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<a name="Compare"></a>
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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.
</p>
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