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Upper bounds for standardizations and an application

Published online by Cambridge University Press:  12 March 2014

Hongwei Xi
Hongwei Xi*
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pa 15213, USA E-mail: [email protected]
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Abstract

We present a new proof for the standardization theorem in λ-calculus, which is largely built upon a structural induction on λ-terms. We then extract some bounds for the number of β-reduction steps in the standard β-reduction sequence obtained from transforming a given β-reduction sequence, sharpening the standardization theorem. As an application, we establish a super exponential bound for the lengths of β-reduction sequences from any given simply typed λ-terms.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 291 - 303
Copyright
Copyright © Association for Symbolic Logic 1999

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