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Algebras for object-oriented query languages

Algebraic query processing and optimization for relational databases is a proven and reasonably well-understood technology. This thesis presents a data model and query language that were developed in part to facilitate the study of algebraic query processing and optimization for advanced data models. It also continues the evolution of the algebraic paradigm by presenting operators and transformation rules that correspond to this data model and thus extend the paradigm in several directions. Additional research into algebraic constructs is also presented; this work was done in the context of a newer system that provides even more features than the previous one. A comprehensive survey of database algebras is included to help place the work in perspective. 
Many of the results were obtained in the context of the EXTRA/EXCESS system, which was intended as a test vehicle for the EXODUS extensible database system toolkit. The EXTRA data model includes support for complex objects (via orthogonal type constructors), sharing, and object and value semantics. The EXCESS query language provides facilities for querying and updating EXTRA data, and it can be extended through the addition of procedures and functions for manipulating EXTRA schema types and generic set functions. 
The algebraic constructs developed for EXTRA/EXCESS include operators and transformations supporting grouping, arrays, references, and multisets. I also propose a new approach to processing and optimizing overridden methods in the presence of multiple inheritance. The thesis presents an intuitive set-theoretic semantics for the domains of object identifiers in the presence of multiple inheritance. I constructively prove that the algebra is equipollent to EXCESS, giving a complete semantics and a translation algorithm for the EXCESS language. 
In the context of a more powerful data model, the thesis will describe techniques for handling abstraction in an algebraic setting; differing notions of equality in an algebra and their relation to non-determinism; and algebraic techniques for processing and optimizing some queries over tree structures. 
Taken as a whole, the techniques and results presented in this thesis indicate that the algebraic approach to query processing and optimization is both feasible and beneficial in object-oriented database systems and beyond.