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<div class="section boost_icl_concepts_map_traits" lang="en">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="boost_icl.concepts.map_traits"></a><a class="link" href="map_traits.html" title="Map Traits">Map Traits</a>
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</h3></div></div></div>
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<p>
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Icl maps differ in their behavior dependent on how they handle <a href="http://en.wikipedia.org/wiki/Identity_element" target="_top"><span class="emphasis"><em><span class="bold"><strong>identity elements</strong></span></em></span></a> of the associated
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type <code class="computeroutput"><span class="identifier">CodomainT</span></code>.
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</p>
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<a name="boost_icl.concepts.map_traits.remarks_on_identity_elements"></a><h5>
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<a name="id1079765"></a>
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<a class="link" href="map_traits.html#boost_icl.concepts.map_traits.remarks_on_identity_elements">Remarks
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on Identity Elements</a>
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</h5>
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<p>
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In the pseudo code snippets below <code class="computeroutput"><span class="number">0</span></code>
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will be used to denote <a href="http://en.wikipedia.org/wiki/Identity_element" target="_top"><code class="computeroutput"><span class="identifier">identity</span> <span class="identifier">elements</span></code></a>,
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which can be different objects like <code class="computeroutput"><span class="keyword">const</span>
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<span class="keyword">double</span> <span class="number">0.0</span></code>,
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empty sets, empty strings, null-vectors etc. dependent of the instance type
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for parameter <code class="computeroutput"><span class="identifier">CodomainT</span></code>.
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The existence of an <span class="emphasis"><em><span class="bold"><strong>identity element</strong></span></em></span>
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wrt. an <code class="computeroutput"><span class="keyword">operator</span><span class="special">+=</span></code>
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is a requirement for template type <code class="computeroutput"><span class="identifier">CodomainT</span></code>.
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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type
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</p>
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</th>
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<th>
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<p>
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operation
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</p>
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</th>
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<th>
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<p>
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identity element
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="keyword">int</span></code>
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</p>
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</td>
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<td>
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<p>
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addition
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</p>
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</td>
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<td>
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<p>
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<code class="computeroutput"><span class="number">0</span></code>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">string</span></code>
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</p>
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</td>
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<td>
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<p>
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concatenation
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</p>
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</td>
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<td>
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<p>
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<code class="computeroutput"><span class="string">""</span></code>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<code class="computeroutput"><span class="identifier">set</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code>
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</p>
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</td>
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<td>
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<p>
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union
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</p>
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</td>
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<td>
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<p>
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<code class="computeroutput"><span class="special">{}</span></code>
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</p>
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</td>
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</tr>
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</tbody>
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</table></div>
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<p>
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In these cases the <code class="computeroutput"><span class="identifier">identity</span> <span class="identifier">element</span></code> value is delivered by the default
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constructor of the maps <code class="computeroutput"><span class="identifier">CodomainT</span></code>
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type. But there are well known exceptions like e.g. numeric multiplication:
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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type
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</p>
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</th>
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<th>
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<p>
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operation
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</p>
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</th>
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<th>
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<p>
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identity element
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</p>
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</th>
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</tr></thead>
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<tbody><tr>
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<td>
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<p>
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<code class="computeroutput"><span class="keyword">int</span></code>
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</p>
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</td>
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<td>
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<p>
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multiplication
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</p>
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</td>
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<td>
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<p>
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<code class="computeroutput"><span class="number">1</span></code>
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</p>
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</td>
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</tr></tbody>
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</table></div>
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<p>
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Therefore icl functors, that serve as <code class="computeroutput"><span class="identifier">Combiner</span></code>
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parameters of icl Maps implement a static function <code class="computeroutput"><span class="identifier">identity_element</span><span class="special">()</span></code> to make sure that the correct <code class="computeroutput"><span class="identifier">identity_element</span><span class="special">()</span></code>
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is used in the implementation of <span class="emphasis"><em>aggregate on overlap</em></span>.
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</p>
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<pre class="programlisting"><span class="identifier">inplace_times</span><span class="special"><</span><span class="keyword">int</span><span class="special">>::</span><span class="identifier">identity_element</span><span class="special">()</span> <span class="special">==</span> <span class="number">1</span>
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<span class="comment">// or more general
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</span><span class="identifier">inplace_times</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">identity_element</span><span class="special">()</span> <span class="special">==</span> <span class="identifier">unit_element</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">value</span><span class="special">()</span>
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</pre>
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<p>
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</p>
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<a name="boost_icl.concepts.map_traits.definedness_and_storage_of_identity_elements"></a><h5>
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<a name="id1081881"></a>
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<a class="link" href="map_traits.html#boost_icl.concepts.map_traits.definedness_and_storage_of_identity_elements">Definedness
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and Storage of Identity Elements</a>
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</h5>
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<p>
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There are two <span class="emphasis"><em>properties</em></span> or <span class="emphasis"><em>traits</em></span>
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of icl maps that can be chosen by a template parameter <code class="computeroutput"><span class="identifier">Traits</span></code>.
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The <span class="emphasis"><em><span class="bold"><strong>first trait</strong></span></em></span> relates
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to the <span class="emphasis"><em><span class="bold"><strong>definedness</strong></span></em></span>
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of the map. Icl maps can be <span class="bold"><strong>partial</strong></span> or
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<span class="bold"><strong>total</strong></span> on the set of values given by domain
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type <code class="computeroutput"><span class="identifier">DomainT</span></code>.
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</p>
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<div class="itemizedlist"><ul type="disc">
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<li>
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A <span class="emphasis"><em><span class="bold"><strong>partial</strong></span></em></span> map is
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only defined on those key elements that have been inserted into the Map.
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This is usually expected and so <span class="emphasis"><em><span class="bold"><strong>partial
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definedness</strong></span></em></span> is the default.
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</li>
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<li>
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Alternatively an icl Map can be <span class="emphasis"><em><span class="bold"><strong>total</strong></span></em></span>.
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It is then considered to contain a <span class="emphasis"><em><span class="bold"><strong>neutral
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value</strong></span></em></span> for all key values that are not stored in the
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map.
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</li>
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</ul></div>
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<p>
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The <span class="emphasis"><em><span class="bold"><strong>second trait</strong></span></em></span> is
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related to the representation of <code class="computeroutput"><span class="identifier">identity</span>
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<span class="identifier">elements</span></code> in the map. An icl map
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can be a <span class="emphasis"><em><span class="bold"><strong>identity absorber</strong></span></em></span>
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or a <span class="emphasis"><em><span class="bold"><strong>identity enricher</strong></span></em></span>.
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</p>
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<div class="itemizedlist"><ul type="disc">
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<li>
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A <span class="emphasis"><em><span class="bold"><strong>identity absorber</strong></span></em></span>
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never stores value pairs <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> that carry identity elements.
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</li>
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<li>
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A <span class="emphasis"><em><span class="bold"><strong>identity enricher</strong></span></em></span>
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stores value pairs <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code>.
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</li>
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</ul></div>
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<p>
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For the template parameter <code class="computeroutput"><span class="identifier">Traits</span></code>
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of icl Maps we have the following four values.
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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</p>
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</th>
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<th>
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<p>
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identity absorber
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</p>
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</th>
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<th>
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<p>
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identity enricher
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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partial
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</p>
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</td>
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<td>
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<p>
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partial_absorber <span class="emphasis"><em>(default)</em></span>
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</p>
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</td>
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<td>
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<p>
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partial_enricher
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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total
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</p>
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</td>
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<td>
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<p>
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total_absorber
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</p>
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</td>
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<td>
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<p>
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total_enricher
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</p>
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</td>
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</tr>
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</tbody>
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</table></div>
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<a name="boost_icl.concepts.map_traits.map_traits_motivated"></a><h5>
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<a name="id1082177"></a>
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<a class="link" href="map_traits.html#boost_icl.concepts.map_traits.map_traits_motivated">Map Traits
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motivated</a>
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</h5>
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<p>
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Map traits are a late extension to the <span class="bold"><strong>icl</strong></span>.
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Interval maps have been used for a couple of years in a variety of applications
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at Cortex Software GmbH with an implementation that resembled the default
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trait. Only the deeper analysis of the icl's <span class="emphasis"><em><span class="bold"><strong>aggregating
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Map's concept</strong></span></em></span> in the course of preparation of the library
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for boost led to the introduction of map Traits.
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</p>
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<a name="boost_icl.concepts.map_traits.add_subtract_antinomy_in_aggregating_maps"></a><h6>
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<a name="id1082204"></a>
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<a class="link" href="map_traits.html#boost_icl.concepts.map_traits.add_subtract_antinomy_in_aggregating_maps">Add-Subtract
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Antinomy in Aggregating Maps</a>
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</h6>
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<p>
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Constitutional for the absorber/enricher propery is a little antinomy.
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</p>
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<p>
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We can insert value pairs to the map by <span class="emphasis"><em><span class="bold"><strong>adding</strong></span></em></span>
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them to the map via operations <code class="computeroutput"><span class="identifier">add</span><span class="special">,</span> <span class="special">+=</span></code> or <code class="computeroutput"><span class="special">+</span></code>:
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</p>
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<pre class="programlisting"><span class="special">{}</span> <span class="special">+</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">1</span><span class="special">)}</span> <span class="special">==</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">1</span><span class="special">)}</span> <span class="comment">// addition</span></pre>
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<p>
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</p>
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<p>
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Further addition on common keys triggers aggregation:
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</p>
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<pre class="programlisting"><span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">1</span><span class="special">)}</span> <span class="special">+</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">1</span><span class="special">)}</span> <span class="special">==</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">2</span><span class="special">)}</span> <span class="comment">// aggregation for common key k</span></pre>
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<p>
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</p>
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<p>
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A subtraction of existing pairs
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</p>
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<pre class="programlisting"><span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">2</span><span class="special">)}</span> <span class="special">-</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">2</span><span class="special">)}</span> <span class="special">==</span> <span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)}</span> <span class="comment">// aggregation for common key k</span></pre>
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<p>
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yields value pairs that are associated with 0-values or <code class="computeroutput"><span class="identifier">identity</span>
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<span class="identifier">elements</span></code>.
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</p>
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<p>
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So once a value pair is created for a key <code class="computeroutput"><span class="identifier">k</span></code>
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it can not be removed from the map via subtraction (<code class="computeroutput"><span class="identifier">subtract</span><span class="special">,</span> <span class="special">-=</span></code> or <code class="computeroutput"><span class="special">-</span></code>).
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</p>
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<p>
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The very basic fact on sets, that we can remove what we have previously added
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</p>
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<pre class="programlisting"><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{}</span></pre>
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<p>
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does not apply.
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</p>
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<p>
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This is the motivation for the <span class="emphasis"><em><span class="bold"><strong>identity absorber</strong></span></em></span>
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Trait. A identity absorber map handles value pairs that carry identity elements
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as <span class="emphasis"><em><span class="bold"><strong>non-existent</strong></span></em></span>, which
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saves the law:
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</p>
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<pre class="programlisting"><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{}</span></pre>
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<p>
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</p>
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<p>
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Yet this introduces a new problem: With such a <span class="emphasis"><em>identity absorber</em></span>
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we are <span class="emphasis"><em>by definition</em></span> unable to store a value <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> in the map.
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This may be unfavorable because it is not inline with the behavior of stl::maps
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and this is not necessarily expected by clients of the library.
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</p>
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<p>
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The solution to the problem is the introduction of the identity enricher
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Trait, so the user can choose a map variant according to her needs.
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</p>
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<a name="boost_icl.concepts.map_traits.partial_and_total_maps"></a><h6>
|
|
<a name="id1082625"></a>
|
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<a class="link" href="map_traits.html#boost_icl.concepts.map_traits.partial_and_total_maps">Partial
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and Total Maps</a>
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</h6>
|
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<p>
|
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The idea of a identity absorbing map is, that an <span class="emphasis"><em><span class="bold"><strong>associated
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identity element</strong></span></em></span> value of a pair <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> <span class="emphasis"><em><span class="bold"><strong>codes non-existence</strong></span></em></span>
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for it's key <code class="computeroutput"><span class="identifier">k</span></code>. So the pair
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<code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code>
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immediately tunnels from a map where it may emerge into the realm of non
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existence.
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</p>
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<pre class="programlisting"><span class="special">{(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)}</span> <span class="special">==</span> <span class="special">{}</span></pre>
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<p>
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</p>
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<p>
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If identity elements do not code <span class="emphasis"><em><span class="bold"><strong>non-existence</strong></span></em></span>
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but <span class="emphasis"><em><span class="bold"><strong>existence with null quantification</strong></span></em></span>,
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we can also think of a map that has an associated identity element <span class="emphasis"><em><span class="bold"><strong>for every</strong></span></em></span> key <code class="computeroutput"><span class="identifier">k</span></code>
|
|
that has no associated value different from 0. So in contrast to modelling
|
|
<span class="bold"><strong>all</strong></span> neutral value pairs <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> as being <span class="emphasis"><em><span class="bold"><strong>non-existent</strong></span></em></span>
|
|
we can model <span class="bold"><strong>all</strong></span> neutral value pairs <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> as being
|
|
<span class="emphasis"><em><span class="bold"><strong>implicitly existent</strong></span></em></span>.
|
|
</p>
|
|
<p>
|
|
A map that is modelled in this way, is one large vector with a value <code class="computeroutput"><span class="identifier">v</span></code> for every key <code class="computeroutput"><span class="identifier">k</span></code>
|
|
of it's domain type <code class="computeroutput"><span class="identifier">DomainT</span></code>.
|
|
But only non-identity values are actually stored. This is the motivation
|
|
for the definedness-Trait on <code class="computeroutput"><span class="identifier">icl</span>
|
|
<span class="identifier">Maps</span></code>.
|
|
</p>
|
|
<p>
|
|
A <span class="emphasis"><em><span class="bold"><strong>partial</strong></span></em></span> map models
|
|
the intuitive view that only value pairs are existent, that are stored in
|
|
the map. A <span class="emphasis"><em><span class="bold"><strong>total</strong></span></em></span> map
|
|
exploits the possibility that all value pairs that are not stored can be
|
|
considered as being existent and <span class="emphasis"><em><span class="bold"><strong>quantified</strong></span></em></span>
|
|
with the identity element.
|
|
</p>
|
|
<a name="boost_icl.concepts.map_traits.pragmatical_aspects_of_map_traits"></a><h5>
|
|
<a name="id1082892"></a>
|
|
<a class="link" href="map_traits.html#boost_icl.concepts.map_traits.pragmatical_aspects_of_map_traits">Pragmatical
|
|
Aspects of Map Traits</a>
|
|
</h5>
|
|
<p>
|
|
From a pragmatic perspective value pairs that carry <code class="computeroutput"><span class="identifier">identity</span>
|
|
<span class="identifier">elements</span></code> as mapped values can often
|
|
be ignored. If we count, for instance, the number of overlaps of inserted
|
|
intervals in an <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>
|
|
(see example <a class="link" href="../examples/overlap_counter.html" title="Overlap counter">overlap counter</a>),
|
|
most of the time, we are not interested in whether an overlap has been counted
|
|
<code class="computeroutput"><span class="number">0</span></code> times or has not been counted
|
|
at all. A identity enricher map is only needed, if we want to distinct between
|
|
non-existence and 0-quantification.
|
|
</p>
|
|
<p>
|
|
The following distinction can <span class="bold"><strong>not</strong></span> be made
|
|
for a <code class="computeroutput"><a class="link" href="../../boost/icl/partial_absorber.html" title="Struct partial_absorber">partial_absorber</a></code>
|
|
map but it can be made for an <code class="computeroutput"><a class="link" href="../../boost/icl/partial_enricher.html" title="Struct partial_enricher">partial_enricher</a></code>
|
|
map:
|
|
</p>
|
|
<pre class="programlisting">(k,v) does not exist in the map: Pair (k,v) has NOT been dealt with
|
|
(k,0) key k carries 0 : Pair (k,v) has been dealt with resulting in v=0
|
|
</pre>
|
|
<p>
|
|
Sometimes this subtle distinction is needed. Then a <code class="computeroutput"><a class="link" href="../../boost/icl/partial_enricher.html" title="Struct partial_enricher">partial_enricher</a></code>
|
|
is the right choice. Also, If we want to give two <code class="computeroutput"><span class="identifier">icl</span><span class="special">::</span><span class="identifier">Maps</span></code>
|
|
a common set of keys in order to, say, iterate synchronously over both maps,
|
|
we need <span class="emphasis"><em>enrichers</em></span>.
|
|
</p>
|
|
</div>
|
|
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2007 -2010 Joachim Faulhaber<br>Copyright © 1999 -2006 Cortex Software GmbH<p>
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|
Distributed under the Boost Software License, Version 1.0. (See accompanying
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|
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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</p>
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</div></td>
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</tr></table>
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