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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><title>The Typed Racket Guide</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="" class="tocviewselflink" data-pltdoc="x">The Typed Racket Guide</a></td></tr></table></div><div class="tocviewsublistonly" style="display: block;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1 </td><td><a href="quick.html" class="tocviewlink" data-pltdoc="x">Quick Start</a></td></tr><tr><td align="right">2 </td><td><a href="beginning.html" class="tocviewlink" data-pltdoc="x">Beginning Typed Racket</a></td></tr><tr><td align="right">3 </td><td><a href="more.html" class="tocviewlink" data-pltdoc="x">Specifying Types</a></td></tr><tr><td align="right">4 </td><td><a href="types.html" class="tocviewlink" data-pltdoc="x">Types in Typed Racket</a></td></tr><tr><td align="right">5 </td><td><a href="occurrence-typing.html" class="tocviewlink" data-pltdoc="x">Occurrence Typing</a></td></tr><tr><td align="right">6 </td><td><a href="typed-untyped-interaction.html" class="tocviewlink" data-pltdoc="x">Typed-<wbr></wbr>Untyped Interaction</a></td></tr><tr><td align="right">7 </td><td><a href="optimization.html" class="tocviewlink" data-pltdoc="x">Optimization in Typed Racket</a></td></tr><tr><td align="right">8 </td><td><a href="caveats.html" class="tocviewlink" data-pltdoc="x">Caveats and Limitations</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 Guide</a></td></tr></table></div></div><div class="maincolumn"><div class="main"><div class="versionbox"><span class="version">6.7</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, "6.7", "../");" onfocus="this.style.color="black"; this.style.textAlign="left"; if (this.value == "...search manuals...") this.value="";" onblur="if (this.value.match(/^ *$/)) { this.style.color="#888"; this.style.textAlign="center"; this.value="...search manuals..."; }"/></form> <a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("6.7");">top</a></span><span class="navright"> <span class="nonavigation">← prev</span> <a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("6.7");">up</a> <a href="quick.html" title="forward to "1 Quick Start"" data-pltdoc="x">next →</a></span> </div><h2 x-source-module="(lib "typed-racket/scribblings/ts-guide.scrbl")" x-source-pkg="typed-racket-doc" x-part-tag=""top""><a name="(part._top)"></a><a name="(idx._(gentag._0._(lib._typed-racket/scribblings/ts-guide..scrbl)))"></a>The Typed Racket Guide</h2><div class="SAuthorListBox"><span class="SAuthorList"><p class="author">Sam Tobin-Hochstadt <<a href="mailto:samth@racket-lang.org">samth@racket-lang.org</a>>,<br/>Vincent St-Amour <<a href="mailto:stamourv@racket-lang.org">stamourv@racket-lang.org</a>>,<br/>Eric Dobson <<a href="mailto:endobson@racket-lang.org">endobson@racket-lang.org</a>>,<br/>and Asumu Takikawa <<a href="mailto:asumu@racket-lang.org">asumu@racket-lang.org</a>></p></span></div><p>Typed Racket is Racket’s gradually-typed sister language which allows
the incremental addition of statically-checked type annotations. This guide is intended for programmers familiar
with Racket. For an introduction to Racket, see <a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=guide&rel=index.html&version=6.7" class="Sq" data-pltdoc="x"><span style="font-weight: bold">The Racket Guide</span></a>.</p><p>For the precise details, also see
<a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=index.html&version=6.7" class="Sq" data-pltdoc="x">The Typed Racket Reference</a>.</p><table cellspacing="0" cellpadding="0"><tr><td><p><span class="hspace"> </span><a href="quick.html" class="toptoclink" data-pltdoc="x">1<span class="hspace"> </span>Quick Start</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="quick.html#%28part._.Using_.Typed_.Racket_from_the_.Racket_.R.E.P.L%29" class="toclink" data-pltdoc="x">1.1<span class="hspace"> </span>Using Typed Racket from the Racket REPL</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace"> </span><a href="beginning.html" class="toptoclink" data-pltdoc="x">2<span class="hspace"> </span>Beginning Typed Racket</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="beginning.html#%28part._.Datatypes_and_.Unions%29" class="toclink" data-pltdoc="x">2.1<span class="hspace"> </span>Datatypes and Unions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="beginning.html#%28part._.Type_.Errors%29" class="toclink" data-pltdoc="x">2.2<span class="hspace"> </span>Type Errors</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html" class="toptoclink" data-pltdoc="x">3<span class="hspace"> </span>Specifying Types</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html#%28part._.Type_.Annotation_and_.Binding_.Forms%29" class="toclink" data-pltdoc="x">3.1<span class="hspace"> </span>Type Annotation and Binding Forms</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html#%28part._.Annotating_.Definitions%29" class="toclink" data-pltdoc="x">3.1.1<span class="hspace"> </span>Annotating Definitions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html#%28part._.Annotating_.Local_.Binding%29" class="toclink" data-pltdoc="x">3.1.2<span class="hspace"> </span>Annotating Local Binding</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html#%28part._.Annotating_.Functions%29" class="toclink" data-pltdoc="x">3.1.3<span class="hspace"> </span>Annotating Functions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html#%28part._.Annotating_.Single_.Variables%29" class="toclink" data-pltdoc="x">3.1.4<span class="hspace"> </span>Annotating Single Variables</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html#%28part._.Annotating_.Expressions%29" class="toclink" data-pltdoc="x">3.1.5<span class="hspace"> </span>Annotating Expressions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html#%28part._.Type_.Inference%29" class="toclink" data-pltdoc="x">3.2<span class="hspace"> </span>Type Inference</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html#%28part._when-annotations~3f%29" class="toclink" data-pltdoc="x">3.2.1<span class="hspace"> </span>When do you need type annotations?</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="more.html#%28part._.New_.Type_.Names%29" class="toclink" data-pltdoc="x">3.3<span class="hspace"> </span>New Type Names</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html" class="toptoclink" data-pltdoc="x">4<span class="hspace"> </span>Types in Typed Racket</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Basic_.Types%29" class="toclink" data-pltdoc="x">4.1<span class="hspace"> </span>Basic Types</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Function_.Types%29" class="toclink" data-pltdoc="x">4.2<span class="hspace"> </span>Function Types</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Types_for_.Functions_with_.Optional_or_.Keyword_.Arguments%29" class="toclink" data-pltdoc="x">4.3<span class="hspace"> </span>Types for Functions with Optional or Keyword Arguments</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Union_.Types%29" class="toclink" data-pltdoc="x">4.4<span class="hspace"> </span>Union Types</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Recursive_.Types%29" class="toclink" data-pltdoc="x">4.5<span class="hspace"> </span>Recursive Types</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Structure_.Types%29" class="toclink" data-pltdoc="x">4.6<span class="hspace"> </span>Structure Types</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Subtyping%29" class="toclink" data-pltdoc="x">4.7<span class="hspace"> </span>Subtyping</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Polymorphism%29" class="toclink" data-pltdoc="x">4.8<span class="hspace"> </span>Polymorphism</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Polymorphic_.Data_.Structures%29" class="toclink" data-pltdoc="x">4.8.1<span class="hspace"> </span>Polymorphic Data Structures</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Polymorphic_.Functions%29" class="toclink" data-pltdoc="x">4.8.2<span class="hspace"> </span>Polymorphic Functions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Lexically_.Scoped_.Type_.Variables%29" class="toclink" data-pltdoc="x">4.8.3<span class="hspace"> </span>Lexically Scoped Type Variables</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._varargs%29" class="toclink" data-pltdoc="x">4.9<span class="hspace"> </span>Variable-Arity Functions: Programming with Rest Arguments</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Uniform_.Variable-.Arity_.Functions%29" class="toclink" data-pltdoc="x">4.9.1<span class="hspace"> </span>Uniform Variable-Arity Functions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="types.html#%28part._.Non-.Uniform_.Variable-.Arity_.Functions%29" class="toclink" data-pltdoc="x">4.9.2<span class="hspace"> </span>Non-Uniform Variable-Arity Functions</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace"> </span><a href="occurrence-typing.html" class="toptoclink" data-pltdoc="x">5<span class="hspace"> </span>Occurrence Typing</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="occurrence-typing.html#%28part._.Basic_.Occurrence_.Typing%29" class="toclink" data-pltdoc="x">5.1<span class="hspace"> </span>Basic Occurrence Typing</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="occurrence-typing.html#%28part._propositions-and-predicates%29" class="toclink" data-pltdoc="x">5.2<span class="hspace"> </span>Propositions and Predicates</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="occurrence-typing.html#%28part._.Other_conditionals_and_assertions%29" class="toclink" data-pltdoc="x">5.3<span class="hspace"> </span>Other conditionals and assertions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="occurrence-typing.html#%28part._.A_caveat_about_set_%29" class="toclink" data-pltdoc="x">5.4<span class="hspace"> </span>A caveat about <span class="RktSym"><span class="RktStxLink">set!</span></span></a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="occurrence-typing.html#%28part._let-aliasing%29" class="toclink" data-pltdoc="x">5.5<span class="hspace"> </span><span class="RktSym"><span class="RktStxLink">let</span></span>-aliasing</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace"> </span><a href="typed-untyped-interaction.html" class="toptoclink" data-pltdoc="x">6<span class="hspace"> </span>Typed-Untyped Interaction</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="typed-untyped-interaction.html#%28part._.Using_.Untyped_.Code_from_.Typed_.Code%29" class="toclink" data-pltdoc="x">6.1<span class="hspace"> </span>Using Untyped Code from Typed Code</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="typed-untyped-interaction.html#%28part._.Using_.Typed_.Code_in_.Untyped_.Code%29" class="toclink" data-pltdoc="x">6.2<span class="hspace"> </span>Using Typed Code in Untyped Code</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="typed-untyped-interaction.html#%28part._.Protecting_.Typed-.Untyped_.Interaction%29" class="toclink" data-pltdoc="x">6.3<span class="hspace"> </span>Protecting Typed-Untyped Interaction</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace"> </span><a href="optimization.html" class="toptoclink" data-pltdoc="x">7<span class="hspace"> </span>Optimization in Typed Racket</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="optimization.html#%28part._.Turning_the_optimizer_off%29" class="toclink" data-pltdoc="x">7.1<span class="hspace"> </span>Turning the optimizer off</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="optimization.html#%28part._.Getting_the_most_out_of_the_optimizer%29" class="toclink" data-pltdoc="x">7.2<span class="hspace"> </span>Getting the most out of the optimizer</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="optimization.html#%28part._.Numeric_types%29" class="toclink" data-pltdoc="x">7.2.1<span class="hspace"> </span>Numeric types</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="optimization.html#%28part._.Lists%29" class="toclink" data-pltdoc="x">7.2.2<span class="hspace"> </span>Lists</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="optimization.html#%28part._.Vectors%29" class="toclink" data-pltdoc="x">7.2.3<span class="hspace"> </span>Vectors</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="optimization.html#%28part._contract-costs%29" class="toclink" data-pltdoc="x">7.2.4<span class="hspace"> </span>Contract boundaries</a></p></td></tr><tr><td><p><span class="hspace"></span></p></td></tr><tr><td><p><span class="hspace"> </span><a href="caveats.html" class="toptoclink" data-pltdoc="x">8<span class="hspace"> </span>Caveats and Limitations</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="caveats.html#%28part._.The_.Integer_type_and_integer_%29" class="toclink" data-pltdoc="x">8.1<span class="hspace"> </span>The <span class="RktSym"><span class="RktStxLink">Integer</span></span> type and <span class="RktSym"><span class="RktValLink">integer?</span></span></a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="caveats.html#%28part._.Type_inference_for_polymorphic_functions%29" class="toclink" data-pltdoc="x">8.2<span class="hspace"> </span>Type inference for polymorphic functions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="caveats.html#%28part._.Typed-untyped_interaction_and_contract_generation%29" class="toclink" data-pltdoc="x">8.3<span class="hspace"> </span>Typed-untyped interaction and contract generation</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="caveats.html#%28part._.Unsupported_features%29" class="toclink" data-pltdoc="x">8.4<span class="hspace"> </span>Unsupported features</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="caveats.html#%28part._.Type_generalization%29" class="toclink" data-pltdoc="x">8.5<span class="hspace"> </span>Type generalization</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="caveats.html#%28part._.Macros_and_compile-time_computation%29" class="toclink" data-pltdoc="x">8.6<span class="hspace"> </span>Macros and compile-time computation</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="caveats.html#%28part._.Expensive_contract_boundaries%29" class="toclink" data-pltdoc="x">8.7<span class="hspace"> </span>Expensive contract boundaries</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, "6.7", "../");" onfocus="this.style.color="black"; this.style.textAlign="left"; if (this.value == "...search manuals...") this.value="";" onblur="if (this.value.match(/^ *$/)) { this.style.color="#888"; this.style.textAlign="center"; this.value="...search manuals..."; }"/></form> <a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return 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