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Our paper [1] contains a serious error. Proposition 4.6 of [1] is actually false and hence our strong normalization proof does not work for the Curry-style λµ-calculus. However, our method still can show that (1) the correction of Proposition 5.4 of [2], and (2) the correction of the proof of strong normalization of Church-style λµ-calculus by… (More)

This paper shows undecidability of type-checking and type-inference problems in domain-free typed lambda-calculi with existential types: a negation and conjunction fragment, and an implicational fragment. These are proved by reducing type-checking and type-inference problems of the domain-free polymorphic typed lambda-calculus to those of the lambda-calculi… (More)

In this paper, we propose a new proof method for strong normal-ization of calculi with control operators, and, by this method, we prove strong normalization of the system λµ → ∧∨⊥ , which is introduced in [3] by de Groote and corresponds to the classical natural deduction with disjunctions and permutative conversions by the Curry-Howard isomorphism. For our… (More)

This paper proves strong normalization of classical natural deduction with disjunc-tion and permutative conversions, by using CPS-translation and augmentations. By them, this paper also proves strong normalization of classical natural deduction with general elimination rules for implication and conjunction, and their permuta-tive conversions. This paper… (More)

This paper introduces a cut-elimination procedure of the in-tuitionistic sequent calculus and shows that it is isomorphic to the proof reduction of the intuitionistic natural deduction with general elimination and explicit substitution. It also proves strong normalization and Church-Rosser property of the cut-elimination procedure by projecting the sequent… (More)

This paper proves undecidability of type checking and type inference problems in some variants of typed lambda calculi with polymorphic and existen-tial types. First, type inference in the domain-free polymorphic lambda calculus is proved to be unde-cidable, and then it is proved that type inference is undecidable in the negation, conjunction, and existence… (More)

This paper shows that type-checking and type-inference problems are equivalent in domain-free lambda calculi with existen-tial types, that is, type-checking problem is Turing reducible to type-inference problem and vice versa. In this paper, the equivalence is proved for two variants of domain-free lambda calculi with existential types: one is an… (More)

We study monadic translations of the call-by-name (cbn) and the call-by-value (cbv) fragments of the classical sequent calculus λµ˜µ by Curien and Herbelin and give modular and syntactic proofs of strong normalization. The target of the translations is a new metalanguage for classical logic, named monadic λµ. It is a monadic reworking of Parigot's… (More)

This paper shows (1) the undecidability of the type checking and the typability problems in the domain-free lambda calculus with negation, product, and existen-tial types, (2) the undecidability of the typability problem in the domain-free poly-morphic lambda calculus, and (3) the undecidability of the type checking and the typability problems in the… (More)