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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><meta name="viewport" content="width=device-width, initial-scale=0.8"/><title>7.5 Contracts on Structures</title><link rel="stylesheet" type="text/css" href="../scribble.css" title="default"/><link rel="stylesheet" type="text/css" href="../racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-style.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../doc-site.css" title="default"/><script type="text/javascript" src="../scribble-common.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../doc-site.js"></script><script type="text/javascript" src="../local-redirect/local-redirect.js"></script><script type="text/javascript" src="../local-redirect/local-user-redirect.js"></script><!--[if IE 6]><style type="text/css">.SIEHidden { overflow: hidden; }</style><![endif]--></head><body id="doc-racket-lang-org"><div class="tocset"><div class="tocview"><div class="tocviewlist tocviewlisttopspace"><div class="tocviewtitle"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_0");">►</a></td><td></td><td><a href="index.html" class="tocviewlink" data-pltdoc="x">The Racket Guide</a></td></tr></table></div><div class="tocviewsublisttop" style="display: none;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1 </td><td><a href="intro.html" class="tocviewlink" data-pltdoc="x">Welcome to Racket</a></td></tr><tr><td align="right">2 </td><td><a href="to-scheme.html" class="tocviewlink" data-pltdoc="x">Racket Essentials</a></td></tr><tr><td align="right">3 </td><td><a href="datatypes.html" class="tocviewlink" data-pltdoc="x">Built-<wbr></wbr>In Datatypes</a></td></tr><tr><td align="right">4 </td><td><a href="scheme-forms.html" class="tocviewlink" data-pltdoc="x">Expressions and Definitions</a></td></tr><tr><td align="right">5 </td><td><a href="define-struct.html" class="tocviewlink" data-pltdoc="x">Programmer-<wbr></wbr>Defined Datatypes</a></td></tr><tr><td align="right">6 </td><td><a href="modules.html" class="tocviewlink" data-pltdoc="x">Modules</a></td></tr><tr><td align="right">7 </td><td><a href="contracts.html" class="tocviewselflink" data-pltdoc="x">Contracts</a></td></tr><tr><td align="right">8 </td><td><a href="i_o.html" class="tocviewlink" data-pltdoc="x">Input and Output</a></td></tr><tr><td align="right">9 </td><td><a href="regexp.html" class="tocviewlink" data-pltdoc="x">Regular Expressions</a></td></tr><tr><td align="right">10 </td><td><a href="control.html" class="tocviewlink" data-pltdoc="x">Exceptions and Control</a></td></tr><tr><td align="right">11 </td><td><a href="for.html" class="tocviewlink" data-pltdoc="x">Iterations and Comprehensions</a></td></tr><tr><td align="right">12 </td><td><a href="match.html" class="tocviewlink" data-pltdoc="x">Pattern Matching</a></td></tr><tr><td align="right">13 </td><td><a href="classes.html" class="tocviewlink" data-pltdoc="x">Classes and Objects</a></td></tr><tr><td align="right">14 </td><td><a href="units.html" class="tocviewlink" data-pltdoc="x">Units</a></td></tr><tr><td align="right">15 </td><td><a href="reflection.html" class="tocviewlink" data-pltdoc="x">Reflection and Dynamic Evaluation</a></td></tr><tr><td align="right">16 </td><td><a href="macros.html" class="tocviewlink" data-pltdoc="x">Macros</a></td></tr><tr><td align="right">17 </td><td><a href="languages.html" class="tocviewlink" data-pltdoc="x">Creating Languages</a></td></tr><tr><td align="right">18 </td><td><a 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class="tocviewlink" data-pltdoc="x">Bibliography</a></td></tr><tr><td align="right"></td><td><a href="doc-index.html" class="tocviewlink" data-pltdoc="x">Index</a></td></tr></table></div></div><div class="tocviewlist"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_1");">▼</a></td><td>7 </td><td><a href="contracts.html" class="tocviewlink" data-pltdoc="x">Contracts</a></td></tr></table><div class="tocviewsublist" style="display: block;" id="tocview_1"><table cellspacing="0" cellpadding="0"><tr><td align="right">7.1 </td><td><a href="contract-boundaries.html" class="tocviewlink" data-pltdoc="x">Contracts and Boundaries</a></td></tr><tr><td align="right">7.2 </td><td><a href="contract-func.html" class="tocviewlink" data-pltdoc="x">Simple Contracts on Functions</a></td></tr><tr><td align="right">7.3 </td><td><a href="contracts-general-functions.html" class="tocviewlink" data-pltdoc="x">Contracts on Functions in General</a></td></tr><tr><td align="right">7.4 </td><td><a href="contracts-first.html" class="tocviewlink" data-pltdoc="x">Contracts:<span class="mywbr"> </span> A Thorough Example</a></td></tr><tr><td align="right">7.5 </td><td><a href="contracts-struct.html" class="tocviewselflink" data-pltdoc="x">Contracts on Structures</a></td></tr><tr><td align="right">7.6 </td><td><a href="contracts-exists.html" class="tocviewlink" data-pltdoc="x">Abstract Contracts using <span class="RktPn">#:<span class="mywbr"> </span>exists</span> and <span class="RktPn">#:<span class="mywbr"> </span>∃</span></a></td></tr><tr><td align="right">7.7 </td><td><a href="contracts-examples.html" class="tocviewlink" data-pltdoc="x">Additional Examples</a></td></tr><tr><td align="right">7.8 </td><td><a href="Building_New_Contracts.html" class="tocviewlink" data-pltdoc="x">Building New Contracts</a></td></tr><tr><td align="right">7.9 </td><td><a href="contracts-gotchas.html" class="tocviewlink" data-pltdoc="x">Gotchas</a></td></tr></table></div></div><div class="tocviewlist"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_2");">►</a></td><td>7.5 </td><td><a href="contracts-struct.html" class="tocviewselflink" data-pltdoc="x">Contracts on Structures</a></td></tr></table><div class="tocviewsublistbottom" style="display: none;" id="tocview_2"><table cellspacing="0" cellpadding="0"><tr><td align="right">7.5.1 </td><td><a href="contracts-struct.html#%28part._contracts-single-struct%29" class="tocviewlink" data-pltdoc="x">Guarantees for a Specific Value</a></td></tr><tr><td align="right">7.5.2 </td><td><a href="contracts-struct.html#%28part._contracts-define-struct%29" class="tocviewlink" data-pltdoc="x">Guarantees for All Values</a></td></tr><tr><td align="right">7.5.3 </td><td><a href="contracts-struct.html#%28part._contracts-lazy-contracts%29" class="tocviewlink" data-pltdoc="x">Checking Properties of Data Structures</a></td></tr></table></div></div></div><div class="tocsub"><div class="tocsubtitle">On this page:</div><table class="tocsublist" cellspacing="0"><tr><td><span class="tocsublinknumber">7.5.1<tt> </tt></span><a href="contracts-struct.html#%28part._contracts-single-struct%29" class="tocsubseclink" data-pltdoc="x">Guarantees for a Specific Value</a></td></tr><tr><td><span class="tocsublinknumber">7.5.2<tt> </tt></span><a href="contracts-struct.html#%28part._contracts-define-struct%29" class="tocsubseclink" data-pltdoc="x">Guarantees for All Values</a></td></tr><tr><td><span class="tocsublinknumber">7.5.3<tt> </tt></span><a href="contracts-struct.html#%28part._contracts-lazy-contracts%29" class="tocsubseclink" data-pltdoc="x">Checking Properties of Data Structures</a></td></tr></table></div></div><div class="maincolumn"><div class="main"><div class="navsettop"><span class="navleft"><form class="searchform"><input class="searchbox" id="searchbox" type="text" tabindex="1" placeholder="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "8.6", "../");"/></form> <a href="https://docs.racket-lang.org/index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("8.6");">top</a><span class="tocsettoggle"> <a href="javascript:void(0);" title="show/hide table of contents" onclick="TocsetToggle();">contents</a></span></span><span class="navright"> <a href="contracts-first.html" title="backward to "7.4 Contracts: A Thorough Example"" data-pltdoc="x">← prev</a> <a href="contracts.html" title="up to "7 Contracts"" data-pltdoc="x">up</a> <a href="contracts-exists.html" title="forward to "7.6 Abstract Contracts using #:exists and #:∃"" data-pltdoc="x">next →</a></span> </div><h4 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-struct"">7.5<tt> </tt><a name="(part._contracts-struct)"></a>Contracts on Structures</h4><p>Modules deal with structures in two ways. First they export
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<span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define-struct.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct</a></span> definitions, i.e., the ability to create
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structs of a certain kind, to access their fields, to modify
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them, and to distinguish structs of this kind against every
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other kind of value in the world. Second, on occasion a
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module exports a specific struct and wishes to promise that
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its fields contain values of a certain kind. This section
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explains how to protect structs with contracts for both
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uses.</p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-single-struct"">7.5.1<tt> </tt><a name="(part._contracts-single-struct)"></a>Guarantees for a Specific Value</h5><p>If your module defines a variable to be a structure value, then you can
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specify the structure’s shape using <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/c</a></span>.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=index.html&version=8.6" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket</span></a></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define-struct.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct</a></span><span class="hspace"> </span><span class="RktSym">posn</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="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">origin</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">posn</span><span class="hspace"> </span><span class="RktVal">0</span><span class="hspace"> </span><span class="RktVal">0</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">origin</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/c</a></span><span class="hspace"> </span><span class="RktSym">posn</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._zero%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">zero?</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._zero%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">zero?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>In this example, the module defines a structure shape for representing
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2-dimensional positions and then creates one specific instance:
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<span class="RktSym">origin</span>. The export of this instance guarantees that its fields
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are <span class="RktVal">0</span>, i.e., they represent <span class="stt">(0,0)</span>, on the Cartesian grid.</p><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>See also <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fvector..rkt%2529._vector%252Fc%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">vector/c</a></span> and similar contract
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combinators for (flat) compound data.</p></blockquote></blockquote></blockquote><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-define-struct"">7.5.2<tt> </tt><a name="(part._contracts-define-struct)"></a>Guarantees for All Values</h5><p>The book <span style="font-style: italic"><a href="https://htdp.org">How to Design Programs</a></span> teaches that <span class="RktSym">posn</span>s should contain only
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numbers in their two fields. With contracts we would enforce this
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informal data definition as follows:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=index.html&version=8.6" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket</span></a></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define-struct.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct</a></span><span class="hspace"> </span><span class="RktSym">posn</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="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define-struct.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct</a></span><span class="hspace"> </span><span class="RktSym">posn</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="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">y</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">p-okay</span><span class="hspace"> </span><span class="RktSym">posn?</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">p-sick</span><span class="hspace"> </span><span class="RktSym">posn?</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">p-okay</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">posn</span><span class="hspace"> </span><span class="RktVal">10</span><span class="hspace"> </span><span class="RktVal">20</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">p-sick</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">posn</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">a</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">b</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>This module exports the entire structure definition: <span class="RktSym">posn</span>,
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<span class="RktSym">posn?</span>, <span class="RktSym">posn-x</span>, <span class="RktSym">posn-y</span>,
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<span class="RktSym">set-posn-x!</span>, and <span class="RktSym">set-posn-y!</span>. Each function enforces
|
|
or promises that the two fields of a <span class="RktSym">posn</span> structure are
|
|
numbers —<wbr></wbr> when the values flow across the module boundary. Thus, if
|
|
a client calls <span class="RktSym">posn</span> on <span class="RktVal">10</span> and <span class="RktVal">'</span><span class="RktVal">a</span>, the
|
|
contract system signals a contract violation.</p><p>The creation of <span class="RktSym">p-sick</span> inside of the <span class="RktSym">posn</span> module,
|
|
however, does not violate the contracts. The function <span class="RktSym">posn</span> is
|
|
used internally, so <span class="RktVal">'</span><span class="RktVal">a</span> and <span class="RktVal">'</span><span class="RktVal">b</span> don’t cross the module
|
|
boundary. Similarly, when <span class="RktSym">p-sick</span> crosses the boundary of
|
|
<span class="RktSym">posn</span>, the contract promises a <span class="RktSym">posn?</span> and nothing
|
|
else. In particular, this check does <span style="font-style: italic">not</span> require that the
|
|
fields of <span class="RktSym">p-sick</span> are numbers.</p><p>The association of contract checking with module boundaries implies that
|
|
<span class="RktSym">p-okay</span> and <span class="RktSym">p-sick</span> look alike from a client’s
|
|
perspective until the client extracts the pieces:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=index.html&version=8.6" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket</span></a></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._require%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">require</a></span><span class="hspace"> </span><span class="RktSym">lang/posn</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">...</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">posn-x</span><span class="hspace"> </span><span class="RktSym">p-sick</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">...</a></span></td></tr></table></blockquote><p>Using <span class="RktSym">posn-x</span> is the only way the client can find out what
|
|
a <span class="RktSym">posn</span> contains in the <span class="RktSym">x</span> field. The application of
|
|
<span class="RktSym">posn-x</span> sends <span class="RktSym">p-sick</span> back into the
|
|
<span class="RktSym">posn</span> module and the result value – <span class="RktVal">'</span><span class="RktVal">a</span> here – back to
|
|
the client, again across the module boundary. At this very point, the contract
|
|
system discovers that a promise is broken. Specifically, <span class="RktSym">posn-x</span>
|
|
doesn’t return a number but a symbol and is therefore blamed.</p><p>This specific example shows that the explanation for a contract violation
|
|
doesn’t always pinpoint the source of the error. The good news is that the
|
|
error is located in the <span class="RktSym">posn</span> module. The bad news is that the
|
|
explanation is misleading. Although it is true that <span class="RktSym">posn-x</span>
|
|
produced a symbol instead of a number, it is the fault of the programmer who
|
|
created a <span class="RktSym">posn</span> from symbols, i.e., the programmer who added</p><blockquote class="SCodeFlow"><p><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">p-sick</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">posn</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">a</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">b</span><span class="RktPn">)</span><span class="RktPn">)</span></p></blockquote><p>to the module. So, when you are looking for bugs based on contract
|
|
violations, keep this example in mind.</p><p>If we want to fix the contract for <span class="RktSym">p-sick</span> so that the error
|
|
is caught when <span class="RktSym">sick</span> is exported, a single change suffices:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">...</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">p-sick</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/c</a></span><span class="hspace"> </span><span class="RktSym">posn</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>That is, instead of exporting <span class="RktSym">p-sick</span> as a plain
|
|
<span class="RktSym">posn?</span>, we use a <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/c</a></span> contract to enforce
|
|
constraints on its components.</p><h5 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-source-pkg="racket-doc" x-part-tag=""contracts-lazy-contracts"">7.5.3<tt> </tt><a name="(part._contracts-lazy-contracts)"></a>Checking Properties of Data Structures</h5><p>Contracts written using <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/c</a></span> immediately
|
|
check the fields of the data structure, but sometimes this
|
|
can have disastrous effects on the performance of a program
|
|
that does not, itself, inspect the entire data structure.</p><p>As an example, consider the binary search tree
|
|
search algorithm. A binary search tree is like a binary
|
|
tree, except that the numbers are organized in the tree to
|
|
make searching the tree fast. In particular, for each
|
|
interior node in the tree, all of the numbers in the left
|
|
subtree are smaller than the number in the node, and all of
|
|
the numbers in the right subtree are larger than the number
|
|
in the node.</p><p><div class="SIntrapara">We can implement a search function <span class="RktSym">in?</span> that takes
|
|
advantage of the structure of the binary search tree.
|
|
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=index.html&version=8.6" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket</span></a></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define-struct.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct</a></span><span class="hspace"> </span><span class="RktSym">node</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">val</span><span class="hspace"> </span><span class="RktSym">left</span><span class="hspace"> </span><span class="RktSym">right</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">determines if `n' is in the binary search tree `b',</span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">exploiting the binary search tree invariant</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">in?</span><span class="hspace"> </span><span class="RktSym">n</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._cond%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">cond</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._null%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">null?</a></span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._else%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">else</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._cond%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">cond</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktSym">n</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-val</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVal">#t</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3c%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x"><</a></span><span class="hspace"> </span><span class="RktSym">n</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-val</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">in?</span><span class="hspace"> </span><span class="RktSym">n</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-left</span><span class="hspace"> </span><span class="RktSym">b</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><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3e%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">></a></span><span class="hspace"> </span><span class="RktSym">n</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-val</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">in?</span><span class="hspace"> </span><span class="RktSym">n</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-right</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">a predicate that identifies binary search trees</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between?</span><span class="hspace"> </span><span class="RktSym">b</span><span class="hspace"> </span><span class="RktSym">low</span><span class="hspace"> </span><span class="RktSym">high</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._or%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">or</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._null%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">null?</a></span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._and%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3c%7E3d%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x"><=</a></span><span class="hspace"> </span><span class="RktSym">low</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-val</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">high</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between?</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-left</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">low</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-val</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between?</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-right</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">node-val</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">high</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst?</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between?</span><span class="hspace"> </span><span class="RktSym">b</span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-i</span>nf.0</span><span class="hspace"> </span><span class="RktVal">+inf.0</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">provide</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct-out%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct-out</a></span><span class="hspace"> </span><span class="RktSym">node</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">bst?</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._boolean%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">in?</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="hspace"> </span><span class="RktSym">bst?</span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._boolean%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div></p><p>In a full binary search tree, this means that
|
|
the <span class="RktSym">in?</span> function only has to explore a
|
|
logarithmic number of nodes.</p><p>The contract on <span class="RktSym">in?</span> guarantees that its input
|
|
is a binary search tree. But a little careful thought
|
|
reveals that this contract defeats the purpose of the binary
|
|
search tree algorithm. In particular, consider the
|
|
inner <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._cond%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">cond</a></span> in the <span class="RktSym">in?</span>
|
|
function. This is where the <span class="RktSym">in?</span> function gets
|
|
its speed: it avoids searching an entire subtree at each
|
|
recursive call. Now compare that to the <span class="RktSym">bst-between?</span>
|
|
function. In the case that it returns <span class="RktVal">#t</span>, it
|
|
traverses the entire tree, meaning that the speedup
|
|
of <span class="RktSym">in?</span> is lost.</p><p>In order to fix that, we can employ a new strategy for
|
|
checking the binary search tree contract. In particular, if
|
|
we only checked the contract on the nodes
|
|
that <span class="RktSym">in?</span> looks at, we can still guarantee that
|
|
the tree is at least partially well-formed, but without
|
|
changing the complexity.</p><p>To do that, we need to use <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fdc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/dc</a></span> to define
|
|
<span class="RktSym">bst-between?</span>. Like <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/c</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fdc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/dc</a></span> defines a
|
|
contract for a structure. Unlike
|
|
<span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/c</a></span>, it allows fields to be marked as lazy, so that
|
|
the contracts are only checked when the matching selector is called.
|
|
Also, it does not allow mutable fields to be marked as lazy.</p><p>The <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fdc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/dc</a></span> form accepts a contract for each
|
|
field of the struct and returns a contract on the
|
|
struct. More interestingly, <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fdc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/dc</a></span> allows us to write dependent
|
|
contracts, i.e., contracts where some of the contracts on
|
|
the fields depend on the values of other fields. We can use
|
|
this to define the binary search tree contract:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><a href="Module_Syntax.html#%28part._hash-lang%29" class="RktModLink" data-pltdoc="x"><span class="RktMod">#lang</span></a><span class="hspace"> </span><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=index.html&version=8.6" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">racket</span></a></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define-struct.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct</a></span><span class="hspace"> </span><span class="RktSym">node</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">val</span><span class="hspace"> </span><span class="RktSym">left</span><span class="hspace"> </span><span class="RktSym">right</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">determines if `n' is in the binary search tree `b'</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">in?</span><span class="hspace"> </span><span class="RktSym">n</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">...</a></span><span class="hspace"> </span><span class="RktSym">as</span><span class="hspace"> </span><span class="RktSym">before</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">...</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">bst-between : number number -> contract</span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">builds a contract for binary search trees</span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">whose values are between low and high</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between/c</span><span class="hspace"> </span><span class="RktSym">low</span><span class="hspace"> </span><span class="RktSym">high</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._or%252Fc%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">or/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._null%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">null?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fdc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/dc</a></span><span class="hspace"> </span><span class="RktSym">node</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">val</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._between%252Fc%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">between/c</a></span><span class="hspace"> </span><span class="RktSym">low</span><span class="hspace"> </span><span class="RktSym">high</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">left</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">val</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">#:lazy</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between/c</span><span class="hspace"> </span><span class="RktSym">low</span><span class="hspace"> </span><span class="RktSym">val</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">right</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">val</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">#:lazy</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between/c</span><span class="hspace"> </span><span class="RktSym">val</span><span class="hspace"> </span><span class="RktSym">high</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">bst/c</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between/c</span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-i</span>nf.0</span><span class="hspace"> </span><span class="RktVal">+inf.0</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">provide</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._struct-out%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct-out</a></span><span class="hspace"> </span><span class="RktSym">node</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">provide</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">contract-out</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">bst/c</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=contract-utilities.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fguts..rkt%2529._contract%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">contract?</a></span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">in?</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="hspace"> </span><span class="RktSym">bst/c</span><span class="hspace"> </span><span class="RktPn">. </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="RktPn"> .</span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._boolean%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>In general, each use of <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fdc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/dc</a></span> must name the
|
|
fields and then specify contracts for each field. In the
|
|
above, the <span class="RktSym">val</span> field is a contract that accepts
|
|
values between <span class="RktSym">low</span> and <span class="RktSym">high</span>.
|
|
The <span class="RktSym">left</span> and <span class="RktSym">right</span> fields are
|
|
dependent on the value of the <span class="RktSym">val</span> field,
|
|
indicated by their second sub-expressions. They are
|
|
also marked with the <span class="RktPn">#:lazy</span> keyword to indicate
|
|
that they should be checked only when the appropriate
|
|
accessor is called on the struct instance. Their contracts
|
|
are built by recursive calls to
|
|
the <span class="RktSym">bst-between/c</span> function. Taken together,
|
|
this contract ensures the same thing that
|
|
the <span class="RktSym">bst-between?</span> function checked in the
|
|
original example, but here the checking only happens
|
|
as <span class="RktSym">in?</span> explores the tree.</p><p>Although this contract improves the performance
|
|
of <span class="RktSym">in?</span>, restoring it to the logarithmic
|
|
behavior that the contract-less version had, it is still
|
|
imposes a fairly large constant overhead. So, the contract
|
|
library also provides <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=contract-utilities.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fopt..rkt%2529._define-opt%252Fc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define-opt/c</a></span> that brings
|
|
down that constant factor by optimizing its body. Its shape
|
|
is just like the <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span> above. It expects its
|
|
body to be a contract and then optimizes that contract.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=contract-utilities.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fopt..rkt%2529._define-opt%252Fc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define-opt/c</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between/c</span><span class="hspace"> </span><span class="RktSym">low</span><span class="hspace"> </span><span class="RktSym">high</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._or%252Fc%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">or/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._null%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">null?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fstruct-dc..rkt%2529._struct%252Fdc%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">struct/dc</a></span><span class="hspace"> </span><span class="RktSym">node</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">val</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._between%252Fc%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">between/c</a></span><span class="hspace"> </span><span class="RktSym">low</span><span class="hspace"> </span><span class="RktSym">high</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">left</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">val</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">#:lazy</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between/c</span><span class="hspace"> </span><span class="RktSym">low</span><span class="hspace"> </span><span class="RktSym">val</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">right</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">val</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">#:lazy</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">bst-between/c</span><span class="hspace"> </span><span class="RktSym">val</span><span class="hspace"> </span><span class="RktSym">high</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 class="navsetbottom"><span class="navleft"><form class="searchform"><input class="searchbox" id="searchbox" type="text" tabindex="1" placeholder="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "8.6", "../");"/></form> <a href="https://docs.racket-lang.org/index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("8.6");">top</a><span class="tocsettoggle"> <a href="javascript:void(0);" title="show/hide table of contents" onclick="TocsetToggle();">contents</a></span></span><span class="navright"> <a href="contracts-first.html" title="backward to "7.4 Contracts: A Thorough Example"" data-pltdoc="x">← prev</a> <a href="contracts.html" title="up to "7 Contracts"" data-pltdoc="x">up</a> <a href="contracts-exists.html" title="forward to "7.6 Abstract Contracts using #:exists and #:∃"" data-pltdoc="x">next →</a></span> </div></div></div><div id="contextindicator"> </div></body></html> |