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