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Checking algorithms for Pure Type Systems

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Types for Proofs and Programs (TYPES 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 806))

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Abstract

We have presented efficient syntax directed presentations of two subclasses of PTS:

  • the semi-full systems, via the ⊢ sdsf relation

  • the functional systems, via the ⊢f relation

The only remaining defect in these presentations lies in the possible failure of tests for conversion in the application rule. Thus for normalizing functional and semi-full systems, everything has been said.

For non-functional systems the situation is less clear. We know of no a priori bound on the amount of reduction necessary to correctly type λ-abstractions, so we must be content with the collective completeness of the family of syntax directed systems ⊢sd−n.

We have made little impact on the Expansion Postponement problem, which we leave as future work. We can however bask in the relative peace of mind gained from the machine-checked presentation of most (i.e. those not concerning schematic judgments) of the above results.

This work was supported by the ESPRIT Basic Research Actions on Logical Frame-works and Types for Proofs and Programs, and by grants from the British Science and Engineering Research Council.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Nijmegen, Toernooiveld 1, 6525, ED Nijmegen, The Netherlands

    L. S. van Benthem Jutting

  2. Laboratory for Foundations of Computer Science, University of Edinburgh, The King's Buildings, EH9 3JZ, Edinburgh, Scotland

    J. McKinna & R. Pollack

Authors
  1. L. S. van Benthem Jutting
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  2. J. McKinna
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  3. R. Pollack
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Editor information

Henk Barendregt Tobias Nipkow

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© 1994 Springer-Verlag Berlin Heidelberg

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van Benthem Jutting, L.S., McKinna, J., Pollack, R. (1994). Checking algorithms for Pure Type Systems. In: Barendregt, H., Nipkow, T. (eds) Types for Proofs and Programs. TYPES 1993. Lecture Notes in Computer Science, vol 806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58085-9_71

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  • DOI: https://doi.org/10.1007/3-540-58085-9_71

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58085-0

  • Online ISBN: 978-3-540-48440-0

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