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Polymorphic Delimited Continuations
 In Proc. Asian Programming Languages and Systems, LNCS 4807
, 2007
"... Abstract. This paper presents a polymorphic type system for a language with delimited control operators, shift and reset. Based on the monomorphic type system by Danvy and Filinski, the proposed type system allows pure expressions to be polymorphic. Thanks to the explicit presence of answer types, o ..."
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Abstract. This paper presents a polymorphic type system for a language with delimited control operators, shift and reset. Based on the monomorphic type system by Danvy and Filinski, the proposed type system allows pure expressions to be polymorphic. Thanks to the explicit presence of answer types, our type system satisfies various important properties, including strong type soundness, existence of principal types and an inference algorithm, and strong normalization. Relationship to CPS translation as well as extensions to impredicative polymorphism are also discussed. These technical results establish the foundation of polymorphic delimited continuations.
Relational parametricity for references and recursive types
 In Proceedings Fourth ACM Workshop on Types in Language Design and Implementation, TLDI’09
, 2009
"... We present a possible world semantics for a callbyvalue higherorder programming language with impredicative polymorphism, general references, and recursive types. The model is one of the first relationally parametric models of a programming language with all these features. To model impredicative ..."
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We present a possible world semantics for a callbyvalue higherorder programming language with impredicative polymorphism, general references, and recursive types. The model is one of the first relationally parametric models of a programming language with all these features. To model impredicative polymorphism we define the semantics of types via parameterized (worldindexed) logical relations over a universal domain. It is wellknown that it is nontrivial to show the existence of logical relations in the presence of recursive types. Here the problems are exacerbated because of general references. We explain what the problems are and present our solution, which makes use of a novel approach to modeling references. We prove that the resulting semantics is adequate with respect to a standard operational semantics and include simple examples of reasoning about contextual equivalence via parametricity.
Undecidability of typechecking in domainfree typed lambdacalculi with existence
 In the 17th EACSL Annual Conference on Computer Science Logic (CSL 2008), LNCS 5213
, 2008
"... Abstract. This paper shows undecidability of typechecking and typeinference problems in domainfree typed lambdacalculi with existential types: a negation and conjunction fragment, and an implicational fragment. These are proved by reducing typechecking and typeinference problems of the domainf ..."
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Abstract. This paper shows undecidability of typechecking and typeinference problems in domainfree typed lambdacalculi with existential types: a negation and conjunction fragment, and an implicational fragment. These are proved by reducing typechecking and typeinference problems of the domainfree polymorphic typed lambdacalculus to those of the lambdacalculi with existential types by continuation passing style translations.
Relational parametricity for control considered as a computational effect
 Electr. Notes Theor. Comput. Sci
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
Relational Parametricity for Computational Effects
"... According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricit ..."
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Cited by 1 (0 self)
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According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Real programs, however, exhibit computational effects. In this paper, we develop a framework for extending the notion of relational parametricity to languages with effects.
Type checking and inference are equivalent in lambda calculi with existential types
 In WFLP ’09: 18th International Workshop on Functional and (Constraint) Logic Programming
, 2009
"... Abstract. This paper shows that typechecking and typeinference problems are equivalent in domainfree lambda calculi with existential types, that is, typechecking problem is Turing reducible to typeinference problem and vice versa. In this paper, the equivalence is proved for two variants of doma ..."
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Abstract. This paper shows that typechecking and typeinference problems are equivalent in domainfree lambda calculi with existential types, that is, typechecking problem is Turing reducible to typeinference problem and vice versa. In this paper, the equivalence is proved for two variants of domainfree lambda calculi with existential types: one is an implication and existence fragment, and the other is a negation, conjunction and existence fragment. This result gives another proof of undecidability of type inference in the domainfree calculi with existence.
Type Checking and Inference for Polymorphic and Existential Types
"... This paper proves undecidability of type checking and type inference problems in some variants of typed lambda calculi with polymorphic and existential types. First, type inference in the domainfree polymorphic lambda calculus is proved to be undecidable, and then it is proved that type inference i ..."
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This paper proves undecidability of type checking and type inference problems in some variants of typed lambda calculi with polymorphic and existential types. First, type inference in the domainfree polymorphic lambda calculus is proved to be undecidable, and then it is proved that type inference is undecidable in the negation, conjunction, and existence fragment of the domainfree typed lambda calculus. Secondly, their variants with multiple quantifier rules are introduced, and their type checking and type inference are proved to be undecidable. Finally, it is proved that we can reduce undecidability of type checking and type inference problems in the Currystyle lambda calculus in negation, conjunction, and existential fragment to undecidability of those problems in another variant of the domainfree polymorphic lambda calculus.
EXISTENTIAL TYPE SYSTEMS BETWEEN CHURCH AND CURRY STYLE
"... Abstract. We study type checking, typability, and type inference problems for typefree style and Curry style secondorder existential systems where the typefree style differs from the Curry style in that the terms of the former contain information on where the existential quantifier elimination an ..."
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Abstract. We study type checking, typability, and type inference problems for typefree style and Curry style secondorder existential systems where the typefree style differs from the Curry style in that the terms of the former contain information on where the existential quantifier elimination and introduction take place but omit the information on which types are involved. We show that all the problems are undecidable employing reduction of secondorder unification in case of the typefree system and semiunification in case of the Curry style system. This provides a fine border between problems yielding to a reduction of secondorder unification problem and the semiunification problem. In addition, we investigate the subject reduction property of the system in the Currystyle. 5 10
Relational Parametricity for Computational Effects
"... According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricit ..."
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According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Many programs, however, exhibit computational effects. In this paper, we develop a framework for extending the notion of relational parametricity to languages with effects. 1.
Type Checking and Typability in DomainFree Lambda Calculi
"... This paper shows (1) the undecidability of the type checking and the typability problems in the domainfree lambda calculus with negation, product, and existential types, (2) the undecidability of the typability problem in the domainfree polymorphic lambda calculus, and (3) the undecidability of th ..."
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This paper shows (1) the undecidability of the type checking and the typability problems in the domainfree lambda calculus with negation, product, and existential types, (2) the undecidability of the typability problem in the domainfree polymorphic lambda calculus, and (3) the undecidability of the type checking and the typability problems in the domainfree lambda calculus with function and existential types. The first and the third results are proved by the second result and CPS translations that reduce those problems in the domainfree polymorphic lambda calculus to those in the the domainfree lambda calculi with existential types. The key idea is the conservativity of the domainfree lambda calculi with existential types over the images of the translations.