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<h5 class="subsubsection">2.7.8.2 Fan</h5>

<p><a name="index-g_t_0040code_007bfan_007d-294"></a>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>A <code>silly</code> definition of <code>fan</code> implying the following theorem is
helpful in expressing such an application.

     <dl>
<dt><em>T14</em><dd>[[<code>fan</code>]] <var>f</var> = <code>((nil,nil),((nil,</code><var>f</var><code>),(nil,nil)))</code>
</dl>

<p class="noindent">The virtual machine recognizes when an application has the form shown
above, and uses <var>f</var> as a function to be applied to both sides
of the argument.

     <dl>
<dt><em>P13</em><dd>([[<code>fan</code>]] <var>f</var>) <code>(</code><var>x</var><code>,</code><var>y</var><code>)</code> = <code>(</code><var>f</var> <var>x</var><code>,</code><var>f</var> <var>y</var><code>)</code>
</dl>

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