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191 <!-- ! Licensed to the Apache Software Foundation (ASF) under one
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207 ! --><h1>AsterixDB Temporal Functions: Allen&#x2019;s Relations</h1>
208<div class="section">
209<h2><a name="Table_of_Contents"></a><a name="toc" id="toc">Table of Contents</a></h2>
210
211<ul>
212
213<li><a href="#AboutAllensRelations">About Allen&#x2019;s Relations</a></li>
214
215<li><a href="#AllensRelatonsFunctions">Allen&#x2019;s Relations Functions</a></li>
216</ul></div>
217<div class="section">
218<h2><a name="About_Allens_Relations_Back_to_TOC"></a><a name="AboutAllensRelations" id="AboutAllensRelations">About Allen&#x2019;s Relations</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
219<p>AsterixDB supports Allen&#x2019;s relations over interval types. Allen&#x2019;s relations are also called Allen&#x2019;s interval algebra. There are totally 13 base relations described by this algebra, and all of them are supported in AsterixDB (note that <tt>interval-equals</tt> is supported by the <tt>=</tt> comparison symbol so there is no extra function for it). </p>
220<p>A detailed description of Allen&#x2019;s relations can be found from its <a class="externalLink" href="http://en.wikipedia.org/wiki/Allen&apos;s_interval_algebra">wikipedia entry</a>. </p></div>
221<div class="section">
222<h2><a name="Allens_Relations_Functions_Back_to_TOC"></a><a name="AllensRelatonsFunctions" id="AllensRelatonsFunctions">Allen&#x2019;s Relations Functions</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
223<div class="section">
224<h3><a name="interval-before_interval-after"></a>interval-before, interval-after</h3>
225
226<ul>
227
228<li>
229<p>Syntax:</p>
230
231<div class="source">
232<div class="source">
233<pre>interval-before(interval1, interval2)
234interval-after(interval1, interval2)
235</pre></div></div></li>
236
237<li>
238<p>These two functions check whether an interval happens before/after another interval. </p></li>
239
240<li>Arguments:
241
242<ul>
243
244<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
245 </ul></li>
246
247<li>
248<p>Return Value:</p>
249<p>A <tt>boolean</tt> value. Specifically, <tt>interval-before(interval1, interval2)</tt> is true if and only if <tt>interval1.end &lt; interval2.start</tt>, and <tt>interval-after(interval1, interval2)</tt> is true if and only if <tt>interval1.start &gt; interval2.end</tt>. If any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
250
251<li>
252<p>Examples:</p>
253
254<div class="source">
255<div class="source">
256<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
257let $itv2 := interval-from-date(&quot;2005-05-01&quot;, &quot;2012-09-09&quot;)
258return {&quot;interval-before&quot;: interval-before($itv1, $itv2), &quot;interval-after&quot;: interval-after($itv2, $itv1)}
259</pre></div></div></li>
260
261<li>
262<p>The expected result is:</p>
263
264<div class="source">
265<div class="source">
266<pre>{ &quot;interval-before&quot;: true, &quot;interval-after&quot;: true }
267</pre></div></div></li>
268</ul></div>
269<div class="section">
270<h3><a name="interval-covers_interval-covered-by"></a>interval-covers, interval-covered-by</h3>
271
272<ul>
273
274<li>
275<p>Syntax:</p>
276
277<div class="source">
278<div class="source">
279<pre>interval-covers(interval1, interval2)
280interval-covered-by(interval1, interval2)
281</pre></div></div></li>
282
283<li>
284<p>These two functions check whether one interval covers the other interval.</p></li>
285
286<li>Arguments:
287
288<ul>
289
290<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
291 </ul></li>
292
293<li>
294<p>Return Value:</p>
295<p>A <tt>boolean</tt> value. Specifically, <tt>interval-covers(interval1, interval2)</tt> is true if and only if</p>
296
297<div class="source">
298<div class="source">
299<pre>interval1.start &lt;= interval2.start
300AND interval1.end &gt;= interval2.end
301</pre></div></div>
302<p><tt>interval-covered-by(interval1, interval2)</tt> is true if and only if</p>
303
304<div class="source">
305<div class="source">
306<pre>interval2.start &lt;= interval1.start
307AND interval2.end &gt;= interval1.end
308</pre></div></div>
309<p>For both functions, if any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
310
311<li>
312<p>Examples:</p>
313
314<div class="source">
315<div class="source">
316<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
317let $itv2 := interval-from-date(&quot;2000-03-01&quot;, &quot;2004-09-09&quot;)
318let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
319let $itv4 := interval-from-date(&quot;2004-09-10&quot;, &quot;2012-08-01&quot;)
320return {&quot;interval-covers&quot;: interval-covers($itv1, $itv2), &quot;interval-covered-by&quot;: interval-covered-by($itv3, $itv4)}
321</pre></div></div></li>
322
323<li>
324<p>The expected result is:</p>
325
326<div class="source">
327<div class="source">
328<pre>{ &quot;interval-covers&quot;: true, &quot;interval-covered-by&quot;: true }
329</pre></div></div></li>
330</ul></div>
331<div class="section">
332<h3><a name="interval-overlaps_interval-overlapped-by"></a>interval-overlaps, interval-overlapped-by</h3>
333
334<ul>
335
336<li>
337<p>Syntax:</p>
338
339<div class="source">
340<div class="source">
341<pre>interval-overlaps(interval1, interval2)
342interval-overlapped-by(interval1, interval2)
343</pre></div></div></li>
344
345<li>
346<p>These functions check whether two intervals overlap with each other.</p></li>
347
348<li>Arguments:
349
350<ul>
351
352<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
353 </ul></li>
354
355<li>
356<p>Return Value:</p>
357<p>A <tt>boolean</tt> value. Specifically, <tt>interval-overlaps(interval1, interval2)</tt> is true if and only if</p>
358
359<div class="source">
360<div class="source">
361<pre>interval1.start &lt; interval2.start
362AND interval2.end &gt; interval1.end
363AND interval1.end &gt; interval2.start
364</pre></div></div>
365<p><tt>interval-overlapped-by(interval1, interval2)</tt> is true if and only if</p>
366
367<div class="source">
368<div class="source">
369<pre>interval2.start &lt; interval1.start
370AND interval1.end &gt; interval2.end
371AND interval2.end &gt; interval1.start
372</pre></div></div>
373<p>For all these functions, if any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p>
374<p>Note that <tt>interval-overlaps</tt> and <tt>interval-overlapped-by</tt> are following the Allen&#x2019;s relations on the definition of overlap.</p></li>
375
376<li>
377<p>Examples:</p>
378
379<div class="source">
380<div class="source">
381<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
382let $itv2 := interval-from-date(&quot;2004-05-01&quot;, &quot;2012-09-09&quot;)
383let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
384let $itv4 := interval-from-date(&quot;2004-09-10&quot;, &quot;2006-12-31&quot;)
385return {&quot;overlaps&quot;: interval-overlaps($itv1, $itv2),
386 &quot;overlapped-by&quot;: interval-overlapped-by($itv3, $itv4)}
387</pre></div></div></li>
388
389<li>
390<p>The expected result is:</p>
391
392<div class="source">
393<div class="source">
394<pre>{ &quot;overlaps&quot;: true, &quot;overlapped-by&quot;: true }
395</pre></div></div></li>
396</ul></div>
397<div class="section">
398<h3><a name="interval-overlapping"></a>interval-overlapping</h3>
399<p>Note that <tt>interval-overlapping</tt> is not an Allen&#x2019;s Relation, but syntactic sugar we added for the case that the intersect of two intervals is not empty. Basically this function returns true if any of these functions return true: <tt>interval-overlaps</tt>, <tt>interval-overlapped-by</tt>, <tt>interval-covers</tt>, or <tt>interval-covered-by</tt>.</p>
400
401<ul>
402
403<li>
404<p>Syntax:</p>
405
406<div class="source">
407<div class="source">
408<pre>interval-overlapping(interval1, interval2)
409</pre></div></div></li>
410
411<li>
412<p>This functions check whether two intervals share any points with each other. </p></li>
413
414<li>Arguments:
415
416<ul>
417
418<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
419 </ul></li>
420
421<li>
422<p>Return Value:</p>
423<p>A <tt>boolean</tt> value. Specifically, <tt>interval-overlapping(interval1, interval2)</tt> is true if</p>
424
425<div class="source">
426<div class="source">
427<pre>(interval2.start &gt;= interval1.start
428AND interval2.start &lt; interval1.end)
429OR
430(interval2.end &gt; interval1.start
431AND interval2.end &lt;= interval1.end)
432</pre></div></div>
433<p>If any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
434
435<li>
436<p>Examples:</p>
437
438<div class="source">
439<div class="source">
440<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
441let $itv2 := interval-from-date(&quot;2004-05-01&quot;, &quot;2012-09-09&quot;)
442let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
443let $itv4 := interval-from-date(&quot;2004-09-10&quot;, &quot;2006-12-31&quot;)
444return {&quot;overlapping1&quot;: interval-overlapping($itv1, $itv2),
445 &quot;overlapping2&quot;: interval-overlapping($itv3, $itv4)}
446</pre></div></div></li>
447
448<li>
449<p>The expected result is:</p>
450
451<div class="source">
452<div class="source">
453<pre>{ &quot;overlapping1&quot;: true, &quot;overlapping2&quot;: true }
454</pre></div></div></li>
455</ul></div>
456<div class="section">
457<h3><a name="interval-meets_interval-met-by"></a>interval-meets, interval-met-by</h3>
458
459<ul>
460
461<li>
462<p>Syntax:</p>
463
464<div class="source">
465<div class="source">
466<pre>interval-meets(interval1, interval2)
467interval-met-by(interval1, interval2)
468</pre></div></div></li>
469
470<li>
471<p>These two functions check whether an interval meets with another interval. </p></li>
472
473<li>Arguments:
474
475<ul>
476
477<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
478 </ul></li>
479
480<li>
481<p>Return Value:</p>
482<p>A <tt>boolean</tt> value. Specifically, <tt>interval-meets(interval1, interval2)</tt> is true if and only if <tt>interval1.end = interval2.start</tt>, and <tt>interval-met-by(interval1, interval2)</tt> is true if and only if <tt>interval1.start = interval2.end</tt>. If any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
483
484<li>
485<p>Examples:</p>
486
487<div class="source">
488<div class="source">
489<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
490let $itv2 := interval-from-date(&quot;2005-01-01&quot;, &quot;2012-09-09&quot;)
491let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
492let $itv4 := interval-from-date(&quot;2004-09-10&quot;, &quot;2006-08-01&quot;)
493return {&quot;meets&quot;: interval-meets($itv1, $itv2), &quot;metby&quot;: interval-met-by($itv3, $itv4)}
494</pre></div></div></li>
495
496<li>
497<p>The expected result is:</p>
498
499<div class="source">
500<div class="source">
501<pre>{ &quot;meets&quot;: true, &quot;metby&quot;: true }
502</pre></div></div></li>
503</ul></div>
504<div class="section">
505<h3><a name="interval-starts_interval-started-by"></a>interval-starts, interval-started-by</h3>
506
507<ul>
508
509<li>
510<p>Syntax:</p>
511
512<div class="source">
513<div class="source">
514<pre>interval-starts(interval1, interval2)
515interval-started-by(interval1, interval2)
516</pre></div></div></li>
517
518<li>
519<p>These two functions check whether one interval starts with the other interval.</p></li>
520
521<li>Arguments:
522
523<ul>
524
525<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
526 </ul></li>
527
528<li>
529<p>Return Value:</p>
530<p>A <tt>boolean</tt> value. Specifically, <tt>interval-starts(interval1, interval2)</tt> returns true if and only if</p>
531
532<div class="source">
533<div class="source">
534<pre>interval1.start = interval2.start
535AND interval1.end &lt;= interval2.end
536</pre></div></div>
537<p><tt>interval-started-by(interval1, interval2)</tt> returns true if and only if</p>
538
539<div class="source">
540<div class="source">
541<pre>interval1.start = interval2.start
542AND interval2.end &lt;= interval1.end
543</pre></div></div>
544<p>For both functions, if any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
545
546<li>
547<p>Examples:</p>
548
549<div class="source">
550<div class="source">
551<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
552let $itv2 := interval-from-date(&quot;2000-01-01&quot;, &quot;2012-09-09&quot;)
553let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
554let $itv4 := interval-from-date(&quot;2006-08-01&quot;, &quot;2006-08-01&quot;)
555return {&quot;interval-starts&quot;: interval-starts($itv1, $itv2), &quot;interval-started-by&quot;: interval-started-by($itv3, $itv4)}
556</pre></div></div></li>
557
558<li>
559<p>The expected result is:</p>
560
561<div class="source">
562<div class="source">
563<pre>{ &quot;interval-starts&quot;: true, &quot;interval-started-by&quot;: true }
564</pre></div></div></li>
565</ul></div>
566<div class="section">
567<h3><a name="interval-ends_interval-ended-by"></a>interval-ends, interval-ended-by</h3>
568
569<ul>
570
571<li>
572<p>Syntax:</p>
573
574<div class="source">
575<div class="source">
576<pre>interval-ends(interval1, interval2)
577interval-ended-by(interval1, interval2)
578</pre></div></div></li>
579
580<li>
581<p>These two functions check whether one interval ends with the other interval.</p></li>
582
583<li>Arguments:
584
585<ul>
586
587<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
588 </ul></li>
589
590<li>
591<p>Return Value:</p>
592<p>A <tt>boolean</tt> value. Specifically, <tt>interval-ends(interval1, interval2)</tt> returns true if and only if</p>
593
594<div class="source">
595<div class="source">
596<pre>interval1.end = interval2.end
597AND interval1.start &gt;= interval2.start
598</pre></div></div>
599<p><tt>interval-ended-by(interval1, interval2)</tt> returns true if and only if</p>
600
601<div class="source">
602<div class="source">
603<pre>interval2.end = interval1.end
604AND interval2.start &gt;= interval1.start
605</pre></div></div>
606<p>For both functions, if any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
607
608<li>
609<p>Examples:</p>
610
611<div class="source">
612<div class="source">
613<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
614let $itv2 := interval-from-date(&quot;1998-01-01&quot;, &quot;2005-01-01&quot;)
615let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
616let $itv4 := interval-from-date(&quot;2006-09-10&quot;, &quot;2007-03-01&quot;)
617return {&quot;interval-ends&quot;: interval-ends($itv1, $itv2), &quot;interval-ended-by&quot;: interval-ended-by($itv3, $itv4) }
618</pre></div></div></li>
619
620<li>
621<p>The expected result is:</p>
622
623<div class="source">
624<div class="source">
625<pre>{ &quot;interval-ends&quot;: true, &quot;interval-ended-by&quot;: true }
626</pre></div></div></li>
627</ul></div></div>
628 </div>
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