Type checking and inference for polymorphic and existential types

Authors:
Koji Nakazawa;Makoto Tatsuta
Affiliations:
Kyoto University, Kyoto, Japan;National Institute of Informatics, Japan
Venue:
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Year:
2009

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Abstract

This paper proves undecidability of type checking and type inference problems in some variants of typed lambda calculi with polymorphic and existential types. First, type inference in the domain-free polymorphic lambda calculus is proved to be undecidable, and then it is proved that type inference is undecidable in the negation, conjunction, and existence fragment of the domain-free typed lambda calculus. Secondly, their variants with multiple quantifier rules are introduced, and their type checking and type inference are proved to be undecidable. Finally, it is proved that we can reduce undecidability of type checking and type inference problems in the Curry-style lambda calculus in negation, conjunction, and existential fragment to undecidability of those problems in another variant of the domain-free polymorphic lambda calculus.