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<A NAME=RULE>

<TITLE>RULE</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>RULE</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>type</B><P>
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 <P>
<P>
A <em>rule</em> is an instruction to replace an algebraic expression 
or a part of an expression by another one. 
 <P> <H3> 
syntax: </H3>
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<P>
&lt;lhs&gt; =&gt; &lt;rhs&gt; or 
&lt;lhs&gt; =&gt; &lt;rhs&gt; <em>when</em> &lt;cond&gt; 
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<P>
<P>
&lt;lhs&gt; is an algebraic expression used as search pattern and 
&lt;rhs&gt; is an algebraic expression which replaces matches of 
&lt;rhs&gt;. <em>=&gt;</em> is the operator 
<A HREF=r37_0026.html>replace</A>. 
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<P>
&lt;lhs&gt; can contain 
<A HREF=r37_0061.html>free variable</A>s which are 
symbols preceded by a tilde <em>~</em> in their leftmost position 
in &lt;lhs&gt;. 
A double tilde marks an 
<A HREF=r37_0062.html>optional free variable</A>. 
If a rule has a <em>when</em> &lt;cond&gt; 
part it will fire only if the evaluation of &lt;cond&gt; has a 
result 
<A HREF=r37_0122.html>true</A>. &lt;cond&gt; may contain references to 
free variables of &lt;lhs&gt;. 
<P>
<P>
Rules can be collected in a 
<A HREF=r37_0053.html>list</A> which then forms a 
 <em>rule list</em>. <em>Rule lists</em> can be used to collect 
algebraic knowledge for a specific evaluation context. 
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<em>Rules</em>and <em>rule lists</em> are globally activated and 
deactivated by 
<A HREF=r37_0199.html>let</A>, 
<A HREF=r37_0195.html>forall</A>, 
<A HREF=r37_0190.html>clearrules</A>. 
For a single evaluation they can be locally activate by 
<A HREF=r37_0227.html>where</A>. 
The active rules for an operator can be visualized by 
<A HREF=r37_0178.html>showrules</A>. 
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<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
operator f,g,h; 

let f(x) =&gt; x^2; 

f(x); 

   2
  x


g_rules:={g(~n,~x)=&gt;h(n/2,x) when evenp n,

g(~n,~x)=&gt;h((1-n)/2,x) when not evenp n}$

let g_rules;

g(3,x); 

  h(-1,x)

</TT></PRE><P>