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  24 </div>
  25 <div class="section boost_icl_concepts_map_traits" lang="en">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_icl.concepts.map_traits"></a><a class="link" href="map_traits.html" title="Map Traits">Map Traits</a>
  28 </h3></div></div></div>
  29 <p>
  30         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
  31         type <code class="computeroutput"><span class="identifier">CodomainT</span></code>.
  32       </p>
  33 <a name="boost_icl.concepts.map_traits.remarks_on_identity_elements"></a><h5>
  34 <a name="id1079765"></a>
  35         <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.remarks_on_identity_elements">Remarks
  36         on Identity Elements</a>
  37       </h5>
  38 <p>
  39         In the pseudo code snippets below <code class="computeroutput"><span class="number">0</span></code>
  40         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>,
  41         which can be different objects like <code class="computeroutput"><span class="keyword">const</span>
  42         <span class="keyword">double</span> <span class="number">0.0</span></code>,
  43         empty sets, empty strings, null-vectors etc. dependent of the instance type
  44         for parameter <code class="computeroutput"><span class="identifier">CodomainT</span></code>.
  45         The existence of an <span class="emphasis"><em><span class="bold"><strong>identity element</strong></span></em></span>
  46         wrt. an <code class="computeroutput"><span class="keyword">operator</span><span class="special">+=</span></code>
  47         is a requirement for template type <code class="computeroutput"><span class="identifier">CodomainT</span></code>.
  48       </p>
  49 <div class="informaltable"><table class="table">
  50 <colgroup>
  51 <col>
  52 <col>
  53 <col>
  54 </colgroup>
  55 <thead><tr>
  56 <th>
  57               <p>
  58                 type
  59               </p>
  60               </th>
  61 <th>
  62               <p>
  63                 operation
  64               </p>
  65               </th>
  66 <th>
  67               <p>
  68                 identity element
  69               </p>
  70               </th>
  71 </tr></thead>
  72 <tbody>
  73 <tr>
  74 <td>
  75               <p>
  76                 <code class="computeroutput"><span class="keyword">int</span></code>
  77               </p>
  78               </td>
  79 <td>
  80               <p>
  81                 addition
  82               </p>
  83               </td>
  84 <td>
  85               <p>
  86                 <code class="computeroutput"><span class="number">0</span></code>
  87               </p>
  88               </td>
  89 </tr>
  90 <tr>
  91 <td>
  92               <p>
  93                 <code class="computeroutput"><span class="identifier">string</span></code>
  94               </p>
  95               </td>
  96 <td>
  97               <p>
  98                 concatenation
  99               </p>
 100               </td>
 101 <td>
 102               <p>
 103                 <code class="computeroutput"><span class="string">""</span></code>
 104               </p>
 105               </td>
 106 </tr>
 107 <tr>
 108 <td>
 109               <p>
 110                 <code class="computeroutput"><span class="identifier">set</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span></code>
 111               </p>
 112               </td>
 113 <td>
 114               <p>
 115                 union
 116               </p>
 117               </td>
 118 <td>
 119               <p>
 120                 <code class="computeroutput"><span class="special">{}</span></code>
 121               </p>
 122               </td>
 123 </tr>
 124 </tbody>
 125 </table></div>
 126 <p>
 127         In these cases the <code class="computeroutput"><span class="identifier">identity</span> <span class="identifier">element</span></code> value is delivered by the default
 128         constructor of the maps <code class="computeroutput"><span class="identifier">CodomainT</span></code>
 129         type. But there are well known exceptions like e.g. numeric multiplication:
 130       </p>
 131 <div class="informaltable"><table class="table">
 132 <colgroup>
 133 <col>
 134 <col>
 135 <col>
 136 </colgroup>
 137 <thead><tr>
 138 <th>
 139               <p>
 140                 type
 141               </p>
 142               </th>
 143 <th>
 144               <p>
 145                 operation
 146               </p>
 147               </th>
 148 <th>
 149               <p>
 150                 identity element
 151               </p>
 152               </th>
 153 </tr></thead>
 154 <tbody><tr>
 155 <td>
 156               <p>
 157                 <code class="computeroutput"><span class="keyword">int</span></code>
 158               </p>
 159               </td>
 160 <td>
 161               <p>
 162                 multiplication
 163               </p>
 164               </td>
 165 <td>
 166               <p>
 167                 <code class="computeroutput"><span class="number">1</span></code>
 168               </p>
 169               </td>
 170 </tr></tbody>
 171 </table></div>
 172 <p>
 173         Therefore icl functors, that serve as <code class="computeroutput"><span class="identifier">Combiner</span></code>
 174         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>
 175         is used in the implementation of <span class="emphasis"><em>aggregate on overlap</em></span>.
 176
 177 </p>
 178 <pre class="programlisting"><span class="identifier">inplace_times</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;::</span><span class="identifier">identity_element</span><span class="special">()</span> <span class="special">==</span> <span class="number">1</span>
 179 <span class="comment">// or more general
 180 </span><span class="identifier">inplace_times</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">identity_element</span><span class="special">()</span> <span class="special">==</span> <span class="identifier">unit_element</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">value</span><span class="special">()</span>
 181 </pre>
 182 <p>
 183       </p>
 184 <a name="boost_icl.concepts.map_traits.definedness_and_storage_of_identity_elements"></a><h5>
 185 <a name="id1081881"></a>
 186         <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.definedness_and_storage_of_identity_elements">Definedness
 187         and Storage of Identity Elements</a>
 188       </h5>
 189 <p>
 190         There are two <span class="emphasis"><em>properties</em></span> or <span class="emphasis"><em>traits</em></span>
 191         of icl maps that can be chosen by a template parameter <code class="computeroutput"><span class="identifier">Traits</span></code>.
 192         The <span class="emphasis"><em><span class="bold"><strong>first trait</strong></span></em></span> relates
 193         to the <span class="emphasis"><em><span class="bold"><strong>definedness</strong></span></em></span>
 194         of the map. Icl maps can be <span class="bold"><strong>partial</strong></span> or
 195         <span class="bold"><strong>total</strong></span> on the set of values given by domain
 196         type <code class="computeroutput"><span class="identifier">DomainT</span></code>.
 197       </p>
 198 <div class="itemizedlist"><ul type="disc">
 199 <li>
 200           A <span class="emphasis"><em><span class="bold"><strong>partial</strong></span></em></span> map is
 201           only defined on those key elements that have been inserted into the Map.
 202           This is usually expected and so <span class="emphasis"><em><span class="bold"><strong>partial
 203           definedness</strong></span></em></span> is the default.
 204         </li>
 205 <li>
 206           Alternatively an icl Map can be <span class="emphasis"><em><span class="bold"><strong>total</strong></span></em></span>.
 207           It is then considered to contain a <span class="emphasis"><em><span class="bold"><strong>neutral
 208           value</strong></span></em></span> for all key values that are not stored in the
 209           map.
 210         </li>
 211 </ul></div>
 212 <p>
 213         The <span class="emphasis"><em><span class="bold"><strong>second trait</strong></span></em></span> is
 214         related to the representation of <code class="computeroutput"><span class="identifier">identity</span>
 215         <span class="identifier">elements</span></code> in the map. An icl map
 216         can be a <span class="emphasis"><em><span class="bold"><strong>identity absorber</strong></span></em></span>
 217         or a <span class="emphasis"><em><span class="bold"><strong>identity enricher</strong></span></em></span>.
 218       </p>
 219 <div class="itemizedlist"><ul type="disc">
 220 <li>
 221           A <span class="emphasis"><em><span class="bold"><strong>identity absorber</strong></span></em></span>
 222           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.
 223         </li>
 224 <li>
 225           A <span class="emphasis"><em><span class="bold"><strong>identity enricher</strong></span></em></span>
 226           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>.
 227         </li>
 228 </ul></div>
 229 <p>
 230         For the template parameter <code class="computeroutput"><span class="identifier">Traits</span></code>
 231         of icl Maps we have the following four values.
 232       </p>
 233 <div class="informaltable"><table class="table">
 234 <colgroup>
 235 <col>
 236 <col>
 237 <col>
 238 </colgroup>
 239 <thead><tr>
 240 <th>
 241               <p>
 242               </p>
 243               </th>
 244 <th>
 245               <p>
 246                 identity absorber
 247               </p>
 248               </th>
 249 <th>
 250               <p>
 251                 identity enricher
 252               </p>
 253               </th>
 254 </tr></thead>
 255 <tbody>
 256 <tr>
 257 <td>
 258               <p>
 259                 partial
 260               </p>
 261               </td>
 262 <td>
 263               <p>
 264                 partial_absorber <span class="emphasis"><em>(default)</em></span>
 265               </p>
 266               </td>
 267 <td>
 268               <p>
 269                 partial_enricher
 270               </p>
 271               </td>
 272 </tr>
 273 <tr>
 274 <td>
 275               <p>
 276                 total
 277               </p>
 278               </td>
 279 <td>
 280               <p>
 281                 total_absorber
 282               </p>
 283               </td>
 284 <td>
 285               <p>
 286                 total_enricher
 287               </p>
 288               </td>
 289 </tr>
 290 </tbody>
 291 </table></div>
 292 <a name="boost_icl.concepts.map_traits.map_traits_motivated"></a><h5>
 293 <a name="id1082177"></a>
 294         <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.map_traits_motivated">Map Traits
 295         motivated</a>
 296       </h5>
 297 <p>
 298         Map traits are a late extension to the <span class="bold"><strong>icl</strong></span>.
 299         Interval maps have been used for a couple of years in a variety of applications
 300         at Cortex Software GmbH with an implementation that resembled the default
 301         trait. Only the deeper analysis of the icl's <span class="emphasis"><em><span class="bold"><strong>aggregating
 302         Map's concept</strong></span></em></span> in the course of preparation of the library
 303         for boost led to the introduction of map Traits.
 304       </p>
 305 <a name="boost_icl.concepts.map_traits.add_subtract_antinomy_in_aggregating_maps"></a><h6>
 306 <a name="id1082204"></a>
 307         <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.add_subtract_antinomy_in_aggregating_maps">Add-Subtract
 308         Antinomy in Aggregating Maps</a>
 309       </h6>
 310 <p>
 311         Constitutional for the absorber/enricher propery is a little antinomy.
 312       </p>
 313 <p>
 314         We can insert value pairs to the map by <span class="emphasis"><em><span class="bold"><strong>adding</strong></span></em></span>
 315         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>:
 316 </p>
 317 <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>
 318 <p>
 319       </p>
 320 <p>
 321         Further addition on common keys triggers aggregation:
 322 </p>
 323 <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>
 324 <p>
 325       </p>
 326 <p>
 327         A subtraction of existing pairs
 328 </p>
 329 <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>
 330 <p>
 331         yields value pairs that are associated with 0-values or <code class="computeroutput"><span class="identifier">identity</span>
 332         <span class="identifier">elements</span></code>.
 333       </p>
 334 <p>
 335         So once a value pair is created for a key <code class="computeroutput"><span class="identifier">k</span></code>
 336         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>).
 337       </p>
 338 <p>
 339         The very basic fact on sets, that we can remove what we have previously added
 340
 341 </p>
 342 <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>
 343 <p>
 344         does not apply.
 345       </p>
 346 <p>
 347         This is the motivation for the <span class="emphasis"><em><span class="bold"><strong>identity absorber</strong></span></em></span>
 348         Trait. A identity absorber map handles value pairs that carry identity elements
 349         as <span class="emphasis"><em><span class="bold"><strong>non-existent</strong></span></em></span>, which
 350         saves the law:
 351 </p>
 352 <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>
 353 <p>
 354       </p>
 355 <p>
 356         Yet this introduces a new problem: With such a <span class="emphasis"><em>identity absorber</em></span>
 357         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.
 358         This may be unfavorable because it is not inline with the behavior of stl::maps
 359         and this is not necessarily expected by clients of the library.
 360       </p>
 361 <p>
 362         The solution to the problem is the introduction of the identity enricher
 363         Trait, so the user can choose a map variant according to her needs.
 364       </p>
 365 <a name="boost_icl.concepts.map_traits.partial_and_total_maps"></a><h6>
 366 <a name="id1082625"></a>
 367         <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.partial_and_total_maps">Partial
 368         and Total Maps</a>
 369       </h6>
 370 <p>
 371         The idea of a identity absorbing map is, that an <span class="emphasis"><em><span class="bold"><strong>associated
 372         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>
 373         for it's key <code class="computeroutput"><span class="identifier">k</span></code>. So the pair
 374         <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>
 375         immediately tunnels from a map where it may emerge into the realm of non
 376         existence.
 377 </p>
 378 <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>
 379 <p>
 380       </p>
 381 <p>
 382         If identity elements do not code <span class="emphasis"><em><span class="bold"><strong>non-existence</strong></span></em></span>
 383         but <span class="emphasis"><em><span class="bold"><strong>existence with null quantification</strong></span></em></span>,
 384         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>
 385         that has no associated value different from 0. So in contrast to modelling
 386         <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>
 387         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
 388         <span class="emphasis"><em><span class="bold"><strong>implicitly existent</strong></span></em></span>.
 389       </p>
 390 <p>
 391         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>
 392         of it's domain type <code class="computeroutput"><span class="identifier">DomainT</span></code>.
 393         But only non-identity values are actually stored. This is the motivation
 394         for the definedness-Trait on <code class="computeroutput"><span class="identifier">icl</span>
 395         <span class="identifier">Maps</span></code>.
 396       </p>
 397 <p>
 398         A <span class="emphasis"><em><span class="bold"><strong>partial</strong></span></em></span> map models
 399         the intuitive view that only value pairs are existent, that are stored in
 400         the map. A <span class="emphasis"><em><span class="bold"><strong>total</strong></span></em></span> map
 401         exploits the possibility that all value pairs that are not stored can be
 402         considered as being existent and <span class="emphasis"><em><span class="bold"><strong>quantified</strong></span></em></span>
 403         with the identity element.
 404       </p>
 405 <a name="boost_icl.concepts.map_traits.pragmatical_aspects_of_map_traits"></a><h5>
 406 <a name="id1082892"></a>
 407         <a class="link" href="map_traits.html#boost_icl.concepts.map_traits.pragmatical_aspects_of_map_traits">Pragmatical
 408         Aspects of Map Traits</a>
 409       </h5>
 410 <p>
 411         From a pragmatic perspective value pairs that carry <code class="computeroutput"><span class="identifier">identity</span>
 412         <span class="identifier">elements</span></code> as mapped values can often
 413         be ignored. If we count, for instance, the number of overlaps of inserted
 414         intervals in an <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>
 415         (see example <a class="link" href="../examples/overlap_counter.html" title="Overlap counter">overlap counter</a>),
 416         most of the time, we are not interested in whether an overlap has been counted
 417         <code class="computeroutput"><span class="number">0</span></code> times or has not been counted
 418         at all. A identity enricher map is only needed, if we want to distinct between
 419         non-existence and 0-quantification.
 420       </p>
 421 <p>
 422         The following distinction can <span class="bold"><strong>not</strong></span> be made
 423         for a <code class="computeroutput"><a class="link" href="../../boost/icl/partial_absorber.html" title="Struct partial_absorber">partial_absorber</a></code>
 424         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>
 425         map:
 426       </p>
 427 <pre class="programlisting">(k,v) does not exist in the map: Pair (k,v) has NOT been dealt with
 428 (k,0) key k carries 0          : Pair (k,v) has     been dealt with resulting in v=0
 429 </pre>
 430 <p>
 431         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>
 432         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>
 433         a common set of keys in order to, say, iterate synchronously over both maps,
 434         we need <span class="emphasis"><em>enrichers</em></span>.
 435       </p>
 436 </div>
 437 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 438 <td align="left"></td>
 439 <td align="right"><div class="copyright-footer">Copyright &#169; 2007 -2010 Joachim Faulhaber<br>Copyright &#169; 1999 -2006 Cortex Software GmbH<p>
 440         Distributed under the Boost Software License, Version 1.0. (See accompanying
 441         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>)
 442       </p>
 443 </div></td>
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