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Characterising Strongly Normalising Intuitionistic Sequent Terms

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Types for Proofs and Programs (TYPES 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4941))

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Abstract

This paper gives a characterisation, via intersection types, of the strongly normalising terms of an intuitionistic sequent calculus (where LJ easily embeds). The soundness of the typing system is reduced to that of a well known typing system with intersection types for the ordinary λ-calculus. The completeness of the typing system is obtained from subject expansion at root position. This paper’s sequent term calculus integrates smoothly the λ-terms with generalised application or explicit substitution. Strong normalisability of these terms as sequent terms characterises their typeability in certain “natural” typing systems with intersection types. The latter are in the natural deduction format, like systems previously studied by Matthes and Lengrand et al., except that they do not contain any extra, exceptional rules for typing generalised applications or substitution.

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Authors and Affiliations

  1. Mathematics Department, University of Minho, Portugal

    J. Espírito Santo

  2. Faculty of Engineering, University of Novi Sad, Serbia

    S. Ghilezan & J. Ivetić

Authors
  1. J. Espírito Santo
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  2. S. Ghilezan
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  3. J. Ivetić
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Marino Miculan Ivan Scagnetto Furio Honsell

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Espírito Santo, J., Ghilezan, S., Ivetić, J. (2008). Characterising Strongly Normalising Intuitionistic Sequent Terms. In: Miculan, M., Scagnetto, I., Honsell, F. (eds) Types for Proofs and Programs. TYPES 2007. Lecture Notes in Computer Science, vol 4941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68103-8_6

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  • DOI: https://doi.org/10.1007/978-3-540-68103-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68084-0

  • Online ISBN: 978-3-540-68103-8

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