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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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