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  3. <title>Representation of Numeric and Textual Data - avram - a virtual machine code interpreter</title>
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  27. <a name="Representation-of-Numeric-and-Textual-Data"></a>
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  29. Next:&nbsp;<a rel="next" accesskey="n" href="Filter-Mode-Interface.html#Filter-Mode-Interface">Filter Mode Interface</a>,
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  33. </div>
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  34. 

  35. <h3 class="section">2.4 Representation of Numeric and Textual Data</h3>
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  36. 

  37. <p>As noted already, virtual code applications are specified by functions
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  38. operating on elements of a set having the properties described in
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  39. <a href="Raw-Material.html#Raw-Material">Raw Material</a>, which are convenient to envision as ordered binary trees or
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  40. <a name="index-trees-158"></a><a name="index-g_t_0040code_007bnil_007d-159"></a>pairs of <code>nil</code>. However, virtual code applications normally deal
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  41. with numeric or textual data, for example when they refer to the
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  42. contents of a text file. It is therefore necessary for the application
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  43. and the virtual machine emulator to agree on a way of describing textual
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  44. or numeric data with these trees.
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  45. 

  46.    <p>The purpose of this section is to explain the basic data structures used
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  47. in the exchange of information between <code>avram</code> and a virtual code
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  48. application.  For example, an explanation is needed for statements like
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  49. &ldquo;an application invoked with the <samp><span class="option">--baz</span></samp> option is expected to
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  50. return a pair <code>(</code><var>foo</var><code>,</code><var>bar</var><code>)</code>, where <var>foo</var> is a
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  51. <a name="index-strings-160"></a><a name="index-character-strings-161"></a><a name="index-lists-162"></a>list of character strings <small class="dots">...</small>&rdquo;, that are made subsequently in this
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  52. document. Such statements should be understood as referring to the trees
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  53. representing the pairs, lists, character strings, etc., according to the
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  54. conventions explained below.
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  55. 

  56.      <dl>
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  57. <dt><em>Characters</em><dd><a name="index-character-codes-163"></a>An arbitrarily chosen set of 256 trees is used to represent the
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  58. character set. They are listed in <a href="Character-Table.html#Character-Table">Character Table</a>. For example,
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  59. the letter <code>A</code> is represented by
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  60. <code>(nil,(((nil,(nil,(nil,nil))),nil),(nil,nil)))</code>.  That means that
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  61. when an application wants the letter <code>A</code> written to a text file, it
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  62. returns something with this tree in it. 
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  63. <br><dt><em>Booleans</em><dd><a name="index-booleans-164"></a>The value of <code>false</code> is represented by <code>nil</code>, and the value of
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  64. <code>true</code> is represented by <code>(nil,nil)</code>. 
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  65. <br><dt><em>Pairs</em><dd><a name="index-pairs-165"></a>Given any two items of data <var>x1</var> and <var>x2</var>, having the respective
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  66. representations <var>r1</var> and <var>r2</var>, the pair <code>(</code><var>x1</var><code>,</code><var>x2</var><code>)</code> has the
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  67. representation <code>cons(</code><var>r1</var><code>,</code><var>r2</var><code>)</code>. 
    68. 

  68. <br><dt><em>Lists</em><dd><a name="index-lists-166"></a>A list of the items <var>x1</var>, <var>x2</var> <small class="dots">...</small> <var>xn</var> with respective
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  69. representations <var>r1</var> through <var>rn</var> is represented by the tree
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  70. <code>cons(</code><var>r1</var><code>,cons(</code><var>r2</var><code>...cons(</code><var>rn</var><code>,nil)...))</code>. In other words,
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  71. lists are represented as pairs whose left sides are the heads and whose
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  72. right sides are the tails. The empty list is identified with
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  73. <code>nil</code>. Lists of arbitrary finite length can be accommodated. 
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  74. <br><dt><em>Naturals</em><dd><a name="index-naturals-167"></a>A number of the form <var>b0</var><code> + 2</code><var>b1</var><code> + 4</code><var>b2</var><code> + ... +
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  75. 2^n </code><var>bn</var>, where each <var>b</var><code>i</code> is <code>0</code> or <code>1</code>, is
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  76. represented by a tree of the form
    77. 

  77. <code>cons(</code><var>t0</var><code>,cons(</code><var>t1</var><code>...cons(</code><var>tn</var><code>,nil)...))</code>
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  78. where each <var>t</var><code>i</code> is <code>nil</code> if the corresponding
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  79. <var>b</var><code>i</code> is <code>0</code>, and <code>(nil,nil)</code> otherwise. Note that
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  80. the numbers <var>b</var><code>i</code> are exactly the bits written in the binary
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  81. expansion of the number, with <var>b0</var> being the least significant
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  82. bit. 
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  83. <br><dt><em>Strings</em><dd><a name="index-strings-168"></a><a name="index-character-strings-169"></a>are represented as lists of characters. 
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  84. </dl>
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  85. 

  86.    <p><a name="index-types-170"></a><code>avram</code> imposes no more of a &ldquo;type discipline&rdquo; than necessary to
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  87. a workable interface between it and an application.  This selection of
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  88. types and constructors should not be seen as constraining what a
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  89. compiler writer may wish to have in a source language.
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  90. 

  91.    </body></html>
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