4a04618b4e
Fix for ticket #6924: Now using insert with hint. ........ Fixed ticket #6924 (reporter: John Reid). Improvements of icl/functors.hpp. ........ Documentation tweaks. Ticket #6967, fixed broken links. ........ Added doxygen generated html to complete broken links. ........ [SVN r79220]
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<link rel="prev" href="sets.html" title="Sets">
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<div class="section boost_icl_semantics_maps" lang="en">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="boost_icl.semantics.maps"></a><a class="link" href="maps.html" title="Maps">Maps</a>
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</h3></div></div></div>
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<p>
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By definition a map is set of pairs. So we would expect maps to obey the
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same laws that are valid for sets. Yet the semantics of the <span class="bold"><strong>icl's</strong></span>
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maps may be a different one, because of it's aggregating facilities, where
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the aggregating combiner operations are passed to combine the map's associated
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values. It turns out, that the aggregation on overlap principle induces semantic
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properties to icl maps in such a way, that the set of equations that are
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valid will depend on the semantics of the type <code class="computeroutput"><span class="identifier">CodomainT</span></code>
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of the map's associated values.
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</p>
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<p>
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This is less magical as it might seem at first glance. If, for instance,
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we instantiate an <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>
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to collect and concatenate <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">strings</span></code>
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associated to intervals,
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</p>
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<p>
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</p>
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<pre class="programlisting"><span class="identifier">interval_map</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span><span class="special">></span> <span class="identifier">cat_map</span><span class="special">;</span>
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<span class="identifier">cat_map</span> <span class="special">+=</span> <span class="identifier">make_pair</span><span class="special">(</span><span class="identifier">interval</span><span class="special"><</span><span class="keyword">int</span><span class="special">>::</span><span class="identifier">rightopen</span><span class="special">(</span><span class="number">1</span><span class="special">,</span><span class="number">5</span><span class="special">),</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span><span class="special">(</span><span class="string">"Hello"</span><span class="special">));</span>
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<span class="identifier">cat_map</span> <span class="special">+=</span> <span class="identifier">make_pair</span><span class="special">(</span><span class="identifier">interval</span><span class="special"><</span><span class="keyword">int</span><span class="special">>::</span><span class="identifier">rightopen</span><span class="special">(</span><span class="number">3</span><span class="special">,</span><span class="number">7</span><span class="special">),</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span><span class="special">(</span><span class="string">" World"</span><span class="special">));</span>
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<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"cat_map: "</span> <span class="special"><<</span> <span class="identifier">cat_map</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
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</pre>
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<p>
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</p>
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<p>
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we won't be able to apply <code class="computeroutput"><span class="keyword">operator</span>
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<span class="special">-=</span></code>
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</p>
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<pre class="programlisting"><span class="comment">// This will not compile because string::operator -= is missing.
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</span><span class="identifier">cat_map</span> <span class="special">-=</span> <span class="identifier">make_pair</span><span class="special">(</span><span class="identifier">interval</span><span class="special"><</span><span class="keyword">int</span><span class="special">>::</span><span class="identifier">rightopen</span><span class="special">(</span><span class="number">3</span><span class="special">,</span><span class="number">7</span><span class="special">),</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span><span class="special">(</span><span class="string">" World"</span><span class="special">));</span>
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</pre>
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<p>
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because, as std::sting does not implement <code class="computeroutput"><span class="special">-=</span></code>
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itself, this won't compile. So all <span class="bold"><strong>laws</strong></span>,
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that rely on <code class="computeroutput"><span class="keyword">operator</span> <span class="special">-=</span></code>
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or <code class="computeroutput"><span class="special">-</span></code> not only will not be valid
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they can not even be stated. This reduces the set of laws that can be valid
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for a richer <code class="computeroutput"><span class="identifier">CodomainT</span></code> type
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to a smaller set of laws and thus to a less restricted semantics.
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</p>
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<p>
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Currently we have investigated and validated two major instantiations of
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icl::Maps,
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</p>
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<div class="itemizedlist"><ul type="disc">
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<li>
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<span class="emphasis"><em><span class="bold"><strong>Maps of Sets</strong></span></em></span> that
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will be called <span class="emphasis"><em><span class="bold"><strong>Collectors</strong></span></em></span>
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and
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</li>
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<li>
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<span class="emphasis"><em><span class="bold"><strong>Maps of Numbers</strong></span></em></span> which
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will be called <span class="emphasis"><em><span class="bold"><strong>Quantifiers</strong></span></em></span>
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</li>
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</ul></div>
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<p>
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both of which seem to have many interesting use cases for practical applications.
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The semantics associated with the term <span class="emphasis"><em>Numbers</em></span> is a
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<a href="http://en.wikipedia.org/wiki/Monoid" target="_top">commutative monoid</a>
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for unsigned numbers and a <a href="http://en.wikipedia.org/wiki/Abelian_group" target="_top">commutative
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or abelian group</a> for signed numbers. From a practical point of view
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we can think of numbers as counting or quantifying the key values of the
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map.
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</p>
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<p>
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Icl <span class="emphasis"><em><span class="bold"><strong>Maps of Sets</strong></span></em></span> or
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<span class="emphasis"><em><span class="bold"><strong>Collectors</strong></span></em></span> are models
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of concept <code class="computeroutput"><span class="identifier">Set</span></code>. This implies
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that all laws that have been stated as a semantics for <code class="computeroutput"><span class="identifier">icl</span><span class="special">::</span><span class="identifier">Sets</span></code>
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in the previous chapter also hold for <code class="computeroutput"><span class="identifier">Maps</span>
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<span class="identifier">of</span> <span class="identifier">Sets</span></code>.
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Icl <span class="emphasis"><em><span class="bold"><strong>Maps of Numbers</strong></span></em></span>
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or <span class="emphasis"><em><span class="bold"><strong>Quantifiers</strong></span></em></span> on the
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contrary are not models of concept <code class="computeroutput"><span class="identifier">Set</span></code>.
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But there is a substantial intersection of laws that apply both for <code class="computeroutput"><span class="identifier">Collectors</span></code> and <code class="computeroutput"><span class="identifier">Quantifiers</span></code>.
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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Kind of Map
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</p>
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</th>
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<th>
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<p>
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Alias
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</p>
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</th>
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<th>
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<p>
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Behavior
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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Maps of Sets
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</p>
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</td>
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<td>
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<p>
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Collector
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</p>
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</td>
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<td>
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<p>
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Collects items <span class="bold"><strong>for</strong></span> key values
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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Maps of Numbers
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</p>
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</td>
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<td>
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<p>
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Quantifier
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</p>
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</td>
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<td>
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<p>
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Counts or quantifies <span class="bold"><strong>the</strong></span> key values
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</p>
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</td>
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</tr>
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</tbody>
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</table></div>
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<p>
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In the next two sections the law based semantics of <span class="emphasis"><em><span class="bold"><strong>Collectors</strong></span></em></span>
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and <span class="emphasis"><em><span class="bold"><strong>Quantifiers</strong></span></em></span> will
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be described in more detail.
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</p>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2007 -2010 Joachim Faulhaber<br>Copyright © 1999 -2006 Cortex Software GmbH<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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</p>
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</div></td>
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</tr></table>
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<hr>
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