123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187 |
- <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 V1.79.1">
- <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">
- <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 class="itemizedlist" style="list-style-type: disc; ">
- <li class="listitem">
- <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 class="listitem">
- <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>)
- </p>
- </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>
|