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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><meta name="viewport" content="width=device-width, initial-scale=0.8"/><title>9.5 Quantifiers</title><link rel="stylesheet" type="text/css" href="../scribble.css" title="default"/><link rel="stylesheet" type="text/css" href="../racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-style.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../doc-site.css" title="default"/><script type="text/javascript" src="../scribble-common.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../doc-site.js"></script><script type="text/javascript" src="../local-redirect/local-redirect.js"></script><script type="text/javascript" src="../local-redirect/local-user-redirect.js"></script><!--[if IE 6]><style type="text/css">.SIEHidden { overflow: hidden; }</style><![endif]--></head><body id="doc-racket-lang-org"><div class="tocset"><div class="tocview"><div class="tocviewlist tocviewlisttopspace"><div class="tocviewtitle"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_0");">►</a></td><td></td><td><a href="index.html" class="tocviewlink" data-pltdoc="x">The Racket Guide</a></td></tr></table></div><div class="tocviewsublisttop" style="display: none;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1 </td><td><a href="intro.html" class="tocviewlink" data-pltdoc="x">Welcome to Racket</a></td></tr><tr><td align="right">2 </td><td><a href="to-scheme.html" class="tocviewlink" data-pltdoc="x">Racket Essentials</a></td></tr><tr><td align="right">3 </td><td><a href="datatypes.html" class="tocviewlink" data-pltdoc="x">Built-<wbr></wbr>In Datatypes</a></td></tr><tr><td align="right">4 </td><td><a href="scheme-forms.html" class="tocviewlink" data-pltdoc="x">Expressions and Definitions</a></td></tr><tr><td align="right">5 </td><td><a href="define-struct.html" class="tocviewlink" data-pltdoc="x">Programmer-<wbr></wbr>Defined Datatypes</a></td></tr><tr><td align="right">6 </td><td><a href="modules.html" class="tocviewlink" data-pltdoc="x">Modules</a></td></tr><tr><td align="right">7 </td><td><a href="contracts.html" class="tocviewlink" data-pltdoc="x">Contracts</a></td></tr><tr><td align="right">8 </td><td><a href="i_o.html" class="tocviewlink" data-pltdoc="x">Input and Output</a></td></tr><tr><td align="right">9 </td><td><a href="regexp.html" class="tocviewselflink" data-pltdoc="x">Regular Expressions</a></td></tr><tr><td align="right">10 </td><td><a href="control.html" class="tocviewlink" data-pltdoc="x">Exceptions and Control</a></td></tr><tr><td align="right">11 </td><td><a href="for.html" class="tocviewlink" data-pltdoc="x">Iterations and Comprehensions</a></td></tr><tr><td align="right">12 </td><td><a href="match.html" class="tocviewlink" data-pltdoc="x">Pattern Matching</a></td></tr><tr><td align="right">13 </td><td><a href="classes.html" class="tocviewlink" data-pltdoc="x">Classes and Objects</a></td></tr><tr><td align="right">14 </td><td><a href="units.html" class="tocviewlink" data-pltdoc="x">Units</a></td></tr><tr><td align="right">15 </td><td><a href="reflection.html" class="tocviewlink" data-pltdoc="x">Reflection and Dynamic Evaluation</a></td></tr><tr><td align="right">16 </td><td><a href="macros.html" class="tocviewlink" data-pltdoc="x">Macros</a></td></tr><tr><td align="right">17 </td><td><a href="languages.html" class="tocviewlink" data-pltdoc="x">Creating Languages</a></td></tr><tr><td align="right">18 </td><td><a href="concurrency.html" class="tocviewlink" d
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match respectively: zero or more, one or more, and zero or one
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instances of the preceding subpattern.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match-positions%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match-positions</a></span><span class="hspace"> </span><span class="RktVal">#rx"c[ad]*r"</span><span class="hspace"> </span><span class="RktVal">"cadaddadddr"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'((0 . 11))</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match-positions%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match-positions</a></span><span class="hspace"> </span><span class="RktVal">#rx"c[ad]*r"</span><span class="hspace"> </span><span class="RktVal">"cr"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'((0 . 2))</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match-positions%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match-positions</a></span><span class="hspace"> </span><span class="RktVal">#rx"c[ad]+r"</span><span class="hspace"> </span><span class="RktVal">"cadaddadddr"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'((0 . 11))</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match-positions%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match-positions</a></span><span class="hspace"> </span><span class="RktVal">#rx"c[ad]+r"</span><span class="hspace"> </span><span class="RktVal">"cr"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match-positions%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match-positions</a></span><span class="hspace"> </span><span class="RktVal">#rx"c[ad]?r"</span><span class="hspace"> </span><span class="RktVal">"cadaddadddr"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match-positions%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match-positions</a></span><span class="hspace"> </span><span class="RktVal">#rx"c[ad]?r"</span><span class="hspace"> </span><span class="RktVal">"cr"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'((0 . 2))</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%
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finer-tuned quantification than is possible with <span class="RktInBG"><span class="hspace"></span><span class="RktIn">*</span><span class="hspace"></span></span>,
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">+</span><span class="hspace"></span></span>, <span class="RktInBG"><span class="hspace"></span><span class="RktIn">?</span><span class="hspace"></span></span>:</p><ul><li><p>The quantifier <span class="RktInBG"><span class="hspace"></span><span class="RktIn">{</span><span class="hspace"></span></span><span style="font-style: italic">m</span><span class="RktInBG"><span class="hspace"></span><span class="RktIn">}</span><span class="hspace"></span></span> matches
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<span class="emph">exactly</span> <span style="font-style: italic">m</span> instances of the preceding
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<a href="regexp-clusters.html#%28tech._subpattern%29" class="techoutside" data-pltdoc="x"><span class="techinside">subpattern</span></a>; <span style="font-style: italic">m</span> must be a nonnegative integer.</p></li><li><p>The quantifier
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">{</span><span class="hspace"></span></span><span style="font-style: italic">m</span><span class="RktInBG"><span class="hspace"></span><span class="RktIn">,</span><span class="hspace"></span></span><span style="font-style: italic">n</span><span class="RktInBG"><span class="hspace"></span><span class="RktIn">}</span><span class="hspace"></span></span> matches
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at least <span style="font-style: italic">m</span> and at most <span style="font-style: italic">n</span> instances. <span class="RktInBG"><span class="hspace"></span><span class="RktIn">m</span><span class="hspace"></span></span>
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and <span class="RktInBG"><span class="hspace"></span><span class="RktIn">n</span><span class="hspace"></span></span> are nonnegative integers with <span style="font-style: italic">m</span> less or
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equal to <span style="font-style: italic">n</span>. You may omit either or both numbers, in
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which case <span style="font-style: italic">m</span> defaults to <span style="font-style: italic"></span>0<span style="font-style: italic"></span> and <span style="font-style: italic">n</span> to
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infinity.</p></li></ul><p>It is evident that <span class="RktInBG"><span class="hspace"></span><span class="RktIn">+</span><span class="hspace"></span></span> and <span class="RktInBG"><span class="hspace"></span><span class="RktIn">?</span><span class="hspace"></span></span> are abbreviations for
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">{1,}</span><span class="hspace"></span></span> and <span class="RktInBG"><span class="hspace"></span><span class="RktIn">{0,1}</span><span class="hspace"></span></span> respectively, and <span class="RktInBG"><span class="hspace"></span><span class="RktIn">*</span><span class="hspace"></span></span>
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abbreviates <span class="RktInBG"><span class="hspace"></span><span class="RktIn">{,}</span><span class="hspace"></span></span>, which is the same as <span class="RktInBG"><span class="hspace"></span><span class="RktIn">{0,}</span><span class="hspace"></span></span>.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match</a></span><span class="hspace"> </span><span class="RktVal">#px"[aeiou]{3}"</span><span class="hspace"> </span><span class="RktVal">"vacuous"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'("uou")</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match</a></span><span class="hspace"> </span><span class="RktVal">#px"[aeiou]{3}"</span><span class="hspace"> </span><span class="RktVal">"evolve"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match</a></span><span class="hspace"> </span><span class="RktVal">#px"[aeiou]{2,3}"</span><span class="hspace"> </span><span class="RktVal">"evolve"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match</a></span><span class="hspace"> </span><span class="RktVal">#px"[aeiou]{2,3}"</span><span class="hspace"> </span><span class="RktVal">"zeugma"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'("eu")</span></p></td></tr></table></blockquote><p>The quantifiers described so far are all <a name="(tech._greedy)"></a><span style="font-style: italic">greedy</span>: they match
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the maximal number of instances that would still lead to an overall
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match for the full pattern.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match</a></span><span class="hspace"> </span><span class="RktVal">#rx"<.*>"</span><span class="hspace"> </span><span class="RktVal">"<tag1> <tag2> <tag3>"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'("<tag1> <tag2> <tag3>")</span></p></td></tr></table></blockquote><p>To make these quantifiers <a name="(tech._non._greedy)"></a><span style="font-style: italic">non-greedy</span>, append a <span class="RktInBG"><span class="hspace"></span><span class="RktIn">?</span><span class="hspace"></span></span>
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to them. Non-greedy quantifiers match the minimal number of instances
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needed to ensure an overall match.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=regexp.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._regexp-match%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">regexp-match</a></span><span class="hspace"> </span><span class="RktVal">#rx"<.*?>"</span><span class="hspace"> </span><span class="RktVal">"<tag1> <tag2> <tag3>"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'("<tag1>")</span></p></td></tr></table></blockquote><p>The non-greedy quantifiers are <span class="RktInBG"><span class="hspace"></span><span class="RktIn">*?</span><span class="hspace"></span></span>, <span class="RktInBG"><span class="hspace"></span><span class="RktIn">+?</span><span class="hspace"></span></span>,
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">??</span><span class="hspace"></span></span>, <span class="RktInBG"><span class="hspace"></span><span class="RktIn">{</span><span class="hspace"></span></span><span style="font-style: italic">m</span><span class="RktInBG"><span class="hspace"></span><span class="RktIn">}?</span><span class="hspace"></span></span>, and
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">{</span><span class="hspace"></span></span><span style="font-style: italic">m</span><span class="RktInBG"><span class="hspace"></span><span class="RktIn">,</span><span class="hspace"></span></span><span style="font-style: italic">n</span><span class="RktInBG"><span class="hspace"></span><span class="RktIn">}?</span><span class="hspace"></span></span>, although
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">{</span><span class="hspace"></span></span><span style="font-style: italic">m</span><span class="RktInBG"><span class="hspace"></span><span class="RktIn">}?</span><span class="hspace"></span></span> is always the same as
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">{</span><span class="hspace"></span></span><span style="font-style: italic">m</span><span class="RktInBG"><span class="hspace"></span><span class="RktIn">}</span><span class="hspace"></span></span>. Note that the metacharacter
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">?</span><span class="hspace"></span></span> has two different uses, and both uses are represented in
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">??</span><span class="hspace"></span></span>.</p><div class="navsetbottom"><span class="navleft"><form class="searchform"><input class="searchbox" id="searchbox" type="text" tabindex="1" placeholder="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "8.6", "../");"/></form> <a href="https://docs.racket-lang.org/index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("8.6");">top</a><span class="tocsettoggle"> <a href="javascript:void(0);" title="show/hide table of contents" onclick="TocsetToggle();">contents</a></span></span><span class="navright"> <a href="regexp-chars.html" title="backward to "9.4 Characters and Character Classes"" data-pltdoc="x">← prev</a> <a href="regexp.html" title="up to "9 Regular Expressions"" data-pltdoc="x">up</a> <a href="regexp-clusters.html" title="forward to "9.6 Clusters"" data-pltdoc="x">next →</a></span> </div></div></div><div id="contextindicator"> </div></body></html>
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