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<a name="Refer-1"></a>
<h4 class="subsubsection">2.7.9.2 Refer</h4>

<a name="index-refer"></a>
<p>In the style of recursive programming compelled by the available
<code>meta</code> primitive, a function effectively requires a copy of its own
machine code as its left argument. Bringing about that state of
affairs is an interesting party trick.
</p>
<a name="index-bu"></a>
<p>If we had a definition of <code>bu</code> in the standard library implying
</p>
<dl compact="compact">
<dt> <em>T16</em></dt>
<dd><p>([[<code>bu</code>]] <code>(<var>f</var>,<var>k</var>)</code>) <code><var>x</var></code> = <code><var>f</var>(<var>k</var>,<var>x</var>)</code>
</p></dd>
</dl>

<p>which for the sake of concreteness can be done like this,
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">bu = (hired compose)(
        left,
        (hired couple)(compose(constant,right),constant identity))
</pre></td></tr></table>

<p>then a definition of <code>refer</code> as
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">refer = (hired bu)(identity,identity)
</pre></td></tr></table>

<p>would be consistent with the following property of the operator.
</p>
<dl compact="compact">
<dt> <em>P15</em></dt>
<dd><p>([[<code>refer</code>]] <code><var>f</var></code>) <code><var>x</var></code> = <code><var>f</var> (<var>f</var>,<var>x</var>)</code>
</p></dd>
</dl>

<p>The proof, as always, is a matter of routine calculation in the manner
of the section on how <code>avram</code> thinks.
</p>
<p>However, this pattern would occur so frequently in recursively defined
functions as to be a significant waste of space and time. Therefore,
rather than requiring it to be defined in terms of other operations, the
virtual machine specification recognizes a pattern of the form below with
respect to property <em>P15</em>,
</p>
<dl compact="compact">
<dt> <em>T17</em></dt>
<dd><p>[[<code>refer</code>]] <code><var>f</var></code> = <code>(((<var>f</var>,nil),nil),nil)</code>
</p></dd>
</dl>

<p>and takes the property to be true by definition of the operator. A
definition of <code>refer</code> consistent with <em>T17</em> is therefore to
<a name="index-standard-library"></a>
be found in the standard library, not the definition proposed above.
</p>

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