Normal Forms and Conservative Extension Properties for Query Languages over Collection Types

Abstract

Strong normalization results are obtained for a general language for collection types. An induced normal form for sets and bags is then used to show that the class of functions whose input has height (that is, the maximal depth of nestings of sets/bags/lists in the complex object) at mostiand output has height at mostodefinable in a nested relational query language withoutpowersetoperator isindependentof the height of intermediate expressions used. Our proof holds regardless of whether the language is used for querying sets, bags, or lists, even in the presence of variant types. Moreover, the normal forms are useful in a general approach to query optimization. Paredaens and Van Gucht (ACM Trans on Database Systems17, No.?1 (1992), 65–93), proved a similar result for the special case wheni=o=1. Their result is complemented by Hull and Su (J. Comput. Systems Sci.43(1991), 219–261) who demonstrated the failure of independence when powerset operator is present andi=o=1. The theorem of Hull and Su was generalized to alliandoby Grumbach and Vianu (in“Proceedings of the 3rd International Conference on Database Theory,” Lecture Notes in Computer Science, Vol.?470, Springer-Verlag, Berlin, 1990). Our result generalizes Paredaens and Van Gucht's to alliando, providing a counterpart to the theorem of Grumbach and Vianu.