Abstract
We present a wide-spectrum algebra and refinement calculus designed to allow one to reason about query optimization in graph-based data models.
A query language is wide-spectrum if it can be used to express both user level queries as well as low-level evaluation strategies or access plans. This property enables rule-based query optimization to be viewed as the process of refining expressions in such a language: “non-procedural” sub-expressions are gradually replaced by more “procedural” sub-expressions until an unambiguous access plan results. We begin by presenting an algebra that is wide-spectrum in this sense. One subset of operations within the algebra can be used to define the formal semantics of a non-procedural query language for graph-based data models. Another subset can express common data access paradigms such as an index scan, the “cut” operator in Prolog or the nested-iteration join processing strategy.
We then present a refinement calculus over the algebra which defines when one algebraic expression subsumes another. The calculus makes it possible to formally prove the correctness of rewrite rules used in rule-based query optimizers, and is sufficiently expressive to admit rules encoding many forms of semantic query optimization.
This research was supported in part by the Natural Sciences and Engineering Research Council of Canada, by Bell-Northern Research Ltd., and by ITRC: Information Technology Research Centre of Ontario.
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Coburn, N., Weddell, G.E. (1993). A logic for rule-based query optimization in graph-based data models. In: Ceri, S., Tanaka, K., Tsur, S. (eds) Deductive and Object-Oriented Databases. DOOD 1993. Lecture Notes in Computer Science, vol 760. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57530-8_8
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DOI: https://doi.org/10.1007/3-540-57530-8_8
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