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- <a name="Compare-1"></a>
- <h4 class="subsubsection">2.7.11.1 Compare</h4>
- <a name="index-compare"></a>
- <p>A function that performs comparison has a the following very simple
- virtual code representation.
- </p>
- <dl compact="compact">
- <dt> <em>T19</em></dt>
- <dd><p>[[<code>compare</code>]] = <code>(nil,nil)</code>
- </p></dd>
- </dl>
- <p>The proof of theorem <em>T19</em> is that the standard <code>silly</code> prelude
- contains the declaration <code>compare = (nil,nil)</code>. Code in this form
- has the following semantics.
- </p>
- <dl compact="compact">
- <dt> <em>P17</em></dt>
- <dd><p>For distinct trees <code><var>x</var></code> and <code><var>y</var></code>, [[<code>compare</code>]] <code>(<var>x</var>,<var>y</var>)</code> = <code>nil</code>
- </p></dd>
- <dt> <em>P18</em></dt>
- <dd><p>[[<code>compare</code>]] <code>(<var>x</var>,<var>x</var>)</code> = <code>(nil,nil)</code>
- </p></dd>
- </dl>
- <a name="index-equality-2"></a>
- <p>In other words, the virtual code <code>(nil,nil)</code> implements a function
- that takes a pair of trees and returns true if and only if they are
- equal.
- </p>
- <p>It would be fairly simple to write an equivalent virtual code
- application that implements this function if it were not realizable in
- this form by definition of the operator. However, this method is
- preferable because it saves space in virtual code and has a highly
- optimized implementation in C.
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