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Exact bounds for lengths of reductions in typed λ-calculus

Published online by Cambridge University Press:  12 March 2014

Arnold Beckmann*
Affiliation:
Institut für Mathematische Logik, und Grundlagenforschung, Der Westfälischen Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany, E-mail: Arnold.Beckmann@math.uni-muenster.de

Abstract

We determine the exact bounds for the length of an arbitrary reduction sequence of a term in the typed λ-calculus with β-, ξ- and η-conversion. There will be two essentially different classifications, one depending on the height and the degree of the term and the other depending on the length and the degree of the term.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2001

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References

[1]Barendregt, H. P., The lambda calculus, Studies in Logic, vol. 103, North-Holland, 1984.Google Scholar
[2]Goguen, H., A typed operational semantics for type theory, Ph.D. thesis, University of Edinburgh, 1994.Google Scholar
[3]Loader, R., Notes on simply typed lambda calculus, Technical Report ECS-LFCS-98-381, Edinburgh.Google Scholar
[4]Schwichtenberg, H., Complexity of normalization in the pure typed lambda - calculus, The L. E. J. Brouwer centenary symposium (Troelstra, A. S. and van Dalen, D., editors), North-Holland, 1982, pp. 453457.CrossRefGoogle Scholar
[5]Schwichtenberg, H., An upper bound for reduction sequences in the typed λ-calculus, Archive of Mathematical Logic, vol. 30 (1991), pp. 405408.CrossRefGoogle Scholar
[6]van Raamsdonk, F. and Severi, P., On normalisation, Computer Science Report CS-R9545, Centrum for Wiskunde en Informatica, 1995.Google Scholar
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