Type inference in a database programming language

Ohori, Atsushi; Buneman, Peter

doi:10.1145/62678.62700

Cited by 62 publications

(37 citation statements)

References 8 publications

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“…The semantics of relational algebra is the well-known one [1,2] and will actually not concern us in the present paper. The set of all relation variables occurring in expression e is denoted 4 Stijn Vansummeren by Relvars(e) and the set of all attributes occurring in e is denoted by…”

Section: Preliminariesmentioning

confidence: 99%

“…We only need to show NP-hardness of T (R Ω ∪,−, ,σ,π,ρ ), for which we modify a reduction invented by Ohori and Buneman [4]. The reduction is from MONOTONE 3SAT [3]: decide whether there is a satisfying truth assignment for a given 3CNF boolean formula φ whose clauses are either all variables (called a positive clause) or all negated variables (called a negative clause).…”

Section: Theoremmentioning

confidence: 99%

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On the complexity of deciding typability in the relational algebra

Vansummeren

2005

Acta Informatica

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Abstract.We investigate the complexity of the typability problem for the relational algebra. This problem consists of deciding, for a given relational algebra expression, whether there exists an assignment of types to variables occurring in the expression such that the expression is well-typed under the assignment. We obtain that the problem is NP-complete in general. In particular, we show that the problem becomes NP-hard due to (1) the cartesian product operator; (2) the selection operator on arbitrary sets of typed predicates; and (3) the selection operator on "well-behaved" sets of typed predicates together with join and projection or renaming. However, the problem is in P when (1) we only allow union, difference, join and selection on "well-behaved" sets of typed predicates; or (2) we allow all operators except cartesian product, where the set of selection predicates can mention at most one base type. Most of these results follow from a close connection of the typability problem to non-uniform constraint satisfaction.

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Section: Preliminariesmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

On the complexity of deciding typability in the relational algebra

Vansummeren

2005

Acta Informatica

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“…The system, however, does not share with ML the property of principal typing (see [OB88, Wan881 for the analysis of the problem and [JM88, Em891 for the refinement of the system.) Based on Wand's general observation, in [OB88] we developed a type inference method which overcomes the difficulty and extends the method to database operations. Instead of using row variables, we introduced syntactic conditions to control substitution of type variables.…”

Section: Type Inference and Polymorphism In Machiavellimentioning

confidence: 99%

“…The typing rule for join operation is associated -a complex condition which can no longer be represented by some kind. To give a type scheme for join, we need t o extend the notion of (kinded) typing schemes to conditional typing schemes [OB88] by adding syntactic conditions on instantiation of type variables. A similar problem was later observed in [Wan891 if one uses a record concatenation operation rather than join.…”

Section: Operat Ions For Generalized Relationsmentioning

confidence: 99%

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Polymorphism and type inference in database programming

Buneman

Ohori

1996

ACM Trans. Database Syst.

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The polymorphic type system of ML can be extended in two ways that make it appropriate as the basis of a database programming language. The first is an extension to the language of types that captures the polymorphic nature of field selection; the second is a technique that generalizes relational operators to arbitrary data structures. The combination provides a statically typed language in which relational databases may be cleanly represented as typed structures. As in ML types are inferred, which relieves the programmer of making the rather complicated type assertions that may be required to express the most general type of a program that involves field selection and generalized relational operators.It is also possible to use these ideas to implement various aspects of object-oriented databases. By implementing database objects as reference types and generating the appropriate views -sets of structures with "identity" -we can achieve a degree of static type checking for object-oriented databases. Moreover it is possible to exploit the type system to check the consistency of object-oriented classes (abstract data types with inheritance). A prototype language based on these ideas has been implemented. While it lacks some important practical features, it demonstrates that a wide variety of database structures can be cleanly represented in a polymorphic programming language. Atsushi Ohorit Department of Computing ScienceUniversity of Glasgow Glasgow GI2 8QQ, Scotland AbstractThe polymorphic type system of ML can be extended in two ways that make it appropriate as the basis of a database programming language. The first is an extension to the language of types that captures the polymorphic nature of field selection; the second is a technique that generalizes relational operators to arbitrary data structures. The combination provides a statically typed language in which relational databases may be cleanly represented as typed structures. As in ML types are inferred, which relieves the programmer of making the rather complicated type assertions that may be required to express the most general type of a program that involves field selection and generalized relational operators.It is also possible to use these ideas to implement various aspects of object-oriented databases. By implementing database objects as reference types and generating the appropriate views -sets of structures with "identityn -we can achieve a degree of static type checking for object-oriented databases. Moreover it is possible to exploit the type system to check the consistency of object-oriented classes (abstract data types with inheritance). A prototype language based on these ideas has been implemented. While it lacks some important practical features, it demonstrates that a wide variety of database structures can be cleanly represented in a polymorphic programming language.

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A Typed Pattern Calculus

Kesner¹,

Puel²,

Tannen³

1996

Information and Computation

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The theory of programming with pattern-matching function definitions has been studied mainly in the framework of first-order rewrite systems. We present a typed functional calculus that emphasizes the strong connection between the structures of whole pattern definitions and their types. In this calculus, type-checking guarantees the absence of runtime errors caused by non-exhaustive pattern-matching definitions. Its operational semantics is deterministic in a natural way, without the imposition of ad hoc solutions such as clause order or``best fit''. In the spirit of the Curry Howard isomorphism, we design the calculus as a computational interpretation of the Gentzen sequent proofs for the intuitionistic propositional logic. We prove the basic properties connecting typing and evaluation: subject reduction and strong normalization. We believe that this calculus offers a rational reconstruction of the pattern-matching features found in successful functional languages.

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Type inference in a database programming language

Cited by 62 publications

References 8 publications

On the complexity of deciding typability in the relational algebra

On the complexity of deciding typability in the relational algebra

Polymorphism and type inference in database programming

A Typed Pattern Calculus

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