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<a name="Representation-of-Numeric-and-Textual-Data"></a>
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<a name="Representation-of-Numeric-and-Textual-Data-1"></a>
<h2 class="section">2.4 Representation of Numeric and Textual Data</h2>

<p>As noted already, virtual code applications are specified by functions
operating on elements of a set having the properties described in
<a href="Raw-Material.html#Raw-Material">Raw Material</a>, which are convenient to envision as ordered binary trees or
<a name="index-trees-2"></a>
<a name="index-nil-1"></a>
pairs of <code>nil</code>. However, virtual code applications normally deal
with numeric or textual data, for example when they refer to the
contents of a text file. It is therefore necessary for the application
and the virtual machine emulator to agree on a way of describing textual
or numeric data with these trees.
</p>
<p>The purpose of this section is to explain the basic data structures used
in the exchange of information between <code>avram</code> and a virtual code
application.  For example, an explanation is needed for statements like
&ldquo;an application invoked with the &lsquo;<samp>--baz</samp>&rsquo; option is expected to
return a pair <code>(<var>foo</var>,<var>bar</var>)</code>, where <code><var>foo</var></code> is a
<a name="index-strings"></a>
<a name="index-character-strings"></a>
<a name="index-lists-2"></a>
list of character strings &hellip;&rdquo;, that are made subsequently in this
document. Such statements should be understood as referring to the trees
representing the pairs, lists, character strings, etc., according to the
conventions explained below.
</p>
<dl compact="compact">
<dt> <em>Characters</em></dt>
<dd><a name="index-character-codes-1"></a>
<p>An arbitrarily chosen set of 256 trees is used to represent the
character set. They are listed in <a href="Character-Table.html#Character-Table">Character Table</a>. For example,
the letter <code>A</code> is represented by
<code>(nil,(((nil,(nil,(nil,nil))),nil),(nil,nil)))</code>.  That means that
when an application wants the letter <code>A</code> written to a text file, it
returns something with this tree in it.
</p></dd>
<dt> <em>Booleans</em></dt>
<dd><a name="index-booleans"></a>
<p>The value of <code>false</code> is represented by <code>nil</code>, and the value of
<code>true</code> is represented by <code>(nil,nil)</code>.
</p></dd>
<dt> <em>Pairs</em></dt>
<dd><a name="index-pairs"></a>
<p>Given any two items of data <var>x1</var> and <var>x2</var>, having the respective
representations <var>r1</var> and <var>r2</var>, the pair <code>(<var>x1</var>,<var>x2</var>)</code> has the
representation <code>cons(<var>r1</var>,<var>r2</var>)</code>.
</p></dd>
<dt> <em>Lists</em></dt>
<dd><a name="index-lists-3"></a>
<p>A list of the items <var>x1</var>, <var>x2</var> &hellip; <var>xn</var> with respective
representations <var>r1</var> through <var>rn</var> is represented by the tree
<code>cons(<var>r1</var>,cons(<var>r2</var>&hellip;cons(<var>rn</var>,nil)&hellip;))</code>. In other words,
lists are represented as pairs whose left sides are the heads and whose
right sides are the tails. The empty list is identified with
<code>nil</code>. Lists of arbitrary finite length can be accommodated.
</p></dd>
<dt> <em>Naturals</em></dt>
<dd><a name="index-naturals"></a>
<p>A number of the form <code><var>b0</var> + 2<var>b1</var> + 4<var>b2</var> + &hellip; +
2^n <var>bn</var></code>, where each <code><var>b</var>i</code> is <code>0</code> or <code>1</code>, is
represented by a tree of the form
<code>cons(<var>t0</var>,cons(<var>t1</var>&hellip;cons(<var>tn</var>,nil)&hellip;))</code>
where each <code><var>t</var>i</code> is <code>nil</code> if the corresponding
<code><var>b</var>i</code> is <code>0</code>, and <code>(nil,nil)</code> otherwise. Note that
the numbers <code><var>b</var>i</code> are exactly the bits written in the binary
expansion of the number, with <code><var>b0</var></code> being the least significant
bit.
</p></dd>
<dt> <em>Strings</em></dt>
<dd><a name="index-strings-1"></a>
<a name="index-character-strings-1"></a>
<p>are represented as lists of characters.
</p></dd>
</dl>

<a name="index-types"></a>
<p><code>avram</code> imposes no more of a &ldquo;type discipline&rdquo; than necessary to
a workable interface between it and an application.  This selection of
types and constructors should not be seen as constraining what a
compiler writer may wish to have in a source language.
</p>

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<td valign="middle" align="left">[<a href="avram_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>
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