/usr/share/doc/racket/guide/contracts-first.html is in racket-doc 6.1-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 | <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><title>7.4 Contracts: A Thorough Example</title><link rel="stylesheet" type="text/css" href="../scribble.css" title="default"/><link rel="stylesheet" type="text/css" href="../racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-style.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../doc-site.css" title="default"/><script type="text/javascript" src="../scribble-common.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../doc-site.js"></script><script type="text/javascript" src="../local-redirect/local-redirect.js"></script><script type="text/javascript" src="../local-redirect/local-user-redirect.js"></script><!--[if IE 6]><style type="text/css">.SIEHidden { overflow: hidden; }</style><![endif]--></head><body id="doc-racket-lang-org"><div class="tocset"><div class="tocview"><div class="tocviewlist tocviewlisttopspace"><div class="tocviewtitle"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_0");">►</a></td><td></td><td><a href="index.html" class="tocviewlink" data-pltdoc="x"><span style="font-weight: bold">The Racket Guide</span></a></td></tr></table></div><div class="tocviewsublisttop" style="display: none;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1 </td><td><a href="intro.html" class="tocviewlink" data-pltdoc="x">Welcome to Racket</a></td></tr><tr><td align="right">2 </td><td><a href="to-scheme.html" class="tocviewlink" data-pltdoc="x">Racket Essentials</a></td></tr><tr><td align="right">3 </td><td><a href="datatypes.html" class="tocviewlink" data-pltdoc="x">Built-<wbr></wbr>In Datatypes</a></td></tr><tr><td align="right">4 </td><td><a href="scheme-forms.html" class="tocviewlink" data-pltdoc="x">Expressions and Definitions</a></td></tr><tr><td align="right">5 </td><td><a href="define-struct.html" class="tocviewlink" data-pltdoc="x">Programmer-<wbr></wbr>Defined Datatypes</a></td></tr><tr><td align="right">6 </td><td><a href="modules.html" class="tocviewlink" data-pltdoc="x">Modules</a></td></tr><tr><td align="right">7 </td><td><a href="contracts.html" class="tocviewselflink" data-pltdoc="x">Contracts</a></td></tr><tr><td align="right">8 </td><td><a href="i_o.html" class="tocviewlink" data-pltdoc="x">Input and Output</a></td></tr><tr><td align="right">9 </td><td><a href="regexp.html" class="tocviewlink" data-pltdoc="x">Regular Expressions</a></td></tr><tr><td align="right">10 </td><td><a href="control.html" class="tocviewlink" data-pltdoc="x">Exceptions and Control</a></td></tr><tr><td align="right">11 </td><td><a href="for.html" class="tocviewlink" data-pltdoc="x">Iterations and Comprehensions</a></td></tr><tr><td align="right">12 </td><td><a href="match.html" class="tocviewlink" data-pltdoc="x">Pattern Matching</a></td></tr><tr><td align="right">13 </td><td><a href="classes.html" class="tocviewlink" data-pltdoc="x">Classes and Objects</a></td></tr><tr><td align="right">14 </td><td><a href="units.html" class="tocviewlink" data-pltdoc="x">Units (Components)</a></td></tr><tr><td align="right">15 </td><td><a href="reflection.html" class="tocviewlink" data-pltdoc="x">Reflection and Dynamic Evaluation</a></td></tr><tr><td align="right">16 </td><td><a href="macros.html" class="tocviewlink" data-pltdoc="x">Macros</a></td></tr><tr><td align="right">17 </td><td><a href="languages.html" class="tocviewlink" data-pltdoc="x">Creating Languages</a></td></tr><tr><td align="right">18 </td><td><a href="concurrency.html" class="tocviewlink" data-pltdoc="x">Concurrency and Synchronization</a></td></tr><tr><td align="right">19 </td><td><a href="performance.html" class="tocviewlink" data-pltdoc="x">Performance</a></td></tr><tr><td align="right">20 </td><td><a href="parallelism.html" class="tocviewlink" data-pltdoc="x">Parallelism</a></td></tr><tr><td align="right">21 </td><td><a href="running.html" class="tocviewlink" data-pltdoc="x">Running and Creating Executables</a></td></tr><tr><td align="right">22 </td><td><a href="More_Libraries.html" class="tocviewlink" data-pltdoc="x">More Libraries</a></td></tr><tr><td align="right">23 </td><td><a href="dialects.html" class="tocviewlink" data-pltdoc="x">Dialects of Racket and Scheme</a></td></tr><tr><td align="right">24 </td><td><a href="other-editors.html" class="tocviewlink" data-pltdoc="x">Command-<wbr></wbr>Line Tools and Your Editor of Choice</a></td></tr><tr><td align="right"></td><td><a href="doc-bibliography.html" class="tocviewlink" data-pltdoc="x">Bibliography</a></td></tr><tr><td align="right"></td><td><a href="doc-index.html" class="tocviewlink" data-pltdoc="x">Index</a></td></tr></table></div></div><div class="tocviewlist"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_1");">▼</a></td><td>7 </td><td><a href="contracts.html" class="tocviewlink" data-pltdoc="x">Contracts</a></td></tr></table><div class="tocviewsublistbottom" 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="" class="tocviewselflink" data-pltdoc="x">Contracts:<span class="mywbr"> </span> A Thorough Example</a></td></tr><tr><td align="right">7.5 </td><td><a href="contracts-struct.html" class="tocviewlink" data-pltdoc="x">Contracts on Structures</a></td></tr><tr><td align="right">7.6 </td><td><a href="contracts-exists.html" class="tocviewlink" data-pltdoc="x">Abstract Contracts using <span class="RktPn">#:<span class="mywbr"> </span>exists</span> and <span class="RktPn">#:<span class="mywbr"> </span>∃</span></a></td></tr><tr><td align="right">7.7 </td><td><a href="contracts-examples.html" class="tocviewlink" data-pltdoc="x">Additional Examples</a></td></tr><tr><td align="right">7.8 </td><td><a href="contracts-gotchas.html" class="tocviewlink" data-pltdoc="x">Gotchas</a></td></tr></table></div></div></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="contracts-general-functions.html" title="backward to "7.3 Contracts on Functions in General"" data-pltdoc="x">← prev</a> <a href="contracts.html" title="up to "7 Contracts"" data-pltdoc="x">up</a> <a href="contracts-struct.html" title="forward to "7.5 Contracts on Structures"" data-pltdoc="x">next →</a></span> </div><h4 x-source-module="(lib "scribblings/guide/guide.scrbl")" x-part-tag=""contracts-first"">7.4<tt> </tt><a name="(part._contracts-first)"></a>Contracts: A Thorough Example</h4><p><div class="SIntrapara">This section develops several different flavors of contracts for one and
the same example: Racket’s <span class="RktSym">argmax</span> function. According to
its Racket documentation, the function consumes a procedure <span class="RktSym">proc</span> and
a non-empty list of values, <span class="RktSym">lst</span>. It
</div><div class="SIntrapara"><blockquote><p>returns the <span style="font-style: italic">first</span> element in the list <span class="RktSym">lst</span> that maximizes
the result of <span class="RktSym">proc</span>.</p></blockquote></div><div class="SIntrapara">The emphasis on <span style="font-style: italic">first</span> is ours.</div></p><p><div class="SIntrapara">Examples:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._add1%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">add1</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">3</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">3</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._sqrt%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">sqrt</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list</a></span><span class="hspace"> </span><span class="RktVal">0.4</span><span class="hspace"> </span><span class="RktVal">0.9</span><span class="hspace"> </span><span class="RktVal">0.16</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">0.9</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym">second</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">(</span><span class="RktVal">a</span><span class="hspace"> </span><span class="RktVal">2</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktVal">(</span><span class="RktVal">b</span><span class="hspace"> </span><span class="RktVal">3</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktVal">(</span><span class="RktVal">c</span><span class="hspace"> </span><span class="RktVal">4</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktVal">(</span><span class="RktVal">d</span><span class="hspace"> </span><span class="RktVal">1</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktVal">(</span><span class="RktVal">e</span><span class="hspace"> </span><span class="RktVal">4</span><span class="RktVal">)</span><span class="RktVal">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'(c 4)</span></p></td></tr></table></blockquote></div></p><p><div class="SIntrapara">Here is the simplest possible contract for this function:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">version 1</span></span></p><blockquote class="Rfilecontent"><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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.1" 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="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.1" 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">argmax</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._and%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._pair%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">pair?</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list?</a></span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></blockquote></div><div class="SIntrapara">This contract captures two essential conditions of the informal
description of <span class="RktSym">argmax</span>:
</div><div class="SIntrapara"><ul><li><p>the given function must produce numbers that are comparable according
to <span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3c%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x"><</a></span>. In particular, the contract <span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">number?</a></span><span class="RktPn">)</span>
would not do, because <span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">number?</a></span> also recognizes complex numbers in
Racket.</p></li><li><p>the given list must contain at least one item.</p></li></ul></div><div class="SIntrapara">When combined with the name, the contract explains the behavior of
<span class="RktSym">argmax</span> at the same level as an ML function type in a
module signature (except for the non-empty list aspect).</div></p><p><div class="SIntrapara">Contracts may communicate significantly more than a type signature,
however. Take a look at this second contract for <span class="RktSym">argmax</span>:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">version 2</span></span></p><blockquote class="Rfilecontent"><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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.1" 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="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.1" 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">argmax</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">lov</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._and%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._pair%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">pair?</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><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">r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">r</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">r</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=for.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._for%252Fand%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">for/and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">v</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3e%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">>=</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">v</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></blockquote></div><div class="SIntrapara">It is a <span style="font-style: italic">dependent</span> contract that names the two arguments and uses
the names to impose a predicate on the result. This predicate computes
<span class="RktPn">(</span><span class="RktSym">f</span><span class="stt"> </span><span class="RktSym">r</span><span class="RktPn">)</span> – where <span class="RktSym">r</span> is the result of <span class="RktSym">argmax</span> – and
then validates that this value is greater than or equal to all values
of <span class="RktSym">f</span> on the items of <span class="RktSym">lov</span>.</div></p><p><div class="SIntrapara">Is it possible that <span class="RktSym">argmax</span> could cheat by returning a random value
that accidentally maximizes <span class="RktSym">f</span> over all elements of <span class="RktSym">lov</span>?
With a contract, it is possible to rule out this possibility:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">version 2 rev. a</span></span></p><blockquote class="Rfilecontent"><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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.1" 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="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.1" 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">argmax</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">lov</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._and%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._pair%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">pair?</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><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">r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">r</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">r</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._and%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._memq%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">memq</a></span><span class="hspace"> </span><span class="RktSym">r</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=for.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._for%252Fand%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">for/and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">v</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3e%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">>=</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">v</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></blockquote></div><div class="SIntrapara">The <span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._memq%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">memq</a></span> function ensures that <span class="RktSym">r</span> is <span style="font-style: italic">intensionally equal</span>
<span class="refelem"><span class="refcolumn"><span class="refcontent">That is, "pointer equality" for those who prefer to think at
the hardware level.</span></span></span> to one of the members of <span class="RktSym">lov</span>. Of course, a
moment’s worth of reflection shows that it is impossible to make up such a
value. Functions are opaque values in Racket and without applying a
function, it is impossible to determine whether some random input value
produces an output value or triggers some exception. So we ignore this
possibility from here on.</div></p><p><div class="SIntrapara">Version 2 formulates the overall sentiment of <span class="RktSym">argmax</span>’s
documentation, but it fails to bring across that the result is the
<span style="font-style: italic">first</span> element of the given list that maximizes the given function
<span class="RktSym">f</span>. Here is a version that communicates this second aspect of
the informal documentation:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">version 3</span></span></p><blockquote class="Rfilecontent"><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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.1" 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="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.1" 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">argmax</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">lov</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._and%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._pair%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">pair?</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><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">r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">r</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">r</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._and%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=for.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._for%252Fand%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">for/and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">v</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3e%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">>=</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">v</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._eq%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">eq?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">first</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Flist..rkt%2529._memf%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">memf</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">v</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">v</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym">r</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></blockquote></div><div class="SIntrapara">That is, the <span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Flist..rkt%2529._memf%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">memf</a></span> function determines the first element of
<span class="RktSym">lov</span> whose value under <span class="RktSym">f</span> is equal to <span class="RktSym">r</span>’s value
under <span class="RktSym">f</span>. If this element is intensionally equal to <span class="RktSym">r</span>,
the result of <span class="RktSym">argmax</span> is correct.</div></p><p>This second refinement step introduces two problems. First, both conditions
recompute the values of <span class="RktSym">f</span> for all elements of <span class="RktSym">lov</span>. Second,
the contract is now quite difficult to read. Contracts should have a concise
formulation that a client can comprehend with a simple scan. Let us
eliminate the readability problem with two auxiliary functions that have
reasonably meaningful names:</p><p><div class="SIntrapara"><blockquote class="SCodeFlow"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">version 3 rev. a</span></span></p><blockquote class="Rfilecontent"><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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.1" 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="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.1" 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">argmax</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">lov</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._and%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._pair%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">pair?</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><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">r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">r</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">r</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._and%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">is-first-max?</span><span class="hspace"> </span><span class="RktSym">r</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">dominates-all</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">where</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt"><span class="stt"><span class="RktSym">f@r</span> is greater or equal to all <span class="RktPn">(</span><span class="RktSym">f</span><span class="stt"> </span><span class="RktSym">v</span><span class="RktPn">)</span> for <span class="RktSym">v</span> in <span class="RktSym">lov</span></span></span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">dominates-all</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=for.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._for%252Fand%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">for/and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">v</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3e%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">>=</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">v</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"><span class="stt"><span class="RktSym">r</span> is <span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._eq%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">eq?</a></span> to the first element <span class="RktSym">v</span> of <span class="RktSym">lov</span>
for which <span class="RktPn">(</span><span class="RktSym">pred?</span><span class="stt"> </span><span class="RktSym">v</span><span class="RktPn">)</span></span></span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">is-first-max?</span><span class="hspace"> </span><span class="RktSym">r</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._eq%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">eq?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">first</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Flist..rkt%2529._memf%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">memf</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">v</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">v</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">r</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></blockquote></div><div class="SIntrapara">The names of the two predicates express their functionality and, in
principle, render it unnecessary to read their definitions.</div></p><p>This step leaves us with the problem of the newly introduced inefficiency.
To avoid the recomputation of <span class="RktPn">(</span><span class="RktSym">f</span><span class="stt"> </span><span class="RktSym">v</span><span class="RktPn">)</span> for all <span class="RktSym">v</span> on
<span class="RktSym">lov</span>, we change the contract so that it computes these values and
reuses them as needed:</p><p><div class="SIntrapara"><blockquote class="SCodeFlow"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">version 3 rev. b</span></span></p><blockquote class="Rfilecontent"><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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.1" 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="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.1" 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">argmax</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">lov</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._and%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._pair%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">pair?</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><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">r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">r</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">r</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">flov</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fmap..rkt%2529._map%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">map</a></span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._and%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">is-first-max?</span><span class="hspace"> </span><span class="RktSym">r</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fmap..rkt%2529._map%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">map</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list</a></span><span class="hspace"> </span><span class="RktSym">lov</span><span class="hspace"> </span><span class="RktSym">flov</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">dominates-all</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">flov</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">where</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt"><span class="stt"><span class="RktSym">f@r</span> is greater or equal to all <span class="RktSym">f@v</span> in <span class="RktSym">flov</span></span></span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">dominates-all</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">flov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=for.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._for%252Fand%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">for/and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">f@v</span><span class="hspace"> </span><span class="RktSym">flov</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3e%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">>=</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">f@v</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"><span class="stt"><span class="RktSym">r</span> is <span class="RktPn">(</span><span class="RktSym">first</span><span class="stt"> </span><span class="RktSym">x</span><span class="RktPn">)</span> for the first
<span class="RktSym">x</span> in <span class="RktSym">lov+flov</span> s.t. <span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym">second</span><span class="stt"> </span><span class="RktSym">x</span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym">f@r</span><span class="RktPn">)</span></span></span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">is-first-max?</span><span class="hspace"> </span><span class="RktSym">r</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">lov+flov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">fst</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">first</span><span class="hspace"> </span><span class="RktSym">lov+flov</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._if%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">if</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">second</span><span class="hspace"> </span><span class="RktSym">fst</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._eq%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">eq?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">first</span><span class="hspace"> </span><span class="RktSym">fst</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">r</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">is-first-max?</span><span class="hspace"> </span><span class="RktSym">r</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">rest</span><span class="hspace"> </span><span class="RktSym">lov+flov</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></blockquote></div><div class="SIntrapara">Now the predicate on the result once again computes all values of <span class="RktSym">f</span>
for elements of <span class="RktSym">lov</span> once.</div></p><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>The word "eager" comes from the literature on the linguistics
of contracts.</p></blockquote></blockquote></blockquote><p>Version 3 may still be too eager when it comes to calling <span class="RktSym">f</span>. While
Racket’s <span class="RktSym">argmax</span> always calls <span class="RktSym">f</span> no matter how many items
<span class="RktSym">lov</span> contains, let us imagine for illustrative purposes that our
own implementation first checks whether the list is a singleton. If so,
the first element would be the only element of <span class="RktSym">lov</span> and in that
case there would be no need to compute <span class="RktPn">(</span><span class="RktSym">f</span><span class="stt"> </span><span class="RktSym">r</span><span class="RktPn">)</span>.
<span class="refelem"><span class="refcolumn"><span class="refcontent">The <span class="RktSym">argmax</span> of Racket implicitly argues that it not
only promises the first value that maximizes <span class="RktSym">f</span> over <span class="RktSym">lov</span>
but also that <span class="RktSym">f</span> produces/produced a value for the result.</span></span></span>
As a matter of fact, since <span class="RktSym">f</span> may diverge or raise an exception
for some inputs, <span class="RktSym">argmax</span> should avoid calling <span class="RktSym">f</span> when
possible.</p><p>The following contract demonstrates how a higher-order dependent contract
needs to be adjusted so as to avoid being over-eager:</p><p><div class="SIntrapara"><blockquote class="SCodeFlow"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">version 4</span></span></p><blockquote class="Rfilecontent"><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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=index.html&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">argmax</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._if%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">if</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">empty?</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">rest</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">first</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">...</a></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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._provide%2529%2529&version=6.1" 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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=attaching-contracts-to-values.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._contract-out%2529%2529&version=6.1" 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">argmax</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3ei%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span>i</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=function-contracts.html%23%2528form._%2528%2528lib._racket%252Fcontract%252Fbase..rkt%2529._-%7E3e%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._any%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">any/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">real?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktSym">lov</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=data-structure-contracts.html%23%2528def._%2528%2528lib._racket%252Fcontract%252Fprivate%252Fmisc..rkt%2529._and%252Fc%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">and/c</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._pair%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">pair?</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list?</a></span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><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">r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=lambda.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._lambda%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">r</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._cond%2529%2529&version=6.1" 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">empty?</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">rest</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._eq%7E3f%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">eq?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">first</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">r</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._else%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">else</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">r</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">flov</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fmap..rkt%2529._map%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">map</a></span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">lov</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="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._and%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">is-first-max?</span><span class="hspace"> </span><span class="RktSym">r</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fmap..rkt%2529._map%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">map</a></span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=pairs.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._list%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">list</a></span><span class="hspace"> </span><span class="RktSym">lov</span><span class="hspace"> </span><span class="RktSym">flov</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">dominates-all</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">flov</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><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">where</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt"><span class="stt"><span class="RktSym">f@r</span> is greater or equal to all <span class="RktSym">f@v</span> in <span class="RktSym">flov</span></span></span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">dominates-all</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">lov</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.1" 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"><span class="stt"><span class="RktSym">r</span> is <span class="RktPn">(</span><span class="RktSym">first</span><span class="stt"> </span><span class="RktSym">x</span><span class="RktPn">)</span> for the first
<span class="RktSym">x</span> in <span class="RktSym">lov+flov</span> s.t. <span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym">second</span><span class="stt"> </span><span class="RktSym">x</span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym">f@r</span><span class="RktPn">)</span></span></span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">is-first-max?</span><span class="hspace"> </span><span class="RktSym">r</span><span class="hspace"> </span><span class="RktSym">f@r</span><span class="hspace"> </span><span class="RktSym">lov+flov</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=stx-patterns.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fstxcase-scheme..rkt%2529._......%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">...</a></span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></blockquote></div><div class="SIntrapara">Note that such considerations don’t apply to the world of first-order
contracts. Only a higher-order (or lazy) language forces the programmer to
express contracts with such precision.</div></p><p>The problem of diverging or exception-raising functions should alert the
reader to the even more general problem of functions with side-effects. If
the given function <span class="RktSym">f</span> has visible effects – say it logs its calls
to a file – then the clients of <span class="RktSym">argmax</span> will be able to observe
two sets of logs for each call to <span class="RktSym">argmax</span>. To be precise, if the
list of values contains more than one element, the log will contain two
calls of <span class="RktSym">f</span> per value on <span class="RktSym">lov</span>. If <span class="RktSym">f</span> is expensive
to compute, doubling the calls imposes a high cost.</p><p>To avoid this cost and to signal problems with overly eager contracts, a
contract system could record the i/o of contracted function arguments and
use these hashtables in the dependency specification. This is a topic of
on-going research in PLT. Stay tuned.</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="contracts-general-functions.html" title="backward to "7.3 Contracts on Functions in General"" data-pltdoc="x">← prev</a> <a href="contracts.html" title="up to "7 Contracts"" data-pltdoc="x">up</a> <a href="contracts-struct.html" title="forward to "7.5 Contracts on Structures"" data-pltdoc="x">next →</a></span> </div></div></div><div id="contextindicator"> </div></body></html>
|