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190 <!-- ! Licensed to the Apache Software Foundation (ASF) under one
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206 ! --><h1>AsterixDB Temporal Functions: Allen&#x2019;s Relations</h1>
207<div class="section">
208<h2><a name="Table_of_Contents"></a><a name="toc" id="toc">Table of Contents</a></h2>
209
210<ul>
211
212<li><a href="#AboutAllensRelations">About Allen&#x2019;s Relations</a></li>
213
214<li><a href="#AllensRelatonsFunctions">Allen&#x2019;s Relations Functions</a></li>
215</ul></div>
216<div class="section">
217<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>
218<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>
219<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>
220<div class="section">
221<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>
222<div class="section">
223<h3><a name="interval-before_interval-after"></a>interval-before, interval-after</h3>
224
225<ul>
226
227<li>
228<p>Syntax:</p>
229
230<div class="source">
231<div class="source">
232<pre>interval-before(interval1, interval2)
233interval-after(interval1, interval2)
234</pre></div></div></li>
235
236<li>
237<p>These two functions check whether an interval happens before/after another interval. </p></li>
238
239<li>Arguments:
240
241<ul>
242
243<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
244 </ul></li>
245
246<li>
247<p>Return Value:</p>
248<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>
249
250<li>
251<p>Examples:</p>
252
253<div class="source">
254<div class="source">
255<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
256let $itv2 := interval-from-date(&quot;2005-05-01&quot;, &quot;2012-09-09&quot;)
257return {&quot;interval-before&quot;: interval-before($itv1, $itv2), &quot;interval-after&quot;: interval-after($itv2, $itv1)}
258</pre></div></div></li>
259
260<li>
261<p>The expected result is:</p>
262
263<div class="source">
264<div class="source">
265<pre>{ &quot;interval-before&quot;: true, &quot;interval-after&quot;: true }
266</pre></div></div></li>
267</ul></div>
268<div class="section">
269<h3><a name="interval-covers_interval-covered-by"></a>interval-covers, interval-covered-by</h3>
270
271<ul>
272
273<li>
274<p>Syntax:</p>
275
276<div class="source">
277<div class="source">
278<pre>interval-covers(interval1, interval2)
279interval-covered-by(interval1, interval2)
280</pre></div></div></li>
281
282<li>
283<p>These two functions check whether one interval covers the other interval.</p></li>
284
285<li>Arguments:
286
287<ul>
288
289<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
290 </ul></li>
291
292<li>
293<p>Return Value:</p>
294<p>A <tt>boolean</tt> value. Specifically, <tt>interval-covers(interval1, interval2)</tt> is true if and only if</p>
295
296<div class="source">
297<div class="source">
298<pre>interval1.start &lt;= interval2.start
299AND interval1.end &gt;= interval2.end
300</pre></div></div>
301<p><tt>interval-covered-by(interval1, interval2)</tt> is true if and only if</p>
302
303<div class="source">
304<div class="source">
305<pre>interval2.start &lt;= interval1.start
306AND interval2.end &gt;= interval1.end
307</pre></div></div>
308<p>For both functions, if any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
309
310<li>
311<p>Examples:</p>
312
313<div class="source">
314<div class="source">
315<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
316let $itv2 := interval-from-date(&quot;2000-03-01&quot;, &quot;2004-09-09&quot;)
317let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
318let $itv4 := interval-from-date(&quot;2004-09-10&quot;, &quot;2012-08-01&quot;)
319return {&quot;interval-covers&quot;: interval-covers($itv1, $itv2), &quot;interval-covered-by&quot;: interval-covered-by($itv3, $itv4)}
320</pre></div></div></li>
321
322<li>
323<p>The expected result is:</p>
324
325<div class="source">
326<div class="source">
327<pre>{ &quot;interval-covers&quot;: true, &quot;interval-covered-by&quot;: true }
328</pre></div></div></li>
329</ul></div>
330<div class="section">
331<h3><a name="interval-overlaps_interval-overlapped-by"></a>interval-overlaps, interval-overlapped-by</h3>
332
333<ul>
334
335<li>
336<p>Syntax:</p>
337
338<div class="source">
339<div class="source">
340<pre>interval-overlaps(interval1, interval2)
341interval-overlapped-by(interval1, interval2)
342</pre></div></div></li>
343
344<li>
345<p>These functions check whether two intervals overlap with each other.</p></li>
346
347<li>Arguments:
348
349<ul>
350
351<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
352 </ul></li>
353
354<li>
355<p>Return Value:</p>
356<p>A <tt>boolean</tt> value. Specifically, <tt>interval-overlaps(interval1, interval2)</tt> is true if and only if</p>
357
358<div class="source">
359<div class="source">
360<pre>interval1.start &lt; interval2.start
361AND interval2.end &gt; interval1.end
362AND interval1.end &gt; interval2.start
363</pre></div></div>
364<p><tt>interval-overlapped-by(interval1, interval2)</tt> is true if and only if</p>
365
366<div class="source">
367<div class="source">
368<pre>interval2.start &lt; interval1.start
369AND interval1.end &gt; interval2.end
370AND interval2.end &gt; interval1.start
371</pre></div></div>
372<p>For all these functions, if any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p>
373<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>
374
375<li>
376<p>Examples:</p>
377
378<div class="source">
379<div class="source">
380<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
381let $itv2 := interval-from-date(&quot;2004-05-01&quot;, &quot;2012-09-09&quot;)
382let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
383let $itv4 := interval-from-date(&quot;2004-09-10&quot;, &quot;2006-12-31&quot;)
384return {&quot;overlaps&quot;: interval-overlaps($itv1, $itv2),
385 &quot;overlapped-by&quot;: interval-overlapped-by($itv3, $itv4)}
386</pre></div></div></li>
387
388<li>
389<p>The expected result is:</p>
390
391<div class="source">
392<div class="source">
393<pre>{ &quot;overlaps&quot;: true, &quot;overlapped-by&quot;: true }
394</pre></div></div></li>
395</ul></div>
396<div class="section">
397<h3><a name="interval-overlapping"></a>interval-overlapping</h3>
398<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>
399
400<ul>
401
402<li>
403<p>Syntax:</p>
404
405<div class="source">
406<div class="source">
407<pre>interval-overlapping(interval1, interval2)
408</pre></div></div></li>
409
410<li>
411<p>This functions check whether two intervals share any points with each other. </p></li>
412
413<li>Arguments:
414
415<ul>
416
417<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
418 </ul></li>
419
420<li>
421<p>Return Value:</p>
422<p>A <tt>boolean</tt> value. Specifically, <tt>interval-overlapping(interval1, interval2)</tt> is true if</p>
423
424<div class="source">
425<div class="source">
426<pre>(interval2.start &gt;= interval1.start
427AND interval2.start &lt; interval1.end)
428OR
429(interval2.end &gt; interval1.start
430AND interval2.end &lt;= interval1.end)
431</pre></div></div>
432<p>If any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
433
434<li>
435<p>Examples:</p>
436
437<div class="source">
438<div class="source">
439<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
440let $itv2 := interval-from-date(&quot;2004-05-01&quot;, &quot;2012-09-09&quot;)
441let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
442let $itv4 := interval-from-date(&quot;2004-09-10&quot;, &quot;2006-12-31&quot;)
443return {&quot;overlapping1&quot;: interval-overlapping($itv1, $itv2),
444 &quot;overlapping2&quot;: interval-overlapping($itv3, $itv4)}
445</pre></div></div></li>
446
447<li>
448<p>The expected result is:</p>
449
450<div class="source">
451<div class="source">
452<pre>{ &quot;overlapping1&quot;: true, &quot;overlapping2&quot;: true }
453</pre></div></div></li>
454</ul></div>
455<div class="section">
456<h3><a name="interval-meets_interval-met-by"></a>interval-meets, interval-met-by</h3>
457
458<ul>
459
460<li>
461<p>Syntax:</p>
462
463<div class="source">
464<div class="source">
465<pre>interval-meets(interval1, interval2)
466interval-met-by(interval1, interval2)
467</pre></div></div></li>
468
469<li>
470<p>These two functions check whether an interval meets with another interval. </p></li>
471
472<li>Arguments:
473
474<ul>
475
476<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
477 </ul></li>
478
479<li>
480<p>Return Value:</p>
481<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>
482
483<li>
484<p>Examples:</p>
485
486<div class="source">
487<div class="source">
488<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
489let $itv2 := interval-from-date(&quot;2005-01-01&quot;, &quot;2012-09-09&quot;)
490let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
491let $itv4 := interval-from-date(&quot;2004-09-10&quot;, &quot;2006-08-01&quot;)
492return {&quot;meets&quot;: interval-meets($itv1, $itv2), &quot;metby&quot;: interval-met-by($itv3, $itv4)}
493</pre></div></div></li>
494
495<li>
496<p>The expected result is:</p>
497
498<div class="source">
499<div class="source">
500<pre>{ &quot;meets&quot;: true, &quot;metby&quot;: true }
501</pre></div></div></li>
502</ul></div>
503<div class="section">
504<h3><a name="interval-starts_interval-started-by"></a>interval-starts, interval-started-by</h3>
505
506<ul>
507
508<li>
509<p>Syntax:</p>
510
511<div class="source">
512<div class="source">
513<pre>interval-starts(interval1, interval2)
514interval-started-by(interval1, interval2)
515</pre></div></div></li>
516
517<li>
518<p>These two functions check whether one interval starts with the other interval.</p></li>
519
520<li>Arguments:
521
522<ul>
523
524<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
525 </ul></li>
526
527<li>
528<p>Return Value:</p>
529<p>A <tt>boolean</tt> value. Specifically, <tt>interval-starts(interval1, interval2)</tt> returns true if and only if</p>
530
531<div class="source">
532<div class="source">
533<pre>interval1.start = interval2.start
534AND interval1.end &lt;= interval2.end
535</pre></div></div>
536<p><tt>interval-started-by(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 interval2.end &lt;= interval1.end
542</pre></div></div>
543<p>For both functions, if any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
544
545<li>
546<p>Examples:</p>
547
548<div class="source">
549<div class="source">
550<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
551let $itv2 := interval-from-date(&quot;2000-01-01&quot;, &quot;2012-09-09&quot;)
552let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
553let $itv4 := interval-from-date(&quot;2006-08-01&quot;, &quot;2006-08-01&quot;)
554return {&quot;interval-starts&quot;: interval-starts($itv1, $itv2), &quot;interval-started-by&quot;: interval-started-by($itv3, $itv4)}
555</pre></div></div></li>
556
557<li>
558<p>The expected result is:</p>
559
560<div class="source">
561<div class="source">
562<pre>{ &quot;interval-starts&quot;: true, &quot;interval-started-by&quot;: true }
563</pre></div></div></li>
564</ul></div>
565<div class="section">
566<h3><a name="interval-ends_interval-ended-by"></a>interval-ends, interval-ended-by</h3>
567
568<ul>
569
570<li>
571<p>Syntax:</p>
572
573<div class="source">
574<div class="source">
575<pre>interval-ends(interval1, interval2)
576interval-ended-by(interval1, interval2)
577</pre></div></div></li>
578
579<li>
580<p>These two functions check whether one interval ends with the other interval.</p></li>
581
582<li>Arguments:
583
584<ul>
585
586<li><tt>interval1</tt>, <tt>interval2</tt>: two intervals to be compared</li>
587 </ul></li>
588
589<li>
590<p>Return Value:</p>
591<p>A <tt>boolean</tt> value. Specifically, <tt>interval-ends(interval1, interval2)</tt> returns true if and only if</p>
592
593<div class="source">
594<div class="source">
595<pre>interval1.end = interval2.end
596AND interval1.start &gt;= interval2.start
597</pre></div></div>
598<p><tt>interval-ended-by(interval1, interval2)</tt> returns true if and only if</p>
599
600<div class="source">
601<div class="source">
602<pre>interval2.end = interval1.end
603AND interval2.start &gt;= interval1.start
604</pre></div></div>
605<p>For both functions, if any of the two inputs is <tt>null</tt>, <tt>null</tt> is returned.</p></li>
606
607<li>
608<p>Examples:</p>
609
610<div class="source">
611<div class="source">
612<pre>let $itv1 := interval-from-date(&quot;2000-01-01&quot;, &quot;2005-01-01&quot;)
613let $itv2 := interval-from-date(&quot;1998-01-01&quot;, &quot;2005-01-01&quot;)
614let $itv3 := interval-from-date(&quot;2006-08-01&quot;, &quot;2007-03-01&quot;)
615let $itv4 := interval-from-date(&quot;2006-09-10&quot;, &quot;2007-03-01&quot;)
616return {&quot;interval-ends&quot;: interval-ends($itv1, $itv2), &quot;interval-ended-by&quot;: interval-ended-by($itv3, $itv4) }
617</pre></div></div></li>
618
619<li>
620<p>The expected result is:</p>
621
622<div class="source">
623<div class="source">
624<pre>{ &quot;interval-ends&quot;: true, &quot;interval-ended-by&quot;: true }
625</pre></div></div></li>
626</ul></div></div>
627 </div>
628 </div>
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630
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