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Type reconstruction in Fω is undecidable

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Typed Lambda Calculi and Applications (TLCA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 664))

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Abstract

We investigate the Girard's calculus F ω as a “Curry style” type assignment system for pure lambda terms. We prove that the type-reconstruction problem for F ω is undecidable (even with quantification restricted to constructor variables of rank 1). In addition, we show an example of a strongly normalizable pure lambda term that is untypable in F ω.

This work is partly supported by NSF grant CCR-9113196 and by Polish KBN Grant 2 1192 91 01

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097, Warszawa, Poland

    Paweł Urzyczyn

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  1. Paweł Urzyczyn
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Marc Bezem Jan Friso Groote

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© 1993 Springer-Verlag Berlin Heidelberg

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Urzyczyn, P. (1993). Type reconstruction in Fω is undecidable. In: Bezem, M., Groote, J.F. (eds) Typed Lambda Calculi and Applications. TLCA 1993. Lecture Notes in Computer Science, vol 664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0037122

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  • DOI: https://doi.org/10.1007/BFb0037122

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56517-8

  • Online ISBN: 978-3-540-47586-6

  • eBook Packages: Springer Book Archive

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