Extended algebra and calculus for nested relational databases

Abstract

Relaxing the assumption that relations are always in First-Normal-Form (1NF) necessitates a reexamination of the fundamentals of relational database theory. In this paper we take a first step towards unifying the various theories of ¬1NF databases. We start by determining an appropriate model to couch our formalisms in. We then define an extended relational calculus as the theoretical basis for our ¬1NF database query language. We define a minimal extended relational algebra and prove its equivalence to the ¬1NF relational calculus. We define a class of ¬1NF relations with certain “good” properties and extend our algebra operators to work within this domain. We prove certain desirable equivalences that hold only if we restrict our language to this domain.