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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><title>7.3 Contracts on Functions in General</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"><span style="font-weight: bold">The Racket Guide</span></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="tocviewselflink" 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="tocviewlink" 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" data-pltdoc="x">Concurrency and Synchronization</a></td></tr><tr><td align="right">19 </td><td><a href="performance.html" class="tocviewlink" data-pltdoc="x">Performance</a></td></tr><tr><td align="right">20 </td><td><a href="parallelism.html" class="tocviewlink" data-pltdoc="x">Parallelism</a></td></tr><tr><td align="right">21 </td><td><a href="running.html" class="tocviewlink" data-pltdoc="x">Running and Creating Executables</a></td></tr><tr><td align="right">22 </td><td><a href="More_Libraries.html" class="tocviewlink" data-pltdoc="x">More Libraries</a></td></tr><tr><td align="right">23 </td><td><a href="dialects.html" class="tocviewlink" data-pltdoc="x">Dialects of Racket and Scheme</a></td></tr><tr><td align="right">24 </td><td><a href="other-editors.html" class="tocviewlink" data-pltdoc="x">Command-<wbr></wbr>Line Tools and Your Editor of Choice</a></td></tr><tr><td align="right"></td><td><a href="doc-bibliography.html" class="tocviewlink" data-pltdoc="x">Bibliography</a></td></tr><tr><td align="right"></td><td><a href="doc-index.html" class="tocviewlink" data-pltdoc="x">Index</a></td></tr></table></div></div><div class="tocviewlist"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_1");">▼</a></td><td>7 </td><td><a href="contracts.html" class="tocviewlink" data-pltdoc="x">Contracts</a></td></tr></table><div class="tocviewsublist" style="display: block;" id="tocview_1"><table cellspacing="0" cellpadding="0"><tr><td align="right">7.1 </td><td><a href="contract-boundaries.html" class="tocviewlink" data-pltdoc="x">Contracts and Boundaries</a></td></tr><tr><td align="right">7.2 </td><td><a href="contract-func.html" class="tocviewlink" data-pltdoc="x">Simple Contracts on Functions</a></td></tr><tr><td align="right">7.3 </td><td><a href="" class="tocviewselflink" data-pltdoc="x">Contracts on Functions in General</a></td></tr><tr><td align="right">7.4 </td><td><a href="contracts-first.html" class="tocviewlink" data-pltdoc="x">Contracts:<span class="mywbr"> </span> A Thorough Example</a></td></tr><tr><td align="right">7.5 </td><td><a href="contracts-struct.html" class="tocviewlink" data-pltdoc="x">Contracts on Structures</a></td></tr><tr><td align="right">7.6 </td><td><a href="contracts-exists.html" class="tocviewlink" data-pltdoc="x">Abstract Contracts using <span class="RktPn">#:<span class="mywbr"> </span>exists</span> and <span class="RktPn">#:<span class="mywbr"> </span>∃</span></a></td></tr><tr><td align="right">7.7 </td><td><a href="contracts-examples.html" class="tocviewlink" data-pltdoc="x">Additional Examples</a></td></tr><tr><td align="right">7.8 </td><td><a href="Building_New_Contracts.html" class="tocviewlink" data-pltdoc="x">Building New Contracts</a></td></tr><tr><td align="right">7.9 </td><td><a href="contracts-gotchas.html" class="tocviewlink" data-pltdoc="x">Gotchas</a></td></tr></table></div></div><div class="tocviewlist"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_2");">►</a></td><td>7.3 </td><td><a href="" class="tocviewselflink" data-pltdoc="x">Contracts on Functions in General</a></td></tr></table><div class="tocviewsublistbottom" style="display: none;" id="tocview_2"><table cellspacing="0" cellpadding="0"><tr><td align="right">7.3.1 </td><td><a href="#%28part._contracts-optional%29" class="tocviewlink" data-pltdoc="x">Optional Arguments</a></td></tr><tr><td align="right">7.3.2 </td><td><a href="#%28part._contracts-rest-args%29" class="tocviewlink" data-pltdoc="x">Rest Arguments</a></td></tr><tr><td align="right">7.3.3 </td><td><a href="#%28part._contracts-keywords%29" class="tocviewlink" data-pltdoc="x">Keyword Arguments</a></td></tr><tr><td align="right">7.3.4 </td><td><a href="#%28part._contracts-optional-keywords%29" class="tocviewlink" data-pltdoc="x">Optional Keyword Arguments</a></td></tr><tr><td align="right">7.3.5 </td><td><a href="#%28part._contracts-case-lambda%29" class="tocviewlink" data-pltdoc="x">Contracts for <span class="RktSym"><span class="RktStxLink">case-<wbr></wbr>lambda</span></span></a></td></tr><tr><td align="right">7.3.6 </td><td><a href="#%28part._contracts-arrow-d%29" class="tocviewlink" data-pltdoc="x">Argument and Result Dependencies</a></td></tr><tr><td align="right">7.3.7 </td><td><a href="#%28part._contracts-arrow-d-eval-order%29" class="tocviewlink" data-pltdoc="x">Checking State Changes</a></td></tr><tr><td align="right">7.3.8 </td><td><a href="#%28part._contracts-multiple%29" class="tocviewlink" data-pltdoc="x">Multiple Result Values</a></td></tr><tr><td align="right">7.3.9 </td><td><a href="#%28part._contracts-no-domain%29" class="tocviewlink" data-pltdoc="x">Fixed but Statically Unknown Arities</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">7.3.1<tt> </tt></span><a href="#%28part._contracts-optional%29" class="tocsubseclink" data-pltdoc="x">Optional Arguments</a></td></tr><tr><td><span class="tocsublinknumber">7.3.2<tt> </tt></span><a href="#%28part._contracts-rest-args%29" class="tocsubseclink" data-pltdoc="x">Rest Arguments</a></td></tr><tr><td><span class="tocsublinknumber">7.3.3<tt> </tt></span><a href="#%28part._contracts-keywords%29" class="tocsubseclink" data-pltdoc="x">Keyword Arguments</a></td></tr><tr><td><span class="tocsublinknumber">7.3.4<tt> </tt></span><a href="#%28part._contracts-optional-keywords%29" class="tocsubseclink" data-pltdoc="x">Optional Keyword Arguments</a></td></tr><tr><td><span class="tocsublinknumber">7.3.5<tt> </tt></span><a href="#%28part._contracts-case-lambda%29" class="tocsubseclink" data-pltdoc="x">Contracts for <span class="RktSym"><span class="RktStxLink">case-<wbr></wbr>lambda</span></span></a></td></tr><tr><td><span class="tocsublinknumber">7.3.6<tt> </tt></span><a href="#%28part._contracts-arrow-d%29" class="tocsubseclink" data-pltdoc="x">Argument and Result Dependencies</a></td></tr><tr><td><span class="tocsublinknumber">7.3.7<tt> </tt></span><a href="#%28part._contracts-arrow-d-eval-order%29" class="tocsubseclink" data-pltdoc="x">Checking State Changes</a></td></tr><tr><td><span class="tocsublinknumber">7.3.8<tt> </tt></span><a href="#%28part._contracts-multiple%29" class="tocsubseclink" data-pltdoc="x">Multiple Result Values</a></td></tr><tr><td><span class="tocsublinknumber">7.3.9<tt> </tt></span><a href="#%28part._contracts-no-domain%29" class="tocsubseclink" data-pltdoc="x">Fixed but Statically Unknown Arities</a></td></tr></table></div></div><div class="maincolumn"><div class="main"><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"> <a href="contract-func.html" title="backward to "7.2 Simple Contracts on Functions"" data-pltdoc="x">← prev</a> <a href="contracts.html" title="up to "7 Contracts"" data-pltdoc="x">up</a> <a href="contracts-first.html" title="forward to "7.4 Contracts: A Thorough Example"" data-pltdoc="x">next →</a></span> </div><h4 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-general-functions"">7.3<tt> </tt><a name="(part._contracts-general-functions)"></a>Contracts on Functions in General</h4><p>The <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span> contract constructor works for functions that take a
fixed number of arguments and where the result contract is independent
of the input arguments. To support other kinds of functions, Racket
supplies additional contract constructors, notably <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span> and
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span>.</p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-optional"">7.3.1<tt> </tt><a name="(part._contracts-optional)"></a>Optional Arguments</h5><p>Take a look at this excerpt from a string-processing module, inspired by the
<a href="http://schemecookbook.org">Scheme cookbook</a>:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.7" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket</span></a></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">pad the given str left and right with</span></td></tr><tr><td><span class="hspace"> </span><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">the (optional) char so that it is centered</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">string-pad-center</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._natural-number%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">natural-number/c</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">string-pad-center</span><span class="hspace"> </span><span class="RktSym">str</span><span class="hspace"> </span><span class="RktSym">width</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">pad</span><span class="hspace"> </span><span class="RktVal">#\space</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">field-width</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._min%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">min</a></span><span class="hspace"> </span><span class="RktSym">width</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string-length%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string-length</a></span><span class="hspace"> </span><span class="RktSym">str</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">rmargin</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._ceiling%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">ceiling</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252F%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">/</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._-%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><span class="nobreak">-</span></a></span><span class="hspace"> </span><span class="RktSym">width</span><span class="hspace"> </span><span class="RktSym">field-width</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">2</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">lmargin</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._floor%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">floor</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252F%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">/</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._-%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><span class="nobreak">-</span></a></span><span class="hspace"> </span><span class="RktSym">width</span><span class="hspace"> </span><span class="RktSym">field-width</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">2</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string-append%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string-append</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Flist..rkt%2529._build-string%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">build-string</a></span><span class="hspace"> </span><span class="RktSym">lmargin</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._%7Ece%7Ebb%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">λ</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">x</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">pad</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym">str</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Flist..rkt%2529._build-string%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">build-string</a></span><span class="hspace"> </span><span class="RktSym">rmargin</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._%7Ece%7Ebb%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">λ</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">x</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">pad</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>The module exports <span class="RktSym">string-pad-center</span>, a function
that creates a string of a given <span class="RktSym">width</span> with the
given string in the center. The default fill character is
<span class="RktVal">#\space</span>; if the client module wishes to use a
different character, it may call <span class="RktSym">string-pad-center</span>
with a third argument, a <span class="RktSym">char</span>, overwriting the
default.</p><p>The function definition uses optional arguments, which is
appropriate for this kind of functionality. The interesting
point here is the formulation of the contract for the
<span class="RktSym">string-pad-center</span>.</p><p>The contract combinator <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span>, demands several groups of contracts:</p><ul><li><p>The first one is a parenthesized group of contracts for all required
arguments. In this example, we see two: <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span> and
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._natural-number%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">natural-number/c</a></span>. </p></li><li><p>The second one is a parenthesized group of contracts for all optional
arguments: <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span>. </p></li><li><p>The last one is a single contract: the result of the function.</p></li></ul><p>Note that if a default value does not satisfy a contract, you won’t get a
contract error for this interface. If you can’t trust yourself to get
the initial value right, you need to communicate the initial value
across a boundary.</p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-rest-args"">7.3.2<tt> </tt><a name="(part._contracts-rest-args)"></a>Rest Arguments</h5><p>The <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._max%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">max</a></span> operator consumes at least one real number, but it
accepts any number of additional arguments. You can write other such
functions using a <a href="lambda.html#%28tech._rest._argument%29" class="techoutside" data-pltdoc="x"><span class="techinside">rest argument</span></a>, such as in <span class="RktSym">max-abs</span>:</p><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>See <a href="lambda.html#%28part._rest-args%29" data-pltdoc="x">Declaring a Rest Argument</a> for an introduction to rest
arguments.</p></blockquote></blockquote></blockquote><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">max-abs</span><span class="hspace"> </span><span class="RktSym">n</span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym">rst</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Flist..rkt%2529._foldr%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">foldr</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">n</span><span class="hspace"> </span><span class="RktSym">m</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._max%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">max</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._abs%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">abs</a></span><span class="hspace"> </span><span class="RktSym">n</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">m</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._abs%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">abs</a></span><span class="hspace"> </span><span class="RktSym">n</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">rst</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>Describing this function through a contract requires a further
extension of <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span>: a <span class="RktPn">#:rest</span> keyword specifies a
contract on a list of arguments after the required and optional
arguments:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">max-abs</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">#:rest</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>As always for <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span>, the contracts for the required arguments
are enclosed in the first pair of parentheses, which in this case is a
single real number. The empty pair of parenthesis indicates that there
are no optional arguments (not counting the rest arguments). The
contract for the rest argument follows <span class="RktPn">#:rest</span>; since all
additional arguments must be real numbers, the list of rest arguments
must satisfy the contract <span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="stt"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span>.</p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-keywords"">7.3.3<tt> </tt><a name="(part._contracts-keywords)"></a>Keyword Arguments</h5><p>It turns out that the <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span> contract constructor also contains
support for keyword arguments. For example, consider this function,
which creates a simple GUI and asks the user a yes-or-no question:</p><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>See <a href="lambda.html#%28part._lambda-keywords%29" data-pltdoc="x">Declaring Keyword Arguments</a> for an introduction to
keyword arguments.</p></blockquote></blockquote></blockquote><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=gui&rel=index.html&version=6.7" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket/gui</span></a></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">ask-yes-or-no-question</span><span class="hspace"> </span><span class="RktSym">question</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:default</span><span class="hspace"> </span><span class="RktSym">answer</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:title</span><span class="hspace"> </span><span class="RktSym">title</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:width</span><span class="hspace"> </span><span class="RktSym">w</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:height</span><span class="hspace"> </span><span class="RktSym">h</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">d</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=objcreation.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fclass-internal..rkt%2529._new%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">new</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=gui&rel=dialog_.html&version=6.7" class="RktValLink Sq" data-pltdoc="x">dialog%</a></span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">label</span><span class="hspace"> </span><span class="RktSym">title</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">width</span><span class="hspace"> </span><span class="RktSym">w</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">height</span><span class="hspace"> </span><span class="RktSym">h</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">msg</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=objcreation.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fclass-internal..rkt%2529._new%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">new</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=gui&rel=message_.html&version=6.7" class="RktValLink Sq" data-pltdoc="x">message%</a></span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">label</span><span class="hspace"> </span><span class="RktSym">question</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">parent</span><span class="hspace"> </span><span class="RktSym">d</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">yes</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=set_.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._set%2521%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">set!</a></span><span class="hspace"> </span><span class="RktSym">answer</span><span class="hspace"> </span><span class="RktVal">#t</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=ivaraccess.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fclass-internal..rkt%2529._send%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">send</a></span><span class="hspace"> </span><span class="RktSym">d</span><span class="hspace"> </span><span class="RktSym">show</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">no</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=set_.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._set%2521%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">set!</a></span><span class="hspace"> </span><span class="RktSym">answer</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=ivaraccess.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fclass-internal..rkt%2529._send%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">send</a></span><span class="hspace"> </span><span class="RktSym">d</span><span class="hspace"> </span><span class="RktSym">show</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">yes-b</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=objcreation.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fclass-internal..rkt%2529._new%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">new</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=gui&rel=button_.html&version=6.7" class="RktValLink Sq" data-pltdoc="x">button%</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">label</span><span class="hspace"> </span><span class="RktVal">"Yes"</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">parent</span><span class="hspace"> </span><span class="RktSym">d</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">callback</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._%7Ece%7Ebb%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">λ</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktSym">y</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">yes</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">style</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._if%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">if</a></span><span class="hspace"> </span><span class="RktSym">answer</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">border</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">no-b</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=objcreation.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fclass-internal..rkt%2529._new%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">new</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=gui&rel=button_.html&version=6.7" class="RktValLink Sq" data-pltdoc="x">button%</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">label</span><span class="hspace"> </span><span class="RktVal">"No"</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">parent</span><span class="hspace"> </span><span class="RktSym">d</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">callback</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._%7Ece%7Ebb%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">λ</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktSym">y</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">no</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">style</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._if%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">if</a></span><span class="hspace"> </span><span class="RktSym">answer</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">border</span><span class="RktVal">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=ivaraccess.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fclass-internal..rkt%2529._send%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">send</a></span><span class="hspace"> </span><span class="RktSym">d</span><span class="hspace"> </span><span class="RktSym">show</span><span class="hspace"> </span><span class="RktVal">#t</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym">answer</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">ask-yes-or-no-question</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:default</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._boolean%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">boolean?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:title</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:width</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._exact-integer%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">exact-integer?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:height</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._exact-integer%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">exact-integer?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._boolean%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>If you really want to ask a yes-or-no question
via a GUI, you should use <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=gui&rel=Windowing_Functions.html%23%2528def._%2528%2528lib._mred%252Fmain..rkt%2529._message-box%252Fcustom%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">message-box/custom</a></span>. For that
matter, it’s usually better to provide buttons with more specific
answers than “yes” and “no.”</p></blockquote></blockquote></blockquote><p>The contract for <span class="RktSym">ask-yes-or-no-question</span> uses <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span>, and
in the same way that <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span> (or <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span>-based
functions) allows a keyword to precede a functions formal argument,
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span> allows a keyword to precede a function contract’s argument
contract. In this case,
the contract says that <span class="RktSym">ask-yes-or-no-question</span> must receive four keyword
arguments, one for each of the keywords
<span class="RktPn">#:default</span>,
<span class="RktPn">#:title</span>,
<span class="RktPn">#:width</span>, and
<span class="RktPn">#:height</span>.
As in a function definition, the order of the keywords in <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span>
relative to each other does not matter for clients of the function;
only the relative order of argument contracts without keywords
matters.</p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-optional-keywords"">7.3.4<tt> </tt><a name="(part._contracts-optional-keywords)"></a>Optional Keyword Arguments</h5><p>Of course, many of the parameters in
<span class="RktSym">ask-yes-or-no-question</span> (from the previous question)
have reasonable defaults and should be made optional:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">ask-yes-or-no-question</span><span class="hspace"> </span><span class="RktSym">question</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:default</span><span class="hspace"> </span><span class="RktSym">answer</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:title</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">title</span><span class="hspace"> </span><span class="RktVal">"Yes or No?"</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:width</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">w</span><span class="hspace"> </span><span class="RktVal">400</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:height</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">h</span><span class="hspace"> </span><span class="RktVal">200</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">...</a></span><span class="RktPn">)</span></td></tr></table></blockquote><p>To specify this function’s contract, we need to use
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span> again. It supports keywords just as you might
expect in both the optional and mandatory argument
sections. In this case, we have the mandatory keyword
<span class="RktPn">#:default</span> and optional keywords
<span class="RktPn">#:title</span>,
<span class="RktPn">#:width</span>, and
<span class="RktPn">#:height</span>. So, we write the contract like this:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">ask-yes-or-no-question</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:default</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._boolean%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">#:title</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:width</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._exact-integer%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">exact-integer?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:height</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._exact-integer%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._boolean%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>That is, we put the mandatory keywords in the first section, and we
put the optional ones in the second section.</p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-case-lambda"">7.3.5<tt> </tt><a name="(part._contracts-case-lambda)"></a>Contracts for <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._case-lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">case-lambda</a></span></h5><p>A function defined with <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._case-lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">case-lambda</a></span> might impose different
constraints on its arguments depending on how many are provided. For
example, a <span class="RktSym">report-cost</span> function might convert either a pair
of numbers or a string into a new string:</p><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>See <a href="lambda.html#%28part._case-lambda%29" data-pltdoc="x">Arity-Sensitive Functions: <span class="RktSym"><span class="RktStxLink">case-lambda</span></span></a> for an introduction to
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._case-lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">case-lambda</a></span>.</p></blockquote></blockquote></blockquote><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">report-cost</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._case-lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">case-lambda</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym">lo</span><span class="hspace"> </span><span class="RktSym">hi</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=Writing.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._format%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">format</a></span><span class="hspace"> </span><span class="RktVal">"between $~a and $~a"</span><span class="hspace"> </span><span class="RktSym">lo</span><span class="hspace"> </span><span class="RktSym">hi</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym">desc</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=Writing.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._format%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">format</a></span><span class="hspace"> </span><span class="RktVal">"~a of dollars"</span><span class="hspace"> </span><span class="RktSym">desc</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p> </p></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym">report-cost</span><span class="hspace"> </span><span class="RktVal">5</span><span class="hspace"> </span><span class="RktVal">8</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">"between $5 and $8"</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym">report-cost</span><span class="hspace"> </span><span class="RktVal">"millions"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">"millions of dollars"</span></p></td></tr></table></td></tr></table></blockquote><p><div class="SIntrapara">The contract for such a function is formed with the <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._case-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">case-></a></span>
combinator, which combines as many functional contracts as needed:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">report-cost</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._case-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">case-></a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._integer%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._integer%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">As you can see, the contract for <span class="RktSym">report-cost</span> combines two
function contracts, which is just as many clauses as the explanation
of its functionality required.</div></p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-arrow-d"">7.3.6<tt> </tt><a name="(part._contracts-arrow-d)"></a>Argument and Result Dependencies</h5><p>The following is an excerpt from an imaginary numerics module:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">real-sqrt</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">argument</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._%7E3e%7E3d%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">>=/c</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">result</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">argument</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._%7E3c%7E3d%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><=/c</a></span><span class="hspace"> </span><span class="RktSym">argument</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p><div class="SIntrapara"><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>The word “indy” is meant to suggest that blame may be
assigned to the contract itself, because the contract must be considered an
independent component. The name was chosen in
response to two existing labels—<wbr></wbr>“lax” and “picky”—<wbr></wbr>for different
semantics of function contracts in the research literature.</p></blockquote></blockquote></blockquote></div><div class="SIntrapara">The contract for the exported function <span class="RktSym">real-sqrt</span> uses the
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> rather than <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span> function contract. The “i”
stands for an <span style="font-style: italic">indy dependent</span> contract, meaning the contract for the
function range depends on the value of the argument. The appearance
of <span class="RktSym">argument</span> in the line for <span class="RktSym">result</span>’s contract means
that the result depends on the argument. In this
particular case, the argument of <span class="RktSym">real-sqrt</span> is greater or
equal to 1, so a very basic correctness check is that the result is
smaller than the argument.</div></p><p>In general, a dependent function contract looks just like
the more general <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span> contract, but with names added
that can be used elsewhere in the contract.</p><p>Going back to the bank-account example, suppose that we generalize the
module to support multiple accounts and that we also include a
withdrawal operation. The improved bank-account module includes an
<span class="RktSym">account</span> structure type and the following functions:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym">account?</span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">withdraw</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym">account?</span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="hspace"> </span><span class="RktSym">account?</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">deposit</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym">account?</span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="hspace"> </span><span class="RktSym">account?</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>Besides requiring that a client provide a valid amount for a
withdrawal, however, the amount should be less than or equal to the specified
account’s balance, and the resulting account will have less money than
it started with. Similarly, the module might promise that a deposit
produces an account with money added to the account. The following
implementation enforces those constraints and guarantees through
contracts:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.7" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket</span></a></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">section 1: the contract definitions</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define-struct.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">struct</a></span><span class="hspace"> </span><span class="RktSym">account</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._natural-number%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">natural-number/c</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">section 2: the exports</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">create</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">amount/c</span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym">account?</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account?</span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">withdraw</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">account?</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">amt</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">acc</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._and%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._%7E3c%7E3d%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><=/c</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">acc</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">result</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._and%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym">account?</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">res</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3e%7E3d%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">>=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">res</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._-%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><span class="nobreak">-</span></a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">acc</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">deposit</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">account?</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">amt</span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">result</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._and%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym">account?</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">res</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3e%7E3d%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">>=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">res</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252B%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">+</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">acc</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">section 3: the function definitions</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">account-balance</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">create</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">withdraw</span><span class="hspace"> </span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._-%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><span class="nobreak">-</span></a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account-balance</span><span class="hspace"> </span><span class="RktSym">a</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">deposit</span><span class="hspace"> </span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252B%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">+</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account-balance</span><span class="hspace"> </span><span class="RktSym">a</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>The contracts in section 2 provide typical type-like guarantees for
<span class="RktSym">create</span> and <span class="RktSym">balance</span>. For <span class="RktSym">withdraw</span> and
<span class="RktSym">deposit</span>, however, the contracts check and guarantee the more
complicated constraints on <span class="RktSym">balance</span> and <span class="RktSym">deposit</span>. The
contract on the second argument to <span class="RktSym">withdraw</span> uses
<span class="RktPn">(</span><span class="RktSym">balance</span><span class="stt"> </span><span class="RktSym">acc</span><span class="RktPn">)</span> to check whether the supplied withdrawal amount
is small enough, where <span class="RktSym">acc</span> is the name given within
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> to the function’s first argument. The contract on the
result of <span class="RktSym">withdraw</span> uses both <span class="RktSym">acc</span> and <span class="RktSym">amt</span> to
guarantee that no more than that requested amount was withdrawn. The
contract on <span class="RktSym">deposit</span> similarly uses <span class="RktSym">acc</span> and
<span class="RktSym">amount</span> in the result contract to guarantee that at least as
much money as provided was deposited into the account.</p><p>As written above, when a contract check fails, the error message is
not great. The following revision uses <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._flat-named-contract%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">flat-named-contract</a></span>
within a helper function <span class="RktSym">mk-account-contract</span> to provide
better error messages.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.7" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket</span></a></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">section 1: the contract definitions</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define-struct.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">struct</a></span><span class="hspace"> </span><span class="RktSym">account</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._natural-number%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">natural-number/c</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">msg></span><span class="hspace"> </span><span class="RktVal">"account a with balance larger than ~a expected"</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">msg<</span><span class="hspace"> </span><span class="RktVal">"account a with balance less than ~a expected"</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">mk-account-contract</span><span class="hspace"> </span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="hspace"> </span><span class="RktSym">op</span><span class="hspace"> </span><span class="RktSym">msg</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">balance0</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">acc</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">ctr</span><span class="hspace"> </span><span class="RktSym">a</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._and%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account?</span><span class="hspace"> </span><span class="RktSym">a</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">op</span><span class="hspace"> </span><span class="RktSym">balance0</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">a</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._flat-named-contract%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">flat-named-contract</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=Writing.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._format%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">format</a></span><span class="hspace"> </span><span class="RktSym">msg</span><span class="hspace"> </span><span class="RktSym">balance0</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">ctr</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">section 2: the exports</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">create</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">amount/c</span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym">account?</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account?</span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">withdraw</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">account?</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">amt</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">acc</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._and%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._%7E3c%7E3d%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><=/c</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">acc</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">result</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">mk-account-contract</span><span class="hspace"> </span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3e%7E3d%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">>=</a></span><span class="hspace"> </span><span class="RktSym">msg></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">deposit</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">account?</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">amt</span><span class="hspace"> </span><span class="RktSym">amount/c</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">result</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">mk-account-contract</span><span class="hspace"> </span><span class="RktSym">acc</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3c%7E3d%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><=</a></span><span class="hspace"> </span><span class="RktSym">msg<</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">section 3: the function definitions</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">balance</span><span class="hspace"> </span><span class="RktSym">account-balance</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">create</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">withdraw</span><span class="hspace"> </span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._-%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><span class="nobreak">-</span></a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account-balance</span><span class="hspace"> </span><span class="RktSym">a</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">deposit</span><span class="hspace"> </span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252B%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">+</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">account-balance</span><span class="hspace"> </span><span class="RktSym">a</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">amt</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-arrow-d-eval-order"">7.3.7<tt> </tt><a name="(part._contracts-arrow-d-eval-order)"></a>Checking State Changes</h5><p><div class="SIntrapara">The <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> contract combinator can also ensure that a
function only modifies state according to certain
constraints. For example, consider this contract
(it is a slightly simplified version from the function
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=framework&rel=Preferences.html%23%2528def._%2528%2528lib._framework%252Fmain..rkt%2529._preferences%7E3aadd-panel%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">preferences:add-panel</a></span> in the framework):
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">parent</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=Object_and_Class_Contracts.html%23%2528def._%2528%2528lib._racket%252Fclass..rkt%2529._is-a%7E3f%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">is-a?/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=gui&rel=area-container-window___.html&version=6.7" class="RktValLink Sq" data-pltdoc="x">area-container-window<%></a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529.__%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">_</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">parent</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=let.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._let%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">let</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">old-children</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=ivaraccess.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fclass-internal..rkt%2529._send%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">send</a></span><span class="hspace"> </span><span class="RktSym">parent</span><span class="hspace"> </span><span class="RktSym">get-children</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._%7Ece%7Ebb%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">λ</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">child</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fmap..rkt%2529._andmap%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">andmap</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._eq%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">eq?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._append%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">append</a></span><span class="hspace"> </span><span class="RktSym">old-children</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">list</a></span><span class="hspace"> </span><span class="RktSym">child</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=ivaraccess.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fclass-internal..rkt%2529._send%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">send</a></span><span class="hspace"> </span><span class="RktSym">parent</span><span class="hspace"> </span><span class="RktSym">get-children</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">It says that the function accepts a single argument, named
<span class="RktSym">parent</span>, and that <span class="RktSym">parent</span> must be
an object matching the interface <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=gui&rel=area-container-window___.html&version=6.7" class="RktValLink Sq" data-pltdoc="x">area-container-window<%></a></span>.</div></p><p>The range contract ensures that the function only modifies
the children of <span class="RktSym">parent</span> by adding a new child to the
front of the list. It accomplishes this by using the
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529.__%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">_</a></span> instead of a normal identifier, which tells the
contract library that the range contract does not depend on
the values of any of the results, and thus the contract
library evaluates the expression following the <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529.__%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">_</a></span>
when the function is called, instead of when it
returns. Therefore the call to the <span class="RktSym">get-children</span> method
happens before the function under the contract is called.
When the function under contract returns, its result is
passed in as <span class="RktSym">child</span>, and the contract ensures that
the children after the function return are the same as the
children before the function called, but with one more
child, at the front of the list.</p><p><div class="SIntrapara">To see the difference in a toy example that focuses
on this point, consider this program
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.7" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket</span></a></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">get-x</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">x</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=set_.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._set%2521%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">set!</a></span><span class="hspace"> </span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._cons%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">cons</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">f</span><span class="hspace"> </span><span class="RktSym">x</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529.__%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">_</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=begin.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._begin%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">begin</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=set_.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._set%2521%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">set!</a></span><span class="hspace"> </span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._cons%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">cons</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">ctc</span><span class="hspace"> </span><span class="RktSym">x</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">get-x</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=symbols.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._symbol%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">symbol?</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">If you were to require this module, call <span class="RktSym">f</span>, then
the result of <span class="RktSym">get-x</span> would be <span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">f</span><span class="stt"> </span><span class="RktVal">ctc</span><span class="RktVal">)</span>. In
contrast, if the contract for <span class="RktSym">f</span> were
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><p><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">res</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=begin.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._begin%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">begin</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=set_.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._set%2521%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">set!</a></span><span class="hspace"> </span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._cons%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">cons</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">ctc</span><span class="hspace"> </span><span class="RktSym">x</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></p></blockquote></div><div class="SIntrapara">(only changing the underscore to <span class="RktSym">res</span>), then
the result of <span class="RktSym">get-x</span> would be <span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">ctc</span><span class="stt"> </span><span class="RktVal">f</span><span class="RktVal">)</span>.</div></p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-multiple"">7.3.8<tt> </tt><a name="(part._contracts-multiple)"></a>Multiple Result Values</h5><p><div class="SIntrapara">The function <span class="RktSym">split</span> consumes a list of <span class="RktSym">char</span>s
and delivers the string that occurs before the first occurrence of
<span class="RktVal">#\newline</span> (if any) and the rest of the list:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">split</span><span class="hspace"> </span><span class="RktSym">l</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">split</span><span class="hspace"> </span><span class="RktSym">l</span><span class="hspace"> </span><span class="RktSym">w</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._cond%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">cond</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._null%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">null?</a></span><span class="hspace"> </span><span class="RktSym">l</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=values.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._values%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list-%7E3estring%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">list->string</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Flist..rkt%2529._reverse%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">reverse</a></span><span class="hspace"> </span><span class="RktSym">w</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">)</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3d%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char=?</a></span><span class="hspace"> </span><span class="RktVal">#\newline</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._car%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">car</a></span><span class="hspace"> </span><span class="RktSym">l</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=values.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._values%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list-%7E3estring%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">list->string</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Flist..rkt%2529._reverse%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">reverse</a></span><span class="hspace"> </span><span class="RktSym">w</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._cdr%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">cdr</a></span><span class="hspace"> </span><span class="RktSym">l</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._else%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">else</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">split</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._cdr%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">cdr</a></span><span class="hspace"> </span><span class="RktSym">l</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._cons%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">cons</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._car%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">car</a></span><span class="hspace"> </span><span class="RktSym">l</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">w</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">split</span><span class="hspace"> </span><span class="RktSym">l</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">It is a typical multiple-value function, returning two values by
traversing a single list.</div></p><p><div class="SIntrapara">The contract for such a function can use the ordinary
function arrow <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span>, since <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span>
treats <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=values.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._values%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">values</a></span> specially when it appears as the
last result:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">split</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=values.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._values%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div></p><p><div class="SIntrapara">The contract for such a function can also be written
using <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span>:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">split</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=values.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._values%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">As before, the contract for the argument with <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span> is wrapped in an
extra pair of parentheses (and must always be wrapped like
that) and the empty pair of parentheses indicates that
there are no optional arguments. The contracts for the
results are inside <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=values.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._values%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">values</a></span>: a string and a list of
characters.</div></p><p><div class="SIntrapara">Now, suppose that we also want to ensure that the first result of
<span class="RktSym">split</span> is a prefix of the given word in list format. In that
case, we need to use the <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> contract combinator:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">substring-of?</span><span class="hspace"> </span><span class="RktSym">s</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._flat-named-contract%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">flat-named-contract</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=Writing.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._format%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">format</a></span><span class="hspace"> </span><span class="RktVal">"substring of ~s"</span><span class="hspace"> </span><span class="RktSym">s</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">s2</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._and%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string?</a></span><span class="hspace"> </span><span class="RktSym">s2</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3c%7E3d%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string-length%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string-length</a></span><span class="hspace"> </span><span class="RktSym">s2</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string-length%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string-length</a></span><span class="hspace"> </span><span class="RktSym">s</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._equal%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">equal?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._substring%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">substring</a></span><span class="hspace"> </span><span class="RktSym">s</span><span class="hspace"> </span><span class="RktVal">0</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._string-length%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string-length</a></span><span class="hspace"> </span><span class="RktSym">s2</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">s2</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">split</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">fl</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=values.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._values%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">s</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fl</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">substring-of?</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=strings.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list-%7E3estring%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">list->string</a></span><span class="hspace"> </span><span class="RktSym">fl</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">c</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">Like <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span>, the <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> combinator uses a function over the
argument to create the range contracts. Yes, it doesn’t just return one
contract but as many as the function produces values: one contract per
value. In this case, the second contract is the same as before, ensuring
that the second result is a list of <span class="RktSym">char</span>s. In contrast, the
first contract strengthens the old one so that the result is a prefix of
the given word.</div></p><p><div class="SIntrapara">This contract is expensive to check, of course. Here is a slightly
cheaper version:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">split</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">fl</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=values.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._values%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">s</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fl</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._string-len%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">string-len/c</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._length%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">length</a></span><span class="hspace"> </span><span class="RktSym">fl</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">c</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=characters.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._char%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">char?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div></p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-no-domain"">7.3.9<tt> </tt><a name="(part._contracts-no-domain)"></a>Fixed but Statically Unknown Arities</h5><p>Imagine yourself writing a contract for a function that accepts some other
function and a list of numbers that eventually applies the former to the
latter. Unless the arity of the given function matches the length of the
given list, your procedure is in trouble.</p><p><div class="SIntrapara">Consider this <span class="RktSym">n-step</span> function:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">(number ... -> (union #f number?)) (listof number) -> void</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">n-step</span><span class="hspace"> </span><span class="RktSym">proc</span><span class="hspace"> </span><span class="RktSym">inits</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=let.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._let%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">let</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">inc</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=procedures.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._apply%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">apply</a></span><span class="hspace"> </span><span class="RktSym">proc</span><span class="hspace"> </span><span class="RktSym">inits</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=when_unless.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._when%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">when</a></span><span class="hspace"> </span><span class="RktSym">inc</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">n-step</span><span class="hspace"> </span><span class="RktSym">proc</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fmap..rkt%2529._map%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">map</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._%7Ece%7Ebb%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">λ</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">x</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252B%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">+</a></span><span class="hspace"> </span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktSym">inc</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">inits</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div></p><p>The argument of <span class="RktSym">n-step</span> is <span class="RktSym">proc</span>, a function
<span class="RktSym">proc</span> whose results are either numbers or false, and a list. It
then applies <span class="RktSym">proc</span> to the list <span class="RktSym">inits</span>. As long as
<span class="RktSym">proc</span> returns a number, <span class="RktSym">n-step</span> treats that number
as an increment for each of the numbers in <span class="RktSym">inits</span> and
recurs. When <span class="RktSym">proc</span> returns <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528lib._racket%252Fbool..rkt%2529._false%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">false</a></span>, the loop stops.</p><p><div class="SIntrapara">Here are two uses:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">nat -> nat</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">x</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=Writing.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._printf%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">printf</a></span><span class="hspace"> </span><span class="RktVal">"~s\n"</span><span class="hspace"> </span><span class="RktSym">x</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._if%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">if</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktVal">0</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-1</span></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym">n-step</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">2</span><span class="RktVal">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">nat nat -> nat</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">g</span><span class="hspace"> </span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktSym">y</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">z</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252B%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">+</a></span><span class="hspace"> </span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktSym">y</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=Writing.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._printf%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">printf</a></span><span class="hspace"> </span><span class="RktVal">"~s\n"</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">list</a></span><span class="hspace"> </span><span class="RktSym">x</span><span class="hspace"> </span><span class="RktSym">y</span><span class="hspace"> </span><span class="RktSym">z</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._if%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">if</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktSym">z</span><span class="hspace"> </span><span class="RktVal">0</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-1</span></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym">n-step</span><span class="hspace"> </span><span class="RktSym">g</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1</span><span class="RktVal">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div></p><p><div class="SIntrapara">A contract for <span class="RktSym">n-step</span> must specify two aspects of
<span class="RktSym">proc</span>’s behavior: its arity must include the number of elements
in <span class="RktSym">inits</span>, and it must return either a number or
<span class="RktVal">#f</span>. The latter is easy, the former is difficult. At first
glance, this appears to suggest a contract that assigns a
<span style="font-style: italic">variable-arity</span> to <span class="RktSym">proc</span>:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%252A%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>*</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:rest</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._or%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">or/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._false%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">false/c</a></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">This contract, however, says that the function must accept <span style="font-style: italic">any</span>
number of arguments, not a <span style="font-style: italic">specific</span> but
<span style="font-style: italic">undetermined</span> number. Thus, applying <span class="RktSym">n-step</span> to
<span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym">x</span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym">x</span><span class="RktPn">)</span> and <span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">list</a></span><span class="stt"> </span><span class="RktVal">1</span><span class="RktPn">)</span> breaks the contract
because the given function accepts only one argument.</div></p><p><div class="SIntrapara">The correct contract uses the <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._unconstrained-domain-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">unconstrained-domain-></a></span>
combinator, which specifies only the range of a function, not its
domain. It is then possible to combine this contract with an arity test to
specify the correct contract for <span class="RktSym">n-step</span>:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">n-step</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">proc</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">inits</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._and%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._unconstrained-domain-%7E3e%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">unconstrained-domain-></a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._or%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">or/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._false%252Fc%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">false/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._%7Ece%7Ebb%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">λ</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=procedures.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._procedure-arity-includes%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">procedure-arity-includes?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym">f</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._length%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">length</a></span><span class="hspace"> </span><span class="RktSym">inits</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">inits</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._listof%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">any</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div></p><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"; 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