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Lower and upper bounds for reductions of types in λ and λP (extended abstract)

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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

For several important systems of the λ-cube we study the time-complexity of type conversion. Non-elementary lower bounds are given for the type-conversion problem for λ\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\omega }\)and λP and hence for the systems that include one of these systems. For λ\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\omega }\)and λP a super-exponential upper bound is given to the length of reduction sequences starting from types that are legal in these systems.

The investigations were supported by the Foundation for Computer Science in the Netherlands (SION) with financial support from the Netherlands Organization for Scientific Research (NWO).

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References

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Authors and Affiliations

  1. Department of Philosophy, University of Utrecht, P.O. Box 80126, 3508, TC Utrecht, The Netherlands

    Jan Springintveld

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  1. Jan Springintveld
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Marc Bezem Jan Friso Groote

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© 1993 Springer-Verlag Berlin Heidelberg

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Springintveld, J. (1993). Lower and upper bounds for reductions of types in λ and λP (extended abstract). 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/BFb0037120

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  • DOI: https://doi.org/10.1007/BFb0037120

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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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