin</strong> for representing the paper at a committee meeting when Gašper could not make it in person, and his various papers that touch ours, and for pre-reviewing our wording and suggesting we make the customisation points CPOs, and reworking his paper to support the <code class="highlight"><c- mi>3</c-><c- n>WAY</c-><c- o>&lt;</c-><c- n>strength</c-><c- o>></c-><c- p>(</c-><c- n>x</c-><c- p>,</c-> <c- n>y</c-><c- p>)</c-></code> syntax.</p>
    <li data-md>
     <p><strong>Herb Sutter</strong> for his comments and support for getting ordering right.</p>
   </ul>
   <p>And, <em>again</em>, a special thank-you to Walter Brown, who, with his final lightning talk in Bellevue, reminded us to remember whose shoulders we are standing on.</p>
   <p>Thank you all!</p>
   <h2 class="heading settled" id="example-cust-point"><span class="content">Appendix A: Proof <code class="highlight"><c- n>strong_order</c-></code> is not a valid customisation point</span><a class="self-link" href="#example-cust-point"></a></h2>
   <p>Say we have a template struct representing the Gaussian integers, with a <em>natural order</em> defined by the Manhattan distance from <code class="highlight"><c- mi>0</c-><c- o>+</c-><c- mi>0</c-><c- n>i</c-></code>. This struct still defines a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>strong_order</c-></code> to model <strong>Regular</strong>.</p>
   <p class="note" role="note"><span>Note:</span> The <strong>Regular</strong> above refers to the <em>Elements of Programming</em> concept, not the ISO C++ <strong>Regular</strong>, which is weaker.</p>
   <p class="note" role="note"><span>Note:</span> There is no natural order on Gaussian integers, but humor this example, please.</p>
<pre class="language-cpp highlight"><c- k>namespace</c-> <c- n>user</c-> <c- p>{</c->
  <c- k>template</c-> <c- o>&lt;</c-><c- k>typename</c-> <c- n>T</c-><c- o>></c->
  <c- k>struct</c-> <c- n>gaussian</c-> <c- p>{</c->
    <c- k>static_assert</c-><c- p>(</c-><c- n>std</c-><c- o>::</c-><c- n>is_integral_v</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-><c- p>);</c->
    <c- n>T</c-> <c- n>re</c-><c- p>;</c->
    <c- n>T</c-> <c- n>im</c-><c- p>;</c->

    <c- k>constexpr</c-> <c- n>std</c-><c- o>::</c-><c- n>strong_equality</c-> <c- k>operator</c-><c- o>==</c-><c- p>(</c-><c- n>gassian</c-> <c- k>const</c-><c- o>&amp;</c-> <c- n>other</c-><c- p>)</c-> <c- k>const</c-> <c- p>{</c->
      <c- k>return</c-> <c- n>re</c-> <c- o>==</c-> <c- n>other</c-><c- p>.</c-><c- n>re</c-> <c- o>&amp;&amp;</c-> <c- n>im</c-> <c- o>==</c-> <c- n>other</c-><c- p>.</c-><c- n>im</c-><c- p>;</c->
    <c- p>}</c->
    <c- k>constexpr</c-> <c- n>std</c-><c- o>::</c-><c- n>weak_ordering</c-> <c- k>operator</c-><c- o>&lt;=></c-><c- p>(</c-><c- n>gaussian</c-> <c- k>const</c-><c- o>&amp;</c-> <c- n>other</c-><c- p>)</c-> <c- k>const</c-> <c- p>{</c->
      <c- k>return</c-> <c- p>(</c-><c- o>*</c-><c- k>this</c-> <c- o>==</c-> <c- n>other</c-><c- p>)</c-> <c- o>?</c-> <c- n>std</c-><c- o>::</c-><c- n>weak_ordering</c-><c- o>::</c-><c- nl>equal</c->
                              <c- p>:</c-> <c- p>(</c-><c- n>abs</c-><c- p>(</c-><c- o>*</c-><c- k>this</c-><c- p>)</c-> <c- o>==</c-> <c- n>abs</c-><c- p>(</c-><c- n>other</c-><c- p>))</c-> <c- o>?</c-> <c- n>std</c-><c- o>::</c-><c- n>weak_ordering</c-><c- o>::</c-><c- nl>equivalent</c->
                                                           <c- p>:</c-> <c- n>abs</c-><c- p>(</c-><c- o>*</c-><c- k>this</c-><c- p>)</c-> <c- o>&lt;=></c-> <c- n>abs</c-><c- p>(</c-><c- n>other</c-><c- p>);</c->
    <c- p>}</c->
    <c- k>friend</c-> <c- k>constexpr</c-> <c- n>T</c-> <c- n>abs</c-><c- p>(</c-><c- n>gaussian</c-> <c- k>const</c-><c- o>&amp;</c-><c- p>)</c-> <c- p>{</c->
      <c- k>using</c-> <c- n>std</c-><c- o>::</c-><c- n>abs</c-><c- p>;</c->
      <c- k>return</c-> <c- nf>abs</c-><c- p>(</c-><c- n>re</c-><c- p>)</c-> <c- o>+</c-> <c- n>abs</c-><c- p>(</c-><c- n>im</c-><c- p>);</c->
    <c- p>}</c->

    <c- k>friend</c-> <c- k>constexpr</c-> <c- n>std</c-><c- o>::</c-><c- n>strong_ordering</c-> <c- n>strong_order</c-><c- p>(</c-><c- n>gaussian</c-> <c- k>const</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>,</c->
                                                       <c- n>gaussian</c-> <c- k>const</c-><c- o>&amp;</c-> <c- n>y</c-><c- p>)</c-> <c- p>{</c->
      <c- c1>// compare lexicographically</c->
      <c- k>return</c-> <c- n>std</c-><c- o>::</c-><c- n>tie</c-><c- p>(</c-><c- n>x</c-><c- p>.</c-><c- n>re</c-><c- p>,</c-> <c- n>x</c-><c- p>.</c-><c- n>im</c-><c- p>)</c-> <c- o>&lt;=></c-> <c- n>std</c-><c- o>::</c-><c- n>tie</c-><c- p>(</c-><c- n>y</c-><c- p>.</c-><c- n>re</c-><c- p>,</c-> <c- n>y</c-><c- p>.</c-><c- n>im</c-><c- p>);</c->
    <c- p>}</c->
  <c- p>};</c->
<c- p>}</c->
</pre>
   <p>Consider a transparent ordering operator for <code class="highlight"><c- n>map</c-></code>:</p>
<pre class="language-cpp highlight"><c- k>struct</c-> <c- n>strong_less</c->
  <c- k>template</c-> <c- o>&lt;</c-><c- k>typename</c-> <c- n>T</c-><c- p>,</c-> <c- k>typename</c-> <c- n>U</c-><c- o>></c->
  <c- b>bool</c-> <c- k>operator</c-><c- p>()(</c-><c- n>T</c-> <c- k>const</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>,</c-> <c- n>U</c-> <c- k>const</c-><c- o>&amp;</c-> <c- n>y</c-><c- p>)</c-> <c- p>{</c->
    <c- k>using</c-> <c- n>std</c-><c- o>::</c-><c- n>strong_order</c-><c- p>;</c->  <c- c1>// use ADL</c->
    <c- k>return</c-> <c- nf>strong_order</c-><c- p>(</c-><c- n>x</c-><c- p>,</c-> <c- n>y</c-><c- p>)</c-> <c- o>&lt;</c-> <c- mi>0</c-><c- p>;</c->
  <c- p>}</c->
  <c- k>using</c-> <c- n>is_transparent</c-> <c- o>=</c-> <c- n>std</c-><c- o>::</c-><c- n>true_type</c-><c- p>;</c->
<c- p>};</c->
</pre>
   <p>Also say we had a type with an implicit conversion to our <code class="highlight"><c- n>gaussian</c-></code>:</p>
<pre class="language-cpp highlight"><c- k>template</c-> <c- o>&lt;</c-><c- k>typename</c-> <c- n>T</c-><c- o>></c->
<c- k>struct</c-> <c- n>lazy</c-> <c- p>{</c->
  <c- n>std</c-><c- o>::</c-><c- n>function</c-><c- o>&lt;</c-><c- n>T</c-><c- p>()</c-><c- o>></c-> <c- n>make</c-><c- p>;</c->
  <c- k>operator</c-> <c- nf>T</c-><c- p>()</c-> <c- k>const</c-> <c- p>{</c-> <c- k>return</c-> <c- n>make</c-><c- p>();</c-> <c- p>}</c->
<c- p>};</c->
</pre>
   <p>This function now fails to compile, because the chosen <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>strong_order</c-></code> is deleted.</p>
<pre class="language-cpp highlight"><c- b>bool</c-> <c- nf>exists</c-><c- p>(</c-><c- n>lazy</c-><c- o>&lt;</c-><c- n>gaussian</c-><c- o>&lt;</c-><c- b>int</c-><c- o>>></c-> <c- k>const</c-><c- o>&amp;</c-> <c- n>x</c-><c- p>,</c->
            <c- n>std</c-><c- o>::</c-><c- n>set</c-><c- o>&lt;</c-><c- n>gaussian</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-><c- p>,</c-> <c- n>strong_less</c-><c- o>></c-> <c- k>const</c-><c- o>&amp;</c-> <c- n>in</c-><c- p>)</c-> <c- p>{</c->
  <c- d>/* imagine this being a template in both parameters - it’s pretty normal */</c->
  <c- k>return</c-> <c- n>in</c-><c- p>.</c-><c- n>count</c-><c- p>(</c-><c- n>x</c-><c- p>);</c->
<c- p>}</c->
</pre>
   <p>The std-provided <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>strong_order</c-></code> is deleted because it cannot be synthesized from <code class="highlight"><c- n>gaussian</c-></code>'s <code class="highlight"><c- k>operator</c-><c- o>&lt;=></c-></code>. The reason it is chosen over the friend function, however, is because the standard template matches better than the friend which would require an implicit conversion.</p>
   <p>If the std-provided <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>strong_order</c-></code> did not participate in overload resolution, however, this example would work just fine.</p>
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  <h2 class="no-num no-ref heading settled" id="index"><span class="content">Index</span><a class="self-link" href="#index"></a></h2>
  <h3 class="no-num no-ref heading settled" id="index-defined-here"><span class="content">Terms defined by this specification</span><a class="self-link" href="#index-defined-here"></a></h3>
  <ul class="index">
   <li><a href="#ambiguity-of-legacy">Ambiguity of Legacy</a><span>, in §4</span>
   <li><a href="#consistency">Consistency</a><span>, in §4</span>
   <li><a href="#corollary-1">Corollary 1</a><span>, in §4</span>
   <li><a href="#corollary-2">Corollary 2</a><span>, in §4</span>
   <li><a href="#corollary-3">Corollary 3</a><span>, in §4</span>
   <li><a href="#corollary-4">Corollary 4</a><span>, in §4</span>
   <li><a href="#corollary-5">Corollary 5</a><span>, in §4</span>
   <li><a href="#corollary-6">Corollary 6</a><span>, in §4</span>
   <li><a href="#customisation">Customisation</a><span>, in §4</span>
   <li><a href="#fallback">Fallback</a><span>, in §4</span>
   <li><a href="#weakening">Weakening</a><span>, in §4</span>
  </ul>
  <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="normative"><span class="content">Normative References</span><a class="self-link" href="#normative"></a></h3>
  <dl>
   <dt id="biblio-d1186r1">[D1186R1]
   <dd><a href="https://wg21.link/d1186r1">(Untitled)</a>. URL: <a href="https://wg21.link/d1186r1">https://wg21.link/d1186r1</a>
   <dt id="biblio-p0551r3">[P0551R3]
   <dd>Walter E. Brown. <a href="https://wg21.link/p0551r3">Thou Shalt Not Specialize std Function Templates!</a>. 16 March 2018. URL: <a href="https://wg21.link/p0551r3">https://wg21.link/p0551r3</a>
  </dl>
  <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-p0100r2">[P0100R2]
   <dd>Lawrence Crowl. <a href="https://wg21.link/p0100r2">Comparison in C++</a>. 27 November 2016. URL: <a href="https://wg21.link/p0100r2">https://wg21.link/p0100r2</a>
   <dt id="biblio-p0515r3">[P0515R3]
   <dd>Herb Sutter, Jens Maurer, Walter E. Brown. <a href="https://wg21.link/p0515r3">Consistent comparison</a>. 10 November 2017. URL: <a href="https://wg21.link/p0515r3">https://wg21.link/p0515r3</a>
   <dt id="biblio-p0768r1">[P0768R1]
   <dd>Walter E. Brown. <a href="https://wg21.link/p0768r1">Library Support for the Spaceship (Comparison) Operator</a>. 10 November 2017. URL: <a href="https://wg21.link/p0768r1">https://wg21.link/p0768r1</a>
   <dt id="biblio-p0863r1">[P0863R1]
   <dd>Jeff Snyder. <a href="https://wg21.link/p0863r1">Fixing the partial_order comparison algorithm</a>. 8 October 2018. URL: <a href="https://wg21.link/p0863r1">https://wg21.link/p0863r1</a>
   <dt id="biblio-p0891r0">[P0891R0]
   <dd>Gašper Ažman. <a href="https://wg21.link/p0891r0">Let strong_order Truly Be a Customization Point!</a>. 10 February 2018. URL: <a href="https://wg21.link/p0891r0">https://wg21.link/p0891r0</a>
   <dt id="biblio-p0891r1">[P0891R1]
   <dd>Gašper Ažman. <a href="https://wg21.link/p0891r1">Everyone Deserves a Little Order</a>. 27 October 2018. URL: <a href="https://wg21.link/p0891r1">https://wg21.link/p0891r1</a>
   <dt id="biblio-p1185r0">[P1185R0]
   <dd>Barry Revzin. <a href="https://wg21.link/p1185r0">&lt;=> != ==</a>. 7 October 2018. URL: <a href="https://wg21.link/p1185r0">https://wg21.link/p1185r0</a>
  </dl>
  <aside class="dfn-panel" data-for="consistency">
   <b><a href="#consistency">#consistency</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-consistency">4. Principles</a> <a href="#ref-for-consistency①">(2)</a> <a href="#ref-for-consistency②">(3)</a> <a href="#ref-for-consistency③">(4)</a>
    <li><a href="#ref-for-consistency④">6. Questions for LEWG:</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="weakening">
   <b><a href="#weakening">#weakening</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-weakening">4. Principles</a>
    <li><a href="#ref-for-weakening①">6. Questions for LEWG:</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="ambiguity-of-legacy">
   <b><a href="#ambiguity-of-legacy">#ambiguity-of-legacy</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-ambiguity-of-legacy">4. Principles</a>
    <li><a href="#ref-for-ambiguity-of-legacy①">6. Questions for LEWG:</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="customisation">
   <b><a href="#customisation">#customisation</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-customisation">4. Principles</a> <a href="#ref-for-customisation①">(2)</a>
    <li><a href="#ref-for-customisation②">5.1. Discussion of the Customisation principle</a>
    <li><a href="#ref-for-customisation③">6. Questions for LEWG:</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="fallback">
   <b><a href="#fallback">#fallback</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-fallback">4. Principles</a> <a href="#ref-for-fallback①">(2)</a>
    <li><a href="#ref-for-fallback②">5.2. Discussion of the Fallback principle</a>
    <li><a href="#ref-for-fallback③">6. Questions for LEWG:</a>
    <li><a href="#ref-for-fallback④">7.5. Add fallback functions</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="corollary-4">
   <b><a href="#corollary-4">#corollary-4</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-corollary-4">4. Principles</a>
   </ul>
  </aside>
  <aside class="dfn-panel" data-for="corollary-5">
   <b><a href="#corollary-5">#corollary-5</a></b><b>Referenced in:</b>
   <ul>
    <li><a href="#ref-for-corollary-5">4. Principles</a>
   </ul>
  </aside>
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