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<title>avram - a virtual machine code interpreter: 2.7.17 Vacant Address Space</title>

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<a name="Vacant-Address-Space"></a>
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<hr size="1">
<a name="Vacant-Address-Space-1"></a>
<h3 class="subsection">2.7.17 Vacant Address Space</h3>

<p>Not every possible pattern has been used by the virtual machine as a way
of encoding a function. The following patterns, where <code><var>a</var></code>,
<code><var>b</var></code>, and <code><var>c</var></code> are non-<code>nil</code> trees, do not
represent anything useful.
</p>
<dl compact="compact">
<dt> unary forms</dt>
<dd><p><code>((nil,nil),((nil,nil),(nil,((nil,<var>a</var>),nil))))</code><br>
<code>((nil,nil),((nil,nil),(nil,(nil,(nil,<var>a</var>)))))</code>
</p></dd>
<dt> binary forms</dt>
<dd><p><code>((nil,nil),((nil,nil),(<var>a</var>,<var>b</var>)))</code><br>
<code>((nil,nil),((<var>a</var>,nil),(<var>b</var>,nil)))</code><br>
<code>((nil,nil),((<var>a</var>,nil),(nil,<var>b</var>)))</code>
</p></dd>
<dt> ternary forms</dt>
<dd><p><code>((nil,nil),((<var>a</var>,<var>b</var>),(<var>c</var>,nil)))</code><br>
<code>((nil,nil),((<var>a</var>,<var>b</var>),(nil,<var>c</var>)))</code><br>
<code>((nil,nil),((<var>a</var>,nil),(<var>b</var>,<var>c</var>)))</code><br>
<code>((nil,nil),((nil,<var>a</var>),(<var>b</var>,<var>c</var>)))</code>
</p></dd>
</dl>

<p>These patterns are detected by the virtual machine simply to avoid blowing
it up, but they always cause an error message to be reported.
<a name="index-unsupported-hook-2"></a>
<a name="index-unrecognized-combinator-1"></a>
</p>
<dl compact="compact">
<dt> <em>P55</em></dt>
<dd><p>For <code><var>f</var></code> matching any of the first three trees in the above list,<br>
   <code><var>f</var>_<var>n</var> <var>x</var>_<var>n</var></code> =
[[<code>('unsupported hook',nil)</code>]]<code>_(<var>n</var>+1)</code>
</p></dd>
<dt> <em>P56</em></dt>
<dd><p>For the remaining trees <code><var>f</var></code> in the above list,<br>
   <code><var>f</var>_<var>n</var> <var>x</var>_<var>n</var></code> =
[[<code>('unrecognized combinator (code <var>m</var>)',nil)</code>]]<code>_(<var>n</var>+1)</code>
</p></dd>
</dl>

<p>Here, <code><var>m</var></code> is a numeric constant dependent on which tree
<code><var>f</var></code> was used. The unsupported hook message is meant to be
more informative than the unrecognized combinator message, suggesting
that a feature intended for future use is not yet available.
</p>
<p>This list has been assembled for the benefit of readers considering the
addition of backward compatible extensions to the virtual code
semantics, who are undeterred by the facts that 
</p><ul>
<li> 
the computational model
<a name="index-universality-1"></a>
is already universal
</li><li>
virtual code applications are already
interoperable with all kinds of high performance software having a text
based or console interface by way of the <code>interact</code> combinator
</li><li>
an unlimited number of built in library functions can be added
by way of the <code>library</code> combinator as described in
<a href="Implementing-new-library-functions.html#Implementing-new-library-functions">Implementing new library functions</a>
</li><li>
the C code in <code>avram</code> makes fairly
<a name="index-pointers-2"></a>
intricate use of pointers with a careful policy of reference counting
and storage reclamation
</li><li>
there is also a performance penalty incurred by
<a name="index-reference-count"></a>
further extensions to the semantics, even for applications that don&rsquo;t
use them, because a pattern recognition algorithm in the interpreter has
more cases to consider.
</li></ul>

<p>Nevertheless, a new functional form combining a pair of functions to be
interpreted in a new way by the virtual machine could be defined using
any of the binary forms above, for example, with <code><var>a</var></code> as the
virtual code for one of the functions and <code><var>b</var></code> as that of the
other. Such a form would not conflict with any existing applications,
provided that both <code><var>a</var></code> and <code><var>b</var></code> are not <code>nil</code>,
which is true of any valid representation for a function.
</p>
<p>Virtual machine architects, take note. There are infinitely many trees
<a name="index-trees-4"></a>
fitting these patterns, but it would be possible to use them up by
assigning them without adequate foresight. For example, if
interpretations were assigned to the four ternary forms, the three binary
forms, and one of the remaining unary forms, then the only
unassigned pattern could be of the form
</p>
<table><tr><td>&nbsp;</td><td><pre class="display"><code>((nil,nil),((nil,nil),(nil,(nil,(nil,<var>a</var>)))))</code>
</pre></td></tr></table>

<p>Assigning an interpretation to it would leave no further room for
backward compatible expansion. On the other hand, any tree of the
following form also fits the above pattern,
</p>
<table><tr><td>&nbsp;</td><td><pre class="display"><code>((nil,nil),((nil,nil),(nil,(nil,(nil,(<var>b</var>,<var>c</var>))))))</code>
</pre></td></tr></table>

<p>with any values for <code><var>b</var></code> and <code><var>c</var></code>. Different
meanings could be chosen for the case where both are <code>nil</code>, both
are non-<code>nil</code>, or one is <code>nil</code> and the other non-<code>nil</code>,
allowing two unary forms, one binary, and one constant. If at least one
of these patterns is reserved for future enhancements, then a
potentially inexhaustible supply of address space remains and there will
be no need for incompatible changes later.
</p>
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