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.

Efficiently instantiating view-objects from remote relational databases

“…Fischer and Thomas (1983) introduced NEST as an operator for restructuring a flat relation into a nested relation. Similar concepts were also discussed by Abiteboul and Bidoit (1984) and Roth et al (1988). Our nesting process is an instance of implementing the NEST operator.…”

“…The query is used to materialize necessary data into a relation, and the function is used to restructure the materialized relation into a nested relation (Abiteboul and Bidoit, 1984;Roth et al, 1988).…”

Advanced query language for manipulating complex entities

“…2 relations or non-first normal form relations are also based on the valueoriented approach, but support the complex entity notion (Roth et al, 1988). They allow relation-valued attributes, which may contain relation-valued attributes, etc.…”

NF-NR: A practical normal form for nested relations

“…Examples of such applications are picture data processing, CAD and some business data processing applications whose data is hierarchically structured. The motivations behind considering nested relation as a database model are discussed in [4,11,13,15]. Research work in semantic data model and objectoriented data model shows that the capability of a data model to represent and manipulate complex structures is highly desirable [1].…”

“…[14,15] extend the relational algebra and calculus to manipulate nested relations. There are numerous prototype systems built based on nested relation data model [5].…”