AsterixDB Temporal Functions: Allen’s Relations

interval-before, interval-after

• Syntax:

  interval-before(interval1, interval2)
  interval-after(interval1, interval2)
  

• These two functions check whether an interval happens before/after another interval.

• Arguments:
  • interval1, interval2: two intervals to be compared

• Return Value:

  A boolean value. Specifically, interval-before(interval1, interval2) is true if and only if interval1.end < interval2.start, and interval-after(interval1, interval2) is true if and only if interval1.start > interval2.end. If any of the two inputs is null, null is returned.

• Examples:

  let $itv1 := interval-from-date("2000-01-01", "2005-01-01")
  let $itv2 := interval-from-date("2005-05-01", "2012-09-09")
  return {"interval-before": interval-before($itv1, $itv2), "interval-after": interval-after($itv2, $itv1)}
  

• The expected result is:

  { "interval-before": true, "interval-after": true }
  

interval-covers, interval-covered-by

• Syntax:

  interval-covers(interval1, interval2)
  interval-covered-by(interval1, interval2)
  

• These two functions check whether one interval covers the other interval.

• Arguments:
  • interval1, interval2: two intervals to be compared

• Return Value:

  A boolean value. Specifically, interval-covers(interval1, interval2) is true if and only if

  interval1.start <= interval2.start
  AND interval1.end >= interval2.end
  

  interval-covered-by(interval1, interval2) is true if and only if

  interval2.start <= interval1.start
  AND interval2.end >= interval1.end
  

  For both functions, if any of the two inputs is null, null is returned.

• Examples:

  let $itv1 := interval-from-date("2000-01-01", "2005-01-01")
  let $itv2 := interval-from-date("2000-03-01", "2004-09-09")
  let $itv3 := interval-from-date("2006-08-01", "2007-03-01")
  let $itv4 := interval-from-date("2004-09-10", "2012-08-01")
  return {"interval-covers": interval-covers($itv1, $itv2), "interval-covered-by": interval-covered-by($itv3, $itv4)}
  

• The expected result is:

  { "interval-covers": true, "interval-covered-by": true }
  

interval-overlaps, interval-overlapped-by

• Syntax:

  interval-overlaps(interval1, interval2)
  interval-overlapped-by(interval1, interval2)
  

• These functions check whether two intervals overlap with each other.

• Arguments:
  • interval1, interval2: two intervals to be compared

• Return Value:

  A boolean value. Specifically, interval-overlaps(interval1, interval2) is true if and only if

  interval1.start < interval2.start
  AND interval2.end > interval1.end
  AND interval1.end > interval2.start
  

  interval-overlapped-by(interval1, interval2) is true if and only if

  interval2.start < interval1.start
  AND interval1.end > interval2.end
  AND interval2.end > interval1.start
  

  For all these functions, if any of the two inputs is null, null is returned.

  Note that interval-overlaps and interval-overlapped-by are following the Allen’s relations on the definition of overlap.

• Examples:

  let $itv1 := interval-from-date("2000-01-01", "2005-01-01")
  let $itv2 := interval-from-date("2004-05-01", "2012-09-09")
  let $itv3 := interval-from-date("2006-08-01", "2007-03-01")
  let $itv4 := interval-from-date("2004-09-10", "2006-12-31")
  return {"overlaps": interval-overlaps($itv1, $itv2), 
          "overlapped-by": interval-overlapped-by($itv3, $itv4)}
  

• The expected result is:

  { "overlaps": true, "overlapped-by": true }
  

interval-overlapping

Note that interval-overlapping is not an Allen’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: interval-overlaps, interval-overlapped-by, interval-covers, or interval-covered-by.

• Syntax:

  interval-overlapping(interval1, interval2)
  

• This functions check whether two intervals share any points with each other.

• Arguments:
  • interval1, interval2: two intervals to be compared

• Return Value:

  A boolean value. Specifically, interval-overlapping(interval1, interval2) is true if

  (interval2.start >= interval1.start
  AND interval2.start < interval1.end)
  OR
  (interval2.end > interval1.start
  AND interval2.end <= interval1.end)
  

  If any of the two inputs is null, null is returned.

• Examples:

  let $itv1 := interval-from-date("2000-01-01", "2005-01-01")
  let $itv2 := interval-from-date("2004-05-01", "2012-09-09")
  let $itv3 := interval-from-date("2006-08-01", "2007-03-01")
  let $itv4 := interval-from-date("2004-09-10", "2006-12-31")
  return {"overlapping1": interval-overlapping($itv1, $itv2), 
          "overlapping2": interval-overlapping($itv3, $itv4)}
  

• The expected result is:

  { "overlapping1": true, "overlapping2": true }
  

interval-meets, interval-met-by

• Syntax:

  interval-meets(interval1, interval2)
  interval-met-by(interval1, interval2)
  

• These two functions check whether an interval meets with another interval.

• Arguments:
  • interval1, interval2: two intervals to be compared

• Return Value:

  A boolean value. Specifically, interval-meets(interval1, interval2) is true if and only if interval1.end = interval2.start, and interval-met-by(interval1, interval2) is true if and only if interval1.start = interval2.end. If any of the two inputs is null, null is returned.

• Examples:

  let $itv1 := interval-from-date("2000-01-01", "2005-01-01")
  let $itv2 := interval-from-date("2005-01-01", "2012-09-09")
  let $itv3 := interval-from-date("2006-08-01", "2007-03-01")
  let $itv4 := interval-from-date("2004-09-10", "2006-08-01")
  return {"meets": interval-meets($itv1, $itv2), "metby": interval-met-by($itv3, $itv4)}
  

• The expected result is:

  { "meets": true, "metby": true }
  

interval-starts, interval-started-by

• Syntax:

  interval-starts(interval1, interval2)
  interval-started-by(interval1, interval2)
  

• These two functions check whether one interval starts with the other interval.

• Arguments:
  • interval1, interval2: two intervals to be compared

• Return Value:

  A boolean value. Specifically, interval-starts(interval1, interval2) returns true if and only if

  interval1.start = interval2.start
  AND interval1.end <= interval2.end
  

  interval-started-by(interval1, interval2) returns true if and only if

  interval1.start = interval2.start
  AND interval2.end <= interval1.end
  

  For both functions, if any of the two inputs is null, null is returned.

• Examples:

  let $itv1 := interval-from-date("2000-01-01", "2005-01-01")
  let $itv2 := interval-from-date("2000-01-01", "2012-09-09")
  let $itv3 := interval-from-date("2006-08-01", "2007-03-01")
  let $itv4 := interval-from-date("2006-08-01", "2006-08-01")
  return {"interval-starts": interval-starts($itv1, $itv2), "interval-started-by": interval-started-by($itv3, $itv4)}
  

• The expected result is:

  { "interval-starts": true, "interval-started-by": true }
  

interval-ends, interval-ended-by

• Syntax:

  interval-ends(interval1, interval2)
  interval-ended-by(interval1, interval2)
  

• These two functions check whether one interval ends with the other interval.

• Arguments:
  • interval1, interval2: two intervals to be compared

• Return Value:

  A boolean value. Specifically, interval-ends(interval1, interval2) returns true if and only if

  interval1.end = interval2.end
  AND interval1.start >= interval2.start
  

  interval-ended-by(interval1, interval2) returns true if and only if

  interval2.end = interval1.end
  AND interval2.start >= interval1.start
  

  For both functions, if any of the two inputs is null, null is returned.

• Examples:

  let $itv1 := interval-from-date("2000-01-01", "2005-01-01")
  let $itv2 := interval-from-date("1998-01-01", "2005-01-01")
  let $itv3 := interval-from-date("2006-08-01", "2007-03-01")
  let $itv4 := interval-from-date("2006-09-10", "2007-03-01")
  return {"interval-ends": interval-ends($itv1, $itv2), "interval-ended-by": interval-ended-by($itv3, $itv4) }
  

• The expected result is:

  { "interval-ends": true, "interval-ended-by": true }