Database programming in Machiavelli—a polymorphic language with static type inference
SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
A simple proof of a theorem of Statman
Theoretical Computer Science
Functional database query languages as typed lambda calculi of fixed order (extended abstract)
PODS '94 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Finite model theory in the simply typed lambda calculus
Finite model theory in the simply typed lambda calculus
Answering queries using limited external query processors (extended abstract)
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Complexity of nonrecursive logic programs with complex values
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Complexity and expressive power of logic programming
ACM Computing Surveys (CSUR)
FQL: a functional query language
SIGMOD '79 Proceedings of the 1979 ACM SIGMOD international conference on Management of data
Naturally Embedded Query Languages
ICDT '92 Proceedings of the 4th International Conference on Database Theory
On the Expressive Power of Simply Typed and Let-Polymorphic Lambda Calculi
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
On the complexity of single-rule datalog queries
Information and Computation - Special issue: ICC '99
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
On the complexity of nonrecursive XQuery and functional query languages on complex values
ACM Transactions on Database Systems (TODS)
The complexity of β-reduction in low orders
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Optimizing linear counting queries under differential privacy
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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While relational algebra and calculus are a well-established foundation for classical database query languages, it is less clear what the analog is for higher-order functions, such as query transformations. Here we study a natural way to add higher-order functionality to query languages, by adding database query operators to the λ-calculus as constants. This framework, which we refer to as λ-embedded query languages, was introduced in [BPV10]. That work had a restricted focus: the containment and equivalence problems for query-to-query functions, in the case where only positive relational operators are allowed as constants. In this work we take an in-depth look at the most basic issue for such languages: the evaluation problem. We give a full picture of the complexity of evaluation for λ-embedded query languages, looking at a number of variations: with negation and without; with only relational algebra operators, and also with a recursion mechanism in the form of a query iteration operator; in a strongly-typed calculus as well as a weakly-typed one. We give tight bounds on both the combined complexity and the query complexity of evaluation in all these settings, in the process explaining connections with Datalog and prior work on λ-calculus evaluation.