Extended algebra and calculus for nested relational databases
- 1 October 1988
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Database Systems
- Vol. 13 (4), 389-417
- https://doi.org/10.1145/49346.49347
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.Keywords
This publication has 17 references indexed in Scilit:
- SQL/NF: A query language for ¬1NF relational databasesInformation Systems, 1987
- A new normal form for nested relationsACM Transactions on Database Systems, 1987
- The relational model with relation-valued attributesInformation Systems, 1986
- Interactions between dependencies and nested relational structuresJournal of Computer and System Sciences, 1985
- The Format ModelJournal of the ACM, 1984
- Synthesis of unnormalized relations incorporating more meaningInformation Sciences, 1983
- Equivalence of Relational Algebra and Relational Calculus Query Languages Having Aggregate FunctionsJournal of the ACM, 1982
- On Database LogicJournal of the ACM, 1982
- Horizontal decomposition to improve a non-BCNF schemeACM SIGMOD Record, 1981
- Database abstractionsACM Transactions on Database Systems, 1977