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Positive Higher-Order Queries
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BibTeX
@MISC{Benedikt_positivehigher-order,
author = {Michael Benedikt and Huy Vu},
title = {Positive Higher-Order Queries},
year = {}
}
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Abstract
We investigate a higher-order query language that embeds operators of the positive relational algebra within the simply-typed λ-calculus. Our language allows one to succinctly define ordinary positive relational algebra queries (conjunctive queries and unions of conjunctive queries) and, in addition, second-order query functionals, which allow the transformation of CQs and UCQs in a generic (i.e., syntaxindependent) way. We investigate the equivalence and containment problems for this calculus, which subsumes traditional CQ/UCQ containment. Query functionals are said to be equivalent if the output queries are equivalent, for each possible input query, and similarly for containment. These notions of containment and equivalence depend on the class of (ordinary relational algebra) queries considered. We show that containment and equivalence are decidable when query variables are restricted to positive relational algebra and we identify the precise complexity of the problem. We also identify classes of functionals where containment is tractable. Finally, we provide upper bounds to the complexity of the containment problem when functionals act over other classes.
Keyphrases
positive higher-order query conjunctive query containment problem positive relational algebra query variable precise complexity upper bound ordinary positive relational algebra query ordinary relational algebra second-order query functionals equivalence depend possible input query output query simply-typed calculus higher-order query language query functionals traditional cq ucq containment
