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<title>APRON 0.9.10: Abstract values and operations of level 1 (ap_abstract1.h)</title>
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<a name="Abstract-values-and-operations-of-level-1"></a>
<table cellpadding="1" cellspacing="1" border="0">
<tr><td valign="middle" align="left">[<a href="apron_30.html#Arrays-of-tree-constraints-of-level-1" title="Previous section in reading order"> < </a>]</td>
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<td valign="middle" align="left">[Contents]</td>
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<a name="Abstract-values-and-operations-of-level-1-_0028ap_005fabstract1_002eh_0029"></a>
<h2 class="section">Abstract values and operations of level 1 (‘<tt>ap_abstract1.h</tt>’)</h2>
<dl>
<dt><a name="index-ap_005fabstract1_005ft"></a><u>datatype:</u> <b>ap_abstract1_t</b></dt>
<dd><p>Datatype for abstract values at level 1.
</p>
<p>For information:
</p><table><tr><td> </td><td><pre class="example">typedef struct ap_abstract1_t {
ap_abstract0_t* abstract0;
ap_environment_t* env;
} ap_abstract1_t;
/* data structure invariant:
ap_abstract0_integer_dimension(man,abstract0)== env->intdim &&
ap_abstract0_real_dimension(man,abstract0)== env->realdim */
</pre></td></tr></table>
</dd></dl>
<dl>
<dt><a name="index-ap_005fbox1_005ft"></a><u>datatype:</u> <b>ap_box1_t</b></dt>
<dd><table><tr><td> </td><td><pre class="example">typedef struct ap_box1_t {
ap_interval_t** p;
ap_environment_t* env;
} ap_box1_t;
void ap_box1_fprint(FILE* stream, ap_box1_t* box);
void ap_box1_clear(ap_box1_t* box);
</pre></td></tr></table>
</dd></dl>
<p>Most operations are offered in 2 versions: <em>functional</em> or
<em>destructive</em> See section <a href="apron_39.html#Abstract-values-and-operations-of-level-0">Abstract values and operations of level 0 (‘<tt>ap_abstract0.h</tt>’)</a>.
</p>
<p>We remind the policy for redimensioning (see section <a href="apron_23.html#Level-1-of-the-interface">Level 1 of the interface</a>):
</p>
<ul>
<li>
For functions taking one abstract value and one expression (or
constraint or generator, or array of ...), the environment of the
expression should be a sub-environment of the environment of the
abstract value. The environment of the result is the environment of
the argument abstract value.
</li><li>
For functions taking several abstract values, their environments
should be the same. Otherwise, it is up to the user to move them to a
common super-environment (see section <a href="apron_25.html#Environments">Environments (‘<tt>ap_environment.h</tt>’)</a>).
</li></ul>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top"><a href="#Allocating-abstract-values-of-level-1">Allocating abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Control-of-internal-representation-of-abstract-values-of-level-1">Control of internal representation of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Printing-abstract-values-of-level-1">Printing abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Serialization-of-abstract-values-of-level-1">Serialization of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Constructors, Accessors, Tests and Extraction of properties
</pre></th></tr><tr><td align="left" valign="top"><a href="#Constructors-for-abstract-values-of-level-1">Constructors for abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Accessors-for-abstract-values-of-level-1">Accessors for abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Tests-on-abstract-values-of-level-1">Tests on abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Extraction-of-properties-of-abstract-values-of-level-1">Extraction of properties of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Operations
</pre></th></tr><tr><td align="left" valign="top"><a href="#Meet-and-Join-of-abstract-values-of-level-1">Meet and Join of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Assignements-and-Substitutions-of-abstract-values-of-level-1">Assignements and Substitutions of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Existential-quantification-of-abstract-values-of-level-1">Existential quantification of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Change-of-environments-of-abstract-values-of-level-1">Change of environments of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Expansion-and-Folding-of-dimensions-in-abstract-values-of-level-1">Expansion and Folding of dimensions of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Widening-of-abstract-values-of-level-1">Widening of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Topological-closure-of-abstract-values-of-level-1">Topological closure of abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Additional functions
</pre></th></tr><tr><td align="left" valign="top"><a href="#Additional-functions-on-abstract-values-of-level-1">Additional functions on abstract values of level 1</a></td><td> </td><td align="left" valign="top">
</td></tr>
</table>
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<a name="Allocating-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Allocating abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fcopy"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_copy</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Return a copy of <var>a</var>, on which destructive update does not
affect <var>a</var>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fclear"></a><u>Function:</u> void <b>ap_abstract1_clear</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Free all the memory used by <var>a</var>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fsize"></a><u>Function:</u> size_t <b>ap_abstract1_size</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Return the abstract size of <var>a</var>.
</p></dd></dl>
<hr size="6">
<a name="Control-of-internal-representation-of-abstract-values-of-level-1"></a>
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<td valign="middle" align="left">[Contents]</td>
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</tr></table>
<a name="Control-of-internal-representation-of-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Control of internal representation of abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fminimize"></a><u>Function:</u> void <b>ap_abstract1_minimize</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Minimize the size of the representation of <var>a</var>. This may result in
a later recomputation of internal information.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fcanonicalize"></a><u>Function:</u> void <b>ap_abstract1_canonicalize</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Put <var>a</var> in canonical form. (not yet clear definition).
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fhash"></a><u>Function:</u> int <b>ap_abstract1_hash</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Return an hash value for <var>a</var>. Two abstract values in canonical
from (according to <code>ap_abstract1_canonicalize</code>) and considered as
equal by the function <code>ap_abstract1_is_eq</code> are given the
same hash value.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fapproximate"></a><u>Function:</u> void <b>ap_abstract1_approximate</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, int <var>algorithm</var>)</i></dt>
<dd><p>Perform some transformation on <var>a</var>, guided by the field
algorithm.
</p>
<p>The transformation may lose information. The argument
<var>algorithm</var> overrides the field algorithm of the structure of
type <code>ap_funopt_t</code> associated to
<code>ap_abstract1_approximate</code>.
</p></dd></dl>
<hr size="6">
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<a name="Printing-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Printing abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005ffprint"></a><u>Function:</u> void <b>ap_abstract1_fprint</b><i> (FILE* <var>stream</var>, ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Print <var>a</var> in a pretty way on the stream.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005ffprintdiff"></a><u>Function:</u> void <b>ap_abstract1_fprintdiff</b><i> (FILE* <var>stream</var>, ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a1</var>, ap_abstract1_t* <var>a2</var>)</i></dt>
<dd><p>Print the difference between <var>a1</var> (old value) and <var>a2</var> (new
value). The meaning of difference is library dependent.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005ffdump"></a><u>Function:</u> void <b>ap_abstract1_fdump</b><i> (FILE* <var>stream</var>, ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Dump the internal representation of <var>a</var> for debugging
purposes.
</p></dd></dl>
<hr size="6">
<a name="Serialization-of-abstract-values-of-level-1"></a>
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<a name="Serialization-of-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Serialization of abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fserialize_005fraw"></a><u>Function:</u> ap_membuf_t <b>ap_abstract1_serialize_raw</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Allocate a memory buffer (with <code>malloc</code>), output <var>a</var>
in raw binary format to it and return a pointer on the memory
buffer and the number of bytes written. It is the user
responsability to free the memory afterwards (with <code>free</code>).
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fdeserialize_005fraw"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_deserialize_raw</b><i> (ap_manager_t* <var>man</var>, void* <var>ptr</var>, size_t* <var>size</var>)</i></dt>
<dd><p>Return the abstract value read in raw binary format from the
buffer pointed by <var>ptr</var> and store in size the number of bytes
read.
</p></dd></dl>
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<a name="Constructors-for-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Constructors for abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fbottom"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_bottom</b><i> (ap_manager_t* <var>man</var>, ap_environment_t* <var>env</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005ftop"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_top</b><i> (ap_manager_t* <var>man</var>, ap_environment_t* <var>env</var>)</i></dt>
<dd><p>Create resp. a bottom (empty) value and a top (universe) value defined
on the environment <var>env</var>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fof_005fbox"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_of_box</b><i> (ap_manager_t* <var>man</var>, ap_environment_t* <var>env</var>, ap_var_t* <var>tvar</var>, ap_interval_t** <var>tinterval</var>, size_t <var>size</var>)</i></dt>
<dd><p>Abstract an hypercube defined by the arrays <var>tvar</var> and
<var>tintnerval</var> of size <var>size</var>.
</p>
<p>If no inclusion is specified for a variable in the environment, its
value is no constrained in the resulting abstract value.
</p></dd></dl>
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<a name="Accessors-for-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Accessors for abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fenvironment"></a><u>Function:</u> ap_dimension_t <b>ap_abstract1_environment</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Get a reference to the environment of <var>a</var>. Do not free it.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fmanager"></a><u>Function:</u> ap_manager_t* <b>ap_abstract1_manager</b><i> (ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Get a reference to the manager contained in <var>a</var>.
Do not free it.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fabstract0"></a><u>Function:</u> ap_dimension_t <b>ap_abstract1_abstract0</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Get a reference to the underlying abstract value of level 0 in
<var>a</var>. Do not free it.
</p></dd></dl>
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<a name="Tests-on-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Tests on abstract values of level 1</h3>
<p>In abstract tests,
</p><ul>
<li>
true means that the predicate is certainly true;
</li><li>
false means false <em>or</em> don’t know (an exception has occurred, or
the exact computation was considered too expensive to be performed,
according to the options).
</li></ul>
<dl>
<dt><a name="index-ap_005fabstract1_005fis_005fbottom"></a><u>Function:</u> bool <b>ap_abstract1_is_bottom</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fis_005ftop"></a><u>Function:</u> bool <b>ap_abstract1_is_top</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Emtpiness and universality tests.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fis_005fleq"></a><u>Function:</u> bool <b>ap_abstract1_is_leq</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a1</var>, ap_abstract1_t* <var>a2</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fis_005feq"></a><u>Function:</u> bool <b>ap_abstract1_is_eq</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a1</var>, ap_abstract1_t* <var>a2</var>)</i></dt>
<dd><p>Inclusion and equality tests.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fsat_005finterval"></a><u>Function:</u> bool <b>ap_abstract1_sat_interval</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, ap_var_t <var>var</var>, ap_interval_t* <var>interval</var>)</i></dt>
<dd><p>Is the variable <var>var</var> included in the interval <var>interval</var> in the abstract value <var>a</var> ?
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fsat_005flincons"></a><u>Function:</u> bool <b>ap_abstract1_sat_lincons</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, ap_lincons1_t* <var>cons</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fsat_005ftcons"></a><u>Function:</u> bool <b>ap_abstract1_sat_tcons</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, ap_tcons1_t* <var>cons</var>)</i></dt>
<dd><p>Does the abstract value <var>a</var> satisfy the constraint <var>cons</var> ?
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fis_005fvariable_005funconstrained"></a><u>Function:</u> bool <b>ap_abstract1_is_variable_unconstrained</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, ap_var_t <var>var</var>)</i></dt>
<dd><p>Is the dimension <var>dim</var> unconstrained in the abstract value <var>a</var> ?
If it is the case, we have <code>forget(man,a,dim) == a</code>.
</p></dd></dl>
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<a name="Extraction-of-properties-of-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Extraction of properties of abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fbound_005fvariable"></a><u>Function:</u> ap_interval_t* <b>ap_abstract1_bound_variable</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, ap_var_t <var>var</var>)</i></dt>
<dd><p>Return the interval taken by the variable <var>var</var> over the abstract
value <var>a</var>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fbound_005flinexpr"></a><u>Function:</u> ap_interval_t* <b>ap_abstract1_bound_linexpr</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, ap_linexpr1_t* <var>expr</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fbound_005ftexpr"></a><u>Function:</u> ap_interval_t* <b>ap_abstract1_bound_texpr</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, ap_texpr1_t* <var>expr</var>)</i></dt>
<dd><p>Return the interval taken by the expression <var>expr</var> over
the abstract value <var>a</var>.
</p>
<p>In the case of truly linear expression, this function allows to solve
a Linear Programming (LP) problem, but depending on the underlying
domain the solution may be not optimal.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fto_005fbox"></a><u>Function:</u> ap_box1_t <b>ap_abstract1_to_box</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Convert <var>a</var> to an interval/hypercube.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fto_005flincons_005farray"></a><u>Function:</u> ap_lincons1_array_t <b>ap_abstract1_to_lincons_array</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fto_005ftcons_005farray"></a><u>Function:</u> ap_tcons1_array_t <b>ap_abstract1_to_tcons_array</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Convert <var>a</var> to a conjunction of linear (resp. tree)
constraints.
</p>
<p>The constraints are normally guaranteed to be without intervals.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fto_005fgenerator_005farray"></a><u>Function:</u> ap_generator1_array_t <b>ap_abstract1_to_generator_array</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Convert <var>a</var> to an array of generators.
</p></dd></dl>
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<a name="Meet-and-Join-of-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Meet and Join of abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fmeet"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_meet</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a1</var>, ap_abstract1_t* <var>a2</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fjoin"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_join</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a1</var>, ap_abstract1_t* <var>a2</var>)</i></dt>
<dd><p>Meet and Join of 2 abstract values
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fmeet_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_meet_array</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>array</var>, size_t <var>size</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fjoin_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_join_array</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>array</var>, size_t <var>size</var>)</i></dt>
<dd><p>Meet and Join of the array <var>array</var> of abstract values of size
<var>size</var>.
</p>
<p>Raise an <code>AP_EXC_INVALID_ARGUMENT</code> exception if
<code>size==1</code> (no way to define the environment of the result
in such a case).
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fmeet_005flincons_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_meet_lincons_array</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>, ap_lincons1_array_t* <var>array</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fmeet_005ftcons_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_meet_tcons_array</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>, ap_tcons1_array_t* <var>array</var>)</i></dt>
<dd><p>Meet of the abstract value <var>a</var> with the set of constraints
<var>array</var>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fadd_005fray_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_add_ray_array</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>, ap_generator1_array_t* <var>array</var>)</i></dt>
<dd><p>Generalized time elapse operator.
</p>
<p><var>array</var> is supposed to contain only rays or lines, no vertices.
</p></dd></dl>
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<a name="Assignements-and-Substitutions-of-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Assignements and Substitutions of abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fassign_005flinexpr_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_assign_linexpr_array</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>org</var>, ap_var_t* <var>tvar</var>, ap_linexpr1_t* <var>texpr</var>, size_t <var>size</var>, ap_abstract1_t* <var>dest</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fsubstitute_005flinexpr_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_substitute_linexpr_array</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>org</var>, ap_var_t* <var>tvar</var>, ap_linexpr1_t* <var>texpr</var>, size_t <var>size</var>, ap_abstract1_t* <var>dest</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fassign_005ftexpr_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_assign_texpr_array</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>org</var>, ap_var_t* <var>tvar</var>, ap_texpr1_t* <var>texpr</var>, size_t <var>size</var>, ap_abstract1_t* <var>dest</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fsubstitute_005ftexpr_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_substitute_texpr_array</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>org</var>, ap_var_t* <var>tvar</var>, ap_texpr1_t* <var>texpr</var>, size_t <var>size</var>, ap_abstract1_t* <var>dest</var>)</i></dt>
<dd><p>Parallel Assignement and Substitution of several variables by
expressions in abstract value <var>org</var>.
</p>
<p><var>dest</var> is an optional argument. If not NULL, semantically speaking,
the result of the transformation is intersected with <var>dest</var>. This is
useful for precise backward transformations in lattices like intervals or
octagons.
</p></dd></dl>
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<a name="Existential-quantification-of-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Existential quantification of abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fforget_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_forget_array</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>, ap_var_t* <var>tvar</var>, size_t <var>size</var>, bool <var>project</var>)</i></dt>
<dd><p>Forget (<code>project=false</code>) or Project (<code>project=true</code>) the
array of variables <var>tvar</var> of size <var>size</var> in the abstract
value <var>a</var>.
</p></dd></dl>
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<a name="Change-of-environments-of-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Change of environments of abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fchange_005fenvironment"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_change_environment</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>, ap_environment_t* <var>nenv</var>, bool <var>project</var>)</i></dt>
<dd><p>Change the environment of the abstract values. Variables that are
removed are first existentially quantified, and variables that are
introduced are either unconstrained (<code>project==false</code>) or
initialized to 0 (<code>project==false</code>).
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fminimize_005fenvironment"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_minimize_environment</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Remove from the environment of the abstract value and from the
abstract value itself variables that are unconstrained in it.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005frename_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_rename_array</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>, ap_var_t* <var>tvar</var>, ap_var_t* <var>ntvar</var>, size_t <var>size</var>)</i></dt>
<dd><p>Parallel renaming of the environment of the abstract value. The new
variables should not interfere with the variables that are not
renamed.
</p></dd></dl>
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<a name="Expansion-and-Folding-of-dimensions-of-abstract-values-of-level-1"></a>
<h3 class="subsection">Expansion and Folding of dimensions of abstract values of level 1</h3>
<p>Formally, expanding <code>z</code> into <code>z</code> and <code>w</code> in
abstract value (predicate) <code>P</code> is defined by
<em>expand(P(x,y,z),z,w) = P(x,y,z) and P(x,y,w)</em>.
</p>
<p>Conversely, folding <code>z</code> and <code>w</code> into <code>z</code> in
abstract value (predicate) <code>Q</code> is defined by
<em>fold(Q(x,y,z,w),z,w) = (exists w: Q(x,y,z,w)) or (exists z:Q(x,y,z,w)[z<-w])</em>.
</p>
<dl>
<dt><a name="index-ap_005fabstract1_005fexpand"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_expand</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>, ap_var_t <var>var</var>, ap_var_t* <var>tvar</var>, size_t <var>size</var>)</i></dt>
<dd><p>Expand the variable <var>var</var> into itself + the <var>size</var> additional
variables of the array <var>tvar</var>, which are given the same type as
<var>var</var>. The additional variables are added to the environment of
the argument for making the environment of the result, so they should
not belong to the initial environment.
</p>
<p>It results in <code>size+1</code> unrelated variables having same relations
with other dimensions.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005ffold"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_fold</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>, ap_var_t* <var>tvar</var>, size_t <var>size</var>)</i></dt>
<dd><p>Fold the variables in the array <var>tvar</var> of size <var>size</var>>=1 and
put the result in the first variable in the array. The other variables
of the array are then forgot and removed from the environment.
</p></dd></dl>
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<a name="Widening-of-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Widening of abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fwidening"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_widening</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a1</var>, ap_abstract1_t* <var>a2</var>)</i></dt>
<dd><p>Widening of <var>a1</var> with <var>a2</var>. <var>a1</var> is supposed to be
included in <var>a2</var>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fwidening_005fthreshold"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_widening_threshold</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a1</var>, ap_abstract1_t* <var>a2</var>, ap_lincons1_array_t* <var>array</var>)</i></dt>
<dd><p>Widening with threshold.
</p>
<p>Intersect the result of the standard widening with all the
constraints in <var>array</var> that are satisfied by both <var>a1</var> and
<var>a2</var>.
</p></dd></dl>
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<a name="Topological-closure-of-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Topological closure of abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fclosure"></a><u>Function:</u> ap_abstract1_t* <b>ap_abstract1_closure</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a</var>)</i></dt>
<dd><p>Relax strict constraints into non strict constraints.
</p></dd></dl>
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<a name="Additional-functions-on-abstract-values-of-level-1-1"></a>
<h3 class="subsection">Additional functions on abstract values of level 1</h3>
<dl>
<dt><a name="index-ap_005fabstract1_005fof_005flincons_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_of_lincons_array</b><i> (ap_manager_t* <var>man</var>, ap_environment_t* <var>env</var>, ap_lincons1_array_t* <var>array</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fof_005ftcons_005farray"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_of_tcons_array</b><i> (ap_manager_t* <var>man</var>, ap_environment_t* <var>env</var>, ap_tcons1_array_t* <var>array</var>)</i></dt>
<dd><p>Abstract a conjunction of constraints. The environment of the array should be
a subset of the environment <var>env</var>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fassign_005flinexpr"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_assign_linexpr</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>org</var>, ap_var_t <var>var</var>, ap_linexpr1_t* <var>expr</var>, ap_abstract1_t* <var>dest</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fsubstitute_005flinexpr"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_substitute_linexpr</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>org</var>, ap_var_t <var>var</var>, ap_linexpr1_t* <var>expr</var>, ap_abstract1_t* <var>dest</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fassign_005ftexpr"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_assign_texpr</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>org</var>, ap_var_t <var>var</var>, ap_texpr1_t* <var>expr</var>, ap_abstract1_t* <var>dest</var>)</i></dt>
<dt><a name="index-ap_005fabstract1_005fsubstitute_005ftexpr"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_substitute_texpr</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>org</var>, ap_var_t <var>var</var>, ap_texpr1_t* <var>expr</var>, ap_abstract1_t* <var>dest</var>)</i></dt>
<dd><p>Assignement and Substitution of the dimension <var>dim</var> by the
expression <var>expr</var> in abstract value <var>org</var>.
</p>
<p><var>dest</var> is an optional argument. If not NULL, semantically
speaking, the result of the transformation is intersected with
<var>dest</var>. This is useful for precise backward transformations in
lattices like intervals or octagons.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005funify"></a><u>Function:</u> ap_abstract1_t <b>ap_abstract1_unify</b><i> (ap_manager_t* <var>man</var>, bool <var>destructive</var>, ap_abstract1_t* <var>a1</var>, ap_abstract1_t* <var>a2</var>)</i></dt>
<dd><p>Unify two abstract values on their common variables, that is,
embed them on the least common environment and then compute their
meet. The result is defined on the least common environment.
</p>
<p>For instance, the unification of <code>1<=x<=3 and x=y</code> defined on
<code>{ x, y }</code> and <code>2<=z<=4 and z=y</code> defined on
<code>{y,z }</code> results in <code>2<=x<=3 and x=y=z</code> defined on
<code>{x,y,z}</code>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fquasilinear_005fof_005fintlinear"></a><u>Function:</u> ap_linexpr1_t <b>ap_abstract1_quasilinear_of_intlinear</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, ap_linexpr1_t* <var>expr</var>)</i></dt>
<dd><p>Evaluate the interval linear expression <var>expr</var> on the abstract
value <var>a</var> and approximate it by a quasilinear expression.
</p>
<p>This implies calls to <code>ap_abstract0_bound_dimension</code>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fabstract1_005fintlinear_005fof_005ftree"></a><u>Function:</u> ap_linexpr1_t <b>ap_abstract1_intlinear_of_tree</b><i> (ap_manager_t* <var>man</var>, ap_abstract1_t* <var>a</var>, ap_texpr1_t* <var>expr</var>, bool quasilinear)</i></dt>
<dd><p>Evaluate the tree expression <var>expr</var> on the abstract value <var>a</var>
and approximate it by an interval linear (resp. quasilinear if
<var>quasilinear</var> is true) expression.
</p>
<p>This implies calls to <code>ap_abstract0_bound_dimension</code>.
</p></dd></dl>
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