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Hierarchies of Decidable Extensions of Bounded Quantification
 IN 22ND ACM SYMP. ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 1994
"... The system F , the wellknown secondorder polymorphic typed calculus with subtyping and bounded universal type quantification [CW85, BL90, CG92, Pie92, CMMS94], appears to be undecidable [Pie92] because of undecidability of its subtyping component. Attempts were made to obtain decidable type sys ..."
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Cited by 7 (5 self)
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The system F , the wellknown secondorder polymorphic typed calculus with subtyping and bounded universal type quantification [CW85, BL90, CG92, Pie92, CMMS94], appears to be undecidable [Pie92] because of undecidability of its subtyping component. Attempts were made to obtain decidable type systems with subtyping by weakening F [CP94, KS92], and also by reinforcing or extending it [Vor94a, Vor94b, Vor95]. However, for the moment, these extensions lack the important prooftheoretic minimum type property, which holds for F and guarantees that each typable term has the minimum type, being a subtype of any other type of the term in the same context [CG92, Vor94c]. As a preparation step to introducing the extensions of F with the minimum type property and the decidable term typing relation (which we do in [Vor94e]), we define and study here the hierarchies of decidable extensions of the F subtyping relation. We demonstrate conditions providing that each theory in a hierarchy: 1. ext...
Extensions of... with Decidable Typing
 Centre
, 1994
"... Both subtyping and typing relations in the system F , the wellknown secondorder polymorphic typed  calculus with subtyping [CW85, BL90, BTCCS91, CG92, CMMS94] appeared to be undecidable [Pie92]. We demonstrate an infinite class F of extensions of the system F , where both relations are decidable ..."
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Cited by 3 (3 self)
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Both subtyping and typing relations in the system F , the wellknown secondorder polymorphic typed  calculus with subtyping [CW85, BL90, BTCCS91, CG92, CMMS94] appeared to be undecidable [Pie92]. We demonstrate an infinite class F of extensions of the system F , where both relations are decidable. Our extensions are based on the converging hierarchies of decidable extensions of the Fsubtyping relation introduced in [Vor94c]. Every system c F from the class F satisfies the following properties: ffl all subtyping \Gamma ` oe and typing \Gamma ` t : judgments provable in F are also c Fprovable; in particular, every F typable term is also c F typable, but not conversely: an F typable term may have additional types in c F , and there exist c F typable terms that are not F typable; ffl the c F canonical types, analogous to the Fminimum types [CG92], are effectively computable (as opposed to F ); there exists a decision procedure, which given a context \Gamma and a term t a...
Proof Normalization and Subject Reduction in Extensions of Fsub
, 1995
"... System F , the secondorder polymorphic typed calculus with subtyping appeared to be undecidable because of the undecidability of its subtyping component. The discovery of decidable extensions of the F subtyping relation put forward a challenging problem of incorporating these extensions into an F ..."
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Cited by 1 (1 self)
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System F , the secondorder polymorphic typed calculus with subtyping appeared to be undecidable because of the undecidability of its subtyping component. The discovery of decidable extensions of the F subtyping relation put forward a challenging problem of incorporating these extensions into an F like typing in a decidable and coherent manner. In this paper we describe a family of systems combining the standard F typing rules with converging hierarchies of decidable extensions of the F subtyping and give decidable criteria for successful proof normalization and subject reduction.
Incremental Type Inference for Software Engineering
"... Software engineering focused type inference can enhance programmer productivity in statically typed objectoriented languages. Type inference is a system of automatically inferring the argument and return types of a function. It provides considerable programming convenience, because the programmer ca ..."
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Software engineering focused type inference can enhance programmer productivity in statically typed objectoriented languages. Type inference is a system of automatically inferring the argument and return types of a function. It provides considerable programming convenience, because the programmer can realize the benefits of a statically typed language without manually entering the type annotations. We study the problem of type inference in objectoriented languages and propose an incremental, programmeraided approach. Code is added one method at a time and missing types are inferred if possible. We present a specification and algorithm for inferring simple objectoriented types in this kind of incremental development environment. 1. Introduction Type inference was popularized by the ML language [Milner et al., 1990]. ML is made up of functions and simple data types such as records, tuples, and lists. Every function in ML has a welldefined type that includes the required types of it...
Fsub with Recursive Types: "TypesAsPropositions" Interpretation in M. Rabin's S2S
, 1995
"... Subtyping judgments of the polymorphic secondorder typed calculus F extended by recursive types and different known inference rules for these types could be interpreted in S2S, M.Rabin's monadic secondorder theory of two successor functions. On the one hand, this provides a comprehensible ..."
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Subtyping judgments of the polymorphic secondorder typed calculus F extended by recursive types and different known inference rules for these types could be interpreted in S2S, M.Rabin's monadic secondorder theory of two successor functions. On the one hand, this provides a comprehensible model of the parametric and inheritance polymorphisms over recursive types, on the other, proves that the corresponding subtyping theories are not essentially undecidable, i.e., possess consistent decidable extensions.
Incremental Type Inference for Software Engineering
"... Software engineering focused type inference can enhance programmer productivity in statically typed objectoriented languages. Type inference is a system of automatically inferring the argument and return types of a function. It provides considerable programming convenience, because the programmer ca ..."
Abstract
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Software engineering focused type inference can enhance programmer productivity in statically typed objectoriented languages. Type inference is a system of automatically inferring the argument and return types of a function. It provides considerable programming convenience, because the programmer can realize the benefits of a statically typed language without manually entering the type annotations. We study the problem of type inference in objectoriented languages and propose an incremental, programmeraided approach. Code is added one method at a time and missing types are inferred if possible. We present a specification and algorithm for inferring simple objectoriented types in this kind of incremental development environment.