Tridirectional typechecking

Dunfield, Jana; Pfenning, Frank

doi:10.1145/964001.964025

Cited by 64 publications

(47 citation statements)

References 22 publications

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“…However, arguments cannot change state, and state transitions have to be deterministic. We overcome these limitations by adapting type refinements with union and intersection types [9] to our setting. The basic notation is as follows:…”

Section: Methods Specification and Refinementmentioning

confidence: 99%

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Lightweight object specification with typestates

Bierhoff

Aldrich

2005

Proceedings of the 10th European Software Engineering Conference Held Jointly With 13th ACM SIGSOFT International Symposium on

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Previous work has proven typestates to be useful for modeling protocols in object-oriented languages. We build on this work by addressing substitutability of subtypes as well as improving precision and conciseness of specifications. We propose a specification technique for objects based on abstract states that incorporates state refinement, method refinement, and orthogonal state dimensions. Union and intersection types form the underlying semantics of method specifications. The approach guarantees substitutability and behavioral subtyping. We designed a dynamic analysis to check existing object-oriented software for protocol conformance and validated our approach by specifying two standard Java libraries. We provide preliminary evidence for the usefulness of our approach.

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Section: Methods Specification and Refinementmentioning

confidence: 99%

“…Behavioral subtyping results from using union and intersection types [9] in method specifications. They can express non-determinism and case-by-case behavior, increasing expressiveness and precision over specifications in Fugue.…”

Section: Introductionmentioning

confidence: 99%

Lightweight object specification with typestates

Bierhoff

Aldrich

2005

Proceedings of the 10th European Software Engineering Conference Held Jointly With 13th ACM SIGSOFT International Symposium on

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“…In contrast with [8,6,19], this does not force the whole calculus to be call-by-value. We build on [15,16], where a general notion of Girard's candidates is proposed.…”

Section: Introductionmentioning

confidence: 94%

“…This suggests either to adapt the elimination rules to the calculus, or to adapt the calculus to the elimination rules. In call-by-value settings, the first solution is studied in [6,19] for systems with union and implicit existential quantification. Both works propose elimination rules restricted to call-by-value evaluation contexts.…”

Section: Introductionmentioning

confidence: 99%

On the Values of Reducibility Candidates

Riba

2009

Lecture Notes in Computer Science

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Abstract. The straightforward elimination of union types is known to break subject reduction, and for some extensions of the lambda-calculus, to break strong normalization as well. Similarly, the straightforward elimination of implicit existential types breaks subject reduction. We propose elimination rules for union types and implicit existential quantification which use a form call-by-value issued from Girard's reducibility candidates. We show that these rules remedy the above mentioned difficulties, for strong normalization and, for the existential quantification, for subject reduction as well. Moreover, for extensions of the lambda-calculus based on intuitionistic logic, we show that the obtained existential quantification is equivalent to its usual impredicative encoding w.r.t. provability in realizability models built from reducibility candidates and biorthogonals.

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“…This syntactic approach is typically formalized by an inductively or co-inductively defined set of rules (Pierce, 2002). Unfortunately, deriving an algorithm from such a set of rules can be difficult, especially for advanced features such as intersection and union types (Dunfield & Pfenning, 2004;Dunfield, 2007).…”

Section: Related Workmentioning

confidence: 99%

Semantic subtyping with an SMT solver

Bierman¹,

Gordon²,

Hriţcu³

et al. 2012

J. Funct. Prog.

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We study a first-order functional language with the novel combination of the ideas of refinement type (the subset of a type to satisfy a Boolean expression) and type-test (a Boolean expression testing whether a value belongs to a type). Our core calculus can express a rich variety of typing idioms; for example, intersection, union, negation, singleton, nullable, variant, and algebraic types are all derivable. We formulate a semantics in which expressions denote terms, and types are interpreted as first-order logic formulas. Subtyping is defined as valid implication between the semantics of types. The formulas are interpreted in a specific model that we axiomatize using standard first-order theories. On this basis, we present a novel type-checking algorithm able to eliminate many dynamic tests and to detect many errors statically. The key idea is to rely on a Satisfiability Modulo Theories solver to compute subtyping efficiently. Moreover, using a satisfiability modulo theories solver allows us to show the uniqueness of normal forms for non-deterministic expressions, provide precise counterexamples when type-checking fails, detect empty types, and compute instances of types statically and at run-time.

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Tridirectional typechecking

Cited by 64 publications

References 22 publications

Lightweight object specification with typestates

Lightweight object specification with typestates

On the Values of Reducibility Candidates

Semantic subtyping with an SMT solver

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