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| <div class="section boost_icl_concepts_sets_and_maps" 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="id1076180"></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="id1077070"></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="id1077199"></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> |
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