A Framework for the Investigation of Aggregate Functions in Database Queries

13 years 8 months ago

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Abstract. In this paper we present a new approach for studying aggregations in the context of database query languages. Starting from a broad de nition of aggregate function, we address our investigation from two di erent perspectives. We rst propose a declarative notion of uniform aggregate function that refers to a family of scalar functions uniformly constructed over a vocabulary of basic operators by a bounded Turing Machine. This notion yields an e ective tool to study the e ect of the embedding of a class of built-in aggregate functions in a query language. All the aggregate functions most used in practice are included in this classi cation. We then present an operational notion of aggregate function, by considering a high-order folding constructor, based on structural recursion, devoted to compute numeric aggregations over complex values. We show that numeric folding over a given vocabulary is sometimes not able to compute, by itself, the whole class of uniform aggregate functio...

Luca Cabibbo, Riccardo Torlone

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