Abstract

We define a standard of effectiveness for a database calculus relative to a query language. Effectiveness judges suitability to serve as a processing framework for the query language, and comprises aspects of coverage, manipulability and efficient evaluation. We present the monoid calculus, and argue its effectiveness for object-oriented query languages, exemplified by OQL of ODMG-93. The monoid calculus readily captures such features as multiple collection types, aggregations, arbitrary composition of type constructors and nested query expressions. We also show how to extend the monoid calculus to deal with vectors and arrays in more expressive ways than current query languages do, and illustrate how it can handle identity and updates. 1 Introduction A much-touted advantage of the relational data model is the existence of a formal calculus and algebra to model database queries. In practice, these formalisms fail to model many of the features present in commercial query languages (e.g...

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