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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><title>8.2 Function Contracts</title><link rel="stylesheet" type="text/css" href="../scribble.css" title="default"/><link rel="stylesheet" type="text/css" href="extras.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 Reference</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="model.html" class="tocviewlink" data-pltdoc="x">Language Model</a></td></tr><tr><td align="right">2 </td><td><a href="notation.html" class="tocviewlink" data-pltdoc="x">Notation for Documentation</a></td></tr><tr><td align="right">3 </td><td><a href="syntax.html" class="tocviewlink" data-pltdoc="x">Syntactic Forms</a></td></tr><tr><td align="right">4 </td><td><a href="data.html" class="tocviewlink" data-pltdoc="x">Datatypes</a></td></tr><tr><td align="right">5 </td><td><a href="structures.html" class="tocviewlink" data-pltdoc="x">Structures</a></td></tr><tr><td align="right">6 </td><td><a href="mzlib_class.html" class="tocviewlink" data-pltdoc="x">Classes and Objects</a></td></tr><tr><td align="right">7 </td><td><a href="mzlib_unit.html" class="tocviewlink" data-pltdoc="x">Units</a></td></tr><tr><td align="right">8 </td><td><a href="contracts.html" class="tocviewselflink" data-pltdoc="x">Contracts</a></td></tr><tr><td align="right">9 </td><td><a href="match.html" class="tocviewlink" data-pltdoc="x">Pattern Matching</a></td></tr><tr><td align="right">10 </td><td><a href="control.html" class="tocviewlink" data-pltdoc="x">Control Flow</a></td></tr><tr><td align="right">11 </td><td><a href="concurrency.html" class="tocviewlink" data-pltdoc="x">Concurrency and Parallelism</a></td></tr><tr><td align="right">12 </td><td><a href="Macros.html" class="tocviewlink" data-pltdoc="x">Macros</a></td></tr><tr><td align="right">13 </td><td><a href="input-and-output.html" class="tocviewlink" data-pltdoc="x">Input and Output</a></td></tr><tr><td align="right">14 </td><td><a href="security.html" class="tocviewlink" data-pltdoc="x">Reflection and Security</a></td></tr><tr><td align="right">15 </td><td><a href="os.html" class="tocviewlink" data-pltdoc="x">Operating System</a></td></tr><tr><td align="right">16 </td><td><a href="memory.html" class="tocviewlink" data-pltdoc="x">Memory Management</a></td></tr><tr><td align="right">17 </td><td><a href="unsafe.html" class="tocviewlink" data-pltdoc="x">Unsafe Operations</a></td></tr><tr><td align="right">18 </td><td><a href="running.html" class="tocviewlink" data-pltdoc="x">Running Racket</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>8 </td><td><a href="contracts.html" class="tocviewlink" data-pltdoc="x">Contracts</a></td></tr></table><div class="tocviewsublistbottom" style="display: block;" id="tocview_1"><table cellspacing="0" cellpadding="0"><tr><td align="right">8.1 </td><td><a href="data-structure-contracts.html" class="tocviewlink" data-pltdoc="x">Data-<wbr></wbr>structure Contracts</a></td></tr><tr><td align="right">8.2 </td><td><a href="" class="tocviewselflink" data-pltdoc="x">Function Contracts</a></td></tr><tr><td align="right">8.3 </td><td><a href="parametric-contracts.html" class="tocviewlink" data-pltdoc="x">Parametric Contracts</a></td></tr><tr><td align="right">8.4 </td><td><a href="Lazy_Data-structure_Contracts.html" class="tocviewlink" data-pltdoc="x">Lazy Data-<wbr></wbr>structure Contracts</a></td></tr><tr><td align="right">8.5 </td><td><a href="Structure_Type_Property_Contracts.html" class="tocviewlink" data-pltdoc="x">Structure Type Property Contracts</a></td></tr><tr><td align="right">8.6 </td><td><a href="attaching-contracts-to-values.html" class="tocviewlink" data-pltdoc="x">Attaching Contracts to Values</a></td></tr><tr><td align="right">8.7 </td><td><a href="Building_New_Contract_Combinators.html" class="tocviewlink" data-pltdoc="x">Building New Contract Combinators</a></td></tr><tr><td align="right">8.8 </td><td><a href="contract-utilities.html" class="tocviewlink" data-pltdoc="x">Contract Utilities</a></td></tr><tr><td align="right">8.9 </td><td><a href="racket_contract_base.html" class="tocviewlink" data-pltdoc="x"><span class="RktModLink"><span class="RktSym">racket/<span class="mywbr"> </span>contract/<span class="mywbr"> </span>base</span></span></a></td></tr><tr><td align="right">8.10 </td><td><a href="Legacy_Contracts.html" class="tocviewlink" data-pltdoc="x">Legacy Contracts</a></td></tr><tr><td align="right">8.11 </td><td><a href="Random_generation.html" class="tocviewlink" data-pltdoc="x">Random generation</a></td></tr></table></div></div></div><div class="tocsub"><div class="tocsubtitle">On this page:</div><table class="tocsublist" cellspacing="0"><tr><td><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="tocsublink" data-pltdoc="x"><span class="RktSym"><span class="RktStxLink"><span class="nobreak">-<wbr></wbr>></span></span></span></a></td></tr><tr><td><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%2A%29%29" class="tocsublink" data-pltdoc="x"><span class="RktSym"><span class="RktStxLink"><span class="nobreak">-<wbr></wbr>></span>*</span></span></a></td></tr><tr><td><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="tocsublink" data-pltdoc="x"><span class="RktSym"><span class="RktStxLink"><span class="nobreak">-<wbr></wbr>></span>i</span></span></a></td></tr><tr><td><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ed%29%29" class="tocsublink" data-pltdoc="x"><span class="RktSym"><span class="RktStxLink"><span class="nobreak">-<wbr></wbr>></span>d</span></span></a></td></tr><tr><td><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._case-~3e%29%29" class="tocsublink" data-pltdoc="x"><span class="RktSym"><span class="RktStxLink">case-<wbr></wbr>></span></span></a></td></tr><tr><td><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._unconstrained-domain-~3e%29%29" class="tocsublink" data-pltdoc="x"><span class="RktSym"><span class="RktStxLink">unconstrained-<wbr></wbr>domain-<wbr></wbr>></span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._predicate%2Fc%29%29" class="tocsublink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">predicate/<span class="mywbr"> </span>c</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._the-unsupplied-arg%29%29" class="tocsublink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">the-<wbr></wbr>unsupplied-<wbr></wbr>arg</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._unsupplied-arg~3f%29%29" class="tocsublink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">unsupplied-<wbr></wbr>arg?</span></span></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, "6.1", "../");" 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("6.1");">top</a></span><span class="navright"> <a href="data-structure-contracts.html" title="backward to "8.1 Data-structure Contracts"" data-pltdoc="x">← prev</a> <a href="contracts.html" title="up to "8 Contracts"" data-pltdoc="x">up</a> <a href="parametric-contracts.html" title="forward to "8.3 Parametric Contracts"" data-pltdoc="x">next →</a></span> </div><h4 x-source-module="(lib "scribblings/reference/reference.scrbl")" x-part-tag=""function-contracts"">8.2<tt> </tt><a name="(part._function-contracts)"></a>Function Contracts</h4><p>A <a name="(tech._function._contract)"></a><span style="font-style: italic">function contract</span> wraps a procedure to delay
checks for its arguments and results. There are three
primary function contract combinators that have increasing
amounts of expressiveness and increasing additional
overheads. The first <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span> is the cheapest. It
generates wrapper functions that can call the original
function directly. Contracts built with <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%2A%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>*</a></span> require
packaging up arguments as lists in the wrapper function and
then using either <span class="RktSym"><a href="procedures.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._keyword-apply%29%29" class="RktValLink" data-pltdoc="x">keyword-apply</a></span> or
<span class="RktSym"><a href="procedures.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._apply%29%29" class="RktValLink" data-pltdoc="x">apply</a></span>. Finally, <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span>
is the most expensive (along with <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ed%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>d</a></span>),
because it requires delaying the evaluation of the contract
expressions for the domain and range until the function
itself is called or returns.</p><p>The <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._case-~3e%29%29" class="RktStxLink" data-pltdoc="x">case-></a></span> contract is a specialized contract,
designed to match <span class="RktSym"><a href="lambda.html#%28form._%28%28quote._~23~25kernel%29._case-lambda%29%29" class="RktStxLink" data-pltdoc="x">case-lambda</a></span> and
<span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._unconstrained-domain-~3e%29%29" class="RktStxLink" data-pltdoc="x">unconstrained-domain-></a></span> allows range checking
without requiring that the domain have any particular shape
(see below for an example use).</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>syntax</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(form._((lib._racket/contract/base..rkt)._-~3e))"></a><span title="Provided from: racket/contract/base, racket/contract, racket | Package: base"><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxDef RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span></span><span class="hspace"> </span><span class="RktVar">dom</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="hspace"> </span><span class="RktVar">range</span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="stt"> </span></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="specgrammar"><tr><td align="right" valign="baseline"><span class="RktVar">dom</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">dom-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">keyword</span><span class="hspace"> </span><span class="RktVar">dom-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">range</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">range-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">(</span><span class="RktSym"><a href="values.html#%28def._%28%28quote._~23~25kernel%29._values%29%29" class="RktValLink" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktVar">range-expr</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Produces a contract for a function that accepts a fixed
number of arguments and returns either a fixed number of
results or completely unspecified results (the latter when
<span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span> is specified).</div></p><p>Each <span class="RktVar">dom-expr</span> is a contract on an argument to a
function, and each <span class="RktVar">range-expr</span> is a contract on a
result of the function.</p><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>Using a <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span> between two whitespace-delimited
<span class="RktPn">.</span>s is the same as putting the <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span> right
after the enclosing opening parenthesis. See
<a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=guide&rel=Pairs__Lists__and_Racket_Syntax.html%23%2528part._lists-and-syntax%2529&version=6.1" class="Sq" data-pltdoc="x">Lists and Racket Syntax</a> or <a href="reader.html#%28part._parse-pair%29" data-pltdoc="x">Reading Pairs and Lists</a> for more
information.</p></blockquote></blockquote></blockquote><p>For example,</p><blockquote class="SCodeFlow"><p><span class="RktPn">(</span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></span><span class="RktPn">)</span></p></blockquote><p>produces a contract on functions of two arguments. The first argument
must be an integer, and the second argument must be a boolean. The
function must produce an integer.</p><p>A domain specification may include a keyword. If so, the function must
accept corresponding (mandatory) keyword arguments, and the values for
the keyword arguments must match the corresponding contracts. For
example:</p><blockquote class="SCodeFlow"><p><span class="RktPn">(</span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktPn">#:x</span><span class="hspace"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></span><span class="RktPn">)</span></p></blockquote><p>is a contract on a function that accepts a by-position argument that
is an integer and a <span class="RktPn">#:x</span> argument that is a boolean.</p><p>If <span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span> is used as the last sub-form for <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span>, no
contract checking is performed on the result of the function, and
thus any number of values is legal (even different numbers on different
invocations of the function).</p><p>If <span class="RktPn">(</span><span class="RktSym"><a href="values.html#%28def._%28%28quote._~23~25kernel%29._values%29%29" class="RktValLink" data-pltdoc="x">values</a></span><span class="stt"> </span><span class="RktVar">range-expr</span><span class="stt"> </span><span class="RktMeta"><a href="stx-patterns.html#%28form._%28%28lib._racket%2Fprivate%2Fstxcase-scheme..rkt%29._......%29%29" class="RktStxLink" data-pltdoc="x">...</a></span><span class="RktPn">)</span> is used as the last sub-form of
<span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span>, the function must produce a result for each contract, and
each value must match its respective contract.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>syntax</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(form._((lib._racket/contract/base..rkt)._-~3e*))"></a><span title="Provided from: racket/contract/base, racket/contract, racket | Package: base"><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%2A%29%29" class="RktStxDef RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>*</a></span></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">mandatory-dom</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVar">optional-doms</span><span class="hspace"> </span><span class="RktVar">rest</span><span class="hspace"> </span><span class="RktVar">pre</span><span class="hspace"> </span><span class="RktVar">range</span><span class="hspace"> </span><span class="RktVar">post</span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="stt"> </span></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="specgrammar"><tr><td align="right" valign="baseline"><span class="RktVar">mandatory-dom</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">dom-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">keyword</span><span class="hspace"> </span><span class="RktVar">dom-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">optional-doms</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">(</span><span class="RktVar">optional-dom</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">optional-dom</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">dom-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">keyword</span><span class="hspace"> </span><span class="RktVar">dom-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">rest</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">#:rest</span><span class="hspace"> </span><span class="RktVar">rest-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">pre</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">#:pre</span><span class="hspace"> </span><span class="RktVar">pre-cond-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">range</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">range-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">(</span><span class="RktSym"><a href="values.html#%28def._%28%28quote._~23~25kernel%29._values%29%29" class="RktValLink" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktVar">range-expr</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">post</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">#:post</span><span class="hspace"> </span><span class="RktVar">post-cond-expr</span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">The <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%2A%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>*</a></span> contract combinator produces contracts for functions
that accept optional arguments (either keyword or positional) and/or
arbitrarily many arguments. The first clause of a <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%2A%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>*</a></span>
contract describes the mandatory arguments, and is similar to the
argument description of a <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span> contract. The second clause
describes the optional arguments. The range of description can either
be <span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span> or a sequence of contracts, indicating that the
function must return multiple values.</div></p><p><div class="SIntrapara">If present, the
<span class="RktVar">rest-expr</span> contract governs the arguments in the rest
parameter. Note that the <span class="RktVar">rest-expr</span> contract governs only
the arguments in the rest parameter, not those in mandatory arguments.
For example, this contract:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><p><span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%2A%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>*</a></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="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._cons%2Fc%29%29" class="RktValLink" data-pltdoc="x">cons/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._listof%29%29" class="RktValLink" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span><span class="RktPn">)</span></p></blockquote></div><div class="SIntrapara">does not match the function
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><p><span class="RktPn">(</span><span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._~ce~bb%29%29" class="RktStxLink" 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="RktPn">. </span><span class="RktVar">rest</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">x</span><span class="RktPn">)</span></p></blockquote></div><div class="SIntrapara">because the contract insists that the function accept zero arguments
(because there are no mandatory arguments listed in the contract). The
<span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> contract does not know that the contract on the rest argument is
going to end up disallowing empty argument lists.</div></p><p>The <span class="RktVar">pre-cond-expr</span> and <span class="RktVar">post-cond-expr</span>
expressions are checked as the function is called and returns,
respectively, and allow checking of the environment without an
explicit connection to an argument (or a result).</p><p><div class="SIntrapara">As an example, the contract
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><p><span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%2A%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>*</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="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="hspace"> </span><span class="RktPn">#:x</span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></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="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._listof%29%29" class="RktValLink" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym"><a href="symbols.html#%28def._%28%28quote._~23~25kernel%29._symbol~3f%29%29" class="RktValLink" data-pltdoc="x">symbol?</a></span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="symbols.html#%28def._%28%28quote._~23~25kernel%29._symbol~3f%29%29" class="RktValLink" data-pltdoc="x">symbol?</a></span><span class="RktPn">)</span></p></blockquote></div><div class="SIntrapara">matches functions that optionally accept a boolean, an
integer keyword argument <span class="RktPn">#:x</span> and arbitrarily more
symbols, and that return a symbol.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>syntax</p></div></div><table cellspacing="0" cellpadding="0" class="RktBlk RForeground"><tr><td><span class="RktPn">(</span><a name="(form._((lib._racket/contract/base..rkt)._-~3ei))"></a><span title="Provided from: racket/contract/base, racket/contract, racket | Package: base"><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxDef RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">mandatory-dependent-dom</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">dependent-rest</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">pre-condition</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">dependent-range</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">post-condition</span><span class="RktPn">)</span></td></tr></table></blockquote></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxDef RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">mandatory-dependent-dom</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">optional-dependent-dom</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">dependent-rest</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">pre-condition</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">dependent-range</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">post-condition</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><span class="stt"> </span></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="specgrammar"><tr><td align="right" valign="baseline"><span class="RktVar">mandatory-dependent-dom</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">id+ctc</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">keyword</span><span class="hspace"> </span><span class="RktVar">id+ctc</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">optional-dependent-dom</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">id+ctc</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">keyword</span><span class="hspace"> </span><span class="RktVar">id+ctc</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">dependent-rest</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">#:rest</span><span class="hspace"> </span><span class="RktVar">id+ctc</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">pre-condition</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">#:pre</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktVar">boolean-expr</span><span class="hspace"> </span><span class="RktVar">pre-condition</span></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">#:pre/name</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktVar">string</span><span class="hspace"> </span><span class="RktVar">boolean-expr</span><span class="hspace"> </span><span class="RktVar">pre-condition</span></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">dependent-range</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">id+ctc</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">un+ctc</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">(</span><span class="RktSym"><a href="values.html#%28def._%28%28quote._~23~25kernel%29._values%29%29" class="RktValLink" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktVar">id+ctc</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">(</span><span class="RktSym"><a href="values.html#%28def._%28%28quote._~23~25kernel%29._values%29%29" class="RktValLink" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktVar">un+ctc</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">post-condition</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">#:post</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktVar">boolean-expr</span><span class="hspace"> </span><span class="RktVar">post-condition</span></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">#:post/name</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktVar">string</span><span class="hspace"> </span><span class="RktVar">boolean-expr</span><span class="hspace"> </span><span class="RktVar">post-condition</span></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">id+ctc</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">[</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktVar">contract-expr</span><span class="RktPn">]</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">[</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVar">contract-expr</span><span class="RktPn">]</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">un+ctc</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">[</span><span class="RktVar">_</span><span class="hspace"> </span><span class="RktVar">contract-expr</span><span class="RktPn">]</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">[</span><span class="RktVar">_</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVar">contract-expr</span><span class="RktPn">]</span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">The <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> contract combinator differs from the <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%2A%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>*</a></span>
combinator in that the support pre- and post-condition clauses and
in that each argument and result is named. These names can then
be used in the subcontracts and in the pre-/post-condition clauses.
In short, contracts now express dependencies among arguments and results.</div></p><p>The first sub-form of a <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> contract covers the mandatory and the
second sub-form covers the optional arguments. Following that is an optional
rest-args contract, and an optional pre-condition. The pre-condition is
introduced with the <span class="RktPn">#:pre</span> keyword followed by the list of names on
which it depends. If the <span class="RktPn">#:pre/name</span> keyword is used, the string
supplied is used as part of the error message; similarly with <span class="RktPn">#:post/name</span>.</p><p>The <span class="RktSym">dep-range</span> non-terminal specifies the possible result
contracts. If it is <span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span>, then any value is allowed. Otherwise, the
result contract pairs a name and a contract or a multiple values return
with names and contracts. In the last two cases, the range contract may be
optionally followed by a post-condition; the post-condition expression is
not allowed if the range contract is <span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span>. Like the pre-condition,
the post-condition must specify the variables on which it depends.</p><p><div class="SIntrapara">Consider this sample contract:
</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="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxLink" 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">x</span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._number~3f%29%29" class="RktValLink" data-pltdoc="x">number?</a></span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">y</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="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._~3e~3d%2Fc%29%29" class="RktValLink" data-pltdoc="x">>=/c</a></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="hspace"> </span><span class="RktPn">[</span><span class="RktSym">result</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"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._and%2Fc%29%29" class="RktValLink" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._number~3f%29%29" class="RktValLink" data-pltdoc="x">number?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._~3e~3d%2Fc%29%29" class="RktValLink" data-pltdoc="x">>=/c</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2B%29%29" class="RktValLink" 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><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">It specifies a function of two arguments, both numbers. The contract on the
second argument (<span class="RktSym">y</span>) demands that it is greater than the first
argument. The result contract promises a number that is greater than the
sum of the two arguments. While the dependency specification for <span class="RktSym">y</span>
signals that the argument contract depends on the value of the first
argument, the dependency sequence for <span class="RktSym">result</span> indicates that the
contract depends on both argument values. <span class="refelem"><span class="refcolumn"><span class="refcontent">In general, an
empty sequence is (nearly) equivalent to not adding
a sequence at all except that the former is more expensive than the latter.</span></span></span>
Since the contract for <span class="RktSym">x</span> does not depend on anything else, it does
not come with any dependency sequence, not even <span class="RktPn">(</span><span class="RktPn">)</span>.</div></p><p>The contract expressions are not always evaluated in
order. First, if there is no dependency for a given contract expression,
the contract expression is evaluated at the time that the <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span>
expression is evaluated rather than the time when the function is called or
returns. These dependency-free contract expressions are evaluated in the
order in which they are listed.
Second, the dependent contract sub-expressions are evaluated when the
contracted function is called or returns in some order that satisfies the
dependencies. That is, if a contract for an argument depends on the value
of some other contract, the former is evaluated first (so that the
argument, with its contract checked, is available for the other). When
there is no dependency between two arguments (or the result and an
argument), then the contract that appears earlier in the source text is
evaluated first.</p><p>Finally, if all of the identifier positions of the range
contract are <span class="RktVar">_</span>s (underscores), then the range contract expressions
are evaluated when the function is called and the underscore is not bound
in the range, after the argument contracts are evaluated and
checked. Otherwise, the range expressions are evaluated when the function
returns.</p><p>If there are optional arguments that are not supplied, then
the corresponding variables will be bound to a special value
called <span class="RktSym"><a href="#%28def._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._the-unsupplied-arg%29%29" class="RktValLink" data-pltdoc="x">the-unsupplied-arg</a></span> value.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>syntax</p></div></div><table cellspacing="0" cellpadding="0" class="RktBlk RForeground"><tr><td><span class="RktPn">(</span><a name="(form._((lib._racket/contract/base..rkt)._-~3ed))"></a><span title="Provided from: racket/contract/base, racket/contract, racket | Package: base"><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ed%29%29" class="RktStxDef RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>d</a></span></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">mandatory-dependent-dom</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">dependent-rest</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">pre-condition</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">dependent-range</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">post-condition</span><span class="RktPn">)</span></td></tr></table></blockquote></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ed%29%29" class="RktStxDef RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>d</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">mandatory-dependent-dom</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktVar">optional-dependent-dom</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">dependent-rest</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">pre-condition</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">dependent-range</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">post-condition</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><span class="stt"> </span></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="specgrammar"><tr><td align="right" valign="baseline"><span class="RktVar">mandatory-dependent-dom</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">[</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktVar">dom-expr</span><span class="RktPn">]</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">keyword</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktVar">dom-expr</span><span class="RktPn">]</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">optional-dependent-dom</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">[</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktVar">dom-expr</span><span class="RktPn">]</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">keyword</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktVar">dom-expr</span><span class="RktPn">]</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">dependent-rest</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">#:rest</span><span class="hspace"> </span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktVar">rest-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">pre-condition</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">#:pre</span><span class="hspace"> </span><span class="RktVar">boolean-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">#:pre-cond</span><span class="hspace"> </span><span class="RktVar">boolean-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">dependent-range</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">[</span><span class="RktVar">_</span><span class="hspace"> </span><span class="RktVar">range-expr</span><span class="RktPn">]</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">(</span><span class="RktSym"><a href="values.html#%28def._%28%28quote._~23~25kernel%29._values%29%29" class="RktValLink" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktVar">_</span><span class="hspace"> </span><span class="RktVar">range-expr</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">[</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktVar">range-expr</span><span class="RktPn">]</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">(</span><span class="RktSym"><a href="values.html#%28def._%28%28quote._~23~25kernel%29._values%29%29" class="RktValLink" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktVar">id</span><span class="hspace"> </span><span class="RktVar">range-expr</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">post-condition</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">#:post-cond</span><span class="hspace"> </span><span class="RktVar">boolean-expr</span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">This contract is here for backwards compatibility; any new code should
use <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> instead.</div></p><p><div class="SIntrapara">This contract is similar to <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span>, but is “lax”, meaning
that it does not enforce contracts internally. For example, using
this contract
</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="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ed%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>d</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</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">#:pre</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._zero~3f%29%29" class="RktValLink" data-pltdoc="x">zero?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</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="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">will allow <span class="RktSym">f</span> to be called with <span class="RktVal">#f</span>, trigger whatever bad
behavior the author of <span class="RktSym">f</span> was trying to prohibit by insisting that
<span class="RktSym">f</span>’s contract accept only integers.</div></p><p>The <span class="RktPn">#:pre-cond</span> and <span class="RktPn">#:post-cond</span> keywords are aliases for
<span class="RktPn">#:pre</span> and <span class="RktPn">#:post</span> and are provided for backwards compatibility.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>syntax</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(form._((lib._racket/contract/base..rkt)._case-~3e))"></a><span title="Provided from: racket/contract/base, racket/contract, racket | Package: base"><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._case-~3e%29%29" class="RktStxDef RktStxLink" data-pltdoc="x">case-></a></span></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktVar">dom-expr</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="hspace"> </span><span class="RktVar">rest</span><span class="hspace"> </span><span class="RktVar">range</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="stt"> </span></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="specgrammar"><tr><td align="right" valign="baseline"><span class="RktVar">rest</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td></td></tr></table></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">#:rest</span><span class="hspace"> </span><span class="RktVar">rest-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td></tr><tr><td align="right" valign="baseline"><span class="RktVar">range</span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">=</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktVar">range-expr</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktPn">(</span><span class="RktSym"><a href="values.html#%28def._%28%28quote._~23~25kernel%29._values%29%29" class="RktValLink" data-pltdoc="x">values</a></span><span class="hspace"> </span><span class="RktVar">range-expr</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></td></tr><tr><td align="right" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="center" valign="baseline">|</td><td align="left" valign="baseline"><span class="stt"> </span></td><td align="left" valign="baseline"><span class="RktSym"><a href="data-structure-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%29%29" class="RktStxLink" data-pltdoc="x">any</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">This contract form is designed to match
<span class="RktSym"><a href="lambda.html#%28form._%28%28quote._~23~25kernel%29._case-lambda%29%29" class="RktStxLink" data-pltdoc="x">case-lambda</a></span>. Each argument to <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._case-~3e%29%29" class="RktStxLink" data-pltdoc="x">case-></a></span> is a
contract that governs a clause in the
<span class="RktSym"><a href="lambda.html#%28form._%28%28quote._~23~25kernel%29._case-lambda%29%29" class="RktStxLink" data-pltdoc="x">case-lambda</a></span>. If the <span class="RktPn">#:rest</span> keyword is
present, the corresponding clause must accept an arbitrary
number of arguments. The <span class="RktVar">range</span> specification is
just like that for <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span> and <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%2A%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>*</a></span>.</div></p><p><div class="SIntrapara">For example, this contract matches a function with two
cases, one that accepts an integer, returning void, and one
that accepts no arguments and returns an integer.
</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="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._case-~3e%29%29" class="RktStxLink" data-pltdoc="x">case-></a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktSym"><a href="void.html#%28def._%28%28quote._~23~25kernel%29._void~3f%29%29" class="RktValLink" data-pltdoc="x">void?</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._integer~3f%29%29" class="RktValLink" data-pltdoc="x">integer?</a></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">Such a contract could be used to guard a function that controls
access to a single shared integer.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>syntax</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(form._((lib._racket/contract/base..rkt)._unconstrained-domain-~3e))"></a><span title="Provided from: racket/contract/base, racket/contract, racket | Package: base"><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._unconstrained-domain-~3e%29%29" class="RktStxDef RktStxLink" data-pltdoc="x">unconstrained-domain-></a></span></span><span class="hspace"> </span><span class="RktVar">range-expr</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span></p></blockquote></td></tr></table></blockquote></div><div class="SIntrapara">Constructs a contract that accepts a function, but makes no constraint
on the function’s domain. The <span class="RktVar">range-expr</span>s determine the number
of results and the contract for each result.</div></p><p>Generally, this contract must be combined with another contract to
ensure that the domain is actually known to be able to safely call the
function itself.</p><p>For example, the contract</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="require.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._provide%29%29" class="RktStxLink" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="attaching-contracts-to-values.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._contract-out%29%29" class="RktStxLink" 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="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ed%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>d</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">size</span><span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._natural-number%2Fc%29%29" class="RktValLink" 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">proc</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._and%2Fc%29%29" class="RktValLink" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._unconstrained-domain-~3e%29%29" class="RktStxLink" data-pltdoc="x">unconstrained-domain-></a></span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._number~3f%29%29" class="RktValLink" data-pltdoc="x">number?</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._lambda%29%29" class="RktStxLink" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">p</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="procedures.html#%28def._%28%28quote._~23~25kernel%29._procedure-arity-includes~3f%29%29" class="RktValLink" data-pltdoc="x">procedure-arity-includes?</a></span><span class="hspace"> </span><span class="RktSym">p</span><span class="hspace"> </span><span class="RktSym">size</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="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym"><a href="stx-patterns.html#%28form._%28%28lib._racket%2Fprivate%2Fstxcase-scheme..rkt%29.__%29%29" class="RktStxLink" data-pltdoc="x">_</a></span><span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._number~3f%29%29" class="RktValLink" data-pltdoc="x">number?</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><p>says that the function <span class="RktSym">f</span> accepts a natural number
and a function. The domain of the function that <span class="RktSym">f</span>
accepts must include a case for <span class="RktSym">size</span> arguments,
meaning that <span class="RktSym">f</span> can safely supply <span class="RktSym">size</span>
arguments to its input.</p><p>For example, the following is a definition of <span class="RktSym">f</span> that cannot
be blamed using the above contract:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" 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">i</span><span class="hspace"> </span><span class="RktSym">g</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="procedures.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._apply%29%29" class="RktValLink" data-pltdoc="x">apply</a></span><span class="hspace"> </span><span class="RktSym">g</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="pairs.html#%28def._%28%28lib._racket%2Fprivate%2Flist..rkt%29._build-list%29%29" class="RktValLink" data-pltdoc="x">build-list</a></span><span class="hspace"> </span><span class="RktSym">i</span><span class="hspace"> </span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._add1%29%29" class="RktValLink" data-pltdoc="x">add1</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._racket/contract/base..rkt)._predicate/c))"></a><span title="Provided from: racket/contract/base, racket/contract, racket | Package: base"><span class="RktSym"><a href="#%28def._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._predicate%2Fc%29%29" class="RktValDef RktValLink" data-pltdoc="x">predicate/c</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="contract-utilities.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._contract~3f%29%29" class="RktValLink" data-pltdoc="x">contract?</a></span></p></blockquote></td></tr></table></blockquote></div><div class="SIntrapara">Use this contract to indicate that some function
is a predicate. It is semantically equivalent to
<span class="RktPn">(</span><span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span>.</div></p><p>This contract also includes an optimization so that functions returning
<span class="RktVal">#t</span> from <span class="RktSym"><a href="structutils.html#%28def._%28%28quote._~23~25kernel%29._struct-predicate-procedure~3f%29%29" class="RktValLink" data-pltdoc="x">struct-predicate-procedure?</a></span> are just returned directly, without
being wrapped. This contract is used by <span class="RktSym"><a href="attaching-contracts-to-values.html#%28form._%28%28lib._racket%2Fcontract%2Fprivate%2Fprovide..rkt%29._provide%2Fcontract%29%29" class="RktStxLink" data-pltdoc="x">provide/contract</a></span>’s
<span class="RktSym"><a href="define-struct.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._struct%29%29" class="RktStxLink" data-pltdoc="x">struct</a></span> subform so that struct predicates end up not being wrapped.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._racket/contract/base..rkt)._the-unsupplied-arg))"></a><span title="Provided from: racket/contract/base, racket/contract, racket | Package: base"><span class="RktSym"><a href="#%28def._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._the-unsupplied-arg%29%29" class="RktValDef RktValLink" data-pltdoc="x">the-unsupplied-arg</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28def._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._unsupplied-arg~3f%29%29" class="RktValLink" data-pltdoc="x">unsupplied-arg?</a></span></p></blockquote></td></tr></table></blockquote></div><div class="SIntrapara">Used by <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ei%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>i</a></span> (and <span class="RktSym"><a href="#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3ed%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span>d</a></span>) to bind
optional arguments that are not supplied by a call site.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._racket/contract/base..rkt)._unsupplied-arg~3f))"></a><span title="Provided from: racket/contract/base, racket/contract, racket | Package: base"><span class="RktSym"><a href="#%28def._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._unsupplied-arg~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">unsupplied-arg?</a></span></span><span class="hspace"> </span><span class="RktVar">v</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></td></tr></table></blockquote></div><div class="SIntrapara">A predicate to determine whether <span class="RktVar">v</span> is
<span class="RktSym"><a href="#%28def._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._the-unsupplied-arg%29%29" class="RktValLink" data-pltdoc="x">the-unsupplied-arg</a></span>.</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, "6.1", "../");" 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("6.1");">top</a></span><span class="navright"> <a href="data-structure-contracts.html" title="backward to "8.1 Data-structure Contracts"" data-pltdoc="x">← prev</a> <a href="contracts.html" title="up to "8 Contracts"" data-pltdoc="x">up</a> <a href="parametric-contracts.html" title="forward to "8.3 Parametric Contracts"" data-pltdoc="x">next →</a></span> </div></div></div><div id="contextindicator"> </div></body></html>
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