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<title>APRON 0.9.10: Functionalities of the interface at level 1</title>

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<a name="Functionalities-of-the-interface-at-level-1"></a>
<table cellpadding="1" cellspacing="1" border="0">
<tr><td valign="middle" align="left">[<a href="apron_5.html#Functionalities-of-the-interface-at-level-0" title="Previous section in reading order"> &lt; </a>]</td>
<td valign="middle" align="left">[<a href="apron_7.html#APRON-Guidelines" title="Next section in reading order"> &gt; </a>]</td>
<td valign="middle" align="left"> &nbsp; </td>
<td valign="middle" align="left">[<a href="apron_3.html#APRON-Rationale-and-Functionalities" title="Beginning of this chapter or previous chapter"> &lt;&lt; </a>]</td>
<td valign="middle" align="left">[<a href="apron_3.html#APRON-Rationale-and-Functionalities" title="Up section"> Up </a>]</td>
<td valign="middle" align="left">[<a href="apron_7.html#APRON-Guidelines" title="Next chapter"> &gt;&gt; </a>]</td>
<td valign="middle" align="left"> &nbsp; </td>
<td valign="middle" align="left"> &nbsp; </td>
<td valign="middle" align="left"> &nbsp; </td>
<td valign="middle" align="left"> &nbsp; </td>
<td valign="middle" align="left">[<a href="apron.html#Top" title="Cover (top) of document">Top</a>]</td>
<td valign="middle" align="left">[Contents]</td>
<td valign="middle" align="left">[<a href="apron_42.html#Appendices" title="Index">Index</a>]</td>
<td valign="middle" align="left">[<a href="apron_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
</tr></table>
<a name="Functionalities-of-the-interface-at-level-1-1"></a>
<h2 class="section">Functionalities of the interface at level 1</h2>

<p>We focus on the changes brought by the level 1 w.r.t. the level 0.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top"><a href="#Variables-and-Environments">&bull; Variables and Environments</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">  
</td></tr>
<tr><td align="left" valign="top"><a href="#Semantics-and-Representation-of-an-abstract-value">&bull; Semantics and Representation of an abstract value</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">  
</td></tr>
<tr><td align="left" valign="top"><a href="#Operations-on-environments">&bull; Operations on environments</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">  
</td></tr>
<tr><td align="left" valign="top"><a href="#Dynamic-typing-w_002er_002et_002e-environments">&bull; Dynamic typing w.r.t. environments</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">  
</td></tr>
<tr><td align="left" valign="top"><a href="#Operations-on-variables-in-abstract-values">&bull; Operations on variables in abstract values</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">  
</td></tr>
</table>

<a name="Variables-and-Environments"></a>
<a name="Variables"></a>
<h4 class="subsubheading">Variables</h4>

<p>Dimensions are replaced by <em>variables</em>.
</p>
<p>In the C interface, variables are defined by a generic type
(<code>char*</code>, structured type, ...), equipped with the operations
<code>compare</code>, <code>copy</code>, <code>free</code>, <code>to_string</code>. In the
<small>OCAML</small>, for technical reasons, the type is just the <code>string</code>
type.
</p>
<p><em>Environments</em> manages the correspondance between the numerical
dimensions of level 0 and the variables of level 1.
</p>
<a name="Semantics-and-Representation-of-an-abstract-value"></a>
<a name="Semantics-and-Representation-of-an-abstract-value-1"></a>
<h4 class="subsubheading">Semantics and Representation of an abstract value</h4>

<p>The semantics of an abstract value is a subset
</p><blockquote><p>X -&gt; (N+R).
</p></blockquote>
<p>where <em>X</em> is a set of variables.
Abstract values are typed according to their environment.
</p>
<p>It is represented by a structure
</p><pre class="verbatim">struct ap_abstract1_t {
  ap_abstract0_t    *abstract0;
  ap_environment_t  *env;
};
</pre><p>Other datatypes of level 0 are extend in the same way. For instance,
</p><pre class="verbatim">struct ap_linexpr1_t {
  ap_linexpr0_t    *linexpr0;
  ap_environment_t *env;
};
</pre>
<a name="Operations-on-environments"></a>
<a name="Operations-on-environments-1"></a>
<h4 class="subsubheading">Operations on environments</h4>

<ul>
<li> creation, merging, destruction
</li><li> addition/removal/renaming of variables
</li></ul>

<a name="Dynamic-typing-w_002er_002et_002e-environments"></a>
<a name="Dynamic-typing-w_002er_002et_002e-environments-1"></a>
<h4 class="subsubheading">Dynamic typing w.r.t. environments</h4>

<p>For binary operations on abstract values, the environments should be
the same.
</p>
<p>For operations involving an abstract value and an other datatype
(expression, constraint, ...), one checks that the environment of
the expression is a subenvironment of the environment of the abstract
value, and one resize if necessary.
</p>
<a name="Operations-on-variables-in-abstract-values"></a>
<a name="Operations-on-variables-in-abstract-values-1"></a>
<h4 class="subsubheading">Operations on variables in abstract values</h4>

<p>Operations on dimensions are lifted to operations on variables:
</p>
<ul>
<li>
Projection/Elimination of one or several variables with constant
environment;
</li><li>
Addition/Removal/Renaming of variables with corresponding change
of environment;
</li><li>
Change of environment (possibly combining removal and addition of variables);
</li><li>
Expansion and folding of variables. 
</li></ul>

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