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<a name="Field"></a>
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<hr size="1">
<a name="Field-1"></a>
<h4 class="subsubsection">2.7.8.1 Field</h4>

<p>The virtual machine supports a generalization of the <code>left</code> and
<a name="index-left-1"></a>
<a name="index-right-1"></a>
<code>right</code> deconstruction operations that is applicable to deeply nested
structures. Use of this feature is conducive to code that is faster and
more compact than is possible by relying on the primitive deconstructors
alone. It may also be easier for a code optimizer to recognize and
transform.
</p>
<p>The general form of a virtual code application to perform deconstruction
is that it is a pair with a <code>nil</code> left side, and a non-<code>nil</code>
right side. The right side indicates the nature of the deconstruction to
be performed when the function is evaluated on an argument.
</p>
<p>To make the expression of deconstruction functions more readable in
<code>silly</code>, the standard library contains the declaration
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">field = couple(constant nil,identity)
</pre></td></tr></table>

<p>which implies the following theorem.
</p>
<dl compact="compact">
<dt> <em>T13</em></dt>
<dd><p>[[<code>field</code>]] <code><var>w</var></code> = <code>(nil,<var>w</var>)</code>
</p></dd>
</dl>

<a name="index-field"></a>
<p>The virtual machine recognizes an application in this form and evaluates
it according to the following properties, where <code><var>u</var></code> and
<code><var>v</var></code> are other than <code>nil</code>, but <code><var>x</var></code>,
<code><var>y</var></code>, and <code><var>z</var></code> are unrestricted.
</p>
<dl compact="compact">
<dt> <em>P10</em></dt>
<dd><p>([[<code>field</code>]] <code>(<var>u</var>,nil)</code>) <code>(<var>x</var>,<var>y</var>)</code> = ([[<code>field</code>]] <code><var>u</var></code>) <code><var>x</var></code>
</p></dd>
<dt> <em>P11</em></dt>
<dd><p>([[<code>field</code>]] <code>(nil,<var>v</var>)</code>) <code>(<var>x</var>,<var>y</var>)</code> = ([[<code>field</code>]] <code><var>v</var></code>) <code><var>y</var></code>
</p></dd>
<dt> <em>P12</em></dt>
<dd><p>([[<code>field</code>]] <code>(<var>u</var>,<code>v</code>)</code>) <code><var>z</var></code> = <code>((</code>[[<code>field</code>]] <code><var>u</var>) <var>z</var>,(</code>[[<code>field</code>]] <code><var>v</var>) <var>z</var>)</code>
</p></dd>
</dl>

<p>One might also add that ([[<code>field</code>]] <code>(nil,nil)</code>)
<code><var>z</var></code> = <code><var>z</var></code>, but this statement would be equivalent to
<em>P0</em>.
</p>
<p>A suitable choice of the <code>field</code> operand permits the implementation
of any deconstruction function expressible in terms of <code>compose</code>,
<code>couple</code>, <code>identity</code>, <code>left</code> and <code>right</code>. For
example, the application <code>couple(compose(right,right),left)</code> has an
equivalent representation in
<code>field((nil,(nil,(nil,nil))),((nil,nil),nil))</code>. The latter looks
longer in <code>silly</code> but is smaller and faster in virtual code.
</p>
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