On the complexity of deciding typability in the relational algebra

Vansummeren, Stijn

doi:10.1007/s00236-005-0162-6

Cited by 5 publications

(6 citation statements)

References 4 publications

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“…is NP-complete for both the relational algebra [54,59] and N RC(=, drop, ×, 1) [56]. Notice that in contrast, typability for N RC(=, drop) is in polynomial time by Theorem 16.…”

Section: Type Inferencementioning

confidence: 99%

A crash course on database queries

Bussche

Gucht

Vansummeren

2007

Proceedings of the Twenty-Sixth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

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Complex database queries, like programs in general, can 'crash', i.e., can raise runtime errors. We want to avoid crashes without losing expressive power, or we want to correctly predict the absence of crashes. We show how concepts and techniques from programming language theory, notably type systems and reflection, can be adapted to this end. Of course, the specific nature of database queries (as opposed to general programs), also requires some new methods, and raises new questions.

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“…is NP-complete for both the relational algebra [54,59] and N RC(=, drop, ×, 1) [56]. Notice that in contrast, typability for N RC(=, drop) is in polynomial time by Theorem 16.…”

Section: Type Inferencementioning

confidence: 99%

A crash course on database queries

Bussche

Gucht

Vansummeren

2007

Proceedings of the Twenty-Sixth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

Self Cite

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“…The ML type-checking algorithms therefore typically run in linear time in practice [19]. The NP-hardness of type-checking in the NNRC on the other hand arises in many expressions, due to many different reasons [32]. It is therefore likely that type-checking the integrated ML-NNRC language will in practice be slower than type-checking ML.…”

Section: Discussionmentioning

confidence: 99%

“…It is already known that typability for the relational algebra is NPcomplete [31,32]. It is also well-known that the relational algebra can be simulated in the NNRC [9,34].…”

Section: Lemma 3 If ϕ Is a Type Formula And H Is A T -Valuation Suchmentioning

confidence: 99%

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Polymorphic type inference for the named nested relational calculus

Bussche

Vansummeren

2007

ACM Trans. Comput. Logic

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The named nested relational calculus is the canonical query language for the complex object database model and is equipped with a natural static type system. Given an expression in the language, without type declarations for the input variables, there is the problem of whether there are any input type declarations under which the expression is well-typed. Moreover, if there are, then which are they, and what is the corresponding output type for each of these? This problem is solved by a logic-based approach, and the decision problem is shown to be NP-complete.

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“…We call this variant join-like, and name it Riviera J , because the type behavior of this rule is identical to the type-level behavior of the join operator in relational algebras [15,25]. It is not common for modules or records (an exception is the Church-style calculus of [32]), but we mention it to highlight the similarities between type problems in relational calculi and in calculi with concatenation and linking.…”

Section: Asymmetric Variantsmentioning

confidence: 99%

Type inference, principal typings, and let-polymorphism for first-class mixin modules

Makholm

Wells²

2005

Proceedings of the Tenth ACM SIGPLAN International Conference on Functional Programming

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A mixin module is a programming abstraction that simultaneously generalizes λ-abstractions, records, and mutually recursive definitions. Although various mixin module type systems have been developed, no one has investigated principal typings or developed type inference for first-class mixin modules, nor has anyone added Milner's let-polymorphism to such a system. This paper proves that typability is NP-complete for the naive approach followed by previous mixin module type systems. Because a λ-calculus extended with record concatenation is a simple restriction of our mixin module calculus, we also prove the folk belief that typability is NP-complete for the naive early type systems for record concatenation.To allow feasible type inference, we present Martini, a new system of simple types for mixin modules with principal typings. Martini is conceptually simple, with no subtyping and a clean and balanced separation between unification-based type inference with type and row variables and constraint solving for safety of linking and field extraction. We have implemented a type inference algorithm and we prove its complexity to be O(n 2 ), or O(n) given a fixed bound on the number of field labels. 1 To prove the complexity, we need to present an algorithm for row unification that may have been implemented by others, but which we could not find written down anywhere. Because Martini has principal typings, we successfully extend it with Milner's let-polymorphism.

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On the complexity of deciding typability in the relational algebra

Cited by 5 publications

References 4 publications

A crash course on database queries

A crash course on database queries

Polymorphic type inference for the named nested relational calculus

Type inference, principal typings, and let-polymorphism for first-class mixin modules

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