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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><title>2 Predicates</title><link rel="stylesheet" type="text/css" href="../scribble.css" title="default"/><link rel="stylesheet" type="text/css" href="../racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-style.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../doc-site.css" title="default"/><script type="text/javascript" src="../scribble-common.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../doc-site.js"></script><script type="text/javascript" src="../local-redirect/local-redirect.js"></script><script type="text/javascript" src="../local-redirect/local-user-redirect.js"></script><!--[if IE 6]><style type="text/css">.SIEHidden { overflow: hidden; }</style><![endif]--></head><body id="doc-racket-lang-org"><div class="tocset"><div class="tocview"><div class="tocviewlist tocviewlisttopspace"><div class="tocviewtitle"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_0");">▼</a></td><td></td><td><a href="index.html" class="tocviewlink" data-pltdoc="x">Racklog:<span class="mywbr"> </span> Prolog-<wbr></wbr>Style Logic Programming</a></td></tr></table></div><div class="tocviewsublisttop" style="display: block;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1 </td><td><a href="simple.html" class="tocviewlink" data-pltdoc="x">Simple Goals and Queries</a></td></tr><tr><td align="right">2 </td><td><a href="" class="tocviewselflink" data-pltdoc="x">Predicates</a></td></tr><tr><td align="right">3 </td><td><a href="racket-w-logic.html" class="tocviewlink" data-pltdoc="x">Using Conventional Racket Expressions in Racklog</a></td></tr><tr><td align="right">4 </td><td><a href="backtracking.html" class="tocviewlink" data-pltdoc="x">Backtracking</a></td></tr><tr><td align="right">5 </td><td><a href="unification.html" class="tocviewlink" data-pltdoc="x">Unification</a></td></tr><tr><td align="right">6 </td><td><a href="and-or.html" class="tocviewlink" data-pltdoc="x">Conjuctions and Disjunctions</a></td></tr><tr><td align="right">7 </td><td><a href="lv-manip.html" class="tocviewlink" data-pltdoc="x">Manipulating Racklog Variables</a></td></tr><tr><td align="right">8 </td><td><a href="cut.html" class="tocviewlink" data-pltdoc="x">The Cut (<span class="RktSym"><span class="RktStxLink">!</span></span>)</a></td></tr><tr><td align="right">9 </td><td><a href="set-of.html" class="tocviewlink" data-pltdoc="x">Set Predicates</a></td></tr><tr><td align="right">10 </td><td><a href="Racklog_Module_Language.html" class="tocviewlink" data-pltdoc="x">Racklog Module Language</a></td></tr><tr><td align="right">11 </td><td><a href="glossary.html" class="tocviewlink" data-pltdoc="x">Glossary of Racklog Primitives</a></td></tr><tr><td align="right"></td><td><a href="doc-bibliography.html" class="tocviewlink" data-pltdoc="x">Bibliography</a></td></tr></table></div></div><div class="tocviewlist"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_1");">►</a></td><td>2 </td><td><a href="" class="tocviewselflink" data-pltdoc="x">Predicates</a></td></tr></table><div class="tocviewsublistbottom" style="display: none;" id="tocview_1"><table cellspacing="0" cellpadding="0"><tr><td align="right">2.1 </td><td><a href="#%28part._facts%29" class="tocviewlink" data-pltdoc="x">Predicates Introducing Facts</a></td></tr><tr><td align="right">2.2 </td><td><a href="#%28part._rules%29" class="tocviewlink" data-pltdoc="x">Predicates with Rules</a></td></tr><tr><td align="right">2.3 </td><td><a href="#%28part._solving-goals%29" class="tocviewlink" data-pltdoc="x">Solving Goals</a></td></tr><tr><td align="right">2.4 </td><td><a href="#%28part._assert%29" class="tocviewlink" data-pltdoc="x">Asserting Extra Clauses</a></td></tr><tr><td align="right">2.5 </td><td><a href="#%28part._local-vars%29" class="tocviewlink" data-pltdoc="x">Local Variables</a></td></tr></table></div></div></div><div class="tocsub"><div class="tocsubtitle">On this page:</div><table class="tocsublist" cellspacing="0"><tr><td><span class="tocsublinknumber">2.1<tt> </tt></span><a href="#%28part._facts%29" class="tocsubseclink" data-pltdoc="x">Predicates Introducing Facts</a></td></tr><tr><td><span class="tocsublinknumber">2.2<tt> </tt></span><a href="#%28part._rules%29" class="tocsubseclink" data-pltdoc="x">Predicates with Rules</a></td></tr><tr><td><span class="tocsublinknumber">2.3<tt> </tt></span><a href="#%28part._solving-goals%29" class="tocsubseclink" data-pltdoc="x">Solving Goals</a></td></tr><tr><td><span class="tocsublinknumber">2.4<tt> </tt></span><a href="#%28part._assert%29" class="tocsubseclink" data-pltdoc="x">Asserting Extra Clauses</a></td></tr><tr><td><span class="tocsublinknumber">2.5<tt> </tt></span><a href="#%28part._local-vars%29" class="tocsubseclink" data-pltdoc="x">Local Variables</a></td></tr></table></div></div><div class="maincolumn"><div class="main"><div class="navsettop"><span class="navleft"><form class="searchform"><input class="searchbox" style="color: #888;" type="text" value="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "6.1", "../");" onfocus="this.style.color="black"; this.style.textAlign="left"; if (this.value == "...search manuals...") this.value="";" onblur="if (this.value.match(/^ *$/)) { this.style.color="#888"; this.style.textAlign="center"; this.value="...search manuals..."; }"/></form> <a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("6.1");">top</a></span><span class="navright"> <a href="simple.html" title="backward to "1 Simple Goals and Queries"" data-pltdoc="x">← prev</a> <a href="index.html" title="up to "Racklog: Prolog-Style Logic Programming"" data-pltdoc="x">up</a> <a href="racket-w-logic.html" title="forward to "3 Using Conventional Racket Expressions in Racklog"" data-pltdoc="x">next →</a></span> </div><h3 x-source-module="(lib "racklog/racklog.scrbl")" x-part-tag=""predicates"">2<tt> </tt><a name="(part._predicates)"></a>Predicates</h3><p>More interesting goals are created by applying a special
kind of Racklog object called a <span style="font-style: italic">predicate</span> (or
<span style="font-style: italic">relation</span>) to other
Racklog objects. Racklog comes with some primitive
predicates, such as the arithmetic operators
<span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3d~3a~3d%29%29" class="RktValLink" data-pltdoc="x">%=:=</a></span> and <span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3c%29%29" class="RktValLink" data-pltdoc="x">%<</a></span>,
standing for arithmetic “equal” and “less than”
respectively. For example, the following are some goals
involving these predicates:</p><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="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3d~3a~3d%29%29" class="RktValLink" data-pltdoc="x">%=:=</a></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="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'()</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3c%29%29" class="RktValLink" data-pltdoc="x">%<</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">2</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'()</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3d~3a~3d%29%29" class="RktValLink" data-pltdoc="x">%=:=</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">2</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="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3c%29%29" class="RktValLink" data-pltdoc="x">%<</a></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="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr></table></blockquote><p>Other arithmetic predicates are
<span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3e%29%29" class="RktValLink" data-pltdoc="x">%></a></span> (“greater than”),
<span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3c~3d%29%29" class="RktValLink" data-pltdoc="x">%<=</a></span> (“less than or equal”),
<span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3e~3d%29%29" class="RktValLink" data-pltdoc="x">%>=</a></span> (“greater than or equal”), and
<span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25~3d%2F~3d%29%29" class="RktValLink" data-pltdoc="x">%=/=</a></span> (“not equal”).</p><p>Racklog predicates are not to be confused with conventional
Racket predicates (such as <span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3c%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x"><</a></span> and <span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.1" class="RktValLink Sq" data-pltdoc="x">=</a></span>). Racklog
predicates, when applied to arguments, produce goals
that
may either succeed or fail. Racket predicates, when applied
to arguments, yield a boolean value. Henceforth, we will
use the term “predicate” to mean Racklog predicates.
Conventional predicates will be explicitly called “Racket
predicates”.</p><h4 x-source-module="(lib "racklog/racklog.scrbl")" x-part-tag=""facts"">2.1<tt> </tt><a name="(part._facts)"></a>Predicates Introducing Facts</h4><p>Users can create their own predicates using the Racklog form
<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span>. For example, let’s
define the predicate <span class="RktSym">%knows</span>:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">%knows</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">TeX</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Racket</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Prolog</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Penelope</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Penelope</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">TeX</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Penelope</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Prolog</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Penelope</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Telemachus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">TeX</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Telemachus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">calculus</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>The expression has the expected meaning. Each
<span style="font-style: italic">clause</span> in the <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span> establishes a <span style="font-style: italic">fact</span>:
Odysseus
knows TeX, Telemachus knows calculus, &c. In general, if we
apply the predicate to the arguments in any one of its
clauses, we will get a successful goal. Thus, since
<span class="RktSym">%knows</span> has a clause that reads
<span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="stt"> </span><span class="RktVal">'</span><span class="RktVal">TeX</span><span class="RktPn">)</span><span class="RktPn">]</span>, the goal
<span class="RktPn">(</span><span class="RktSym">%knows</span><span class="stt"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="stt"> </span><span class="RktVal">'</span><span class="RktVal">TeX</span><span class="RktPn">)</span>
will be true.</p><p>We can now get answers for the following types of queries:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">TeX</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p><span class="RktRes">'()</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="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Telemachus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Racket</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr></table></blockquote><h4 x-source-module="(lib "racklog/racklog.scrbl")" x-part-tag=""rules"">2.2<tt> </tt><a name="(part._rules)"></a>Predicates with Rules</h4><p>Predicates can be more complicated than the above bald
recitation of facts. The predicate clauses can be <span style="font-style: italic">rules</span>, eg,</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">%computer-literate</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">person</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym">person</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktSym">person</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">TeX</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktSym">person</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Racket</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym">person</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktSym">person</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">TeX</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktSym">person</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Prolog</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>This defines the predicate
<span class="RktSym">%computer-literate</span> in
terms of the predicate <span class="RktSym">%knows</span>. In effect, a person is
defined as computer-literate if they know TeX and
Racket, <span style="font-style: italic">or</span> TeX and Prolog.</p><p>Note that this use of
<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span> employs a local <span style="font-style: italic">logic variable</span> called <span class="RktVar">person</span>.
In general, a <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span>-expression can have a list of symbols
as its second subform. These name new logic variables that
can be used within the body of the <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span>.</p><p>The following query can now be answered:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%computer-literate</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Penelope</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p><span class="RktRes">'()</span></p></td></tr></table></blockquote><p>Since Penelope knows TeX and Prolog, she is computer-literate.</p><h4 x-source-module="(lib "racklog/racklog.scrbl")" x-part-tag=""solving-goals"">2.3<tt> </tt><a name="(part._solving-goals)"></a>Solving Goals</h4><p>The above queries are yes/no questions. Racklog programming
allows more: We can formulate a goal with <span style="font-style: italic">uninstantiated</span>
logic variables and then ask the querying process to
provide, if possible, values for these variables that cause
the goal to succeed. For instance, the query:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">what</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktSym">what</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p><span class="RktRes">'((what . TeX))</span></p></td></tr></table></blockquote><p>asks for an instantiation of the logic variable <span class="RktVar">what</span>
that satisfies the goal <span class="RktPn">(</span><span class="RktSym">%knows</span><span class="stt"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="stt"> </span><span class="RktSym">what</span><span class="RktPn">)</span>.
In other words, we are asking, “What does Odysseus know?”</p><p>Note that this use of <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span> —<wbr></wbr> like <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span>
in the definition of <span class="RktSym">%computer-literate</span> —<wbr></wbr>
uses a local logic
variable, <span class="RktVar">what</span>. In general, the second subform of
<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span> can be a list of local logic variables. The
<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span>-query returns an answer that is a list of
bindings, one for each logic variable mentioned in its
second subform. Thus,</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">what</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktSym">what</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p><span class="RktRes">'((what . TeX))</span></p></td></tr></table></blockquote><p>But that is not all that wily Odysseus knows. Racklog
provides a zero-argument procedure (“thunk”) called
<span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25more%29%29" class="RktValLink" data-pltdoc="x">%more</a></span>
that <span style="font-style: italic">retries</span> the goal in the last
<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span>-query for a different solution.</p><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="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25more%29%29" class="RktValLink" data-pltdoc="x">%more</a></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'((what . Racket))</span></p></td></tr></table></blockquote><p>We can keep pumping for more solutions:</p><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="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25more%29%29" class="RktValLink" data-pltdoc="x">%more</a></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'((what . Prolog))</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25more%29%29" class="RktValLink" data-pltdoc="x">%more</a></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'((what . Penelope))</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25more%29%29" class="RktValLink" data-pltdoc="x">%more</a></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr></table></blockquote><p>The final <span class="RktVal">#f</span> shows that there are no more
solutions. This is because there are no more clauses in the
<span class="RktSym">%knows</span> predicate that list Odysseus as knowing anything
else.</p><h4 x-source-module="(lib "racklog/racklog.scrbl")" x-part-tag=""assert"">2.4<tt> </tt><a name="(part._assert)"></a>Asserting Extra Clauses</h4><p>We can add more clauses to a predicate after it has already
been defined with a <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span>. Racklog provides the
<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert%21%29%29" class="RktStxLink" data-pltdoc="x">%assert!</a></span> form for this purpose. Eg,</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert%21%29%29" class="RktStxLink" data-pltdoc="x">%assert!</a></span><span class="hspace"> </span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">archery</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr></table></blockquote><p>tacks on a new clause at the end of the existing clauses
of the <span class="RktSym">%knows</span>
predicate. Now, the query:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">what</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktSym">what</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p><span class="RktRes">'((what . TeX))</span></p></td></tr></table></blockquote><p>gives TeX, Racket, Prolog, and Penelope, as before, but
a subsequent <span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25more%29%29" class="RktValLink" data-pltdoc="x">%more</a></span><span class="RktPn">)</span> yields a new result:</p><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="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25more%29%29" class="RktValLink" data-pltdoc="x">%more</a></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">'((what . archery))</span></p></td></tr></table></blockquote><p>The Racklog form <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert-after%21%29%29" class="RktStxLink" data-pltdoc="x">%assert-after!</a></span> is similar to <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert%21%29%29" class="RktStxLink" data-pltdoc="x">%assert!</a></span> but
adds clauses <span style="font-style: italic">before</span> any of the current clauses.</p><p>Both <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert%21%29%29" class="RktStxLink" data-pltdoc="x">%assert!</a></span> and <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert-after%21%29%29" class="RktStxLink" data-pltdoc="x">%assert-after!</a></span> assume that the variable
they are adding to already names a predicate (presumably
defined using <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span>).
In order to allow defining a predicate entirely through
<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert%21%29%29" class="RktStxLink" data-pltdoc="x">%assert!</a></span>s, Racklog provides an empty predicate value
<span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25empty-rel%29%29" class="RktValLink" data-pltdoc="x">%empty-rel</a></span>. <span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25empty-rel%29%29" class="RktValLink" data-pltdoc="x">%empty-rel</a></span> takes any number of arguments
and always fails. A typical use of the
<span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25empty-rel%29%29" class="RktValLink" data-pltdoc="x">%empty-rel</a></span> and <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert%21%29%29" class="RktStxLink" data-pltdoc="x">%assert!</a></span> combination:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktSym">%parent</span><span class="hspace"> </span><span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25empty-rel%29%29" class="RktValLink" data-pltdoc="x">%empty-rel</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert%21%29%29" class="RktStxLink" data-pltdoc="x">%assert!</a></span><span class="hspace"> </span><span class="RktSym">%parent</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Laertes</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</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="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25assert%21%29%29" class="RktStxLink" data-pltdoc="x">%assert!</a></span><span class="hspace"> </span><span class="RktSym">%parent</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Telemachus</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktVal">'</span><span class="RktVal">Penelope</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Telemachus</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr></table></blockquote><p>(Racklog does not provide a predicate for <span style="font-style: italic">retracting</span>
assertions, since we can keep track of older versions of
predicates using conventional Racket features (<span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=let.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fletstx-scheme..rkt%2529._let%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">let</a></span> and <span class="RktSym"><a href="http://download.racket-lang.org/docs/6.1/html/local-redirect/index.html?doc=reference&rel=set_.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._set%2521%2529%2529&version=6.1" class="RktStxLink Sq" data-pltdoc="x">set!</a></span>).)</p><h4 x-source-module="(lib "racklog/racklog.scrbl")" x-part-tag=""local-vars"">2.5<tt> </tt><a name="(part._local-vars)"></a>Local Variables</h4><p>The local logic variables of <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span>- and
<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span>-expressions are in reality introduced by the
Racklog syntactic form called <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25let%29%29" class="RktStxLink" data-pltdoc="x">%let</a></span>. (<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25rel%29%29" class="RktStxLink" data-pltdoc="x">%rel</a></span> and
<span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span> are macros written using <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25let%29%29" class="RktStxLink" data-pltdoc="x">%let</a></span>.)</p><p><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25let%29%29" class="RktStxLink" data-pltdoc="x">%let</a></span> introduces new lexically scoped logic variables.
Supposing, instead of</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">what</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktSym">what</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p><span class="RktRes">'((what . TeX))</span></p></td></tr></table></blockquote><p>we had asked</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25let%29%29" class="RktStxLink" data-pltdoc="x">%let</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">what</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="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">%knows</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">Odysseus</span><span class="hspace"> </span><span class="RktSym">what</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p><span class="RktRes">'()</span></p></td></tr></table></blockquote><p>This query, too, succeeds five times, since
Odysseus knows five things. However, <span class="RktSym"><a href="glossary.html#%28form._%28%28lib._racklog%2Fmain..rkt%29._~25which%29%29" class="RktStxLink" data-pltdoc="x">%which</a></span> emits
bindings only for the local variables that <span style="font-style: italic">it</span>
introduces. Thus, this query emits <span class="RktRes">()</span> five times before
<span class="RktPn">(</span><span class="RktSym"><a href="glossary.html#%28def._%28%28lib._racklog%2Fmain..rkt%29._~25more%29%29" class="RktValLink" data-pltdoc="x">%more</a></span><span class="RktPn">)</span> finally returns <span class="RktVal">#f</span>.</p><div class="navsetbottom"><span class="navleft"><form class="searchform"><input class="searchbox" style="color: #888;" type="text" value="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "6.1", "../");" onfocus="this.style.color="black"; this.style.textAlign="left"; if (this.value == "...search manuals...") this.value="";" onblur="if (this.value.match(/^ *$/)) { this.style.color="#888"; this.style.textAlign="center"; this.value="...search manuals..."; }"/></form> <a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("6.1");">top</a></span><span class="navright"> <a href="simple.html" title="backward to "1 Simple Goals and Queries"" data-pltdoc="x">← prev</a> <a href="index.html" title="up to "Racklog: Prolog-Style Logic Programming"" data-pltdoc="x">up</a> <a href="racket-w-logic.html" title="forward to "3 Using Conventional Racket Expressions in Racklog"" data-pltdoc="x">next →</a></span> </div></div></div><div id="contextindicator"> </div></body></html>
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