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<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Maps</title> <link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.74.0"> <link rel="home" href="../../index.html" title="Chapter 1. Boost.Icl"> <link rel="up" href="../semantics.html" title="Semantics"> <link rel="prev" href="sets.html" title="Sets"> <link rel="next" href="collectors__maps_of_sets.html" title="Collectors: Maps of Sets"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> <td align="center"><a href="../../../../../../index.html">Home</a></td> <td align="center"><a href="../../../../../libraries.htm">Libraries</a></td> <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> <td align="center"><a href="../../../../../../more/index.htm">More</a></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="sets.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../semantics.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="collectors__maps_of_sets.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> </div> <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> 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 icl's 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">CodomainT</code> of the map's associated values. 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">std::strings</code> associated to intervals, <pre class="programlisting">interval_map<int,std::string> cat_map; cat_map += make_pair(interval<int>::rightopen(1,5),std::string("Hello")); cat_map += make_pair(interval<int>::rightopen(3,7),std::string(" World")); cout << "cat_map: " << cat_map << endl; </pre> we won't be able to apply <code class="computeroutput">operator -=</code> <pre class="programlisting">// This will not compile because string::operator -= is missing. cat_map -= make_pair(interval<int>::rightopen(3,7),std::string(" World")); </pre> because, as std::sting does not implement <code class="computeroutput">-=</code> itself, this won't compile. So all laws, that rely on <code class="computeroutput">operator -=</code> or <code class="computeroutput">-</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">CodomainT</code> type to a smaller set of laws and thus to a less restricted semantics. Currently we have investigated and validated two major instantiations of icl::Maps, <div class="itemizedlist"><ul type="disc"> <li> Maps of Sets that will be called Collectors and </li> <li> Maps of Numbers which will be called Quantifiers </li> </ul></div> both of which seem to have many interesting use cases for practical applications. The semantics associated with the term Numbers 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. Icl Maps of Sets or Collectors are models of concept <code class="computeroutput">Set</code>. This implies that all laws that have been stated as a semantics for <code class="computeroutput">icl::Sets</code> in the previous chapter also hold for <code class="computeroutput">Maps of Sets</code>. Icl Maps of Numbers or Quantifiers on the contrary are not models of concept <code class="computeroutput">Set</code>. But there is a substantial intersection of laws that apply both for <code class="computeroutput">Collectors</code> and <code class="computeroutput">Quantifiers</code>. <div class="informaltable"><table class="table"> <colgroup> <col> <col> <col> </colgroup> <thead><tr> <th> Kind of Map </th> <th> Alias </th> <th> Behavior </th> </tr></thead> <tbody> <tr> <td> Maps of Sets </td> <td> Collector </td> <td> Collects items for key values </td> </tr> <tr> <td> Maps of Numbers </td> <td> Quantifier </td> <td> Counts or quantifies the key values </td> </tr> </tbody> </table></div> In the next two sections the law based semantics of Collectors and Quantifiers will be described in more detail. </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 Copyright © 1999 -2006 Cortex Software GmbH 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>) </div></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="sets.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../semantics.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="collectors__maps_of_sets.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>