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<title>avram - a virtual machine code interpreter: 2.7.13.5 Transfer</title>

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<a name="Transfer"></a>
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<a name="Transfer-1"></a>
<h4 class="subsubsection">2.7.13.5 Transfer</h4>

<a name="index-transfer"></a>
<p>A particular interpretation is given to virtual code in the following form.
</p>
<dl compact="compact">
<dt> <em>T26</em></dt>
<dd><p>[[<code>transfer</code>]] <code><var>f</var></code> = <code>((nil,nil),(nil,(nil,<var>f</var>)))</code>
</p></dd>
</dl>

<p>When code in this form is evaluated with an argument, the tree
<a name="index-state-transition-function"></a>
<code><var>f</var></code> is used as a state transition function, and the argument
is used as a list to be traversed. The traversal begins with
<code><var>f</var></code> being evaluated on <code>nil</code> to get the initial state
and the initial output. Thereafter, each item of the list is paired with
the current state to be evaluated with <code><var>f</var></code>, resulting in a
list of output and the next state. The output resulting from the entire
application is the cumulative concatenation of all outputs obtained in
the course of evaluating <code><var>f</var></code>. The computation
terminates when <code><var>f</var></code> yields a <code>nil</code> result. If the list
of inputs runs out before the computation terminates, <code>nil</code> values
are used as inputs.
</p>
<p>This behavior is specified more precisely in the following property
of the operator, which applies in the case of non-<code>nil</code> <code><var>f</var></code>.
<a name="index-transition"></a>
</p>
<dl compact="compact">
<dt> <em>P33</em></dt>
<dd><p>([[<code>transfer</code>]] <code><var>f</var></code>) <code><var>x</var></code> =
([[<code>transition</code>]] <code><var>f</var></code>) <code>(nil,(<var>f</var> nil,<var>x</var>))</code>
</p></dd>
</dl>

<p>Much of the <code>transfer</code> semantics is implicit in the meaning of
<code>transition</code>. For any given application <code><var>f</var></code>,
[[<code>transition</code>]] <code><var>f</var></code> is the virtual code for a function
that takes the list traversal from one configuration to the next.
A configuration is represented as a tuple, usually in the form
<code>(<var>previous outputs</var>,((<var>state</var>,<var>output</var>),(<var>next input</var>,<var>subsequent
inputs</var>)))</code>. A terminal configuration has the form
<code>(<var>previous outputs</var>,(nil,(<var>next input</var>,<var>subsequent
inputs</var>)))</code>. A configuration may also have <code>nil</code> in place of the
pair <code>(<var>next input</var>,<var>subsequent inputs</var>)</code> if no more input
remains.
</p>
<p>In the non-degenerate case, the meaning of [[<code>transition</code>]]
<code><var>f</var></code> is consistent with the following equation.
</p>
<dl compact="compact">
<dt> <em>E7</em></dt>
<dd><p>([[<code>transition</code>]] <code><var>f</var></code>) <code>(<var>y</var>,((<var>s</var>,<var>o</var>),(<var>i</var>,<var>x</var>)))</code> =<br>
    ([[<code>transition</code>]] <code><var>f</var></code>) <code>((<var>o</var>,<var>y</var>),(<var>f</var> (<var>s</var>,<var>i</var>),<var>x</var>))</code>
</p></dd>
</dl>

<p>That is, the current output <code><var>o</var></code> is stored with previous outputs <code><var>y</var></code>, the next
input <code><var>i</var></code> is removed from the configuration, and the next state and output
are obtained from the evaluation of <code><var>f</var></code> with the state <code><var>s</var></code> and
the next input <code><var>i</var></code>.
</p>
<p>In the case where no input remains, the transition function is
consistent with the following equation.
</p>
<dl compact="compact">
<dt> <em>E8</em></dt>
<dd><p>([[<code>transition</code>]] <code><var>f</var></code>) <code>(<var>y</var>,((<var>s</var>,<var>o</var>),nil))</code> = <br>
    ([[<code>transition</code>]] <code><var>f</var></code>) <code>((<var>o</var>,<var>y</var>),(<var>f</var> (<var>s</var>,nil),nil))</code>
</p></dd>
</dl>

<p>This case is similar to the previous one except that the <code>nil</code>
value is used in place of the next input. Note that in either case,
nothing about <code><var>f</var></code> depends on the particular way
configurations are represented, except that it should have a state as
its left argument and an input as its right argument.
</p>
<p>Finally, in the case of a terminal configuration, the transition
function returns the cumulative output.
</p>
<dl compact="compact">
<dt> <em>E9</em></dt>
<dd><p>([[<code>transition</code>]] <code><var>f</var></code>) <code>(<var>y</var>,(nil,<var>x</var>))</code> =
[[<code>reduce(cat,nil)</code>]] [[<code>reverse</code>]] <code><var>y</var></code>
</p></dd>
</dl>

<p>The <code>silly</code> code <code>reduce(cat,nil)</code> has the effect of
<a name="index-cat-1"></a>
<a name="index-concatenation"></a>
flattening a list of lists into one long list, which is necessary
insofar as the transition function will have generated not necessarily a
single output but a list of outputs on each iteration. The <code>cat</code>
mnemonic stands for list concatenation and is explained in <a href="Cat.html#Cat">Cat</a>.
The reversal is necessary to cause the first generated output to be at
the head of the list. List reversal is a built in operation of the
virtual machine and is described in <a href="Reverse.html#Reverse">Reverse</a>.
</p>
<p>If such a function as <code>transition</code> seems implausible, its
implementation in <code>silly</code> can be found in <a href="Transition.html#Transition">Transition</a>.
</p>
<p>It is usually more awkward to express a function in terms of
a <code>transfer</code> than to code it directly using recursion or other list
operations. However, this feature is provided by the virtual machine for
several reasons.
</p>
<ul>
<li> Functions in this form may be an easier translation target if the
source is an imperative language.
</li><li> Translating from virtual code to asynchronous circuits or process
<a name="index-asynchronous-circuits"></a>
networks has been a research interest of the author, and code in this
<a name="index-author-1"></a>
form lends itself to easy recognition and mapping onto discrete components.
</li><li> The &lsquo;<samp>--byte-transducer</samp>&rsquo; and &lsquo;<samp>--interactive</samp>&rsquo; command
line options to <code>avram</code> cause an application to be invoked in a
<a name="index-state-transition-function-1"></a>
similar manner to the transition function in a <code>transfer</code>
function, so this feature allows for easy simulation and troubleshooting
of these applications without actually deploying them.
</li></ul>


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