A-New-Operator.html 4.4 KB

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  57. <a name="A-New-Operator-1"></a>
  58. <h3 class="subsection">2.7.1 A New Operator</h3>
  59. <p>With regard to a set of trees as described in <a href="Raw-Material.html#Raw-Material">Raw Material</a>, we can define
  60. a new binary operator. Unlike the <code>cons</code> operator, this one is not
  61. required to associate an element of the set with every possible pair
  62. of elements. For very many pairs of operands we will have nothing to
  63. say about its result. In fact, we require nothing of it beyond
  64. a few simple properties to be described presently.
  65. </p>
  66. <p>Because this is the only other operator than <code>cons</code>, there is no
  67. <a name="index-cons-1"></a>
  68. need to have a special notation for it, so it will be denoted by empty
  69. space. The tree associated by the operator with a pair of trees <code><var>x</var></code>
  70. and <code><var>y</var></code>, if any, will be expressed in the infix notation
  71. <code><var>x</var> <var>y</var></code>. For convenience, the operator is regarded as
  72. being right associative, so that <code><var>a</var> <var>b</var> <var>c</var></code> can be
  73. written for <code><var>a</var> (<var>b</var> <var>c</var>)</code>.
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