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