An Order-Based Theory of Updates for Closed Database Views

Abstract

The fundamental problem in the design of update strategies for views of database schemata is that of selecting how the view update is to be reflected back to the base schema. This work presents a solution to this problem, based upon the dual philosophies of closed update strategies and order-based database mappings. A closed update strategy is one in which the entire set of updates exhibit natural closure properties, including transitivity and reversibility. The order-based paradigm is a natural one; most database formalisms endow the database states with a natural order structure, under which update by insertion is an increasing operation, and update by deletion is decreasing. Upon augmenting the original constant-complement strategy of Bancilhon and Spyratos – which is an early version of a closed update strategy – with compatible order-based notions, the reflection to the base schema of any update to the view schema which is an insertion, a deletion, or a modification which is realizable as a sequence of insertions and deletions is shown to be unique and independent of the choice of complement. In addition to this uniqueness characterization, the paper also develops a theory which identifies conditions under which a natural, maximal, update strategy exists for a view. This theory is then applied to a ubiquitous example – single-relational schemata constrained by equality-generating dependencies. Within this framework it is shown that for a view defined as a projection of the main relation, the only possibility is that the complement defining the update process is also a projection, and that the reconstruction is based upon functional dependencies.