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  57. <a name="Filter-1"></a>
  58. <h4 class="subsubsection">2.7.13.2 Filter</h4>
  59. <a name="index-filter"></a>
  60. <p>Another well known list operation is that which applies a predicate to
  61. every item of a list, and deletes those for which the predicate is
  62. false. For a predicate with virtual code <code><var>p</var></code>, such an
  63. application can be coded conveniently in this form,
  64. </p>
  65. <dl compact="compact">
  66. <dt> <em>T23</em></dt>
  67. <dd><p>[[<code>filter</code>]] <code><var>p</var></code> = <code>((nil,nil),(nil,(<var>p</var>,nil)))</code>
  68. </p></dd>
  69. </dl>
  70. <p>which is to say that writing <code>((nil,nil),(nil,(<var>p</var>,nil)))</code> in
  71. <code>silly</code> is the same as writing <code>filter <var>p</var></code>.
  72. </p>
  73. <p>The virtual machine detects code of this form provided that
  74. <code><var>p</var></code> is other than <code>nil</code>, and evaluates it consistently
  75. with the following properties, causing it to have the meaning that it
  76. does.
  77. </p>
  78. <dl compact="compact">
  79. <dt> <em>P26</em></dt>
  80. <dd><p>([[<code>filter</code>]] <code><var>p</var></code>) <code>nil</code> = <code>nil</code>
  81. </p></dd>
  82. <dt> <em>P27</em></dt>
  83. <dd><p>([[<code>filter</code>]] <code><var>p</var></code>) <code>(<var>x</var>,<var>y</var>)</code> =
  84. ([[<code>filter</code>]] <code><var>p</var></code>) <code><var>y</var></code> if <code><var>p</var> <code><var>x</var></code></code> = <code>nil</code>
  85. </p></dd>
  86. <dt> <em>P28</em></dt>
  87. <dd><p>([[<code>filter</code>]] <code><var>p</var></code>) <code>(<var>x</var>,<var>y</var>)</code> =
  88. <code>(<var>x</var>,</code>([[<code>filter</code>]] <code><var>p</var></code>) <code><var>y</var>)</code> if <code><var>p</var> <var>x</var></code> is a non-<code>nil</code> tree
  89. </p></dd>
  90. </dl>
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