Type checking and typability in domain-free lambda calculi

Authors:
Koji Nakazawa;Makoto Tatsuta;Yukiyoshi Kameyama;Hiroshi Nakano
Affiliations:
Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;National Institute of Informatics, Japan;Department of Computer Science, University of Tsukuba, Japan;Department of Applied Mathematics and Informatics, Ryukoku University, Japan
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

This paper shows (1) the undecidability of the type checking and the typability problems in the domain-free lambda calculus with negation, product, and existential types, (2) the undecidability of the typability problem in the domain-free polymorphic lambda calculus, and (3) the undecidability of the type checking and the typability problems in the domain-free 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 domain-free polymorphic lambda calculus to those in the domain-free lambda calculi with existential types. The key idea is the conservativity of the domain-free lambda calculi with existential types over the images of the translations.