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  58. <h4 class="subsubsection">2.7.8.2 Fan</h4>
  59. <a name="index-fan"></a>
  60. <p>In cases where a deconstructions would be needed to apply the same
  61. function to both sides of a pair, the overhead can be avoided by means
  62. of a property of the virtual machine intended for that purpose.
  63. </p>
  64. <p>A <code>silly</code> definition of <code>fan</code> implying the following theorem is
  65. helpful in expressing such an application.
  66. </p>
  67. <dl compact="compact">
  68. <dt> <em>T14</em></dt>
  69. <dd><p>[[<code>fan</code>]] <code><var>f</var></code> = <code>((nil,nil),((nil,<var>f</var>),(nil,nil)))</code>
  70. </p></dd>
  71. </dl>
  72. <p>The virtual machine recognizes when an application has the form shown
  73. above, and uses <code><var>f</var></code> as a function to be applied to both sides
  74. of the argument.
  75. </p>
  76. <dl compact="compact">
  77. <dt> <em>P13</em></dt>
  78. <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>
  79. </p></dd>
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