Grammar-like functional rules for representing query optimization alternatives

Extensible query optimization requires that the “repertoire” of alternative strategies for executing queries be represented as data, not embedded in the optimizer code. Recognizing that query optimizers are essentially expert systems, several researchers have suggested using strategy rules to transform query execution plans into alternative or better plans. Though extremely flexible, these systems can be very inefficient at any step in the processing, many rules may be eligible for application and complicated conditions must be tested to determine that eligibility during unification. We present a constructive, “building blocks” approach to defining alternative plans, in which the rules defining alternatives are an extension of the productions of a grammar to resemble the definition of a function in mathematics. The extensions permit each token of the grammar to be parametrized and each of its alternative definitions to have a complex condition. The terminals of the grammar are base-level database operations on tables that are interpreted at run-time. The non-terminals are defined declaratively by production rules that combine those operations into meaningful plans for execution. Each production produces a set of alternative plans, each having a vector of properties, including the estimated cost of producing that plan. Productions can require certain properties of their inputs, such as tuple order and location, and we describe a “glue” mechanism for augmenting plans to achieve the required properties. We give detailed examples to illustrate the power and robustness of our rules and to contrast them with related ideas.