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Type Checking and Inference Are Equivalent in Lambda Calculi with Existential Types

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Functional and Constraint Logic Programming (WFLP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5979))

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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.

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Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Yuki Kato & Koji Nakazawa

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  1. Yuki Kato
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  2. Koji Nakazawa
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Editors and Affiliations

  1. Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Camino de vera, s/n, 46022, Valencia, Spain

    Santiago Escobar

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Kato, Y., Nakazawa, K. (2010). Type Checking and Inference Are Equivalent in Lambda Calculi with Existential Types. In: Escobar, S. (eds) Functional and Constraint Logic Programming. WFLP 2009. Lecture Notes in Computer Science, vol 5979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11999-6_7

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  • DOI: https://doi.org/10.1007/978-3-642-11999-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11998-9

  • Online ISBN: 978-3-642-11999-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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