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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>7.6 Abstract Contracts using #:exists and #:∃</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 href="concurr
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protect abstractions, ensuring that clients of your module
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cannot depend on the precise representation choices you make
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for your data structures.</p><p><div class="SIntrapara"><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>You can type <span class="RktPn">#:exists</span> instead of <span class="RktPn">#:∃</span> if you
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cannot easily type unicode characters; in DrRacket, typing
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">\exists</span><span class="hspace"></span></span> followed by either alt-\ or control-\ (depending
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on your platform) will produce <span class="RktSym">∃</span>.</p></blockquote></blockquote></blockquote></div><div class="SIntrapara">The <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> form allows you to write
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</div><div class="SIntrapara"><blockquote class="SCodeFlow"><p><span class="RktPn">#:∃</span><span class="hspace"> </span><span class="RktVar">name-of-a-new-contract</span></p></blockquote></div><div class="SIntrapara"> as one of its clauses. This declaration
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introduces the variable <span class="RktVar">name-of-a-new-contract</span>, binding it to a new
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contract that hides information about the values it protects.</div></p><p><div class="SIntrapara">As an example, consider this (simple) implementation of a queue data structure:
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</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="RktPn">(</span><span class="RktSym">define</span><span class="hspace"> </span><span class="RktSym">empty</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym">define</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">enq</span><span class="hspace"> </span><span class="RktSym">top</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">append</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">list</span><span class="hspace"> </span><span class="RktSym">top</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym">define</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">next</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">car</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym">define</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">deq</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">cdr</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym">define</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">empty?</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">null?</span><span class="hspace"> </span><span class="RktSym">queue</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">provide</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">empty</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%252Fbase..rkt%2529._listof%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">listof</a></span><span class="hspace"> </span><span class="RktSym">integer?</span><s
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of this data structure might use <span class="RktSym">car</span> and <span class="RktSym">cdr</span> directly on the
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data structure (perhaps accidentally) and thus any change in the representation
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(say to a more efficient representation that supports amortized constant time
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enqueue and dequeue operations) might break client code.</div></p><p><div class="SIntrapara">To ensure that the queue representation is abstract, we can use <span class="RktPn">#:∃</span> in the
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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=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> expression, like this:
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</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym">provide</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="hspace"> </span><span class="RktSym">queue</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">empty</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">enq</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="hspace"> </span><span class="RktSym">integer?</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">next</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="hspace"> </span><span class="RktSym">queue</span><span class="hspace"> </span><span class="RktSym">integer?</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">deq</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="hspace"> </span><span class="RktSym">queue</span><span class="hspace"> </span><span class="RktSym">queue</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">empty?</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="hspace"> </span><span class="RktSym">queue</span><span class="hspace"> </span><span class="RktSym">boolean?</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></div></p><p>Now, if clients of the data structure try to use <span class="RktSym">car</span> and <span class="RktSym">cdr</span>, t
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receive an error, rather than mucking about with the internals of the queues.</p><p>See also <a href="contracts-gotchas.html#%28part._contracts-exists-gotcha%29" data-pltdoc="x">Exists Contracts and Predicates</a>.</p><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-struct.html" title="backward to "7.5 Contracts on Structures"" data-pltdoc="x">← prev</a> <a href="contracts.html" title="up to "7 Contracts"" data-pltdoc="x">up</a> <a href="contracts-examples.html" title="forward to "7.7 Additional Examples"" data-pltdoc="x">next →</a></span> </div></div></div><div id="contextindicator"> </div></body></html>
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