<!doctype html><html lang="en">
 <head>
  <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
  <meta content="width=device-width, initial-scale=1, shrink-to-fit=no" name="viewport">
  <title>P2609R2: Relaxing Ranges Just A Smidge</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
 *     -> ins/del.c### for candidate and proposed changes (amendments)
 *
 * 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)
 *   - .advisement for loud normative statements     (div, p, strong)
 *   - .annoying-warning for spec obsoletion notices (div, aside, details)
 *   - .correction for "candidate corrections"       (div, aside, details, section)
 *   - .addition   for "candidate additions"         (div, aside, details, section)
 *   - .correction.proposed for "proposed corrections" (div, aside, details, section)
 *   - .addition.proposed   for "proposed additions"   (div, aside, details, section)
 *
 * 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
 *
 * Outdated warning for old specs
 *
 * 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)
 *
 ******************************************************************************/

/* color variables included separately for reliability */

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

	html {
	}

	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;

		color: black;
		color: var(--text);
		background: white top left fixed no-repeat;
		background: var(--bg) 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: solid var(--logo-bg);
		border-width: .65rem .7rem .6rem;
		border-radius: .4rem;
		background: #1a5e9a;
		background: var(--logo-bg);
		color: white;
		color: var(--logo-text);
		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;
		background: var(--logo-active-bg);
		border-color: #c00;
		border-color: var(--logo-active-bg);
	}

	/* 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: 3;
			bottom: 0; left: 0;
			margin: 0;
			min-width: 1.33em;
			border-top-right-radius: 2rem;
			box-shadow: 0 0 2px;
			font-size: 1.5em;
		}
		#toc-nav > a {
			display: block;
			white-space: nowrap;

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

			box-shadow: 0 0 2px;
			border: none;
			border-top-right-radius: 1.33em;

			color: #707070;
			color: var(--tocnav-normal-text);
			background: white;
			background: var(--tocnav-normal-bg);
		}
		#toc-nav > a:hover,
		#toc-nav > a:focus {
			color: black;
			color: var(--tocnav-hover-text);
			background: #f8f8f8;
			background: var(--tocnav-hover-bg);
		}
		#toc-nav > a:active {
			color: #c00;
			color: var(--tocnav-active-text);
			background: white;
			background: var(--tocnav-active-bg);
		}

		#toc-nav > #toc-jump {
			padding-bottom: 2em;
			margin-bottom: -1.9em;
		}

		/* 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 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);
			color: black;
			color: var(--tocsidebar-text);
			background: inherit;
			background-color: #f7f8f9;
			background-color: var(--tocsidebar-bg);
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) inset;
			box-shadow: -.1em 0 .25em var(--tocsidebar-shadow) 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);
			color: var(--tocsidebar-heading-text);
		}
		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);
			color: black;
			color: var(--tocsidebar-text);
			background: inherit;
			background-color: #f7f8f9;
			background-color: var(--tocsidebar-bg);
			z-index: 1;
			box-shadow: -.1em 0 .25em rgba(0,0,0,.1) inset;
			box-shadow: -.1em 0 .25em var(--tocsidebar-shadow) 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);
			color: var(--tocsidebar-heading-text);
		}

		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;
		color: var(--heading-text);
	}

	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,
	#profile-and-date {
		/* #profile-and-date 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) > :not(.head) + hr {
		font-size: 1.5em;
		text-align: center;
		margin: 1em auto;
		height: auto;
		color: black;
		color: var(--hr-text);
		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;
	border-left: 0.5em solid var(--algo-border);
	}

	/* Put nice boxes around each algorithm. */
	[data-algorithm]:not(.heading) {
	 padding: .5em;
	 border: thin solid #ddd;
	 border: thin solid var(--algo-border);
	 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: inherit;
	}
	dfn var {
		font-style: normal;
	}

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

	del {
		color: #aa0000;
		color: var(--del-text);
		background: transparent;
		background: var(--del-bg);
		text-decoration: line-through;
	}
	ins {
		color: #006100;
		color: var(--ins-text);
		background: transparent;
		background: var(--ins-bg);
		text-decoration: underline;
	}

	/* for amendments (candidate/proposed changes) */

	.amendment ins, .correction ins, .addition ins,
	ins[class^=c] {
		text-decoration-style: dotted;
	}
	.amendment del, .correction del, .addition del,
	del[class^=c] {
		text-decoration-style: dotted;
	}
	.amendment.proposed ins, .correction.proposed ins, .addition.proposed ins,
	ins[class^=c].proposed {
		text-decoration-style: double;
	}
	.amendment.proposed del, .correction.proposed del, .addition.proposed del,
	del[class^=c].proposed {
		text-decoration-style: double;
	}

/** 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;
		hyphens: none;
		text-transform: none;
		text-align: left;
		text-align: start;
		font-variant: normal;
		orphans: 3;
		widows: 3;
		page-break-before: avoid;
	}
	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;
		color: var(--a-normal-text);
		text-decoration: underline #707070;
		text-decoration: underline var(--a-normal-underline);
		text-decoration-skip-ink: none;
	}
	a:visited {
		color: #034575;
		color: var(--a-visited-text);
		text-decoration-color: #bbb;
		text-decoration-color: var(--a-visited-underline);
	}

	/* Indicate interaction with the link */
	a[href]:focus,
	a[href]:hover {
		text-decoration-thickness: 2px;
	}
	a[href]:active {
		color: #c00;
		color: var(--a-active-text);
		text-decoration-color: #c00;
		text-decoration-color: var(--a-active-underline);
	}

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

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

	img {
		border-style: none;
	}

	img, svg {
		/* Intentionally not color-scheme aware. */
		background: white;
	}

	/* 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;
		height: 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,
	.amendment, .correction, .addition {
		margin: 1em auto;
		padding: .5em;
		border: .5em;
		border-left-style: solid;
		page-break-inside: avoid;
	}
	span.issue, span.note {
		padding: .1em .5em .15em;
		border-right-style: solid;
	}

	blockquote > :first-child,
	.note  > p:first-child,
	.issue > p:first-child,
	.amendment > p:first-child,
	.correction > p:first-child,
	.addition > p:first-child {
		margin-top: 0;
	}
	blockquote > :last-child,
	.note  > p:last-child,
	.issue > p:last-child,
	.amendment > p:last-child,
	.correction > p:last-child,
	.addition > p:last-child {
		margin-bottom: 0;
	}


	.issue::before, .issue > .marker,
	.example::before, .example > .marker,
	.note::before, .note > .marker,
	details.note > summary > .marker,
	.amendment::before, .amendment > .marker,
	details.amendment > summary > .marker,
	.addition::before, .addition > .marker,
	addition.amendment > summary > .marker,
	.correction::before, .correction > .marker,
	correction.amendment > summary > .marker
	{
		text-transform: uppercase;
		padding-right: 1em;
	}

	.example::before, .example > .marker {
		display: block;
		padding-right: 0em;
	}

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

	blockquote {
		border-color: silver;
		border-color: var(--blockquote-border);
		background: transparent;
		background: var(--blockquote-bg);
		color: currentcolor;
		color: var(--blockquote-text);
	}

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

	.issue {
		border-color: #e05252;
		border-color: var(--issue-border);
		background: #fbe9e9;
		background: var(--issue-bg);
		color: black;
		color: var(--issue-text);
		counter-increment: issue;
		overflow: auto;
	}
	.issue::before, .issue > .marker {
		color: #831616;
		color: var(--issueheading-text);
	}
	/* 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;
		border-color: var(--example-border);
		background: #fcfaee;
		background: var(--example-bg);
		color: black;
		color: var(--example-text);
		counter-increment: example;
		overflow: auto;
		clear: both;
	}
	.example::before, .example > .marker {
		color: #574b0f;
		color: var(--exampleheading-text);
	}
	/* 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;
		border-color: var(--note-border);
		background: #e9fbe9;
		background: var(--note-bg);
		color: black;
		color: var(--note-text);
		overflow: auto;
	}

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

	details.note[open] > summary {
		border-bottom: 1px silver solid;
		border-bottom: 1px var(--notesummary-underline) solid;
	}

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

	.assertion {
		border-color: #AAA;
		border-color: var(--assertion-border);
		background: #EEE;
		background: var(--assertion-bg);
		color: black;
		color: var(--assertion-text);
	}

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

	.advisement {
		border-color: orange;
		border-color: var(--advisement-border);
		border-style: none solid;
		background: #fec;
		background: var(--advisement-bg);
		color: black;
		color: var(--advisement-text);
	}
	strong.advisement {
		display: block;
		text-align: center;
	}
	.advisement::before, .advisement > .marker {
		color: #b35f00;
		color: var(--advisementheading-text);
	}

/** Amendment Box *************************************************************/

	.amendment, .correction, .addition {
		border-color: #330099;
		border-color: var(--amendment-border);
		background: #F5F0FF;
		background: var(--amendment-bg);
		color: black;
		color: var(--amendment-text);
	}
	.amendment.proposed, .correction.proposed, .addition.proposed {
		border-style: solid;
		border-block-width: 0.25em;
	}
	.amendment::before, .amendment > .marker,
	details.amendment > summary::before, details.amendment > summary > .marker,
	.correction::before, .correction > .marker,
	details.correction > summary::before, details.correction > summary > .marker,
	.addition::before, .addition > .marker,
	details.addition > summary::before, details.addition > summary > .marker {
		color: #220066;
		color: var(--amendmentheading-text);
	}
	.amendment.proposed::before, .amendment.proposed > .marker,
	details.amendment.proposed > summary::before, details.amendment.proposed > summary > .marker,
	.correction.proposed::before, .correction.proposed > .marker,
	details.correction.proposed > summary::before, details.correction.proposed > summary > .marker,
	.addition.proposed::before, .addition.proposed > .marker,
	details.addition.proposed > summary::before, details.addition.proposed > summary > .marker {
		font-weight: bold;
	}

/** 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: hsla(40,100%,50%,0.95);
		background: var(--warning-bg);
		color: black;
		color: var(--warning-text);
		padding: .75em 1em;
		border: red;
		border: var(--warning-border);
		border-style: solid none;
		box-shadow: 0 2px 8px black;
		text-align: center;
	}
	.annoying-warning :last-child {
		margin-bottom: 0;
	}

@media not print {
	details.annoying-warning[open] {
		position: fixed;
		left: 0;
		right: 0;
		bottom: 2em;
		z-index: 1000;
	}
}

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

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

	.def {
		padding: .5em 1em;
		background: #def;
		background: var(--def-bg);
		margin: 1.2em 0;
		border-left: 0.5em solid #8ccbf2;
		border-left: 0.5em solid var(--def-border);
		color: black;
		color: var(--def-text);
	}

/******************************************************************************/
/*                                    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;
		border-bottom: 1px solid var(--defrow-border);
	}

	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-color: var(--datacell-border);
		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 {
		border-bottom: 2px solid;
	}

	table.data colgroup,
	table.index colgroup {
		border-left: 2px solid;
	}

	table.data  tbody th:first-child,
	table.index tbody th:first-child  {
		border-right: 2px solid;
		border-top: 1px solid silver;
		border-top: 1px solid var(--datacell-border);
		padding-right: 1em;
	}

	table.data th[colspan],
	table.data td[colspan] {
		text-align: center;
	}

	table.complex.data th,
	table.complex.data td {
		border: 1px solid silver;
		border: 1px solid var(--datacell-border);
		text-align: center;
	}

	table.data.longlastcol td:last-child,
	table.data td.long {
		vertical-align: baseline;
		text-align: left;
	}

	table.data img {
		vertical-align: middle;
	}


/*
Alternate table alignment rules

	table.data,
	table.index {
		text-align: center;
	}

	table.data  thead th[scope="row"],
	table.index thead th[scope="row"] {
		text-align: right;
	}

	table.data  tbody th:first-child,
	table.index tbody th:first-child  {
		text-align: right;
	}

Possible extra rowspan handling

	table.data  tbody th[rowspan]:not([rowspan='1']),
	table.index tbody th[rowspan]:not([rowspan='1']),
	table.data  tbody td[rowspan]:not([rowspan='1']),
	table.index tbody td[rowspan]:not([rowspan='1']) {
		border-left: 1px solid silver;
	}

	table.data  tbody th[rowspan]:first-child,
	table.index tbody th[rowspan]:first-child,
	table.data  tbody td[rowspan]:first-child,
	table.index tbody td[rowspan]:first-child{
		border-left: 0;
		border-right: 1px solid silver;
	}
*/

/******************************************************************************/
/*                                  Indices                                   */
/******************************************************************************/


/** Table of Contents *********************************************************/

	.toc a {
		/* More spacing; use padding to make it part of the click target. */
		padding: 0.1rem 1px 0;
		/* Larger, more consistently-sized click target */
		display: block;
		/* Switch to using border-bottom for underlines */
		text-decoration: none;
		border-bottom: 1px solid;
		/* Reverse color scheme */
		color: black;
		color: var(--toclink-text);
		border-color: #3980b5;
		border-color: var(--toclink-underline);
	}
	.toc a:visited {
		color: black;
		color: var(--toclink-visited-text);
		border-color: #054572;
		border-color: var(--toclink-visited-underline);
	}
	.toc a:focus,
	.toc a:hover {
		background: rgba(75%, 75%, 75%, .25);
		background: var(--a-hover-bg);
		border-bottom-width: 3px;
		margin-bottom: -2px;
	}
	.toc a:not(:focus):not(:hover) {
		/* Allow colors to cascade through from link styling */
		border-bottom-color: transparent;
	}

	.toc, .toc ol, .toc ul, .toc li {
		list-style: none; /* Numbers must be inlined into source */
		/* because generated content isn't search/selectable and markers can't do multilevel yet */
		margin:  0;
		padding: 0;
	}
	.toc {
		line-height: 1.1em;
	}

	/* ToC not indented until third level, but font style & margins show hierarchy */
	.toc > li			{ font-weight: bold;   }
	.toc > li li		 { font-weight: normal; }
	.toc > li li li	  { font-size:   95%;	}
	.toc > li li li li	{ font-size:   90%;	}
	.toc > li li li li li { font-size:   85%;	}

	/* @supports not (display:grid) { */
		.toc > li			{ margin: 1.5rem 0;	}
		.toc > li li		 { margin: 0.3rem 0;	}
		.toc > li li li	  { margin-left: 2rem;   }

		/* Section numbers in a column of their own */
		.toc .secno {
			float: left;
			width: 4rem;
			white-space: nowrap;
		}
		.toc > li li li li .secno { font-size: 85%; }
		.toc > li li li li li .secno { font-size: 100%; }

		.toc li {
			clear: both;
		}

		:not(li) > .toc			 { margin-left:  5rem; }
		.toc .secno				 { margin-left: -5rem; }
		.toc > li li li .secno	  { margin-left: -7rem; }
		.toc > li li li li .secno	{ margin-left: -9rem; }
		.toc > li li li li li .secno { margin-left: -11rem; }

		/* Tighten up indentation in narrow ToCs */
		@media (max-width: 30em) {
			:not(li) > .toc			 { margin-left:  4rem; }
			.toc .secno				 { margin-left: -4rem; }
			.toc > li li li			 { margin-left:  1rem; }
			.toc > li li li .secno	  { margin-left: -5rem; }
			.toc > li li li li .secno	{ margin-left: -6rem; }
			.toc > li li li li li .secno { margin-left: -7rem; }
		}
		/* Loosen it on wide screens */
		@media screen and (min-width: 78em) {
			body:not(.toc-inline) :not(li) > .toc			 { margin-left:  4rem; }
			body:not(.toc-inline) .toc .secno				 { margin-left: -4rem; }
			body:not(.toc-inline) .toc > li li li			 { margin-left:  1rem; }
			body:not(.toc-inline) .toc > li li li .secno	  { margin-left: -5rem; }
			body:not(.toc-inline) .toc > li li li li .secno	{ margin-left: -6rem; }
			body:not(.toc-inline) .toc > li li li li li .secno { margin-left: -7rem; }
	}
	/* } */

	@supports (display:grid) and (display:contents) {
		/* Use #toc over .toc to override non-@supports rules. */
		#toc {
			display: grid;
			align-content: start;
			grid-template-columns: auto 1fr;
			grid-column-gap: 1rem;
			column-gap: 1rem;
			grid-row-gap: .6rem;
			row-gap: .6rem;
		}
		#toc h2 {
			grid-column: 1 / -1;
			margin-bottom: 0;
		}
		#toc ol,
		#toc li,
		#toc a {
			display: contents;
			/* Switch <a> to subgrid when supported */
		}
		#toc span {
			margin: 0;
		}
		#toc > .toc > li > a > span {
			/* The spans of the top-level list,
			  comprising the first items of each top-level section. */
			margin-top: 1.1rem;
		}
		#toc#toc .secno { /* Ugh, need more specificity to override base.css */
			grid-column: 1;
			width: auto;
			margin-left: 0;
		}
		#toc .content {
			grid-column: 2;
			width: auto;
			margin-right: 1rem;
		}
		#toc .content:hover,
		#toc .content:focus {
			background: rgba(75%, 75%, 75%, .25);
			background: var(--a-hover-bg);
			border-bottom: 3px solid #054572;
			border-bottom: 3px solid var(--toclink-underline);
			margin-bottom: -3px;
		}
		#toc li li li .content {
			margin-left: 1rem;
		}
		#toc li li li li .content {
			margin-left: 2rem;
		}
	}


/** Index *********************************************************************/

	/* Index Lists: Layout */
	ul.index	  { margin-left: 0; columns: 15em; text-indent: 1em hanging; }
	ul.index li	{ margin-left: 0; list-style: none; break-inside: avoid; }
	ul.index li li { margin-left: 1em; }
	ul.index dl	{ margin-top: 0; }
	ul.index dt	{ margin: .2em 0 .2em 20px;}
	ul.index dd	{ margin: .2em 0 .2em 40px;}
	/* Index Lists: Typography */
	ul.index ul,
	ul.index dl { font-size: smaller; }
	@media not print {
		ul.index li span:not(.dfn-paneled) {
			white-space: nowrap;
			color: transparent; }
		ul.index li a:hover + span,
		ul.index li a:focus + span {
			color: #707070;
			color: var(--indexinfo-text);
		}
	}

/** Index Tables *****************************************************/
	/* See also the data table styling section, which this effectively subclasses */

	table.index {
		font-size: small;
		border-collapse: collapse;
		border-spacing: 0;
		text-align: left;
		margin: 1em 0;
	}

	table.index td,
	table.index th {
		padding: 0.4em;
	}

	table.index tr:hover td:not([rowspan]),
	table.index tr:hover th:not([rowspan]) {
		color: black;
		color: var(--indextable-hover-text);
		background: #f7f8f9;
		background: var(--indextable-hover-bg);
	}

	/* The link in the first column in the property table (formerly a TD) */
	table.index th:first-child a {
		font-weight: bold;
	}

/** Outdated warning **********************************************************/

.outdated-spec {
	color: black;
	color: var(--outdatedspec-text);
	background-color: rgba(0,0,0,0.5);
	background-color: var(--outdatedspec-bg);
}

.outdated-warning {
	position: fixed;
	bottom: 50%;
	left: 0;
	right: 0;
	margin: 0 auto;
	width: 50%;
	background: maroon;
	background: var(--outdated-bg);
	color: white;
	color: var(--outdated-text);
	border-radius: 1em;
	box-shadow: 0 0 1em red;
	box-shadow: 0 0 1em var(--outdated-shadow);
	padding: 2em;
	text-align: center;
	z-index: 2;
}

.outdated-warning a {
	color: currentcolor;
	background: transparent;
}

.edited-rec-warning {
	background: darkorange;
	background: var(--editedrec-bg);
	box-shadow: 0 0 1em;
}

.outdated-warning button {
	color: var(--outdated-text);
	border-radius: 1em;
	box-shadow: 0 0 1em red;
	box-shadow: 0 0 1em var(--outdated-shadow);
	padding: 2em;
	text-align: center;
	z-index: 2;
}

.outdated-warning a {
	color: currentcolor;
	background: transparent;
}

.edited-rec-warning {
	background: darkorange;
	background: var(--editedrec-bg);
	box-shadow: 0 0 1em;
}

.outdated-warning button {
	position: absolute;
	top: 0;
	right:0;
	margin: 0;
	border: 0;
	padding: 0.25em 0.5em;
	background: transparent;
	color: white;
	color: var(--outdated-text);
	font:1em sans-serif;
	text-align:center;
}

.outdated-warning span {
	display: block;
}

.outdated-collapsed {
	bottom: 0;
	border-radius: 0;
	width: 100%;
	padding: 0;
}

/******************************************************************************/
/*                                    Print                                   */
/******************************************************************************/

	@media print {
		/* Pages have their own margins. */
		html {
			margin: 0;
		}
		/* Serif for print. */
		body {
			font-family: serif;
		}

		.outdated-warning {
			position: absolute;
			border-style: solid;
			border-color: red;
		}

		.outdated-warning input {
			display: none;
		}
	}
	@page {
		margin: 1.5cm 1.1cm;
	}



/******************************************************************************/
/*                             Overflow Control                               */
/******************************************************************************/

	.figure .caption, .sidefigure .caption, figcaption {
		/* in case figure is overlarge, limit caption to 50em */
		max-width: 50rem;
		margin-left: auto;
		margin-right: auto;
	}
	.overlarge {
		/* Magic to create good item positioning:
		  "content column" is 50ems wide at max; less on smaller screens.
		  Extra space (after ToC + content) is empty on the right.

		  1. When item < content column, centers item in column.
		  2. When content < item < available, left-aligns.
		  3. When item > available, fills available + scroll bar.
		*/
		display: grid;
		grid-template-columns: minmax(0, 50em);
	}
	.overlarge > table {
		/* limit preferred width of table */
		max-width: 50em;
		margin-left: auto;
		margin-right: auto;
	}

	@media (min-width: 55em) {
		.overlarge {
			margin-right: calc(13px + 26.5rem - 50vw);
			max-width: none;
		}
	}
	@media screen and (min-width: 78em) {
		body:not(.toc-inline) .overlarge {
			/* 30.5em body padding 50em content area */
			margin-right: calc(40em - 50vw) !important;
		}
	}
	@media screen and (min-width: 90em) {
		body:not(.toc-inline) .overlarge {
			/* 4em html margin 30.5em body padding 50em content area */
			margin-right: calc(84.5em - 100vw) !important;
		}
	}

	@media not print {
		.overlarge {
			overflow-x: auto;
			/* See Lea Verou's explanation background-attachment:
			* http://lea.verou.me/2012/04/background-attachment-local/
			*
			background: top left  / 4em 100% linear-gradient(to right,  #ffffff, rgba(255, 255, 255, 0)) local,
						top right / 4em 100% linear-gradient(to left, #ffffff, rgba(255, 255, 255, 0)) local,
						top left  / 1em 100% linear-gradient(to right,  #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						top right / 1em 100% linear-gradient(to left, #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						white;
			background-repeat: no-repeat;
			*/
		}
	}
</style>
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 <body class="h-entry">
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  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P2609R2<br>Relaxing Ranges Just A Smidge</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="profile-and-date"><span class="content">Published Proposal, <time class="dt-updated" datetime="2023-01-21">2023-01-21</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="https://jehelset.gitlab.io/cpp/relaxing-ranges-just-a-smidge/index.html">https://jehelset.gitlab.io/cpp/relaxing-ranges-just-a-smidge/index.html</a>
     <dt class="editor">Author:
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:private@jehelset.no">John Eivind Helset</a>
     <dt>Audience:
     <dd>SG9, LEWG
     <dt>Toggle Diffs:
     <dd>
      <label for="hidedel" id="hidedel-label">Hide deleted text</label>
     <dt>Project:
     <dd>ISO/IEC JTC1/SC22/WG21 14882: Programming Language — C++
     <dt>Subgroup:
     <dd>SG9
     <dt>Source:
     <dd><a href="https://gitlab.com/jehelset/cpp/-/blob/main/sources/relaxing-ranges-just-a-smidge/P2.bs">https://gitlab.com/jehelset/cpp/-/blob/main/sources/relaxing-ranges-just-a-smidge/P2.bs</a>
    </dl>
   </div>
   <div data-fill-with="warning"></div>
   <hr title="Separator for header">
  </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="#abstract"><span class="secno">1</span> <span class="content">Abstract</span></a>
    <li>
     <a href="#revisions"><span class="secno">2</span> <span class="content">Revisions</span></a>
     <ol class="toc">
      <li><a href="#revisions-R1"><span class="secno">2.1</span> <span class="content">R1</span></a>
      <li><a href="#revisions-R2"><span class="secno">2.2</span> <span class="content">R2</span></a>
     </ol>
    <li><a href="#problem"><span class="secno">3</span> <span class="content">Problem</span></a>
    <li><a href="#proposal"><span class="secno">4</span> <span class="content">Proposal</span></a>
    <li>
     <a href="#implementation"><span class="secno">5</span> <span class="content">Implementation</span></a>
     <ol class="toc">
      <li><a href="#implementation-ranges-v3"><span class="secno">5.1</span> <span class="content">ranges-v3</span></a>
      <li><a href="#implementation-libstdc++"><span class="secno">5.2</span> <span class="content">libstdc++</span></a>
     </ol>
    <li>
     <a href="#wording"><span class="secno">6</span> <span class="content">Wording</span></a>
     <ol class="toc">
      <li><a href="#wording.version.synopsis"><span class="secno">6.1</span> <span class="content">17.3.2 Header &lt;version> synopsis <span>[version.synopsis]</span></span></a>
      <li><a href="#wording.iterator.synopsis"><span class="secno">6.2</span> <span class="content">23.2 Header &lt;iterator> synopsis <span>[iterator.synopsis]</span></span></a>
      <li><a href="#wording.indirectcallable.traits"><span class="secno">6.3</span> <span class="content">23.3.2.4 Indirect callable traits [indirectcallable.traits]</span></a>
      <li><a href="#wording.indirectcallable.indirectinvocable"><span class="secno">6.4</span> <span class="content">23.3.6.4 Indirect callables <span>[indirectcallable.indirectinvocable]</span></span></a>
     </ol>
    <li><a href="#acknowledgements"><span class="secno">7</span> <span class="content">Acknowledgements</span></a>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ol>
   </ol>
  </nav>
  <main>
   <h2 class="heading settled" data-level="1" id="abstract"><span class="secno">1. </span><span class="content">Abstract</span><a class="self-link" href="#abstract"></a></h2>
   <p>Ranges algorithms that take a function and a projection should, in the unary case, constrain the
function to enable:</p>
<pre class="highlight"><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>It</c-><c- o>></c-> <c- n>x</c-> <c- o>=</c-> <c- o>*</c-><c- n>it</c-><c- p>;</c->
<c- n>f</c-><c- p>(</c-><c- n>proj</c-><c- p>(</c-><c- n>x</c-><c- p>));</c->
</pre>
   <p>Instead they are constrained to allow:</p>
<pre class="highlight"><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-><c- n>Proj</c-><c- o>>></c-> <c- n>u</c-> <c- o>=</c-> <c- n>proj</c-><c- p>(</c-><c- o>*</c-><c- n>it</c-><c- p>);</c->
<c- n>f</c-><c- p>(</c-><c- n>u</c-><c- p>);</c->
</pre>
   <p>And likewise in the binary case. This is caused by the composition of indirect callable concepts
with <code class="highlight"><c- n>projected</c-></code>, seen for example in the constraints of <code class="highlight"><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code> as <code class="highlight"><c- n>indirect_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-><c- n>P</c-><c- o>>></c-></code>.</p>
   <p>A fix is proposed that introduces a type-trait and makes a slight change to the definitions of the
indirect callable concepts, as well as <code class="highlight"><c- n>iter_common_reference_t</c-></code>. The fix is a slight relaxation of
the algorithmic constraints in ranges that does not break ABI.</p>
   <h2 class="heading settled" data-level="2" id="revisions"><span class="secno">2. </span><span class="content">Revisions</span><a class="self-link" href="#revisions"></a></h2>
   <h3 class="heading settled" data-level="2.1" id="revisions-R1"><span class="secno">2.1. </span><span class="content">R1</span><a class="self-link" href="#revisions-R1"></a></h3>
   <ul>
    <li data-md>
     <p>range-v3 PR now C++14 friendly, gcc implementation now exposition-only.</p>
    <li data-md>
     <p>Cleanup wording.</p>
    <li data-md>
     <p>Make <code class="highlight"><c- n>indirect_value_t</c-></code> exposition-only.</p>
    <li data-md>
     <p>Add note on P2248R4.</p>
    <li data-md>
     <p>Bump <code class="highlight"><c- n>__cpp_lib_ranges</c-></code> feature-test macro.</p>
   </ul>
   <h3 class="heading settled" data-level="2.2" id="revisions-R2"><span class="secno">2.2. </span><span class="content">R2</span><a class="self-link" href="#revisions-R2"></a></h3>
   <ul>
    <li data-md>
     <p>Fixup incorrect edits, and exposition-only syntax.</p>
    <li data-md>
     <p>Ensure <i><code class="highlight"><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-></code></i> can handle nested <code class="highlight"><c- n>projected</c-></code>s.</p>
   </ul>
   <h2 class="heading settled" data-level="3" id="problem"><span class="secno">3. </span><span class="content">Problem</span><a class="self-link" href="#problem"></a></h2>
   <p>In <a data-link-type="biblio" href="#biblio-niebler2015">[Niebler2015]</a> Eric Niebler explains that the constraints put on the predicate of <code class="highlight"><c- n>ranges</c-><c- o>::</c-><c- n>unique_copy</c-></code> must be strong enough to allow the algorithm to invoke it with a reference
formed to a copy of an element:</p>
   <blockquote> Sometimes the algorithms call the predicates with references, sometimes with values, and sometimes — like unique_copy — with a mix of both. </blockquote>
   <p>That iteration of <code class="highlight"><c- n>ranges</c-><c- o>::</c-><c- n>unique_copy</c-></code> did not have projections. The current iteration of <code class="highlight"><c- n>ranges</c-><c- o>::</c-><c- n>unique_copy</c-></code> has projections, and is specified as:</p>
<pre class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- n>input_range</c-> <c- n>R</c-><c- p>,</c-> <c- n>weakly_incrementable</c-> <c- n>O</c-><c- p>,</c-> <c- k>class</c-> <c- nc>Proj</c-> <c- o>=</c-> <c- n>identity</c-><c- p>,</c->
         <c- n>indirect_equivalence_relation</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>C</c-> <c- o>=</c-> <c- n>ranges</c-><c- o>::</c-><c- n>equal_to</c-><c- o>></c->
  <c- k>requires</c-> <c- n>indirectly_copyable</c-><c- o>&lt;</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>O</c-><c- o>></c-> <c- o>&amp;&amp;</c->
           <c- p>(</c-><c- n>forward_iterator</c-><c- o>&lt;</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>>></c-> <c- o>||</c->
            <c- p>(</c-><c- n>input_iterator</c-><c- o>&lt;</c-><c- n>O</c-><c- o>></c-> <c- o>&amp;&amp;</c-> <c- n>same_as</c-><c- o>&lt;</c-><c- n>range_value_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>O</c-><c- o>>></c-><c- p>)</c-> <c- o>||</c->
            <c- n>indirectly_copyable_storable</c-><c- o>&lt;</c-><c- n>iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>O</c-><c- o>></c-><c- p>)</c->
  <c- k>constexpr</c-> <c- n>ranges</c-><c- o>::</c-><c- n>unique_copy_result</c-><c- o>&lt;</c-><c- n>borrowed_iterator_t</c-><c- o>&lt;</c-><c- n>R</c-><c- o>></c-><c- p>,</c-> <c- n>O</c-><c- o>></c->
    <c- n>ranges</c-><c- o>::</c-><c- n>unique_copy</c-><c- p>(</c-><c- n>R</c-><c- o>&amp;&amp;</c-> <c- n>r</c-><c- p>,</c-> <c- n>O</c-> <c- n>result</c-><c- p>,</c-> <c- n>C</c-> <c- n>comp</c-> <c- o>=</c-> <c- p>{},</c-> <c- n>Proj</c-> <c- n>proj</c-> <c- o>=</c-> <c- p>{});</c->
</pre>
   <p>In <a data-link-type="biblio" href="#biblio-revzin2022">[Revzin2022]</a>, Barry Revzin writes that projections are function adaptors, and do not change an
algorithm. Projections as function adaptors is also discussed in <a href="https://github.com/ericniebler/range-v3/issues/211">ranges-v3/issues/233</a>. In the unary
case, projection is reduced to composition:</p>
   <blockquote> Put differently, every algorithm in the standard library that accepts a unary predicate and a projection, such that we have <code class="highlight"><c- n>algo</c-><c- p>(...,</c-> <c- n>pred</c-><c- p>,</c-> <c- n>proj</c-><c- p>)</c-></code> can have its projection dropped without any loss of functionality because users can do the function composition themselves and invoke it as <code class="highlight"><c- n>algo</c-><c- p>(...,</c-> <c- n>hof</c-><c- o>::</c-><c- n>compose</c-><c- p>(</c-><c- n>pred</c-><c- p>,</c-> <c- n>proj</c-><c- p>)))</c-></code>. </blockquote>
   <p>Yet the constraints put on the triplet of iterator, function and projection fail to express
projections as function adaptors. In the unary case they do not express <code class="highlight"><c- n>compose</c-><c- p>(</c-><c- n>f</c-><c- p>,</c-><c- n>proj</c-><c- p>)</c-></code>. <code class="highlight"><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-></code>, for example, takes a unary function <code class="highlight"><c- n>indirectly_unary_invocable</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- n>Fun</c-></code>. The definitions of <code class="highlight"><c- n>indirectly_unary_invocable</c-></code> and <code class="highlight"><c- n>projected</c-></code> are:</p>
<pre class="include-code highlight"><c- k>template</c-><c- o>&lt;</c-> <c- k>class</c-> <c- nc>F</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I</c-> <c- o>></c->
  <c- k>concept</c-> <c- nc>indirectly_unary_invocable</c-> <c- o>=</c->
    <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- o>&amp;&amp;</c->
    <c- n>copy_constructible</c-><c- o>&lt;</c-><c- n>F</c-><c- o>></c-> <c- o>&amp;&amp;</c->
    <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>&amp;></c-> <c- o>&amp;&amp;</c->
    <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
    <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
    <c- n>common_reference_with</c-><c- o>&lt;</c->
      <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>&amp;></c-><c- p>,</c->
      <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>>></c-><c- p>;</c->
</pre>
<pre class="include-code highlight"><c- k>template</c-><c- o>&lt;</c-><c- n>indirectly_readable</c-> <c- n>I</c-><c- p>,</c-> <c- n>indirectly_regular_unary_invocable</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- n>Proj</c-><c- o>></c->
<c- k>struct</c-> <c- nc>projected</c-> <c- p>{</c->
  <c- k>using</c-> <c- n>value_type</c-> <c- o>=</c-> <c- n>remove_cvref_t</c-><c- o>&lt;</c-><c- n>indirect_result_t</c-><c- o>&lt;</c-><c- n>Proj</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>I</c-><c- o>>></c-><c- p>;</c->
  <c- n>indirect_result_t</c-><c- o>&lt;</c-><c- n>Proj</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>I</c-><c- o>></c-> <c- k>operator</c-><c- o>*</c-><c- p>()</c-> <c- k>const</c-><c- p>;</c-> <c- c1>// not defined</c->
<c- p>};</c->
</pre>
   <p>Where <code class="highlight"><c- n>indirect_result_t</c-></code> is:</p>
<pre class="include-code highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>F</c-><c- p>,</c-> <c- k>class</c-><c- p>...</c-> <c- n>Is</c-><c- o>></c->
  <c- k>requires</c-> <c- p>(</c-><c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>Is</c-><c- o>></c-> <c- o>&amp;&amp;</c-> <c- p>...)</c-> <c- o>&amp;&amp;</c-> <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>Is</c-><c- o>></c-><c- p>...</c-><c- o>></c->
    <c- k>using</c-> <c- n>indirect_result_t</c-> <c- o>=</c-> <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>Is</c-><c- o>></c-><c- p>...</c-><c- o>></c-><c- p>;</c->
</pre>
   <p>The problematic constraint is <code class="highlight"><c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-> <c- o>&amp;</c-><c- p>,</c-> <c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Proj</c-><c- o>>></c-> <c- o>&amp;></c-></code>, which becomes
apparent when inlining the definition of <code class="highlight"><c- n>iter_value_t</c-></code>:</p>
<pre class="highlight"><c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-> <c- o>&amp;</c-><c- p>,</c-> <c- n>remove_cvref_t</c-><c- o>&lt;</c-><c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>Proj</c-> <c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;></c->
</pre>
   <p>The code that this constraint is supposed to enable, and the code it actually enables, for copying
and a referencing algorithm is:</p>
   <table>
    <tbody>
     <tr>
      <th>Algorithm
      <th>Expected
      <th>Actual
     <tr>
      <td>Referencing
      <td>
<pre class="highlight"><c- n>f</c-><c- p>(</c-><c- n>proj</c-><c- p>(</c-><c- o>*</c-><c- n>it</c-><c- p>))</c-></pre>
      <td>
<pre class="highlight"><c- n>f</c-><c- p>(</c-><c- n>proj</c-><c- p>(</c-><c- o>*</c-><c- n>it</c-><c- p>))</c-></pre>
     <tr>
      <td>Copying
      <td>
<pre class="highlight"><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>It</c-><c- o>></c-> <c- n>v</c-> <c- o>=</c-> <c- o>*</c-><c- n>it</c-><c- p>;</c->
<c- n>f</c-><c- p>(</c-><c- n>proj</c-><c- p>(</c-><c- n>v</c-><c- p>));</c->
</pre>
      <td>
<pre class="highlight"><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-><c- n>P</c-><c- o>>></c-> <c- n>u</c-> <c- o>=</c-> <c- n>proj</c-><c- p>(</c-><c- o>*</c-><c- n>it</c-><c- p>);</c->
<c- n>f</c-><c- p>(</c-><c- n>u</c-><c- p>);</c->
</pre>
   </table>
   <p>None of the algorithms in ranges are constrained to contain <code class="highlight"><c- n>f</c-><c- p>(</c-><c- n>u</c-><c- p>)</c-></code>. They do not require a copyable
or movable <code class="highlight"><c- n>u</c-></code>. Requiring copyability or movability would not be enough. One would also need to
somehow deal with the validity of <code class="highlight"><c- n>u</c-></code>. There is no guarantee that the validity of <code class="highlight"><c- n>u</c-></code> is not tied to
the element <code class="highlight"><c- o>*</c-><c- n>it</c-></code>.  This was discussed in <a href="https://github.com/ericniebler/range-v3/issues/148">ranges-v3/issues/148</a>,
and partially resolved by <a data-link-type="biblio" href="#biblio-p0740r0">[P0740R0]</a>.</p>
   <p>The actual consequence on user code seems small, as the malformed syntactic requirement of the
constraint is often naturally covered. Valid, but perhaps rare, code will not compile or need
work-arounds. In particular projections returning move-only types become problematic:</p>
<pre class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>for_each</c-><c- p>(</c->
  <c- n>std</c-><c- o>::</c-><c- n>views</c-><c- o>::</c-><c- n>iota</c-><c- p>(</c-><c- mi>0</c-><c- p>,</c-> <c- mi>5</c-><c- p>),</c->
  <c- p>[](</c-><c- n>std</c-><c- o>::</c-><c- n>unique_ptr</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-> <c- n>v</c-><c- p>){</c-> <c- c1>//Can’t be invoked with std::unique_ptr&lt;int> &amp;</c->
    <c- n>std</c-><c- o>::</c-><c- n>cout</c-> <c- o>&lt;&lt;</c-> <c- o>*</c-> <c- n>v</c-> <c- o>&lt;&lt;</c-> <c- n>std</c-><c- o>::</c-><c- n>endl</c-><c- p>;</c->
  <c- p>},</c->
  <c- p>[](</c-><c- b>int</c-> <c- n>v</c-><c- p>){</c->
    <c- k>return</c-> <c- n>std</c-><c- o>::</c-><c- n>make_unique</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-><c- p>(</c-><c- n>v</c-><c- p>);</c->
  <c- p>});</c->
</pre>
   <h2 class="heading settled" data-level="4" id="proposal"><span class="secno">4. </span><span class="content">Proposal</span><a class="self-link" href="#proposal"></a></h2>
   <p>The proposal aims at a minimal fix. First an exposition-only type-trait is defined that
disambiguates between the <code class="highlight"><c- n>value_type</c-></code> of an iterator and a projection:</p>
<pre class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- n>indirectly_readable</c-> <c- n>I</c-><c- o>></c->
<c- k>using</c-> <i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-></i> <c- o>=</c-> <c- n>see</c-> <c- n>below</c-><c- p>;</c-> <c- c1>// exposition only</c->
</pre>
   <p>The implementation technique is unspecified, but <i><code class="highlight"><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-></code></i> must be <code class="highlight"><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- o>&amp;</c-></code> for an iterator and <code class="highlight"><c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>Proj</c-> <c- o>&amp;</c-><c- p>,</c-> <i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-></i><c- o>&lt;</c-><c- n>Iter</c-><c- o>>></c-></code> for <code class="highlight"><c- n>projected</c-><c- o>&lt;</c-><c- n>Proj</c-><c- p>,</c-><c- n>Iter</c-><c- o>></c-></code>. The indirect
callable concepts, as well as <code class="highlight"><c- n>iter_common_reference_t</c-></code> are now redefined to use <i><code class="highlight"><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-></code></i> instead of <code class="highlight"><c- n>iter_value_t</c-></code>, showcased here for <code class="highlight"><c- n>indirectly_unary_invocable</c-></code>:</p>
<pre class="highlight"><c- k>template</c-><c- o>&lt;</c-> <c- k>class</c-> <c- nc>F</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I</c-> <c- o>></c->
  <c- k>concept</c-> <c- nc>indirectly_unary_invocable</c-> <c- o>=</c->
    <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- o>&amp;&amp;</c->
    <c- n>copy_constructible</c-><c- o>&lt;</c-><c- n>F</c-><c- o>></c-> <c- o>&amp;&amp;</c->
    <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>&amp;</c-></del><c- o>></c-> <c- o>&amp;&amp;</c->
    <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
    <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
    <c- n>common_reference_with</c-><c- o>&lt;</c->
      <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>&amp;</c-></del><c- o>></c-><c- p>,</c->
      <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>>></c-><c- p>;</c->
</pre>
   <p class="note" role="note"><span>Note:</span> In the event <a data-link-type="biblio" href="#biblio-p2248r4">[P2248R4]</a> is merged before this proposal, the <code class="highlight"><c- n>projected_value_t</c-></code> alias template of that
proposal should be redefined in terms of <code class="highlight"><c- n>remove_cvref_t</c-><c- o>&lt;</c-><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-></i><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-></code> as they compute
the same type and have the same semantics.</p>
   <h2 class="heading settled" data-level="5" id="implementation"><span class="secno">5. </span><span class="content">Implementation</span><a class="self-link" href="#implementation"></a></h2>
   <p>This proposal has currently been implemented and tested with both <a href="https://github.com/jehelset/range-v3/tree/relax-indirect-callable-concepts">ranges-v3</a> and <a href="https://gitlab.com/jehelset/gcc/-/tree/jehelset/relaxing-ranges-just-a-smidge">libstdc++</a> (on the gcc-12 release branch) without any issues.</p>
   <h3 class="heading settled" data-level="5.1" id="implementation-ranges-v3"><span class="secno">5.1. </span><span class="content">ranges-v3</span><a class="self-link" href="#implementation-ranges-v3"></a></h3>
   <p>ranges-v3 has a firewalled <code class="highlight"><c- n>projected</c-></code> (as proposed in <a data-link-type="biblio" href="#biblio-p2538r1">[P2538R1]</a>). Here the implementation uses a partial specialization that
is constrained on the existence of a "secret" nested alias declaration.</p>
   <h3 class="heading settled" data-level="5.2" id="implementation-libstdc++"><span class="secno">5.2. </span><span class="content">libstdc++</span><a class="self-link" href="#implementation-libstdc++"></a></h3>
   <p>libstdc++ has not yet firewalled <code class="highlight"><c- n>projected</c-></code>, so here a simple partial specialization was used.</p>
<pre class="include-code highlight"><c- k>namespace</c-> <c- nn>__detail</c-><c- p>{</c->

  <c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>_I</c-><c- o>></c->
     <c- k>struct</c-> <c- nc>__indirect_value_impl</c->
     <c- p>{</c-> <c- k>using</c-> <c- n>type</c-> <c- o>=</c-> <c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>_I</c-><c- o>></c-> <c- o>&amp;</c-><c- p>;</c-> <c- p>};</c->

  <c- k>template</c-><c- o>&lt;</c-><c- n>indirectly_readable</c-> <c- n>_I</c-><c- o>></c->
    <c- k>using</c-> <c- n>__indirect_value_t</c-> <c- o>=</c-> <c- k>typename</c-> <c- nc>__detail</c-><c- o>::</c-><c- n>__indirect_value_impl</c-><c- o>&lt;</c-><c- n>_I</c-><c- o>>::</c-><c- n>type</c-><c- p>;</c->

  <c- k>template</c-><c- o>&lt;</c-><c- n>weakly_incrementable</c-> <c- n>_Iter</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>_Proj</c-><c- o>></c->
    <c- k>struct</c-> <c- nc>__indirect_value_impl</c-><c- o>&lt;</c-><c- n>projected</c-><c- o>&lt;</c-><c- n>_Iter</c-><c- p>,</c-> <c- n>_Proj</c-><c- o>>></c->
    <c- p>{</c-> <c- k>using</c-> <c- n>type</c-> <c- o>=</c-> <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>_Proj</c-> <c- o>&amp;</c-><c- p>,</c-><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>_Iter</c-><c- o>></c-> <c- o>&amp;></c-><c- p>;</c-> <c- p>};</c->

<c- p>}</c-> <c- c1>// namespace __detail</c->
</pre>
   <h2 class="heading settled" data-level="6" id="wording"><span class="secno">6. </span><span class="content">Wording</span><a class="self-link" href="#wording"></a></h2>
   <h3 class="heading settled" data-level="6.1" id="wording.version.synopsis"><span class="secno">6.1. </span><span class="content">17.3.2 Header &lt;version> synopsis <a href="https://wg21.link/version.synopsis">[version.synopsis]</a></span><a class="self-link" href="#wording.version.synopsis"></a></h3>
   <p>Bump <code class="highlight"><c- n>__cpp_lib_ranges</c-></code> with the value specified as usual (year and month of adoption).</p>
<pre class="highlight"><c- cp>#define __cpp_lib_ranges YYYYMML  </c-><c- c1>// also in</c->
    <c- c1>// &lt;algorithm>,&lt;functional>,&lt;iterator>,&lt;memory>,&lt;ranges></c->
</pre>
   <h3 class="heading settled" data-level="6.2" id="wording.iterator.synopsis"><span class="secno">6.2. </span><span class="content">23.2 Header &lt;iterator> synopsis <a href="https://wg21.link/iterator.synopsis">[iterator.synopsis]</a></span><a class="self-link" href="#wording.iterator.synopsis"></a></h3>
<pre class="highlight"><c- c1>// [iterator.concepts], iterator concepts</c->
<c- c1>// [iterator.concept.readable], concept indirectly_­readable</c->
<c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>In</c-><c- o>></c->
  <c- k>concept</c-> <c- nc>indirectly_readable</c-> <c- o>=</c-> <c- n>see</c-> <c- n>below</c-><c- p>;</c->

<ins><c- k>template</c-><c- o>&lt;</c-><c- n>indirectly_</c->­<c- n>readable</c-> <c- n>T</c-><c- o>></c->
  <c- k>using</c-> <i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-></i> <c- o>=</c-> <c- n>see</c-> <c- n>below</c-><c- p>;</c-> <c- c1>// exposition only</c-></ins>

<c- k>template</c-><c- o>&lt;</c-><c- n>indirectly_</c->­<c- n>readable</c-> <c- n>T</c-><c- o>></c->
  <c- k>using</c-> <c- n>iter_common_reference_t</c-> <c- o>=</c->
    <c- n>common_reference_t</c-><c- o>&lt;</c-><c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>T</c-><c- o>>&amp;</c-></del><c- o>></c-><c- p>;</c->
</pre>
   <h3 class="heading settled" data-level="6.3" id="wording.indirectcallable.traits"><span class="secno">6.3. </span><span class="content">23.3.2.4 Indirect callable traits [indirectcallable.traits]</span><a class="self-link" href="#wording.indirectcallable.traits"></a></h3>
   <ol>
    <li data-md>
     <p>To implement algorithms taking projections, it is necessary to determine the projected type of an iterators value type. The exposition-only alias template <code class="highlight"><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-></code> denotes</p>
     <ul>
      <li data-md>
       <p><code class="highlight"><c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>Proj</c-><c- o>&amp;</c-><c- p>,</c-> <i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-></i><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-></code> if <code class="highlight"><c- n>T</c-></code> names <code class="highlight"><c- n>projected</c-><c- o>&lt;</c-><c- n>I</c-><c- p>,</c-> <c- n>Proj</c-><c- o>></c-></code></p>
      <li data-md>
       <p>and <code class="highlight"><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>T</c-><c- o>></c-> <c- o>&amp;</c-></code> otherwise.</p>
     </ul>
   </ol>
   <h3 class="heading settled" data-level="6.4" id="wording.indirectcallable.indirectinvocable"><span class="secno">6.4. </span><span class="content">23.3.6.4 Indirect callables <a href="https://wg21.link/indirectcallable.indirectinvocable">[indirectcallable.indirectinvocable]</a></span><a class="self-link" href="#wording.indirectcallable.indirectinvocable"></a></h3>
<pre class="highlight"><c- k>namespace</c-> <c- nn>std</c-> <c- p>{</c->
  <c- k>template</c-><c- o>&lt;</c-> <c- k>class</c-> <c- nc>F</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I</c-> <c- o>></c->
    <c- k>concept</c-> <c- nc>indirectly_unary_invocable</c-> <c- o>=</c->
      <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>copy_constructible</c-><c- o>&lt;</c-><c- n>F</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>&amp;</c-></del><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>common_reference_with</c-><c- o>&lt;</c->
  <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>&amp;</c-></del><c- o>></c-><c- p>,</c->
  <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>>></c-><c- p>;</c->

  <c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>F</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I</c-><c- o>></c->
    <c- k>concept</c-> <c- nc>indirectly_regular_unary_invocable</c-> <c- o>=</c->
      <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>copy_constructible</c-><c- o>&lt;</c-><c- n>F</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>regular_invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>&amp;</c-></del><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>regular_invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>regular_invocable</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>common_reference_with</c-><c- o>&lt;</c->
  <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>&amp;</c-></del><c- o>></c-><c- p>,</c->
  <c- n>invoke_result_t</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>>></c-><c- p>;</c->

  <c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>F</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I</c-><c- o>></c->
    <c- k>concept</c-> <c- nc>indirect_unary_predicate</c-> <c- o>=</c->
      <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>copy_constructible</c-><c- o>&lt;</c-><c- n>F</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>predicate</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>&amp;></c-></del> <c- o>&amp;&amp;</c->
      <c- n>predicate</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>predicate</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I</c-><c- o>>></c-><c- p>;</c->

  <c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>F</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I1</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I2</c-><c- o>></c->
    <c- k>concept</c-> <c- nc>indirect_binary_predicate</c-> <c- o>=</c->
      <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-> <c- o>&amp;&amp;</c-> <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>copy_constructible</c-><c- o>&lt;</c-><c- n>F</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>predicate</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>>&amp;</c-></del><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>&amp;</c-></del><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>predicate</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>>&amp;</c-></del><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>predicate</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>&amp;></c-></del> <c- o>&amp;&amp;</c->
      <c- n>predicate</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>predicate</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>></c-><c- p>;</c->

  <c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>F</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I1</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I2</c-> <c- o>=</c-> <c- n>I1</c-><c- o>></c->
    <c- k>concept</c-> <c- nc>indirect_equivalence_relation</c-> <c- o>=</c->
      <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-> <c- o>&amp;&amp;</c-> <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>copy_constructible</c-><c- o>&lt;</c-><c- n>F</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>equivalence_relation</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>>&amp;</c-></del><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>&amp;</c-></del><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>equivalence_relation</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>>&amp;</c-></del><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>equivalence_relation</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>&amp;</c-></del><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>equivalence_relation</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>equivalence_relation</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>></c-><c- p>;</c->

  <c- k>template</c-><c- o>&lt;</c-><c- k>class</c-> <c- nc>F</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I1</c-><c- p>,</c-> <c- k>class</c-> <c- nc>I2</c-> <c- o>=</c-> <c- n>I1</c-><c- o>></c->
    <c- k>concept</c-> <c- nc>indirect_strict_weak_order</c-> <c- o>=</c->
      <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-> <c- o>&amp;&amp;</c-> <c- n>indirectly_readable</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>copy_constructible</c-><c- o>&lt;</c-><c- n>F</c-><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>strict_weak_order</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>>&amp;</c-></del><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>&amp;</c-></del><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>strict_weak_order</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>>&amp;</c-></del><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>strict_weak_order</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-><c- p>,</c-> <ins><i><c- n>indirect</c-><c- o>-</c-><c- n>value</c-><c- o>-</c-><c- n>t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>></c-></i></ins><del><c- n>iter_value_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>&amp;</c-></del><c- o>></c-> <c- o>&amp;&amp;</c->
      <c- n>strict_weak_order</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-><c- p>,</c-> <c- n>iter_reference_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>></c-> <c- o>&amp;&amp;</c->
      <c- n>strict_weak_order</c-><c- o>&lt;</c-><c- n>F</c-><c- o>&amp;</c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I1</c-><c- o>></c-><c- p>,</c-> <c- n>iter_common_reference_t</c-><c- o>&lt;</c-><c- n>I2</c-><c- o>>></c-><c- p>;</c->
</pre>
   <h2 class="heading settled" data-level="7" id="acknowledgements"><span class="secno">7. </span><span class="content">Acknowledgements</span><a class="self-link" href="#acknowledgements"></a></h2>
   <p>The author would like to thank Barry Revzin, Christopher Di Bella, Arthur O’Dwyer, Hui Xie
and Tim Song for guidance.</p>
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  <h2 class="no-num no-ref heading settled" id="references"><span class="content">References</span><a class="self-link" href="#references"></a></h2>
  <h3 class="no-num no-ref heading settled" id="informative"><span class="content">Informative References</span><a class="self-link" href="#informative"></a></h3>
  <dl>
   <dt id="biblio-niebler2015">[Niebler2015]
   <dd>Eric Niebler. <a href="https://ericniebler.com/2015/03/03/iterators-plus-plus-part-3/"><cite>Iterators++, Part 3</cite></a>. URL: <a href="https://ericniebler.com/2015/03/03/iterators-plus-plus-part-3/">https://ericniebler.com/2015/03/03/iterators-plus-plus-part-3/</a>
   <dt id="biblio-p0740r0">[P0740R0]
   <dd>Casey Carter. <a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2017/p0740r0.html"><cite>Ranges TS "Immediate" Issues from the July 2017 (Toronto) meeting</cite></a>. URL: <a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2017/p0740r0.html">https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2017/p0740r0.html</a>
   <dt id="biblio-p2248r4">[P2248R4]
   <dd>Giuseppe D'Angelo. <a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2022/p2248r4.html"><cite>Enabling list-initialization for algorithms</cite></a>. URL: <a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2022/p2248r4.html">https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2022/p2248r4.html</a>
   <dt id="biblio-p2538r1">[P2538R1]
   <dd>Arthur O'Dwyer; Casey Carter. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2022/p2538r1.html"><cite>ADL-proof std::projected</cite></a>. URL: <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2022/p2538r1.html">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2022/p2538r1.html</a>
   <dt id="biblio-revzin2022">[Revzin2022]
   <dd>Barry Revzin. <a href="https://brevzin.github.io/c++/2022/02/13/projections-function-adaptors/"><cite>Projections are Function Adaptors</cite></a>. URL: <a href="https://brevzin.github.io/c++/2022/02/13/projections-function-adaptors/">https://brevzin.github.io/c++/2022/02/13/projections-function-adaptors/</a>
  </dl>