The relational model with relation-valued attributes
Information Systems
ACM Transactions on Database Systems (TODS)
A recursive algebra for nested relations
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Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
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Principles of programming with complex objects and collection types
ICDT '92 Selected papers of the fourth international conference on Database theory
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ICDT '92 Selected papers of the fourth international conference on Database theory
Descriptive complexity theory over the real numbers
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
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Journal of Computer and System Sciences - special issue on complexity theory
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PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Query languages for bags and aggregate functions
Journal of Computer and System Sciences - Special issue on principles of database systems
Equivalence of Relational Algebra and Relational Calculus Query Languages Having Aggregate Functions
Journal of the ACM (JACM)
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The VLDB Journal — The International Journal on Very Large Data Bases
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ICDT '90 Proceedings of the Third International Conference on Database Theory
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
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ICDT '97 Proceedings of the 6th International Conference on Database Theory
Algebraic query optimisation for database programming languages
The VLDB Journal — The International Journal on Very Large Data Bases
ISMIS '02 Proceedings of the 13th International Symposium on Foundations of Intelligent Systems
Transformation-Based Learning Using Multirelational Aggregation
ILP '01 Proceedings of the 11th International Conference on Inductive Logic Programming
Specifying aggregation functions in multidimensional models with OCL
ER'10 Proceedings of the 29th international conference on Conceptual modeling
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In this paper we present a new approach for studying aggregations in the context of database query languages. Starting from a broad definition of aggregate function, we address our investigation from two different perspectives. We first 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 effective tool to study the effect 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 classification. 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 function over the same vocabulary. It turns out however that this limitation can be partially remedied by the restructuring capabilities of a query language.