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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>
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