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Existential Type Systems with No Types in Terms

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Typed Lambda Calculi and Applications (TLCA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5608))

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Abstract

We study type checking, typability, and type inference problems for type-free style and Curry style second-order existential systems where the type-free style differs from the Curry style in that the terms of the former contain information on where the existential quantifier elimination and introduction take place but omit the information on which types are involved. We show that all the problems are undecidable employing reduction of second-order unification in case of the type-free system and semiunification in case of the Curry style system. This provides a fine border between problems yielding to a reduction of second-order unification problem and the semiunification problem. In addition, we investigate the subject reduction property of the system in the Curry-style.

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Author information

Authors and Affiliations

  1. Gunma University, Tenjin-cho 1-5-1, Kiryu, 376-8515, Japan

    Ken-etsu Fujita

  2. The University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Aleksy Schubert

Authors
  1. Ken-etsu Fujita
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  2. Aleksy Schubert
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Editor information

Editors and Affiliations

  1. Laboratoire PPS (CNRS / Paris 7), Case 7014, Université Paris Diderot - Paris 7, 75205, Paris Cedex 13, France

    Pierre-Louis Curien

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Fujita, Ke., Schubert, A. (2009). Existential Type Systems with No Types in Terms. In: Curien, PL. (eds) Typed Lambda Calculi and Applications. TLCA 2009. Lecture Notes in Computer Science, vol 5608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02273-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-02273-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02272-2

  • Online ISBN: 978-3-642-02273-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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