To Form a More Perfect Union (Intersection, Difference)

The AQUA [16] query algebra allows user-defined equivalence relations as arguments to query operators that generalize standard set operations. These predicates determine what objects are included in the query result, and the duplicates that must be removed. While an expressive enhancement, the use of arbitrary equivalence relations to decide set membership can result in sets with counterintuitive behavior, and therefore can make queries return unreasonable results. In this paper, we show that equality predicates assume two roles with respect to sets. Distinguishers differentiate between set members and implicitly give meaning to standard set properties such as set equality. Constructors determine which object from input sets contribute to the query result. The requirements of distinguishers and constructors differ. AQUA’s set operators are problematic because they use constructors where distinguishers are required. We propose alternatives to AQUA’s set operators that address this limitation.