Intersection type assignment systems

Bakel, Steffen van

doi:10.1016/0304-3975(95)00073-6

Cited by 74 publications

(92 citation statements)

References 18 publications

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“…Since then, intersection types disciplines have been used in a series of papers for characterizing evaluation properties of λ-terms [29,28,3,4,23,2,22,17].…”

Section: Introductionmentioning

confidence: 99%

Reductions, intersection types, and explicit substitutions

Dougherty

Lescanne

2001

Lecture Notes in Computer Science

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We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not complete for strong normalization. An important role is played by the notion of available variable in a term, which is a generalization of the classical notion of free variable.

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“…Since then, intersection types disciplines have been used in a series of papers for characterizing evaluation properties of λ-terms [29,28,3,4,23,2,22,17].…”

Section: Introductionmentioning

confidence: 99%

Reductions, intersection types, and explicit substitutions

Dougherty

Lescanne

2001

Lecture Notes in Computer Science

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“…2. System E more cleanly integrates the notion of expansion from the intersection type literature (see [18] for an overview) with substitution. Unlike in System I, expansion is interleaved with substitution and, as a result, both expansions and substitutions are composable.…”

Section: Summary Of Contributionsmentioning

confidence: 99%

System E: Expansion Variables for Flexible Typing with Linear and Non-linear Types and Intersection Types

Carlier¹,

Polakow²,

Wells³

et al. 2004

Programming Languages and Systems

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Abstract. Types are often used to control and analyze computer programs. Intersection types give great flexibility, but have been difficult to implement. The ! operator, used to distinguish between linear and non-linear types, has good potential for better resource-usage tracking, but has not been as flexible as one might want and has been difficult to use in compositional analysis. We introduce System E, a type system with expansion variables, linear intersection types, and the ! type constructor for creating non-linear types. System E is designed for maximum flexibility in automatic type inference and for ease of automatic manipulation of type information. Expansion variables allow postponing the choice of which typing rules to use until later constraint solving gives enough information to allow making a good choice. System E removes many difficulties that expansion variables had in the earlier System I and extends expansion variables to work with ! in addition to the intersection type constructor. We present subject reduction for call-by-need evaluation and discuss program analysis in System E. Discussion Background and MotivationMany current forms of program analysis, including many type-based analyses, work best when given the entire program to be analyzed [21,7]. However, by their very nature, large software systems are assembled from components that are designed separately and updated at different times. Hence, for large software systems, a program analysis methodology will benefit greatly from being compositional, and thereby usable in a modular and incremental fashion.Type systems for programming languages that are flexible enough to allow safe code reuse and abstract datatypes must support some kind of polymorphic types. Theoretical models for type polymorphism in existing programming languages (starting in the 1980s through now) have generally obtained type polymorphism via ∀ ("for all") [15,6] and ∃ ("there exists") quantifiers [13] or closely related methods. Type systems with ∀ and ∃ quantifiers alone tend to

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“…In this section we define a type assignment system for TRS+β, that can be seen as an extension of the intersection type assignment system presented in [3]. The LC-fragment of our type assignment system corresponds directly to the system presented in [4].…”

Section: Type Assignment In Trs+βmentioning

confidence: 99%

“…Using a combination of the techniques used in [3,4], it is possible to show that the three operations (substitution, expansion, and lifting) are sound on typed terms. .…”

Section: Definition 26 I)mentioning

confidence: 99%