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relations (and discussed temporal relvars) with attributes of this particular
type.
An interval type must be defined over an underlying point type, and an
associated precision must be specified (somehow) for that point type. A suc-
cessor function must be defined for that point type and that precision.
The operators we described include operators on intervals per se, opera-
tors on sets of intervals, and operators on temporal relations. Operators on
intervals per se include START, END, and Allens operators. Operators on
sets of intervals include UNFOLD and COALESCE. Operators on temporal
relations include relational versions of UNFOLD and COALESCE. We
also discussed certain specialized update operators and certain specialized
constraints for temporal relvars. We showed that most of those new opera-
tors and constraints could effectively be regarded as temporal counterparts of
familiar constructs.
We discussed two important canonical forms for sets of intervals of the
same type, the unfolded form and the coalesced form. A set of intervals of
type INTERVAL(PT) is in unfolded form if every interval in the set is a unit
interval—that is, an interval containing just one point, where a point is a
value of the underlying point type PT. A set of intervals of type
INTERVAL(PT ) is in coalesced form if no two distinct intervals in the set
overlap or meet. Both canonical forms have the advantage of avoiding certain
kinds of redundancy; the coalesced form maximizes conciseness and has very
pressing psychological advantages, while the unfolded form is the easiest to
operate on (obviating the need for the special constraints and update opera-
tors discussed in Sections 5.9 and 5.10). We showed how the concept of
these canonical forms is extended to relations with interval attributes, leading
to the important new relational operators, UNFOLD and COALESCE.
We drew attention in Section 5.11 to certain database design issues,
having to do with horizontal and vertical decomposition of certain temporal
relvars. Finally, we posed three questions concerning points that had not
conveniently arisen in any of the earlier sections. We suggested answers for
two of those questions and left the third for the reader to ponder.
Acknowledgement
The authors of this chapter are grateful to Nikos A. Lorentzos of the Agricul-
tural University of Athens for his careful review and useful comments.
