On the Decidability of Subtyping with Bounded Existential Types

Wehr, Stefan; Thiemann, Peter

doi:10.1007/978-3-642-10672-9_10

Cited by 16 publications

(18 citation statements)

References 13 publications

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“…There have been several formalisations of the Java type system, for purposes including formal definition [17], type soundness [4], decidability of type checking [20,14], and to gain better understanding of the mechanism [18,3,15].…”

Section: Wildcards In Javamentioning

confidence: 99%

“…We include assignment, since the presence of mutable state is relevant for the correct treatment of advanced type system features such as wildcards [15]. Our syntactic notion of subtyping is close to those employed in other existential type systems [20,19,13] but with some simplifications in presentation and a closer connection with the logical basis of existential types. Our language is rich enough to denote the types that can be expressed in Java (which is a superset of the types which can be denoted in Java).…”

Section: Syntactic Type Systemmentioning

confidence: 99%

“…Both rules can be seen as the natural extension of the existential elimination and introduction rules in first order logic to an arbitrary number of variables 1 . Similar rules are used in some existing models of wildcards [20,3], while some authors combine them into a single rule (e.g., -Env in [16,2]). …”

Section: Subtypingmentioning

confidence: 99%

“…Soundness and decidability of the Java type system has been studied in the context of existential types [2,20], but there has been little effort to investigate the meaning of wildcards.…”

Section: Introductionmentioning

confidence: 99%

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Towards a semantic model for Java wildcards

Summers

Cameron

Dezani‐Ciancaglini

et al. 2010

Proceedings of the 12th Workshop on Formal Techniques for Java-Like Programs

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Wildcard types enrich the types expressible in Java, and extend the set of typeable Java programs. Syntactic models and proofs of soundness for type systems related to Java wildcards have been suggested in the past, however, the semantics of wildcards has not yet been studied.In this paper we propose a semantic model for Java wildcards, inspired by work on semantic subtyping, which traditionally interprets types as sets of possible values. To easily reflect the nominal type system of Java, our model is defined in terms of runtime types (closed class types) rather than the structure of the runtime values themselves. To reflect the variance introduced by wildcards, our model interprets types as sets of such closed class types.Having defined our model, we employ a standard semantic notion of subtyping. We show soundness of syntactic subtyping with respect to the semantic version, and demonstrate that completeness fails in the general case. We identify a restricted (but nonetheless rich) type language for which the syntactic notion of subtyping is both sound and complete.

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Section: Wildcards In Javamentioning

confidence: 99%

Section: Syntactic Type Systemmentioning

confidence: 99%

Section: Subtypingmentioning

confidence: 99%

“…Soundness and decidability of the Java type system has been studied in the context of existential types [2,20], but there has been little effort to investigate the meaning of wildcards.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Towards a semantic model for Java wildcards

Summers

Cameron

Dezani‐Ciancaglini

et al. 2010

Proceedings of the 12th Workshop on Formal Techniques for Java-Like Programs

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“…First-class quantification easily leads to undecidable type inference [22,23]. To make type inference decidable, we restrict quantification to class variables and integer variables.…”

Section: Introductionmentioning

confidence: 99%

Inferable object-oriented typed assembly language

Tate

Chen

Hawblitzel

2010

Proceedings of the 31st ACM SIGPLAN Conference on Programming Language Design and Implementation

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A certifying compiler preserves type information through compilation to assembly language programs, producing typed assembly language (TAL) programs that can be verified for safety independently so that the compiler does not need to be trusted. There are two challenges for adopting certifying compilation in practice. First, requiring every compiler transformation and optimization to preserve types is a large burden on compilers, especially when adopting certifying compilation into existing optimizing non-certifying compilers. Second, type annotations significantly increase the size of assembly language programs. This paper proposes an alternative to traditional certifying compilers. It presents iTalX, the first inferable TAL type system that supports existential types, arrays, interfaces, and stacks. We have proved our inference algorithm is complete, meaning if an assembly language program is typeable with iTalX then our algorithm will infer an iTalX typing for that program. Furthermore, our algorithm is guaranteed to terminate even if the assembly language program is untypeable. We demonstrate that it is practical to infer such an expressive TAL by showing a prototype implementation of type inference for code compiled by Bartok, an optimizing C# compiler. Our prototype implementation infers complete type annotations for 98% of functions in a suite of realistic C# benchmarks. The typeinference time is about 8% of the compilation time. We needed to change only 2.5% of the compiler code, mostly adding new code for defining types and for writing types to object files. Most transformations are untouched. Type-annotation size is only 17% of the size of pure code and data, reducing type annotations in our previous certifying compiler [4] by 60%. The compiler needs to preserve only essential type information such as method signatures, object-layout information, and types for static data and external labels. Even non-certifying compilers have most of this information available.

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