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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><title>The Typed Racket Reference</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,&quot;tocview_0&quot;);">&#9660;</a></td><td></td><td><a href="" class="tocviewselflink" data-pltdoc="x">The Typed Racket Reference</a></td></tr></table></div><div class="tocviewsublistonly" style="display: block;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1&nbsp;</td><td><a href="type-ref.html" class="tocviewlink" data-pltdoc="x">Type Reference</a></td></tr><tr><td align="right">2&nbsp;</td><td><a href="special-forms.html" class="tocviewlink" data-pltdoc="x">Special Form Reference</a></td></tr><tr><td align="right">3&nbsp;</td><td><a href="Libraries_Provided_With_Typed_Racket.html" class="tocviewlink" data-pltdoc="x">Libraries Provided With Typed Racket</a></td></tr><tr><td align="right">4&nbsp;</td><td><a href="Typed_Classes.html" class="tocviewlink" data-pltdoc="x">Typed Classes</a></td></tr><tr><td align="right">5&nbsp;</td><td><a href="Utilities.html" class="tocviewlink" data-pltdoc="x">Utilities</a></td></tr><tr><td align="right">6&nbsp;</td><td><a href="Exploring_Types.html" class="tocviewlink" data-pltdoc="x">Exploring Types</a></td></tr><tr><td align="right">7&nbsp;</td><td><a href="Typed_Racket_Syntax_Without_Type_Checking.html" class="tocviewlink" data-pltdoc="x">Typed Racket Syntax Without Type Checking</a></td></tr><tr><td align="right">8&nbsp;</td><td><a href="Typed_Regions.html" class="tocviewlink" data-pltdoc="x">Typed Regions</a></td></tr><tr><td align="right">9&nbsp;</td><td><a href="Optimization_in_Typed_Racket.html" class="tocviewlink" data-pltdoc="x">Optimization in Typed Racket</a></td></tr><tr><td align="right">10&nbsp;</td><td><a href="Legacy_Forms.html" class="tocviewlink" data-pltdoc="x">Legacy Forms</a></td></tr><tr><td align="right">11&nbsp;</td><td><a href="Compatibility_Languages.html" class="tocviewlink" data-pltdoc="x">Compatibility Languages</a></td></tr><tr><td align="right">12&nbsp;</td><td><a href="Experimental_Features.html" class="tocviewlink" data-pltdoc="x">Experimental Features</a></td></tr></table></div></div></div><div class="tocsub"><div class="tocsubtitle">On this page:</div><table class="tocsublist" cellspacing="0"><tr><td><span class="tocsublinknumber"></span><a href="#%28part._top%29" class="tocsubseclink" data-pltdoc="x">The Typed Racket Reference</a></td></tr></table></div></div><div class="maincolumn"><div class="main"><div class="versionbox"><span class="version">6.1</span></div><div class="navsettop"><span class="navleft"><form class="searchform"><input class="searchbox" style="color: #888;" type="text" value="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, &quot;6.1&quot;, &quot;../&quot;);" onfocus="this.style.color=&quot;black&quot;; this.style.textAlign=&quot;left&quot;; if (this.value == &quot;...search manuals...&quot;) this.value=&quot;&quot;;" onblur="if (this.value.match(/^ *$/)) { this.style.color=&quot;#888&quot;; this.style.textAlign=&quot;center&quot;; this.value=&quot;...search manuals...&quot;; }"/></form>&nbsp;&nbsp;<a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot(&quot;6.1&quot;);">top</a></span><span class="navright">&nbsp;&nbsp;<span class="nonavigation">&larr; prev</span>&nbsp;&nbsp;<a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot(&quot;6.1&quot;);">up</a>&nbsp;&nbsp;<a href="type-ref.html" title="forward to &quot;1 Type Reference&quot;" data-pltdoc="x">next &rarr;</a></span>&nbsp;</div><h2 x-source-module="(lib &quot;typed-racket/scribblings/ts-reference.scrbl&quot;)" x-part-tag="&quot;top&quot;"><a name="(part._top)"></a><a name="(mod-path._typed/racket/base)"></a><a name="(mod-path._typed/racket)"></a>The Typed Racket Reference</h2><div class="SAuthorListBox"><span class="SAuthorList"><p class="author">Sam Tobin-Hochstadt &lt;<a href="mailto:samth@racket-lang.org">samth@racket-lang.org</a>&gt;,<br/>Vincent St-Amour &lt;<a href="mailto:stamourv@racket-lang.org">stamourv@racket-lang.org</a>&gt;,<br/>Eric Dobson &lt;<a href="mailto:endobson@racket-lang.org">endobson@racket-lang.org</a>&gt;,<br/>and Asumu Takikawa &lt;<a href="mailto:asumu@racket-lang.org">asumu@racket-lang.org</a>&gt;</p></span></div><p>This manual describes the Typed Racket language, a sister language
of Racket with a static type-checker. The types, special forms, and
other tools provided by Typed Racket are documented here.</p><p>For a friendly introduction, see the companion manual
<a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=ts-guide&amp;rel=index.html&amp;version=6.1" class="Sq" data-pltdoc="x">The Typed Racket Guide</a>.</p><p><table cellspacing="0" cellpadding="0" class="defmodule"><tr><td align="left"><span class="hspace">&nbsp;</span><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=guide&amp;rel=Module_Syntax.html%23%2528part._hash-lang%2529&amp;version=6.1" class="RktModLink Sq" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace">&nbsp;</span><a href="" class="RktModLink" data-pltdoc="x"><span class="RktSym">typed/racket/base</span></a></td><td align="right"><span class="RpackageSpec"><span class="Smaller">&nbsp;package:</span> <span class="stt">typed-racket-lib</span></span></td></tr><tr><td align="left" colspan="2"><span class="hspace">&nbsp;</span><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=guide&amp;rel=Module_Syntax.html%23%2528part._hash-lang%2529&amp;version=6.1" class="RktModLink Sq" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace">&nbsp;</span><a href="" class="RktModLink" data-pltdoc="x"><span class="RktSym">typed/racket</span></a></td></tr></table></p><table cellspacing="0" cellpadding="0"><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html" class="toptoclink" data-pltdoc="x">1<span class="hspace">&nbsp;</span>Type Reference</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html#%28part._.Base_.Types%29" class="toclink" data-pltdoc="x">1.1<span class="hspace">&nbsp;</span>Base Types</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html#%28part._.Numeric_.Types%29" class="toclink" data-pltdoc="x">1.1.1<span class="hspace">&nbsp;</span>Numeric Types</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html#%28part._.Other_.Base_.Types%29" class="toclink" data-pltdoc="x">1.1.2<span class="hspace">&nbsp;</span>Other Base Types</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html#%28part._.Singleton_.Types%29" class="toclink" data-pltdoc="x">1.2<span class="hspace">&nbsp;</span>Singleton Types</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html#%28part._.Containers%29" class="toclink" data-pltdoc="x">1.3<span class="hspace">&nbsp;</span>Containers</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html#%28part._.Syntax_.Objects%29" class="toclink" data-pltdoc="x">1.4<span class="hspace">&nbsp;</span>Syntax Objects</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html#%28part._.Control%29" class="toclink" data-pltdoc="x">1.5<span class="hspace">&nbsp;</span>Control</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html#%28part._.Other_.Type_.Constructors%29" class="toclink" data-pltdoc="x">1.6<span class="hspace">&nbsp;</span>Other Type Constructors</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="type-ref.html#%28part._.Other_.Types%29" class="toclink" data-pltdoc="x">1.7<span class="hspace">&nbsp;</span>Other Types</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html" class="toptoclink" data-pltdoc="x">2<span class="hspace">&nbsp;</span>Special Form Reference</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Binding_.Forms%29" class="toclink" data-pltdoc="x">2.1<span class="hspace">&nbsp;</span>Binding Forms</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Anonymous_.Functions%29" class="toclink" data-pltdoc="x">2.2<span class="hspace">&nbsp;</span>Anonymous Functions</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Loops%29" class="toclink" data-pltdoc="x">2.3<span class="hspace">&nbsp;</span>Loops</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Definitions%29" class="toclink" data-pltdoc="x">2.4<span class="hspace">&nbsp;</span>Definitions</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Structure_.Definitions%29" class="toclink" data-pltdoc="x">2.5<span class="hspace">&nbsp;</span>Structure Definitions</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Names_for_.Types%29" class="toclink" data-pltdoc="x">2.6<span class="hspace">&nbsp;</span>Names for Types</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Generating_.Predicates_.Automatically%29" class="toclink" data-pltdoc="x">2.7<span class="hspace">&nbsp;</span>Generating Predicates Automatically</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Type_.Annotation_and_.Instantiation%29" class="toclink" data-pltdoc="x">2.8<span class="hspace">&nbsp;</span>Type Annotation and Instantiation</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Require%29" class="toclink" data-pltdoc="x">2.9<span class="hspace">&nbsp;</span>Require</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="special-forms.html#%28part._.Other_.Forms%29" class="toclink" data-pltdoc="x">2.10<span class="hspace">&nbsp;</span>Other Forms</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Libraries_Provided_With_Typed_Racket.html" class="toptoclink" data-pltdoc="x">3<span class="hspace">&nbsp;</span>Libraries Provided With Typed Racket</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Libraries_Provided_With_Typed_Racket.html#%28part._.Porting_.Untyped_.Modules_to_.Typed_.Racket%29" class="toclink" data-pltdoc="x">3.1<span class="hspace">&nbsp;</span>Porting Untyped Modules to Typed Racket</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Typed_Classes.html" class="toptoclink" data-pltdoc="x">4<span class="hspace">&nbsp;</span>Typed Classes</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Typed_Classes.html#%28part._.Special_forms%29" class="toclink" data-pltdoc="x">4.1<span class="hspace">&nbsp;</span>Special forms</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Typed_Classes.html#%28part._.Types%29" class="toclink" data-pltdoc="x">4.2<span class="hspace">&nbsp;</span>Types</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Utilities.html" class="toptoclink" data-pltdoc="x">5<span class="hspace">&nbsp;</span>Utilities</a></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Utilities.html#%28part._.Untyped_.Utilities%29" class="toclink" data-pltdoc="x">5.1<span class="hspace">&nbsp;</span>Untyped Utilities</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Exploring_Types.html" class="toptoclink" data-pltdoc="x">6<span class="hspace">&nbsp;</span>Exploring Types</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Typed_Racket_Syntax_Without_Type_Checking.html" class="toptoclink" data-pltdoc="x">7<span class="hspace">&nbsp;</span>Typed Racket Syntax Without Type Checking</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Typed_Regions.html" class="toptoclink" data-pltdoc="x">8<span class="hspace">&nbsp;</span>Typed Regions</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Optimization_in_Typed_Racket.html" class="toptoclink" data-pltdoc="x">9<span class="hspace">&nbsp;</span>Optimization in Typed Racket</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Legacy_Forms.html" class="toptoclink" data-pltdoc="x">10<span class="hspace">&nbsp;</span>Legacy Forms</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Compatibility_Languages.html" class="toptoclink" data-pltdoc="x">11<span class="hspace">&nbsp;</span>Compatibility Languages</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;</span><a href="Experimental_Features.html" class="toptoclink" data-pltdoc="x">12<span class="hspace">&nbsp;</span>Experimental Features</a></p></td></tr></table><div class="navsetbottom"><span class="navleft"><form class="searchform"><input class="searchbox" style="color: #888;" type="text" value="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, &quot;6.1&quot;, &quot;../&quot;);" onfocus="this.style.color=&quot;black&quot;; this.style.textAlign=&quot;left&quot;; if (this.value == &quot;...search manuals...&quot;) this.value=&quot;&quot;;" onblur="if (this.value.match(/^ *$/)) { this.style.color=&quot;#888&quot;; this.style.textAlign=&quot;center&quot;; this.value=&quot;...search manuals...&quot;; }"/></form>&nbsp;&nbsp;<a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot(&quot;6.1&quot;);">top</a></span><span class="navright">&nbsp;&nbsp;<span class="nonavigation">&larr; prev</span>&nbsp;&nbsp;<a href="../index.html" title="up 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