Abstract
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 with existential types by continuation passing style translations.
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Nakazawa, K., Tatsuta, M., Kameyama, Y., Nakano, H. (2008). Undecidability of Type-Checking in Domain-Free Typed Lambda-Calculi with Existence. In: Kaminski, M., Martini, S. (eds) Computer Science Logic. CSL 2008. Lecture Notes in Computer Science, vol 5213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87531-4_34
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DOI: https://doi.org/10.1007/978-3-540-87531-4_34
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