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directives1.html
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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<link rel="stylesheet" href="https://openmath.org/public/css/hyde.css"/>
<link rel="stylesheet" href="https://openmath.org/public/css/main.css"/>
<link rel="shortcut icon" sizes="144x144" type="image/png" href="/public/favicon.png"/>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_SVG"> </script>
<script type="text/javascript"> function divfold(_Id){
var thisLevel = document.getElementById(_Id);
var thisLevela = document.getElementById(_Id.concat("a"))
if(thisLevel.style.display != "none"){
thisLevel.style.display = "none";
thisLevela.style.backgroundColor = "#CCCCCC";}
else{
thisLevel.style.display = "block";
thisLevela.style.backgroundColor = "#AAFFAA";}
}
</script>
<title>directives1</title>
<link rel="stylesheet" href="https://openmath.org/cd/omcd.css" type="text/css"/>
</head>
<body class="theme-base-odk">
<div class="sidebar">
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<h1>
<a href="/">
<img src="https://openmath.org/public/logo.png" alt="OpenMath" width="100%"/>
</a>
</h1>
<p class="lead">OpenMath is an extensible standard for representing the semantics of mathematical objects.</p>
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<a href="https://openmath.org/">https://openmath.org</a>
</p>
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<div class="content container">
<div class="page">
<a name="top"/>
<h1>OpenMath Content Dictionary: directives1</h1>
<dl>
<dt>
<span class="dt">Canonical URL:</span>
</dt>
<dd>
<a href="http://www.riaca.win.tue.nl/cds/directives/directives1.ocd">http://www.riaca.win.tue.nl/cds/directives/directives1.ocd</a>
</dd>
<dt>
<span class="dt">CD Base:</span>
</dt>
<dd>
<a href="http://www.openmath.org/cd">http://www.openmath.org/cd</a>
</dd>
<dt>
<span class="dt">CD File:</span>
</dt>
<dd>
<a href="directives1.ocd">directives1.ocd
</a>
</dd>
<dt>
<span class="dt">CD as XML Encoded OpenMath:</span>
</dt>
<dd>
<a href="directives1.omcd">directives1.omcd
</a>
</dd>
<dt>
<span class="dt">Defines:</span>
</dt>
<dd>
<a href="#decide">decide</a>, <a href="#disprove">disprove</a>, <a href="#evaluate">evaluate</a>, <a href="#evaluate_to_type">evaluate_to_type</a>, <a href="#explore">explore</a>, <a href="#find">find</a>, <a href="#look_up">look_up</a>, <a href="#prove">prove</a>, <a href="#prove_in_theory">prove_in_theory</a>, <a href="#response">response</a>
</dd>
<dt>
<span class="dt">Date:</span>
</dt>
<dd>2004-06-01</dd>
<dt>
<span class="dt">Version:</span>
</dt>
<dd>1
(Revision 3)
</dd>
<dt>
<span class="dt">Review Date:</span>
</dt>
<dd>2006-06-01</dd>
<dt>
<span class="dt">Status:</span>
</dt>
<dd>experimental</dd>
</dl>
<hr/>
<p> </p>
<p>The primal objective of OpenMath objects is to represent mathematical
expressions. In this Content Dictionary another objective is
addressed, namely to express an action related to a mathematical
expression. Such a request for an action is generally referred to
as a query. The specific queries are called directives. In this CD
we define some. An entity (software) carrying out the query is
referred to as a service. The service might return an OpenMath
object. To formalize this object, we also introduce the symbol
response in this CD.</p>
<p>amc 2004-03-18: added the directive explore.
amc 2004-03-24: removed redundancies.</p>
<p/>
<hr/>
<h2>
<a name="evaluate">evaluate</a>
</h2>
<dl>
<dt>
<span class="dt">Description:</span>
</dt>
<dd>
<p>
This symbol is a function with one argument, which should be a
mathematical expression.
When applied to a mathematical expression, it asks for an evaluation
or simplification of the expression. The evaluation or simplification
to be carried out by a service is a simpler mathematical expression (in some definition of complexity
of objects) which is equal to the argument.
</p>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Example:</span>
</dt>
<dd> The value of sin(Pi) is zero.
The expression below asks for sin(Pi) to be evaluated, and so
a service receiving the object is supposed to return zero.
<div>
<button id="id.om.11xmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.11xml')">OpenMath XML (source)</button>
<pre id="id.om.11xml" style="display:none"><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA><OMS cd="directives1" name="evaluate"/>
<OMA><OMS cd="transc1" name="sin"/>
<OMS cd="nums1" name="pi"/>
</OMA>
</OMA>
</OMOBJ></pre>
</div>
<div>
<button id="id.om.11cmmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.11cmml')">Strict Content MathML</button>
<pre id="id.om.11cmml" style="display:none; margin-top: 0.5em">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="directives1">evaluate</csymbol>
<apply><csymbol cd="transc1">sin</csymbol><csymbol cd="nums1">pi</csymbol></apply>
</apply>
</math></pre>
</div>
<button id="id.om.11prefa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.11pref')">Prefix</button>
<div id="id.om.11pref" style="display:none; margin-top: 0.5em">
<a href="../../../cd/directives1.html#evaluate">evaluate</a>
(<a href="../../../cd/transc1.html#sin">sin</a>
(<a href="../../../cd/nums1.html#pi">pi</a>)
)
</div>
<div>
<button id="id.om.11popa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.11pop')">Popcorn</button>
<div id="id.om.11pop" style="display:none; margin-top: 0.5em">
directives1.evaluate(sin(nums1.pi))
</div>
</div>
<div>
<button id="id.om.11mmla" style="width:20em; background-color:#AAFFAA"
onclick="divfold('id.om.11mml')">Rendered Presentation MathML</button>
<div id="id.om.11mml" style="display:block; margin-top: 0.5em">
<div style="overflow:auto;font-size:90%">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow xmlns:om="http://www.openmath.org/OpenMath">
<mi>evaluate</mi>
<mo>⁡</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>sin</mi>
<mo>⁡</mo>
<mrow>
<mo>(</mo>
<mi>π</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</math>
</div>
</div>
</div>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Signatures:</span>
</dt>
<dd>
<a href="../../sts/directives1.html#evaluate">
sts
</a>
</dd>
</dl>
<p/>
<hr/>
<table width="100%">
<tr>
<td align="right">
<font size="-1">
[Next: <a href="#evaluate_to_type">evaluate_to_type</a>]
[Last: <a href="#explore">explore</a>]
[<a href="#top">Top</a>]</font>
</td>
</tr>
</table>
<hr/>
<h2>
<a name="evaluate_to_type">evaluate_to_type</a>
</h2>
<dl>
<dt>
<span class="dt">Description:</span>
</dt>
<dd>
<p>
This symbol is a function with two arguments, which should be
a mathematical expression and a type.
When applied to a mathematical expression E and a type T, it asks for an evaluation
or simplification of E to a mathematical expression of type T.
</p>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Example:</span>
</dt>
<dd> The value of (7*6)/2 is a natural number.
The expression below asks for this integer.
<div>
<button id="id.om.21xmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.21xml')">OpenMath XML (source)</button>
<pre id="id.om.21xml" style="display:none"><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA><OMS cd="directives1" name="evaluate"/>
<OMA><OMS cd="arith1" name="divide"/>
<OMA><OMS cd="arith1" name="times"/>
<OMI>7</OMI><OMI>6</OMI>
</OMA>
<OMI>2</OMI>
</OMA>
<OMS cd="setname1" name="N"/>
</OMA>
</OMOBJ></pre>
</div>
<div>
<button id="id.om.21cmmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.21cmml')">Strict Content MathML</button>
<pre id="id.om.21cmml" style="display:none; margin-top: 0.5em">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="directives1">evaluate</csymbol>
<apply><csymbol cd="arith1">divide</csymbol>
<apply><csymbol cd="arith1">times</csymbol>
<cn type="integer">7</cn>
<cn type="integer">6</cn>
</apply>
<cn type="integer">2</cn>
</apply>
<csymbol cd="setname1">N</csymbol>
</apply>
</math></pre>
</div>
<button id="id.om.21prefa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.21pref')">Prefix</button>
<div id="id.om.21pref" style="display:none; margin-top: 0.5em">
<a href="../../../cd/directives1.html#evaluate">evaluate</a>
(<a href="../../../cd/arith1.html#divide">divide</a>
(<a href="../../../cd/arith1.html#times">times</a>
(7, 6)
, 2)
, <a href="../../../cd/setname1.html#N">N</a>)
</div>
<div>
<button id="id.om.21popa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.21pop')">Popcorn</button>
<div id="id.om.21pop" style="display:none; margin-top: 0.5em">
directives1.evaluate((7 * 6) / 2, setname1.N)
</div>
</div>
<div>
<button id="id.om.21mmla" style="width:20em; background-color:#AAFFAA"
onclick="divfold('id.om.21mml')">Rendered Presentation MathML</button>
<div id="id.om.21mml" style="display:block; margin-top: 0.5em">
<div style="overflow:auto;font-size:90%">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow xmlns:om="http://www.openmath.org/OpenMath">
<mi>evaluate</mi>
<mo>⁡</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>7</mn>
<mo>×</mo>
<mn>6</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mi mathvariant="double-struck">N</mi>
<mo>)</mo>
</mrow>
</mrow>
</math>
</div>
</div>
</div>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Commented Mathematical property (CMP):</span>
</dt>
<dd>
The type of the responded object should be equal to the
specification,
that is the second argument of the evaluate_to_type.
</dd>
</dl>
<dl>
<dt>
<span class="dt">Formal Mathematical property (FMP):</span>
</dt>
<dd>
<div>
<button id="id.om.34xmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.34xml')">OpenMath XML (source)</button>
<pre id="id.om.34xml" style="display:none">
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMATTR>
<OMATP><OMS cd="ecc" name="type"/>
<OMV name="T"/>
</OMATP>
<OMA><OMS cd="directives1" name="response"/>
<OMA><OMS cd="directives1" name="evaluate_to_type"/>
<OMV name="x"/> <OMV name="T"/>
</OMA>
</OMA>
</OMATTR>
</OMOBJ></pre>
</div>
<div>
<button id="id.om.34cmmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.34cmml')">Strict Content MathML</button>
<pre id="id.om.34cmml" style="display:none; margin-top: 0.5em">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<apply><csymbol cd="directives1">response</csymbol>
<apply><csymbol cd="directives1">evaluate_to_type</csymbol><ci>x</ci><ci>T</ci></apply>
</apply>
<annotation-xml cd="ecc" name="type"><ci>T</ci></annotation-xml>
</semantics>
</math></pre>
</div>
<button id="id.om.34prefa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.34pref')">Prefix</button>
<div id="id.om.34pref" style="display:none; margin-top: 0.5em">
<b>Attrib</b>([<a href="../../../cd/ecc.html#type">type</a>
<i>T</i>
],
<a href="../../../cd/directives1.html#response">response</a>
(<a href="../../../cd/directives1.html#evaluate_to_type">evaluate_to_type</a>
( <i>x</i>, <i>T</i>)
)
)
</div>
<div>
<button id="id.om.34popa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.34pop')">Popcorn</button>
<div id="id.om.34pop" style="display:none; margin-top: 0.5em">
directives1.response(directives1.evaluate_to_type($x, $T)){ecc.type -> $T}
</div>
</div>
<div>
<button id="id.om.34mmla" style="width:20em; background-color:#AAFFAA"
onclick="divfold('id.om.34mml')">Rendered Presentation MathML</button>
<div id="id.om.34mml" style="display:block; margin-top: 0.5em">
<div style="overflow:auto;font-size:90%">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow xmlns:om="http://www.openmath.org/OpenMath">
<mi>response</mi>
<mo>⁡</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>evaluate_to_type</mi>
<mo>⁡</mo>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>T</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</math>
</div>
</div>
</div>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Signatures:</span>
</dt>
<dd>
<a href="../../sts/directives1.html#evaluate_to_type">
sts
</a>
</dd>
</dl>
<p/>
<hr/>
<table width="100%">
<tr>
<td align="right">
<font size="-1">
[Next: <a href="#look_up">look_up</a>]
[Previous: <a href="#evaluate">evaluate</a>]
[<a href="#top">Top</a>]</font>
</td>
</tr>
</table>
<hr/>
<h2>
<a name="look_up">look_up</a>
</h2>
<dl>
<dt>
<span class="dt">Description:</span>
</dt>
<dd>
<p>
This symbol is a function with one argument, which should be a
mathematical expression.
When applied to a mathematical expression, it asks for mathematical
expressions related to the argument. If the argument is a single
OpenMath symbol, the service might respond by the list of all
properties in the CD containing the argument.
Alternatively, the service can provide a list of CDs which use the CD
in which the argument occurs.</p>
<p>Another service might return all documents in which the symbol occurs.</p>
<p>If the argument is a more complicated object, the same services could
be called for, but then with all OpenMath symbols occurring in the
argument instead of the single one.
</p>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Example:</span>
</dt>
<dd> Looking up sin is expressed as follows:
<div>
<button id="id.om.49xmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.49xml')">OpenMath XML (source)</button>
<pre id="id.om.49xml" style="display:none"><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA><OMS cd="directives1" name="look_up"/>
<OMS cd="transc1" name="sin"/>
</OMA>
</OMOBJ></pre>
</div>
<div>
<button id="id.om.49cmmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.49cmml')">Strict Content MathML</button>
<pre id="id.om.49cmml" style="display:none; margin-top: 0.5em">
<math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol cd="directives1">look_up</csymbol><csymbol cd="transc1">sin</csymbol></apply></math></pre>
</div>
<button id="id.om.49prefa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.49pref')">Prefix</button>
<div id="id.om.49pref" style="display:none; margin-top: 0.5em">
<a href="../../../cd/directives1.html#look_up">look_up</a>
(<a href="../../../cd/transc1.html#sin">sin</a>)
</div>
<div>
<button id="id.om.49popa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.49pop')">Popcorn</button>
<div id="id.om.49pop" style="display:none; margin-top: 0.5em">
directives1.look_up(sin)
</div>
</div>
<div>
<button id="id.om.49mmla" style="width:20em; background-color:#AAFFAA"
onclick="divfold('id.om.49mml')">Rendered Presentation MathML</button>
<div id="id.om.49mml" style="display:block; margin-top: 0.5em">
<div style="overflow:auto;font-size:90%">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow xmlns:om="http://www.openmath.org/OpenMath">
<mi>look_up</mi>
<mo>⁡</mo>
<mrow>
<mo>(</mo>
<mi>sin</mi>
<mo>)</mo>
</mrow>
</mrow>
</math>
</div>
</div>
</div>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Signatures:</span>
</dt>
<dd>
<a href="../../sts/directives1.html#look_up">
sts
</a>
</dd>
</dl>
<p/>
<hr/>
<table width="100%">
<tr>
<td align="right">
<font size="-1">
[Next: <a href="#response">response</a>]
[Previous: <a href="#evaluate_to_type">evaluate_to_type</a>]
[<a href="#top">Top</a>]</font>
</td>
</tr>
</table>
<hr/>
<h2>
<a name="response">response</a>
</h2>
<dl>
<dt>
<span class="dt">Description:</span>
</dt>
<dd>
<p>
This symbol is a function of one argument, which should be a query.
When applied to a query, it refers to the response a service might
give.
It will mainly be used in this CD to express formal mathematical
properties
of queries.
</p>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Signatures:</span>
</dt>
<dd>
<a href="../../sts/directives1.html#response">
sts
</a>
</dd>
</dl>
<p/>
<hr/>
<table width="100%">
<tr>
<td align="right">
<font size="-1">
[Next: <a href="#prove">prove</a>]
[Previous: <a href="#look_up">look_up</a>]
[<a href="#top">Top</a>]</font>
</td>
</tr>
</table>
<hr/>
<h2>
<a name="prove">prove</a>
</h2>
<dl>
<dt>
<span class="dt">Description:</span>
</dt>
<dd>
<p>
This symbol is a function with one argument, which should be a clause.
When applied to a clause C, it asks for a
proof of C.
</p>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Signatures:</span>
</dt>
<dd>
<a href="../../sts/directives1.html#prove">
sts
</a>
</dd>
</dl>
<p/>
<hr/>
<table width="100%">
<tr>
<td align="right">
<font size="-1">
[Next: <a href="#disprove">disprove</a>]
[Previous: <a href="#response">response</a>]
[<a href="#top">Top</a>]</font>
</td>
</tr>
</table>
<hr/>
<h2>
<a name="disprove">disprove</a>
</h2>
<dl>
<dt>
<span class="dt">Description:</span>
</dt>
<dd>
<p>
This symbol is a function with one argument, which should be a clause.
When applied to a clause C, it asks for a
proof of that C does not hold.
</p>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Commented Mathematical property (CMP):</span>
</dt>
<dd>
Asking to disprove C amounts to
asking for a proof that C does not hold.
(In other words, this symbol is completely redundant,
even in multi-valued logic.***)
</dd>
</dl>
<dl>
<dt>
<span class="dt">Formal Mathematical property (FMP):</span>
</dt>
<dd>
<div>
<button id="id.om.64xmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.64xml')">OpenMath XML (source)</button>
<pre id="id.om.64xml" style="display:none">
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA><OMS cd="relation1" name="eq"/>
<OMA><OMS cd="directives1" name="disprove"/>
<OMV name="C"/>
</OMA>
<OMA><OMS cd="directives1" name="prove"/>
<OMA><OMS cd="logic1" name="not"/>
<OMV name="C"/>
</OMA>
</OMA>
</OMA>
</OMOBJ></pre>
</div>
<div>
<button id="id.om.64cmmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.64cmml')">Strict Content MathML</button>
<pre id="id.om.64cmml" style="display:none; margin-top: 0.5em">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="relation1">eq</csymbol>
<apply><csymbol cd="directives1">disprove</csymbol><ci>C</ci></apply>
<apply><csymbol cd="directives1">prove</csymbol>
<apply><csymbol cd="logic1">not</csymbol><ci>C</ci></apply>
</apply>
</apply>
</math></pre>
</div>
<button id="id.om.64prefa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.64pref')">Prefix</button>
<div id="id.om.64pref" style="display:none; margin-top: 0.5em">
<a href="../../../cd/relation1.html#eq">eq</a>
(<a href="../../../cd/directives1.html#disprove">disprove</a>
( <i>C</i>)
, <a href="../../../cd/directives1.html#prove">prove</a>
(<a href="../../../cd/logic1.html#not">not</a>
( <i>C</i>)
)
)
</div>
<div>
<button id="id.om.64popa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.64pop')">Popcorn</button>
<div id="id.om.64pop" style="display:none; margin-top: 0.5em">
directives1.disprove($C) = directives1.prove( not($C))
</div>
</div>
<div>
<button id="id.om.64mmla" style="width:20em; background-color:#AAFFAA"
onclick="divfold('id.om.64mml')">Rendered Presentation MathML</button>
<div id="id.om.64mml" style="display:block; margin-top: 0.5em">
<div style="overflow:auto;font-size:90%">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow xmlns:om="http://www.openmath.org/OpenMath">
<mrow>
<mi>disprove</mi>
<mo>⁡</mo>
<mrow>
<mo>(</mo>
<mi>C</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mrow>
<mi>prove</mi>
<mo>⁡</mo>
<mrow>
<mo>(</mo>
<mo>¬</mo>
<mi>C</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</math>
</div>
</div>
</div>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Signatures:</span>
</dt>
<dd>
<a href="../../sts/directives1.html#disprove">
sts
</a>
</dd>
</dl>
<p/>
<hr/>
<table width="100%">
<tr>
<td align="right">
<font size="-1">
[Next: <a href="#prove_in_theory">prove_in_theory</a>]
[Previous: <a href="#prove">prove</a>]
[<a href="#top">Top</a>]</font>
</td>
</tr>
</table>
<hr/>
<h2>
<a name="prove_in_theory">prove_in_theory</a>
</h2>
<dl>
<dt>
<span class="dt">Description:</span>
</dt>
<dd>
<p>
This symbol is a function with two arguments, the first of which
should be a clause and the second of which should be a symbol
indicating a logic theory.
When applied to arguments C, T, it asks for a
proof of C in theory T.
</p>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Signatures:</span>
</dt>
<dd>
<a href="../../sts/directives1.html#prove_in_theory">
sts
</a>
</dd>
</dl>
<p/>
<hr/>
<table width="100%">
<tr>
<td align="right">
<font size="-1">
[Next: <a href="#find">find</a>]
[Previous: <a href="#disprove">disprove</a>]
[<a href="#top">Top</a>]</font>
</td>
</tr>
</table>
<hr/>
<h2>
<a name="find">find</a>
</h2>
<dl>
<dt>
<span class="dt">Description:</span>
</dt>
<dd>
<p>
This symbol is a binder, whose body should be a clause.
When bound to a variable (or list of variables) x with body P(x), it asks for a
mathematical expression A such that P(A) holds.
</p>
</dd>
</dl>
<dl>
<dt>
<span class="dt">Example:</span>
</dt>
<dd>
Searching for a real number x such that sin(x) = 0
<div>
<button id="id.om.82xmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.82xml')">OpenMath XML (source)</button>
<pre id="id.om.82xml" style="display:none"><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMBIND><OMS cd="directives1" name="find"/>
<OMBVAR><OMV name="x"/></OMBVAR>
<OMA><OMS cd="logic1" name="and"/>
<OMA><OMS cd="set1" name="in"/>
<OMV name="x"/><OMS cd="setname1" name="R"/>
</OMA>
<OMA><OMS cd="relation1" name="eq"/>
<OMA><OMS cd="transc1" name="sin"/><OMV name="x"/></OMA>
<OMI>0</OMI>
</OMA>
</OMA>
</OMBIND>
</OMOBJ></pre>
</div>
<div>
<button id="id.om.82cmmla" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.82cmml')">Strict Content MathML</button>
<pre id="id.om.82cmml" style="display:none; margin-top: 0.5em">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<bind><csymbol cd="directives1">find</csymbol>
<bvar><ci>x</ci></bvar>
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="set1">in</csymbol><ci>x</ci><csymbol cd="setname1">R</csymbol></apply>
<apply><csymbol cd="relation1">eq</csymbol>
<apply><csymbol cd="transc1">sin</csymbol><ci>x</ci></apply>
<cn type="integer">0</cn>
</apply>
</apply>
</bind>
</math></pre>
</div>
<button id="id.om.82prefa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.82pref')">Prefix</button>
<div id="id.om.82pref" style="display:none; margin-top: 0.5em">
<a href="../../../cd/directives1.html#find">find</a>
[ <i>x</i>] .
(<a href="../../../cd/logic1.html#and">and</a>
(<a href="../../../cd/set1.html#in">in</a>
( <i>x</i>, <a href="../../../cd/setname1.html#R">R</a>)
, <a href="../../../cd/relation1.html#eq">eq</a>
(<a href="../../../cd/transc1.html#sin">sin</a>
( <i>x</i>)
, 0)
)
)
</div>
<div>
<button id="id.om.82popa" style="width:20em; background-color:#CCCCCC"
onclick="divfold('id.om.82pop')">Popcorn</button>
<div id="id.om.82pop" style="display:none; margin-top: 0.5em">
directives1.find[$x -> set1.in($x, setname1.R) and sin($x) = 0]
</div>
</div>
<div>
<button id="id.om.82mmla" style="width:20em; background-color:#AAFFAA"
onclick="divfold('id.om.82mml')">Rendered Presentation MathML</button>
<div id="id.om.82mml" style="display:block; margin-top: 0.5em">
<div style="overflow:auto;font-size:90%">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow xmlns:om="http://www.openmath.org/OpenMath">
<mi>find</mi>
<mo> </mo>
<mrow>
<mi>x</mi>
</mrow>
<mo>.</mo>
<mrow>
<mrow>
<mi>x</mi>
<mo>∈</mo>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>∧</mo>
<mrow>
<mrow>
<mi>sin</mi>
<mo>⁡</mo>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mrow>
</mrow>