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To Form a More Perfect Union (Intersection, Difference)
 In Proc. 5th Int'l Workshop on Database Programming Languages
, 1995
"... The AQUA [16] query algebra allows userdefined 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 o ..."
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Cited by 4 (2 self)
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The AQUA [16] query algebra allows userdefined 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 limit...
Deep Equality Revisited
, 1995
"... We revisit the notion of deep equality among objects in an object database from a formal point of view. We present three natural formalizations of deep equality: one based on the infinite valuetrees associated with objects, one based on the greatest fixpoint of an operator on equivalence relati ..."
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We revisit the notion of deep equality among objects in an object database from a formal point of view. We present three natural formalizations of deep equality: one based on the infinite valuetrees associated with objects, one based on the greatest fixpoint of an operator on equivalence relations among objects, and one based on indistinguishability of objects using observations of atomic values reachable from the objects. These three definitions are then shown to be equivalent. The characterization in terms of greatest fixpoints also yields a polynomialtime algorithm for checking deep equality. We also study the expressibility of deep equality in deductive database languages. 1 Introduction In object databases, objects consist of an object identifier (oid) and a value, typically having a complex structure built using the set and tuple constructor, in which both basic values and further oids appear. An intuitive way to think about an oid is thus as a reference to a complex...
Deep Equality Revisited
"... We revisit the notion of deep equality among objects in an object database from a formal point of view. We present three natural formalizations of deep equality: one based on the in nite valuetrees associated with objects, one based on the greatest xpoint ofanoperator on equivalence relations among ..."
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We revisit the notion of deep equality among objects in an object database from a formal point of view. We present three natural formalizations of deep equality: one based on the in nite valuetrees associated with objects, one based on the greatest xpoint ofanoperator on equivalence relations among objects, and one based on indistinguishability of objects using observations of atomic values reachable from the objects. These three de nitions are then shown to be equivalent. The characterization in terms of greatest xpoints also yields a polynomialtime algorithm for checking deep equality. Wealso study the expressibility of deep equality in deductive database languages. 1
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"... ©Copyright in this paper belongs to the author(s) Published in collaboration with the ..."
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©Copyright in this paper belongs to the author(s) Published in collaboration with the