Type checking and inference are equivalent in lambda calculi with existential types

Authors:
Yuki Kato;Koji Nakazawa
Affiliations:
Graduate School of Informatics, Kyoto University, Kyoto, Japan;Graduate School of Informatics, Kyoto University, Kyoto, Japan
Venue:
WFLP'09 Proceedings of the 18th international conference on Functional and Constraint Logic Programming
Year:
2009

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Abstract

This paper shows that type-checking and type-inference problems are equivalent in domain-free lambda calculi with existential 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 implication and existence fragment, and the other is a negation, conjunction and existence fragment. This result gives another proof of undecidability of type inference in the domain-free calculi with existence.