Remarks on the algebra of non first normal form relations

TLDR

The relational model typically requires first normal form, but many office information systems violate this restriction, making the condition inconvenient. The authors propose extending the relational model to include Non First Normal Form (NF2) relations. They enrich relational algebra with nest and unnest operations that convert between NF2 and standard relations, and establish properties and rules for these operations in combination with existing algebraic operations. These rules are crucial for both theoretical soundness and practical implementation of NF2 as an internal data model.

Abstract

Usually, the first normal form condition of the relational model of data is imposed. Presently, a broader class of data base applications like office information systems is considered where this restriction is not convenient. Therefore, an extension of the relational model is proposed consisting of Non First Normal Form (NF2) relations. The relational algebra is enriched mainly by so called nest and unnest operations which transform between NF2 relations and the usual ones. We state some properties of these operations and some rules which occur in combination with the operations of the usual relational algebra. Since we propose to use the NF2 model also for the internal data model these rules are important not only for theoretical reasons but also for a practical implementation.