Some Properties of Query Languages for Bags

Abstract

In this paper we study the expressive power of query languages for nested bags. We define the ambient bag language by generalizing the constructs of the relational language of Breazu-Tannen, Buneman and Wong, which is known to have precisely the power of the nested relational algebra. Relative strength of additional polynomial constructs is studied, and the ambient language endowed with the strongest combination of those constructs is chosen as a candidate for the basic bag language, which is called BQL (Bag Query Language). We prove that achieveing the power of BQL in the relational language amounts to adding simple arithmetic to the latter. We show that BQL has shortcomings of the relational algebra: it can not express recursive queries. In particular, parity test is not definable in BQL. We consider augmenting BQL with powerbag and structural recursion to overcome this deficiency. In contrast to the relational case, where powerset and structural recursion are equivalent, the latter is stronger than the former for bags. We discuss problems with using structural recursion and suggest a new bounded loop construct which works uniformly for bags, sets and lists. It has the power of structural recursion and does not require any preconditions to be verified. We find relational languages equivalent to BQL with powerbag and structural recursion/bounded loop. Finally, we discuss orderings on bags for rigorous treatment of partial information.KeywordsQuery LanguageTransitive ClosureExpressive PowerParity TestRelational AlgebraThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.