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<a name="Fan-1"></a>
<h4 class="subsubsection">2.7.8.2 Fan</h4>

<a name="index-fan"></a>
<p>In cases where a deconstructions would be needed to apply the same
function to both sides of a pair, the overhead can be avoided by means
of a property of the virtual machine intended for that purpose.
</p>
<p>A <code>silly</code> definition of <code>fan</code> implying the following theorem is
helpful in expressing such an application.
</p>
<dl compact="compact">
<dt> <em>T14</em></dt>
<dd><p>[[<code>fan</code>]] <code><var>f</var></code> = <code>((nil,nil),((nil,<var>f</var>),(nil,nil)))</code>
</p></dd>
</dl>

<p>The virtual machine recognizes when an application has the form shown
above, and uses <code><var>f</var></code> as a function to be applied to both sides
of the argument.
</p>
<dl compact="compact">
<dt> <em>P13</em></dt>
<dd><p>([[<code>fan</code>]] <code><var>f</var></code>) <code>(<var>x</var>,<var>y</var>)</code> = <code>(<var>f</var> <var>x</var>,<var>f</var> <var>y</var>)</code>
</p></dd>
</dl>

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