Undecidability of Type-Checking in Domain-Free Typed Lambda-Calculi with Existence

Authors:
Koji Nakazawa;Makoto Tatsuta;Yukiyoshi Kameyama;Hiroshi Nakano
Affiliations:
Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501;National Institute of Informatics, Japan;Department of Computer Science, University of Tsukuba, Japan;Department of Applied Mathematics and Informatics, Ryukoku University, Japan
Venue:
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Year:
2008

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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.