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diff --git a/libs/icl/doc/html/boost_icl/concepts/sets_and_maps.html b/libs/icl/doc/html/boost_icl/concepts/sets_and_maps.html new file mode 100644 index 0000000000..1be5c307b5 --- /dev/null +++ b/libs/icl/doc/html/boost_icl/concepts/sets_and_maps.html @@ -0,0 +1,505 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Sets and 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="../concepts.html" title="Concepts"> +<link rel="prev" href="aspects.html" title="Aspects"> +<link rel="next" href="aggrovering.html" title="Addability, Subtractability and Aggregate on Overlap"> +</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="aspects.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.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="aggrovering.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section" lang="en"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_icl.concepts.sets_and_maps"></a><a class="link" href="sets_and_maps.html" title="Sets and Maps">Sets and Maps</a> +</h3></div></div></div> +<a name="boost_icl.concepts.sets_and_maps.a_set_concept"></a><h6> +<a name="id1071622"></a> + <a class="link" href="sets_and_maps.html#boost_icl.concepts.sets_and_maps.a_set_concept">A Set Concept</a> + </h6> +<p> + On the fundamental aspect all <code class="computeroutput"><a class="link" href="../../boost/icl/interval_base_set.html" title="Class template interval_base_set">interval_sets</a></code> + are models of a concept <code class="computeroutput"><span class="identifier">Set</span></code>. + The <code class="computeroutput"><span class="identifier">Set</span></code> concept of the Interval + Template Library refers to the mathematical notion of a set. + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + Variant + </p> + </th> +<th> + <p> + implemented as + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + empty set + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Set</span><span class="special">::</span><span class="identifier">Set</span><span class="special">()</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + subset relation + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">Set</span><span class="special">::</span><span class="identifier">within</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> + <span class="identifier">s1</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s2</span><span class="special">)</span><span class="keyword">const</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + equality + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> + <span class="identifier">s1</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + set union + </p> + </td> +<td> + <p> + inplace + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Set</span><span class="special">&</span> + <span class="keyword">operator</span> <span class="special">+=</span> + <span class="special">(</span><span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Set</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Set</span> <span class="keyword">operator</span> + <span class="special">+</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Set</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + set difference + </p> + </td> +<td> + <p> + inplace + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Set</span><span class="special">&</span> + <span class="keyword">operator</span> <span class="special">-=</span> + <span class="special">(</span><span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Set</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Set</span> <span class="keyword">operator</span> + <span class="special">-</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Set</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + set intersection + </p> + </td> +<td> + <p> + inplace + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Set</span><span class="special">&</span> + <span class="keyword">operator</span> <span class="special">&=</span> + <span class="special">(</span><span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Set</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Set</span> <span class="keyword">operator</span> + <span class="special">&</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Set</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Set</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +</tbody> +</table></div> +<p> + Equality on <code class="computeroutput"><span class="identifier">Sets</span></code> is not implemented + as <code class="computeroutput"><span class="keyword">operator</span> <span class="special">==</span></code>, + because <code class="computeroutput"><span class="keyword">operator</span> <span class="special">==</span></code> + is used for the stronger lexicographical equality on segments, that takes + the segmentation of elements into account. + </p> +<p> + Being models of concept <code class="computeroutput"><span class="identifier">Set</span></code>, + <a href="http://www.cplusplus.com/reference/stl/set/" target="_top"><code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code> + </a> and all <code class="computeroutput"><a class="link" href="../../boost/icl/interval_base_set.html" title="Class template interval_base_set">interval_sets</a></code> + implement these operations and obey the associated laws on <code class="computeroutput"><span class="identifier">Sets</span></code>. See e.g. <a href="http://en.wikipedia.org/wiki/Algebra_of_sets" target="_top">an + algebra of sets here</a>. + </p> +<a name="boost_icl.concepts.sets_and_maps.making_intervals_complete"></a><h6> +<a name="id1072513"></a> + <a class="link" href="sets_and_maps.html#boost_icl.concepts.sets_and_maps.making_intervals_complete">Making + intervals complete</a> + </h6> +<p> + An <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">interval</a></code> is considered + to be a set of elements as well. With respect to the <code class="computeroutput"><span class="identifier">Set</span></code> + concept presented above <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">interval</a></code> + implements the concept only partially. The reason for that is that addition + and subtraction can not be defined on <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">intervals</a></code>. + Two intervals <code class="computeroutput"><span class="special">[</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">]</span></code> + and <code class="computeroutput"><span class="special">[</span><span class="number">4</span><span class="special">,</span><span class="number">5</span><span class="special">]</span></code> + are not addable to a <span class="emphasis"><em><span class="bold"><strong>single</strong></span></em></span> + new <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">interval</a></code>. In other + words <code class="computeroutput"><a class="link" href="../../boost/icl/interval.html" title="Struct template interval">intervals</a></code> are incomplete + w.r.t. union and difference. <code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">Interval_sets</a></code> + can be defined as the <span class="emphasis"><em><span class="bold"><strong>completion</strong></span></em></span> + of intervals for the union and difference operations. + </p> +<p> + When we claim that addition or subtraction can not be defined on intervals, + we are not considering things like e.g. interval arithmetics, where these + operations can be defined, but with a different semantics. + </p> +<a name="boost_icl.concepts.sets_and_maps.a_map_concept"></a><h6> +<a name="id1072641"></a> + <a class="link" href="sets_and_maps.html#boost_icl.concepts.sets_and_maps.a_map_concept">A Map Concept</a> + </h6> +<p> + On the fundamental aspect <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code> + and all <code class="computeroutput"><a class="link" href="../../boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_maps</a></code> + are models of a concept <code class="computeroutput"><span class="identifier">Map</span></code>. + Since a <code class="computeroutput"><span class="identifier">map</span></code> is a <code class="computeroutput"><span class="identifier">set</span> <span class="identifier">of</span> <span class="identifier">pairs</span></code>, we try to design the <code class="computeroutput"><span class="identifier">Map</span></code> concept in accordance to the <code class="computeroutput"><span class="identifier">Set</span></code> concept above. + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + Variant + </p> + </th> +<th> + <p> + implemented as + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + empty map + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Map</span><span class="special">::</span><span class="identifier">Map</span><span class="special">()</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + subset relation + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">within</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s2</span><span class="special">)</span><span class="keyword">const</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + equality + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">is_element_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> + <span class="identifier">s1</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + map union + </p> + </td> +<td> + <p> + inplace + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Map</span><span class="special">&</span> + <span class="keyword">operator</span> <span class="special">+=</span> + <span class="special">(</span><span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Map</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Map</span> <span class="keyword">operator</span> + <span class="special">+</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Map</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + map difference + </p> + </td> +<td> + <p> + inplace + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Map</span><span class="special">&</span> + <span class="keyword">operator</span> <span class="special">-=</span> + <span class="special">(</span><span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Map</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Map</span> <span class="keyword">operator</span> + <span class="special">-</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Map</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + map intersection + </p> + </td> +<td> + <p> + inplace + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Map</span><span class="special">&</span> + <span class="keyword">operator</span> <span class="special">&=</span> + <span class="special">(</span><span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Map</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +<tr> +<td> + <p> + </p> + </td> +<td> + <p> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">Map</span> <span class="keyword">operator</span> + <span class="special">&</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Map</span><span class="special">&</span> <span class="identifier">s1</span><span class="special">,</span> <span class="keyword">const</span> + <span class="identifier">Map</span><span class="special">&</span> + <span class="identifier">s2</span><span class="special">)</span></code> + </p> + </td> +</tr> +</tbody> +</table></div> +<p> + As one can see, on the abstract kernel the signatures of the icl's <code class="computeroutput"><span class="identifier">Set</span></code> and <code class="computeroutput"><span class="identifier">Map</span></code> + concepts are identical, except for the typename. While signatures are identical + The sets of valid laws are different, which will be described in more detail + in the sections on the <a class="link" href="../semantics/sets.html" title="Sets">semantics + of icl Sets</a> and <a class="link" href="../semantics/maps.html" title="Maps">Maps</a>. + These semantic differences are mainly based on the implementation of the + pivotal member functions <code class="computeroutput"><span class="identifier">add</span></code> + and <code class="computeroutput"><span class="identifier">subtract</span></code> for elements + and intervals that again serve for implementing <code class="computeroutput"><span class="keyword">operator</span> + <span class="special">+=</span></code> and <code class="computeroutput"><span class="keyword">operator</span> + <span class="special">-=</span></code>. + </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="aspects.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.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="aggrovering.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> |