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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><meta name="viewport" content="width=device-width, initial-scale=0.8"/><title>4.1 Equality</title><link rel="stylesheet" type="text/css" href="../scribble.css" title="default"/><link rel="stylesheet" type="text/css" href="extras.css" title="default"/><link rel="stylesheet" type="text/css" href="../racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-style.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../doc-site.css" title="default"/><script type="text/javascript" src="../scribble-common.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../doc-site.js"></script><script type="text/javascript" src="../local-redirect/local-redirect.js"></script><script type="text/javascript" src="../local-redirect/local-user-redirect.js"></script><!--[if IE 6]><style type="text/css">.SIEHidden { overflow: hidden; }</style><![endif]--></head><body id="doc-racket-lang-org"><div class="tocset"><div class="tocview"><div class="tocviewlist tocviewlisttopspace"><div class="tocviewtitle"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_0");">►</a></td><td></td><td><a href="index.html" class="tocviewlink" data-pltdoc="x">The Racket Reference</a></td></tr></table></div><div class="tocviewsublisttop" style="display: none;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1 </td><td><a href="model.html" class="tocviewlink" data-pltdoc="x">Language Model</a></td></tr><tr><td align="right">2 </td><td><a href="notation.html" class="tocviewlink" data-pltdoc="x">Notation for Documentation</a></td></tr><tr><td align="right">3 </td><td><a href="syntax.html" class="tocviewlink" data-pltdoc="x">Syntactic Forms</a></td></tr><tr><td align="right">4 </td><td><a href="data.html" class="tocviewselflink" data-pltdoc="x">Datatypes</a></td></tr><tr><td align="right">5 </td><td><a href="structures.html" class="tocviewlink" data-pltdoc="x">Structures</a></td></tr><tr><td align="right">6 </td><td><a href="mzlib_class.html" class="tocviewlink" data-pltdoc="x">Classes and Objects</a></td></tr><tr><td align="right">7 </td><td><a href="mzlib_unit.html" class="tocviewlink" data-pltdoc="x">Units</a></td></tr><tr><td align="right">8 </td><td><a href="contracts.html" class="tocviewlink" data-pltdoc="x">Contracts</a></td></tr><tr><td align="right">9 </td><td><a href="match.html" class="tocviewlink" data-pltdoc="x">Pattern Matching</a></td></tr><tr><td align="right">10 </td><td><a href="control.html" class="tocviewlink" data-pltdoc="x">Control Flow</a></td></tr><tr><td align="right">11 </td><td><a href="concurrency.html" class="tocviewlink" data-pltdoc="x">Concurrency and Parallelism</a></td></tr><tr><td align="right">12 </td><td><a href="Macros.html" class="tocviewlink" data-pltdoc="x">Macros</a></td></tr><tr><td align="right">13 </td><td><a href="input-and-output.html" class="tocviewlink" data-pltdoc="x">Input and Output</a></td></tr><tr><td align="right">14 </td><td><a href="security.html" class="tocviewlink" data-pltdoc="x">Reflection and Security</a></td></tr><tr><td align="right">15 </td><td><a href="os.html" class="tocviewlink" data-pltdoc="x">Operating System</a></td></tr><tr><td align="right">16 </td><td><a href="memory.html" class="tocviewlink" data-pltdoc="x">Memory Management</a></td></tr><tr><td align="right">17 </td><td><a href="unsafe.html" class="tocviewlink" data-pltdoc="x">Unsafe Operations</a></td></tr><tr><td align="right">18 </td><td><a href="running.html" class="tocviewli
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a few different kinds of equality by default, although <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> is
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preferred for most uses.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((quote._~23~25kernel)._equal~3f))"></a><span title="Provided from: racket/base, racket | Package: base"><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">equal?</a></span></span><span class="hspace"> </span><span class="RktVar">v1</span><span class="hspace"> </span><span class="RktVar">v2</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v1</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v2</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Two values are <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> if and only if they are <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span>,
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unless otherwise specified for a particular datatype.</div></p><p>Datatypes with further specification of <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> include
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strings, byte strings, pairs, mutable pairs, vectors, boxes, hash
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tables, and inspectable structures. In the last six cases, equality
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is recursively defined; if both <span class="RktVar">v1</span> and <span class="RktVar">v2</span> contain
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reference cycles, they are equal when the infinite unfoldings of the
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values would be equal. See also <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal+hash</a></span> and
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<span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._prop~3aimpersonator-of%29%29" class="RktValLink" data-pltdoc="x">prop:impersonator-of</a></span>.</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"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">no</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2A%29%29" class="RktValLink" data-pltdoc="x">*</a></span><span class="hspace"> </span><span class="RktVal">6</span><span class="hspace"> </span><span class="RktVal">7</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">42</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._expt%29%29" class="RktValLink" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">100</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._expt%29%29" class="RktValLink" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">100</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">2.0</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="let.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._let%29%29" class="RktStxLink" data-pltdoc="x">let</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="RktPn">(</span><span class="RktSym"><a href="mpairs.html#%28def._%28%28quote._~23~25kernel%29._mcons%29%29" class="RktValLink" data-pltdoc="x">mcons</a></
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equal independent of <span class="emph">mutations</span>. Generally, for to values to be equal-always, corresponding
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immutable values within <span class="RktVar">v1</span> and <span class="RktVar">v2</span> must be <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>,
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while corresponding mutable values within them must be <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>.</div></p><p>Two values <span class="RktVar">v1</span> and <span class="RktVar">v2</span> are <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span> if and only
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if there exists a third value <span class="RktVar">v3</span> such that <span class="RktVar">v1</span> and
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<span class="RktVar">v2</span> are both chaperones of <span class="RktVar">v3</span>, meaning
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<span class="RktPn">(</span><span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._chaperone-of~3f%29%29" class="RktValLink" data-pltdoc="x">chaperone-of?</a></span><span class="stt"> </span><span class="RktVar">v1</span><span class="stt"> </span><span class="RktVar">v3</span><span class="RktPn">)</span> and <span class="RktPn">(</span><span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._chaperone-of~3f%29%29" class="RktValLink" data-pltdoc="x">chaperone-of?</a></span><span class="stt"> </span><span class="RktVar">v2</span><span class="stt"> </span><span class="RktVar">v3</span><span class="RktPn">)</span> are both
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true.</p><p>For values that include no chaperones or other impersonators,
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<span class="RktVar">v1</span> and <span class="RktVar">v2</span> can be considered equal-always
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if they are <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>, except that corresponding mutable
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vectors, boxes, hash tables, strings, byte strings, <a href="mpairs.html#%28tech._mutable._pair%29" class="techoutside" data-pltdoc="x"><span class="techinside">mutable pairs</span></a>, and
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mutable structures within
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<span class="RktVar">v1</span> and <span class="RktVar">v2</span> must be <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>, and equality on structures
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can be specialized for <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span> through <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal-mode%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal-mode+hash</a></span>.</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"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">no</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2A%29%29" class="RktValLink" data-pltdoc="x">*</a></span><span class="hspace"> </span><span class="RktVal">6</span><span class="hspace"> </span><span class="RktVal">7</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">42</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._expt%29%29" class="RktValLink" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">100</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._expt%29%29" class="RktValLink" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">100</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">2.0</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span><span class="hspace"> </span><spa
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unless otherwise specified for a particular datatype.</div></p><p>The <a href="numbers.html#%28tech._number%29" class="techoutside" data-pltdoc="x"><span class="techinside">number</span></a> and <a href="characters.html#%28tech._character%29" class="techoutside" data-pltdoc="x"><span class="techinside">character</span></a> datatypes are the only ones for which
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<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span> differs from <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>. Two numbers are <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span> when
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they have the same exactness, precision, and are both equal and non-zero, both
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<span class="RktVal">+0.0</span>, both <span class="RktVal">+0.0f0</span>, both <span class="RktVal">-0.0</span>,
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both <span class="RktVal">-0.0f0</span>, both <span class="RktVal">+nan.0</span>, or both
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<span class="RktVal">+nan.f</span>—<wbr></wbr>considering real and imaginary components separately
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in the case of <a href="numbers.html#%28tech._complex._number%29" class="techoutside" data-pltdoc="x"><span class="techinside">complex numbers</span></a>. Two characters are <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span> when
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their <span class="RktSym"><a href="characters.html#%28def._%28%28quote._~23~25kernel%29._char-~3einteger%29%29" class="RktValLink" data-pltdoc="x">char->integer</a></span> results are equal.</p><p>Generally, <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span> is identical to <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> except that the former
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cannot recursively compare the contents of compound data types (such as lists
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and structs) and cannot be customized by user-defined data types. The use of
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<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span> is lightly discouraged in favor of <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>.</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"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">no</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2A%29%29" class="RktValLink" data-pltdoc="x">*</a></span><span class="hspace"> </span><span class="RktVal">6</span><span class="hspace"> </span><span class="RktVal">7</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">42</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._expt%29%29" class="RktValLink" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">100</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._expt%29%29" class="RktValLink" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">100</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">2.0</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="let.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._let%29%29" class="RktStxLink" data-pltdoc="x">let</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="RktPn">(</span><span c
|
||
|
|
object, <span class="RktVal">#f</span> otherwise. As a special case among <a href="numbers.html#%28tech._number%29" class="techoutside" data-pltdoc="x"><span class="techinside">numbers</span></a>,
|
||
|
|
two <a href="numbers.html#%28tech._fixnum%29" class="techoutside" data-pltdoc="x"><span class="techinside">fixnums</span></a> that are <span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3d%29%29" class="RktValLink" data-pltdoc="x">=</a></span> are also the same according
|
||
|
|
to <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>. See also <a href="Equality.html#%28part._model-eq%29" data-pltdoc="x">Object Identity and Comparisons</a>.</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"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">yes</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">no</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2A%29%29" class="RktValLink" data-pltdoc="x">*</a></span><span class="hspace"> </span><span class="RktVal">6</span><span class="hspace"> </span><span class="RktVal">7</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">42</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._expt%29%29" class="RktValLink" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">100</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._expt%29%29" class="RktValLink" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">100</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">2.0</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="let.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._let%29%29" class="RktStxLink" data-pltdoc="x">let</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="RktPn">(</span><span class="RktSym"><a href="mpairs.html#%28def._%28%28quote._~23~25kernel%29._mcons%29%
|
||
|
|
comparisons (which means that reference cycles are not handled
|
||
|
|
automatically). Non-<span class="RktVal">#f</span> results from <span class="RktVar">recur-proc</span> are
|
||
|
|
converted to <span class="RktVal">#t</span> before being returned by
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal?/recur</a></span>.</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"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal?/recur</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._lambda%29%29" class="RktStxLink" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal?/recur</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">1</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">1</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._lambda%29%29" class="RktStxLink" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal?/recur</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">#</span><span class="RktVal">(</span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">#</span><span class="RktVal">(</span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1.2</span><span class="hspace"> </span><span class="RktVal">3/4</span><span class="RktVal">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._lambda%29%29" class="RktStxLink" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3c~3d%29%29" class="RktValLink" data-pltdoc="x"><=</a></span><span class="hspace"> </span><span c
|
||
|
|
comparisons (which means that reference cycles are not handled
|
||
|
|
automatically). Non-<span class="RktVal">#f</span> results from <span class="RktVar">recur-proc</span> are
|
||
|
|
converted to <span class="RktVal">#t</span> before being returned by
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal-always?/recur</a></span>.</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"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal-always?/recur</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._lambda%29%29" class="RktStxLink" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal-always?/recur</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">1</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">(</span><span class="RktVal">1</span><span class="RktVal">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._lambda%29%29" class="RktStxLink" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">#f</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal-always?/recur</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="vectors.html#%28def._%28%28quote._~23~25kernel%29._vector-immutable%29%29" class="RktValLink" data-pltdoc="x">vector-immutable</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="vectors.html#%28def._%28%28quote._~23~25kernel%29._vector-immutable%29%29" class="RktValLink" data-pltdoc="x">vector-immutable</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1.2</span><span class="hspace"> </span><span class="RktVal">3/4</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._lambda%29%29" class="RktStxLink" data-pltdoc="x">lambda</a></span><span class="hspace"> </span><span class="RktPn">(</sp
|
||
|
|
<span class="RktVal">#t</span> when the values refer to the same <a href="eval-model.html#%28tech._object%29" class="techoutside" data-pltdoc="x"><span class="techinside">object</span></a>. This form
|
||
|
|
of equality is suitable for comparing objects that support imperative
|
||
|
|
update (e.g., to determine that the effect of modifying an object
|
||
|
|
through one reference is visible through another reference). Also, an
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span> test evaluates quickly, and <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>-based hashing
|
||
|
|
is more lightweight than <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>-based hashing in hash tables.</p><p>In some cases, however, <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span> is unsuitable as a comparison
|
||
|
|
operator, because the generation of <a href="eval-model.html#%28tech._object%29" class="techoutside" data-pltdoc="x"><span class="techinside">objects</span></a> is not clearly
|
||
|
|
defined. In particular, two applications of <span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2B%29%29" class="RktValLink" data-pltdoc="x">+</a></span> to the same two
|
||
|
|
exact integers may or may not produce results that are <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>,
|
||
|
|
although the results are always <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>. Similarly, evaluation
|
||
|
|
of a <span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._lambda%29%29" class="RktStxLink" data-pltdoc="x">lambda</a></span> form typically generates a new procedure
|
||
|
|
<a href="eval-model.html#%28tech._object%29" class="techoutside" data-pltdoc="x"><span class="techinside">object</span></a>, but it may re-use a procedure <a href="eval-model.html#%28tech._object%29" class="techoutside" data-pltdoc="x"><span class="techinside">object</span></a> previously
|
||
|
|
generated by the same source <span class="RktSym"><a href="lambda.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._lambda%29%29" class="RktStxLink" data-pltdoc="x">lambda</a></span> form.</p><p>The behavior of a datatype with respect to <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span> is generally
|
||
|
|
specified with the datatype and its associated procedures.</p><h5 x-source-module="(lib "scribblings/reference/reference.scrbl")" x-source-pkg="racket-doc" x-part-tag=""Equality_and_Hashing"">4.1.2<tt> </tt><a name="(part._.Equality_and_.Hashing)"></a>Equality and Hashing</h5><p>All comparable values have at least one <a name="(tech._hash._code)"></a><span style="font-style: italic">hash code</span> —<wbr></wbr> an arbitrary
|
||
|
|
integer (more specifically a <a href="numbers.html#%28tech._fixnum%29" class="techoutside" data-pltdoc="x"><span class="techinside">fixnum</span></a>) computed by applying a hash function
|
||
|
|
to the value. The defining property of these hash codes is that <span style="font-weight: bold">equal
|
||
|
|
values have equal hash codes</span>. Note that the reverse is not true: two unequal
|
||
|
|
values can still have equal hash codes. Hash codes are useful for various
|
||
|
|
indexing and comparison operations, especially in the implementation of
|
||
|
|
<a href="hashtables.html#%28tech._hash._table%29" class="techoutside" data-pltdoc="x"><span class="techinside">hash tables</span></a>. See <a href="hashtables.html" data-pltdoc="x">Hash Tables</a> for more information.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((quote._~23~25kernel)._equal-hash-code))"></a><span title="Provided from: racket/base, racket | Package: base"><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValDef RktValLink" data-pltdoc="x">equal-hash-code</a></span></span><span class="hspace"> </span><span class="RktVar">v</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._fixnum~3f%29%29" class="RktValLink" data-pltdoc="x">fixnum?</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns a <a href="Equality.html#%28tech._hash._code%29" class="techoutside" data-pltdoc="x"><span class="techinside">hash code</span></a> consistent with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>. For any two calls
|
||
|
|
with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> values, the returned number is the same. A hash code is
|
||
|
|
computed even when <span class="RktVar">v</span> contains a cycle through pairs, vectors, boxes,
|
||
|
|
and/or inspectable structure fields. Additionally, user-defined data types can
|
||
|
|
customize how this hash code is computed by implementing
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal+hash</a></span> or <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal-mode%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal-mode+hash</a></span>.</div></p><p>For any <span class="RktVar">v</span> that could be produced by <span class="RktSym"><a href="Reading.html#%28def._%28%28quote._~23~25kernel%29._read%29%29" class="RktValLink" data-pltdoc="x">read</a></span>, if <span class="RktSym">v2</span> is
|
||
|
|
produced by <span class="RktSym"><a href="Reading.html#%28def._%28%28quote._~23~25kernel%29._read%29%29" class="RktValLink" data-pltdoc="x">read</a></span> for the same input characters, the
|
||
|
|
<span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span><span class="stt"> </span><span class="RktVar">v</span><span class="RktPn">)</span> is the same as <span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span><span class="stt"> </span><span class="RktSym">v2</span><span class="RktPn">)</span> —<wbr></wbr>
|
||
|
|
even if <span class="RktVar">v</span> and <span class="RktSym">v2</span> do not exist at the same time (and therefore
|
||
|
|
could not be compared by calling <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>).</p><p class="SHistory">Changed in version 6.4.0.12 of package <span class="stt">base</span>: Strengthened guarantee for <span class="RktSym"><a href="Reading.html#%28def._%28%28quote._~23~25kernel%29._read%29%29" class="RktValLink" data-pltdoc="x">read</a></span>able values.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((quote._~23~25kernel)._equal-secondary-hash-code))"></a><span title="Provided from: racket/base, racket | Package: base"><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-secondary-hash-code%29%29" class="RktValDef RktValLink" data-pltdoc="x">equal-secondary-hash-code</a></span></span><span class="hspace"> </span><span class="RktVar">v</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._fixnum~3f%29%29" class="RktValLink" data-pltdoc="x">fixnum?</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Like <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span>, but computes a secondary <a href="Equality.html#%28tech._hash._code%29" class="techoutside" data-pltdoc="x"><span class="techinside">hash code</span></a>
|
||
|
|
suitable for use in double hashing.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((quote._~23~25kernel)._equal-always-hash-code))"></a><span title="Provided from: racket/base, racket | Package: base"><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always-hash-code%29%29" class="RktValDef RktValLink" data-pltdoc="x">equal-always-hash-code</a></span></span><span class="hspace"> </span><span class="RktVar">v</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._fixnum~3f%29%29" class="RktValLink" data-pltdoc="x">fixnum?</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns a <a href="Equality.html#%28tech._hash._code%29" class="techoutside" data-pltdoc="x"><span class="techinside">hash code</span></a> consistent with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span>. For any two
|
||
|
|
calls with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span> values, the returned number is the same.</div></p><p>As <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-always-hash-code</a></span> traverses <span class="RktVar">v</span>, immutable
|
||
|
|
values within <span class="RktVar">v</span> are hashed with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span>,
|
||
|
|
while mutable values within <span class="RktVar">v</span> are hashed with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq-hash-code%29%29" class="RktValLink" data-pltdoc="x">eq-hash-code</a></span>.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((quote._~23~25kernel)._equal-always-secondary-hash-code))"></a><span title="Provided from: racket/base, racket | Package: base"><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always-secondary-hash-code%29%29" class="RktValDef RktValLink" data-pltdoc="x">equal-always-secondary-hash-code</a></span></span><span class="hspace"> </span><span class="RktVar">v</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._fixnum~3f%29%29" class="RktValLink" data-pltdoc="x">fixnum?</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Like <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-always-hash-code</a></span>, but computes a secondary <a href="Equality.html#%28tech._hash._code%29" class="techoutside" data-pltdoc="x"><span class="techinside">hash code</span></a>
|
||
|
|
suitable for use in double hashing.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((quote._~23~25kernel)._eq-hash-code))"></a><span title="Provided from: racket/base, racket | Package: base"><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq-hash-code%29%29" class="RktValDef RktValLink" data-pltdoc="x">eq-hash-code</a></span></span><span class="hspace"> </span><span class="RktVar">v</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._fixnum~3f%29%29" class="RktValLink" data-pltdoc="x">fixnum?</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns a <a href="Equality.html#%28tech._hash._code%29" class="techoutside" data-pltdoc="x"><span class="techinside">hash code</span></a> consistent with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>. For any two calls with
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span> values, the returned number is the same.</div></p><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>Equal <a href="numbers.html#%28tech._fixnum%29" class="techoutside" data-pltdoc="x"><span class="techinside">fixnums</span></a> are always <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>.</p></blockquote></blockquote></blockquote><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((quote._~23~25kernel)._eqv-hash-code))"></a><span title="Provided from: racket/base, racket | Package: base"><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv-hash-code%29%29" class="RktValDef RktValLink" data-pltdoc="x">eqv-hash-code</a></span></span><span class="hspace"> </span><span class="RktVar">v</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._fixnum~3f%29%29" class="RktValLink" data-pltdoc="x">fixnum?</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns a <a href="Equality.html#%28tech._hash._code%29" class="techoutside" data-pltdoc="x"><span class="techinside">hash code</span></a> consistent with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span>. For any two calls
|
||
|
|
with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eqv~3f%29%29" class="RktValLink" data-pltdoc="x">eqv?</a></span> values, the returned number is the same.</div></p><h5 x-source-module="(lib "scribblings/reference/reference.scrbl")" x-source-pkg="racket-doc" x-part-tag=""Implementing_Equality_for_Custom_Types"">4.1.3<tt> </tt><a name="(part._.Implementing_.Equality_for_.Custom_.Types)"></a>Implementing Equality for Custom Types</h5><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._racket/private/base..rkt)._gen~3aequal+hash))"></a><span title="Provided from: racket/base, racket | Package: base"><span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal%2Bhash%29%29" class="RktValDef RktValLink" data-pltdoc="x">gen:equal+hash</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span></p></blockquote></td></tr></table></blockquote></div><div class="SIntrapara">A <a href="struct-generics.html#%28tech._generic._interface%29" class="techoutside" data-pltdoc="x"><span class="techinside">generic interface</span></a> (see <a href="struct-generics.html" data-pltdoc="x">Generic Interfaces</a>) for types that can
|
||
|
|
be compared for equality using <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>. The following methods must be
|
||
|
|
implemented:</div></p><ul><li><p><span class="RktVar">equal-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="RktPn">)</span> —<wbr></wbr>
|
||
|
|
tests whether the first two arguments are equal, where both values are
|
||
|
|
instances of the structure type to which the generic interface is associated
|
||
|
|
(or a subtype of the structure type).</p><p>The third argument is an <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> predicate to use for
|
||
|
|
recursive equality checks; use the given predicate instead of
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> to ensure that data cycles are handled
|
||
|
|
properly and to work with <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal?/recur</a></span> (but beware
|
||
|
|
that an arbitrary function can be provided to
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal?/recur</a></span> for recursive checks, which means that
|
||
|
|
arguments provided to the predicate might be exposed to
|
||
|
|
arbitrary code).</p><p>The <span class="RktVar">equal-proc</span> is called for a pair of structures
|
||
|
|
only when they are not <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>, and only when they both
|
||
|
|
have a <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal+hash</a></span> value inherited from the same
|
||
|
|
structure type. With this strategy, the order in which
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> receives two structures does not matter. It
|
||
|
|
also means that, by default, a structure sub-type inherits the
|
||
|
|
equality predicate of its parent, if any.</p></li><li><p><span class="RktVar">hash-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span> —<wbr></wbr>
|
||
|
|
computes a hash code for the given structure, like <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span>.
|
||
|
|
The first argument is an instance of the structure type (or one of its
|
||
|
|
subtypes) to which the generic interface is associated.</p><p>The second argument is an <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span>-like procedure to use for
|
||
|
|
recursive hash-code computation; use the given procedure instead of
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span> to ensure that data cycles are handled properly.</p><p>Although the result of <span class="RktVar">hash-proc</span> can be any exact
|
||
|
|
integer, it will be truncated for most purposes to a <a href="numbers.html#%28tech._fixnum%29" class="techoutside" data-pltdoc="x"><span class="techinside">fixnum</span></a>
|
||
|
|
(e.g., for the result of <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span>). Roughly,
|
||
|
|
truncation uses <span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._bitwise-and%29%29" class="RktValLink" data-pltdoc="x">bitwise-and</a></span> to take the lower bits of the
|
||
|
|
number. Thus, variation in the hash-code computation should be
|
||
|
|
reflected in the fixnum-compatible bits of <span class="RktVar">hash-proc</span>’s
|
||
|
|
result. Consumers of a hash code are expected to use variation
|
||
|
|
within the fixnum range appropriately, and producers are <span class="emph">not</span>
|
||
|
|
responsible to reflect variation in hash codes across the full
|
||
|
|
range of bits that fit within a fixnum.</p></li><li><p><span class="RktVar">hash2-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span> —<wbr></wbr>
|
||
|
|
computes a secondary hash code for the given structure. This procedure is
|
||
|
|
like <span class="RktVar">hash-proc</span>, but analogous to
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-secondary-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-secondary-hash-code</a></span>.</p></li></ul><p>Take care to ensure that <span class="RktVar">hash-proc</span> and <span class="RktVar">hash2-proc</span>
|
||
|
|
are consistent with <span class="RktVar">equal-proc</span>. Specifically,
|
||
|
|
<span class="RktVar">hash-proc</span> and <span class="RktVar">hash2-proc</span> should produce the same
|
||
|
|
value for any two structures for which <span class="RktVar">equal-proc</span> produces a
|
||
|
|
true value.</p><p>The <span class="RktVar">equal-proc</span> is not only used for
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>, it is also used for <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal?/recur</a></span>,
|
||
|
|
and <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._impersonator-of~3f%29%29" class="RktValLink" data-pltdoc="x">impersonator-of?</a></span>. Furthermore, if the structure type
|
||
|
|
has no mutable fields, <span class="RktVar">equal-proc</span> is used for <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span>, and
|
||
|
|
<span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._chaperone-of~3f%29%29" class="RktValLink" data-pltdoc="x">chaperone-of?</a></span>. Likewise <span class="RktVar">hash-proc</span> and
|
||
|
|
<span class="RktVar">hash2-proc</span> are used for
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-always-hash-code</a></span> and
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always-secondary-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-always-secondary-hash-code</a></span>, respectively, when
|
||
|
|
the structure type has no mutable fields.
|
||
|
|
Instances of these methods should follow the guidelines in
|
||
|
|
<a href="Equality.html#%28part._.Honest_.Custom_.Equality%29" data-pltdoc="x">Honest Custom Equality</a> to implement all of these
|
||
|
|
operations reasonably. In particular, these methods should
|
||
|
|
not access mutable data unless the struct is declared
|
||
|
|
mutable.</p><p>When a structure type has no <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal+hash</a></span> or
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal-mode%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal-mode+hash</a></span> implementation, then
|
||
|
|
transparent structures (i.e., structures with an <a href="inspectors.html#%28tech._inspector%29" class="techoutside" data-pltdoc="x"><span class="techinside">inspector</span></a> that
|
||
|
|
is controlled by the current <a href="inspectors.html#%28tech._inspector%29" class="techoutside" data-pltdoc="x"><span class="techinside">inspector</span></a>) are <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>
|
||
|
|
when they are instances of the same structure type (not counting
|
||
|
|
sub-types), and when they have <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> field values. For
|
||
|
|
transparent structures, <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span> and
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-secondary-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-secondary-hash-code</a></span> (in the case of no mutable fields)
|
||
|
|
derive hash code using the field
|
||
|
|
values. For a transparent structure type with at least one mutable field,
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span> is the same as <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>, and an
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-secondary-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-secondary-hash-code</a></span> result is based only on <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq-hash-code%29%29" class="RktValLink" data-pltdoc="x">eq-hash-code</a></span>.
|
||
|
|
For opaque structure types, <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> is the same as
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq~3f%29%29" class="RktValLink" data-pltdoc="x">eq?</a></span>, and <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-hash-code</a></span> and
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-secondary-hash-code%29%29" class="RktValLink" data-pltdoc="x">equal-secondary-hash-code</a></span> results are based only on
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq-hash-code%29%29" class="RktValLink" data-pltdoc="x">eq-hash-code</a></span>. If a structure has a <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._prop~3aimpersonator-of%29%29" class="RktValLink" data-pltdoc="x">prop:impersonator-of</a></span>
|
||
|
|
property, then the <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._prop~3aimpersonator-of%29%29" class="RktValLink" data-pltdoc="x">prop:impersonator-of</a></span> property takes precedence over
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal+hash</a></span> if the property value’s procedure returns a
|
||
|
|
non-<span class="RktVal">#f</span> value when applied to the structure.</p><p><div class="SIntrapara">Examples:</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">farm=?</span><span class="hspace"> </span><span class="RktSym">farm1</span><span class="hspace"> </span><span class="RktSym">farm2</span><span class="hspace"> </span><span class="RktSym">recursive-equal?</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="if.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._and%29%29" class="RktStxLink" data-pltdoc="x">and</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3d%29%29" class="RktValLink" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">farm-apples</span><span class="hspace"> </span><span class="RktSym">farm1</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">farm-apples</span><span class="hspace"> </span><span class="RktSym">farm2</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="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3d%29%29" class="RktValLink" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">farm-oranges</span><span class="hspace"> </span><span class="RktSym">farm1</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">farm-oranges</span><span class="hspace"> </span><span class="RktSym">farm2</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="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3d%29%29" class="RktValLink" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">farm-sheep</span><span class="hspace"> </span><span class="RktSym">farm1</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">farm-sheep</span><span class="hspace"> </span><span class="RktSym">farm2</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">farm-hash-code</span><span class="hspace"> </span><span class="RktSym">farm</span><span class="hspace"> </span><span class="RktSym">recursive-equal-hash</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2B%29%29" class="RktValLink" data-pltdoc="x">+<
|
||
|
|
may specify differences between <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> and <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span>.
|
||
|
|
The following methods must be implemented:</div></p><ul><li><p><span class="RktVar">equal-mode-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="RktPn">)</span> —<wbr></wbr>
|
||
|
|
the first two arguments are the values to compare, the third argument is an
|
||
|
|
equality function to use for recursive comparisons, and the last argument is
|
||
|
|
the mode: <span class="RktVal">#t</span> for an <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> or <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._impersonator-of~3f%29%29" class="RktValLink" data-pltdoc="x">impersonator-of?</a></span>
|
||
|
|
comparison or <span class="RktVal">#f</span> for an <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span> or
|
||
|
|
<span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._chaperone-of~3f%29%29" class="RktValLink" data-pltdoc="x">chaperone-of?</a></span> comparison.</p></li><li><p><span class="RktVar">hash-mode-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span> —<wbr></wbr>
|
||
|
|
the first argument is the value to compute a hash code for, the second
|
||
|
|
argument is a hashing function to use for recursive hashing, and the last
|
||
|
|
argument is the mode: <span class="RktVal">#t</span> for <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> hashing or <span class="RktVal">#f</span>
|
||
|
|
for <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span> hashing.</p></li></ul><p>The <span class="RktVar">hash-mode-proc</span> implementation is used both for a
|
||
|
|
primary hash code and secondary hash code.</p><p>When implementing these methods, follow the guidelines in
|
||
|
|
<a href="Equality.html#%28part._.Honest_.Custom_.Equality%29" data-pltdoc="x">Honest Custom Equality</a>. In particular, these
|
||
|
|
methods should only access mutable data if the “mode” argument
|
||
|
|
is true to indicate <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> or <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._impersonator-of~3f%29%29" class="RktValLink" data-pltdoc="x">impersonator-of?</a></span>.</p><p><div class="SIntrapara">Implementing <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal-mode%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal-mode+hash</a></span> is most useful for types that
|
||
|
|
specify differences between <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> and <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span>, such
|
||
|
|
as a structure type that wraps mutable data with getter and setter procedures:
|
||
|
|
</div><div class="SIntrapara"><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"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">get</span><span class="hspace"> </span><span class="RktSym">gs</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">(</span><span class="RktSym">getset-getter</span><span class="hspace"> </span><span class="RktSym">gs</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="sets.html#%28def._%28%28lib._racket%2Fset..rkt%29._set%29%29" class="RktValLink" data-pltdoc="x">set</a></span><span class="hspace"> </span><span class="RktSym">gs</span><span class="hspace"> </span><span class="RktSym"><a href="objcreation.html#%28form._%28%28lib._racket%2Fprivate%2Fclass-internal..rkt%29._new%29%29" class="RktStxLink" data-pltdoc="x">new</a></span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">(</span><span class="RktSym">getset-setter</span><span class="hspace"> </span><span class="RktSym">gs</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="objcreation.html#%28form._%28%28lib._racket%2Fprivate%2Fclass-internal..rkt%29._new%29%29" class="RktStxLink" data-pltdoc="x">new</a></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="define-struct.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._struct%29%29" class="RktStxLink" data-pltdoc="x">struct</a></span><span class="hspace"> </span><span class="RktSym">getset</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">getter</span><span class="hspace"> </span><span class="RktSym">setter</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">#:methods</span><span class="hspace"> </span><span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal-mode%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal-mode+hash</a></span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">equal-mode-proc</span><span class="hspace"> </span><span class="RktSym">self</span><span class="hspace"> </span><span class="RktSym">other</span><span class="hspace"> </span><span class="RktSym">rec</span><span class="hspace"> </span><span class="RktSym">mode</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="if.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._and%29%29" class="RktStxLink" data-pltdoc="x">and</a></span><span class="hspace"> </span><span clas
|
||
|
|
that supplies an equality predicate and hashing functions for a structure
|
||
|
|
type. Using the <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._prop~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">prop:equal+hash</a></span> property is an alternative to
|
||
|
|
using the <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal+hash</a></span> or <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal-mode%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal-mode+hash</a></span>
|
||
|
|
<a href="struct-generics.html#%28tech._generic._interface%29" class="techoutside" data-pltdoc="x"><span class="techinside">generic interface</span></a>.</div></p><p>A <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._prop~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">prop:equal+hash</a></span> property value is a list of either three
|
||
|
|
procedures <span class="RktPn">(</span><span class="RktSym"><a href="pairs.html#%28def._%28%28quote._~23~25kernel%29._list%29%29" class="RktValLink" data-pltdoc="x">list</a></span><span class="stt"> </span><span class="RktVar">equal-proc</span><span class="stt"> </span><span class="RktVar">hash-proc</span><span class="stt"> </span><span class="RktVar">hash2-proc</span><span class="RktPn">)</span> or two
|
||
|
|
procedures <span class="RktPn">(</span><span class="RktSym"><a href="pairs.html#%28def._%28%28quote._~23~25kernel%29._list%29%29" class="RktValLink" data-pltdoc="x">list</a></span><span class="stt"> </span><span class="RktVar">equal-mode-proc</span><span class="stt"> </span><span class="RktVar">hash-mode-proc</span><span class="RktPn">)</span>:</p><ul><li><p>The three-procedure case corresponds to the procedures of
|
||
|
|
<span class="RktSym">gen:equal-hash</span>:</p><ul><li><p><span class="RktVar">equal-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="RktPn">)</span></p></li><li><p><span class="RktVar">hash-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span></p></li><li><p><span class="RktVar">hash2-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span
|
||
|
|
<span class="RktSym">gen:equal-mode-hash</span>:</p><ul><li><p><span class="RktVar">equal-mode-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="RktPn">)</span></p></li><li><p><span class="RktVar">hash-mode-proc</span><span class="stt"> </span><span class="RktSym">:</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="function-contracts.html#%28form._%28%28lib._racket%2Fcontract%2Fbase..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-></span></a></span><span class="stt"> </span><span class="RktSym"><a href="data-structure-contracts.html#%28def._%28%28lib._racket%2Fcontract%2Fprivate%2Fmisc..rkt%29._any%2Fc%29%29" class="RktValLink" data-pltdoc="x">any/c</a></span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="booleans.html#%28def._%28%28quote._~23~25kernel%29._boolean~3f%29%29" class="RktValLink" data-pltdoc="x">boolean?</a></span><span class="stt"> </span><span class="RktSym"><a href="number-types.html#%28def._%28%28quote._~23~25kernel%29._exact-integer~3f%29%29" class="RktValLink" data-pltdoc="x">exact-integer?</a></span><span class="RktPn">)</span></p></li></ul></li></ul><p>When implementing these methods, follow the guidelines in
|
||
|
|
<a href="Equality.html#%28part._.Honest_.Custom_.Equality%29" data-pltdoc="x">Honest Custom Equality</a>. In particular, these
|
||
|
|
methods should only access mutable data if the struct is
|
||
|
|
declared mutable or the mode is true.</p><p class="SHistory">Changed in version 8.5.0.3 of package <span class="stt">base</span>: Added support for two-procedure values to customize <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span>.</p><h5 x-source-module="(lib "scribblings/reference/reference.scrbl")" x-source-pkg="racket-doc" x-part-tag=""Honest_Custom_Equality"">4.1.4<tt> </tt><a name="(part._.Honest_.Custom_.Equality)"></a>Honest Custom Equality</h5><p>Since the <span class="RktVar">equal-proc</span> or <span class="RktVar">equal-mode-proc</span>
|
||
|
|
is used for more than just <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span>, instances of
|
||
|
|
them should follow certain guidelines to make sure that they work
|
||
|
|
correctly for <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span>, <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._chaperone-of~3f%29%29" class="RktValLink" data-pltdoc="x">chaperone-of?</a></span>,
|
||
|
|
and <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._impersonator-of~3f%29%29" class="RktValLink" data-pltdoc="x">impersonator-of?</a></span>.</p><p>Due to the differences between these operations, avoid
|
||
|
|
calling <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> within them. Instead, use the third
|
||
|
|
argument to “recur” on the pieces, which allows
|
||
|
|
<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%2Frecur%29%29" class="RktValLink" data-pltdoc="x">equal?/recur</a></span> to work properly, lets the other
|
||
|
|
operations behave in their own distinct ways on the pieces,
|
||
|
|
and enables some cycle detection.</p><p><table cellspacing="0" cellpadding="0" border="1" cellpadding="1"><tr><td width="500" align="left" valign="top"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">good</span></span></p><blockquote class="Rfilecontent"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">equal-proc</span><span class="hspace"> </span><span class="RktSym">self</span><span class="hspace"> </span><span class="RktSym">other</span><span class="hspace"> </span><span class="RktSym">rec</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">rec</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">self</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">other</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></td><td width="500" align="left" valign="top"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">bad</span></span></p><blockquote class="Rfilecontent"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">equal-proc</span><span class="hspace"> </span><span class="RktSym">self</span><span class="hspace"> </span><span class="RktSym">other</span><span class="hspace"> </span><span class="RktSym">rec</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">self</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">other</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></td></tr></table></p><p>The operations <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> and <span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span>
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should be symmetric, so <span class="RktVar">equal-proc</span> instances
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should not change their answer when the arguments swap:</p><p><table cellspacing="0" cellpadding="0" border="1" cellpadding="1"><tr><td width="500" align="left" valign="top"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">good</span></span></p><blockquote class="Rfilecontent"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">equal-proc</span><span class="hspace"> </span><span class="RktSym">self</span><span class="hspace"> </span><span class="RktSym">other</span><span class="hspace"> </span><span class="RktSym">rec</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">rec</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">self</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">other</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></td><td width="500" align="left" valign="top"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">bad</span></span></p><blockquote class="Rfilecontent"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">equal-proc</span><span class="hspace"> </span><span class="RktSym">self</span><span class="hspace"> </span><span class="RktSym">other</span><span class="hspace"> </span><span class="RktSym">rec</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3c~3d%29%29" class="RktValLink" data-pltdoc="x"><=</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">self</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">other</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></td></tr></table></p><p>However, the operations <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._chaperone-of~3f%29%29" class="RktValLink" data-pltdoc="x">chaperone-of?</a></span> and
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<span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._impersonator-of~3f%29%29" class="RktValLink" data-pltdoc="x">impersonator-of?</a></span> are <span class="emph">not</span> symmetric, so when
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calling the third argument to “recur” on pieces, pass the
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pieces in the same order they came in:</p><p><table cellspacing="0" cellpadding="0" border="1" cellpadding="1"><tr><td width="500" align="left" valign="top"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">good</span></span></p><blockquote class="Rfilecontent"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">equal-proc</span><span class="hspace"> </span><span class="RktSym">self</span><span class="hspace"> </span><span class="RktSym">other</span><span class="hspace"> </span><span class="RktSym">rec</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">rec</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">self</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">other</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></td><td width="500" align="left" valign="top"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">bad</span></span></p><blockquote class="Rfilecontent"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">equal-proc</span><span class="hspace"> </span><span class="RktSym">self</span><span class="hspace"> </span><span class="RktSym">other</span><span class="hspace"> </span><span class="RktSym">rec</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">rec</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">other</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">fish-size</span><span class="hspace"> </span><span class="RktSym">self</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote></blockquote></td></tr></table></p><p>Mutable structs will only use the custom equality for
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<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal~3f%29%29" class="RktValLink" data-pltdoc="x">equal?</a></span> and <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._impersonator-of~3f%29%29" class="RktValLink" data-pltdoc="x">impersonator-of?</a></span>, so that
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<span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._equal-always~3f%29%29" class="RktValLink" data-pltdoc="x">equal-always?</a></span> and <span class="RktSym"><a href="chaperones.html#%28def._%28%28quote._~23~25kernel%29._chaperone-of~3f%29%29" class="RktValLink" data-pltdoc="x">chaperone-of?</a></span> don’t
|
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change on mutation. Structs that represent mutable data
|
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should either be declared mutable, or use
|
||
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<span class="RktVar">equal-mode-proc</span> from <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal-mode%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal-mode+hash</a></span>
|
||
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instead of <span class="RktVar">equal-proc</span> from <span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal+hash</a></span>,
|
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and only access mutable data when the mode is true:</p><p><table cellspacing="0" cellpadding="0" border="1" cellpadding="1"><tr><td width="500" align="left" valign="top"><blockquote class="Rfilebox"><p class="Rfiletitle"><span class="Rfilename"><span class="stt">good</span></span></p><blockquote class="Rfilecontent"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="define-struct.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._struct%29%29" class="RktStxLink" data-pltdoc="x">struct</a></span><span class="hspace"> </span><span class="RktSym">mcell</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">value</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">#:mutable</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">#:methods</span><span class="hspace"> </span><span class="RktSym"><a href="Equality.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._gen~3aequal%2Bhash%29%29" class="RktValLink" data-pltdoc="x">gen:equal+hash</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">equal-proc</span><span class="hspace"> </span><span class="RktSym">self</span><span class="hspace"> </span><span class="RktSym">other</span><span class="hspace"> </span><span class="RktSym">rec</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">rec</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">mcell-value</span><span class="hspace"> </span><span class="RktSym">self</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">mcell-value</span><span class="hspace"> </span><span class="RktSym">other</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="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">hash-proc</span><span class="hspace"> </span><span class="RktSym">self</span><span class="hspace"> </span><span class="RktSym">rec</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2B%29%29" class="RktValLink" data-pltdoc="x">+</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="Equality.html#%28def._%28%28quote._~23~25kernel%29._eq-hash-code%29%29" class="RktValLink" data-pltdoc="x">eq-hash-code</a></span><span class="hspace"> </span><span class="RktSym">struct:mcell</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">rec</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">mcell-value</span><span class="hspace"> </span><span class="RktSym">self</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="define.html#%28form._%28%28lib._racket%2Fprivate%2Fbas
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