Constant Complements, Reversibility and Universal View Updates
The algebraic specification of information systems (including databases) has been advanced by the introduction of category theoretic sketches and in particular by the authors’ Sketch Data Model (SkDM). The SkDM led to a new treatment of view updating usin
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Department of Computer Science Macquarie University [email protected] Department of Mathematics and Computer Science Mount Allison University [email protected]
Abstract. The algebraic specification of information systems (including databases) has been advanced by the introduction of category theoretic sketches and in particular by the authors’ Sketch Data Model (SkDM). The SkDM led to a new treatment of view updating using universal properties already studied in category theory. We call the new treatment succinctly ”universal updating”. This paper outlines the theory of universal updating and studies the relationships between it and recent theoretical results of Hegner and Lechtenb¨ orger which in turn studied the classical ”constant complement” approach to view updates. The main results demonstrate that constant complement updates are universal, that on the other hand there are sometimes universal updates even in the absence of constant complements, and that in the SkDM constant complement updates are reversible. We show further that there may be universal updates which are reversible even for views which have no complement. In short, the universal updates provide an attractive option including reversibility, even when constant complements are not available. The paper is predominantly theoretical studying different algebraic approaches to information system software but it also has important practical implications since it shows that universal updates have important properties in common with classical updates but they may be available even when classical approaches fail. Keywords: View update, semantic data model, category theory.
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Introduction
To provide usability, security, access limitation, and even interoperability for database systems, the designer of a database schema may specify a subschema or “view”. Any database state instantiating the database schema determines a view state instantiating the view schema by substitution. A user with access to the view state may perform an update to the view state. The question arising
Research partially supported by grants from the Australian Research Council and NSERC Canada.
J. Meseguer and G. Ro¸su (Eds.): AMAST 2008, LNCS 5140, pp. 238–252, 2008. c Springer-Verlag Berlin Heidelberg 2008
Constant Complements, Reversibility and Universal View Updates
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is how to determine an appropriate update to the state of the total database. This problem, known as the “view update problem” has been widely studied. There is a variety of “solutions”, referred to as “translations”, but many of these are either narrow in their application or not apparently close to actual database models. The implementation of view updates, especially within standards such as SQL, has been largely based on ad hoc and very limiting requirements. Much of the literature on the view update problem is over 15 years old, but in recent years there have been several new contributions. In 2002, Hegner [6] introduced an order based theory of database views and their updates which generalized t
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