Koji Nakazawa

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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 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)