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<link title="Mpfrf" rel="Chapter" href="Mpfrf.html"><title>Dim</title>
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<h1>Module <a href="type_Dim.html">Dim</a></h1>
<pre><span class="keyword">module</span> Dim: <code class="code"><span class="keyword">sig</span></code> <a href="Dim.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><div class="info module top">
APRON Dimensions and related types<br>
</div>
<hr width="100%">
<pre><span id="TYPEt"><span class="keyword">type</span> <code class="type"></code>t</span> = <code class="type">int</code> </pre>
<pre><code><span id="TYPEchange"><span class="keyword">type</span> <code class="type"></code>change</span> = {</code></pre><table class="typetable">
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTchange.dim">dim</span> : <code class="type">int array</code>;</code></td>
</tr>
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTchange.intdim">intdim</span> : <code class="type">int</code>;</code></td>
</tr>
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTchange.realdim">realdim</span> : <code class="type">int</code>;</code></td>
</tr></table>
}
<pre><code><span id="TYPEchange2"><span class="keyword">type</span> <code class="type"></code>change2</span> = {</code></pre><table class="typetable">
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTchange2.add">add</span> : <code class="type"><a href="Dim.html#TYPEchange">change</a> option</code>;</code></td>
</tr>
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTchange2.remove">remove</span> : <code class="type"><a href="Dim.html#TYPEchange">change</a> option</code>;</code></td>
</tr></table>
}
<pre><span id="TYPEperm"><span class="keyword">type</span> <code class="type"></code>perm</span> = <code class="type">int array</code> </pre>
<pre><code><span id="TYPEdimension"><span class="keyword">type</span> <code class="type"></code>dimension</span> = {</code></pre><table class="typetable">
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTdimension.intd">intd</span> : <code class="type">int</code>;</code></td>
</tr>
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTdimension.reald">reald</span> : <code class="type">int</code>;</code></td>
</tr></table>
}
<br>
APRON Dimensions and related types<br>
<br>
<ul>
<li><code class="code">t=int</code> is the type of dimensions.</li>
<li>The semantics of an object <code class="code">(change:change)</code> is the following one:
<ul>
<li><code class="code">change.intdim</code> and <code class="code">change.realdim</code> indicate the number of integer and
real dimensions to add or to remove</li>
<li>In case of the addition of dimensions,
<p>
<code class="code">change.dim[i]=k</code> means: add one dimension at dimension k and shift the
already existing dimensions greater than or equal to k one step on the
right (or increment them).
<p>
if k is equal to the size of the vector, then it means: add a dimension at
the end.
<p>
Repetition are allowed, and means that one inserts more than one dimensions.
<p>
Example:
<code class="code">add_dimensions [i0 i1 r0 r1] { dim=[0 1 2 2 4]; intdim=3; realdim=1 }</code>
returns <code class="code">0 i0 0 i1 0 0 r0 r1 0</code>, considered as a vector with 6 integer
dimensions and 3 real dimensions.</li>
<li>In case of the removal of dimensions,
<p>
dimchange.dim<code class="code">i</code>=k means: remove the dimension k and shift the dimensions
greater than k one step on the left (or decrement them).
<p>
Repetitions are meaningless (and are not correct specification)
<p>
Example: <code class="code">remove_dimensions [i0 i1 i2 r0 r1 r2] { dim=[0 2 4]; intdim=2;
realdim=1 }</code> returns <code class="code">i1 r0 r2</code>, considered as a vector with 1 integer
dimensions and 2 real dimensions.
</li>
</ul>
</li>
<li>The semantics of an object <code class="code">(change2:change2)</code> is the combination of the
two following transformations:
<ul>
<li><code class="code">change2.add</code> indicates an optional addition of dimensions.</li>
<li><code class="code">change2.remove</code> indicates an optional removal of dimensions.</li>
</ul>
</li>
<li><code class="code">perm</code> defines a permutation.</li>
<li><code class="code">dimension</code> defines the dimensionality of an abstract value (number of
integer and real dimensions).
</li>
</ul>
<br>
<pre><span id="VALchange_add_invert"><span class="keyword">val</span> change_add_invert</span> : <code class="type"><a href="Dim.html#TYPEchange">change</a> -> unit</code></pre><div class="info ">
Assuming a transformation for add_dimensions, invert it in-place to
obtain the inverse transformation using remove_dimensions<br>
</div>
<pre><span id="VALperm_compose"><span class="keyword">val</span> perm_compose</span> : <code class="type"><a href="Dim.html#TYPEperm">perm</a> -> <a href="Dim.html#TYPEperm">perm</a> -> <a href="Dim.html#TYPEperm">perm</a></code></pre><div class="info ">
<code class="code">perm_compose perm1 perm2</code> composes the 2 permutations perm1 and perm2
(in this order). The sizes of permutations are supposed to be equal.<br>
</div>
<pre><span id="VALperm_invert"><span class="keyword">val</span> perm_invert</span> : <code class="type"><a href="Dim.html#TYPEperm">perm</a> -> <a href="Dim.html#TYPEperm">perm</a></code></pre><div class="info ">
Invert a permutation<br>
</div>
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