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Exact Bounds for lengths of reductions in typed λ-calculus
Journal of Symbolic Logic 66 (3):1277-1285 (2001)
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 termLinks
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Citations of this work
Extracting Herbrand disjunctions by functional interpretation.Philipp Gerhardy & Ulrich Kohlenbach - 2005 - Archive for Mathematical Logic 44 (5):633-644.
Elementary Proof of Strong Normalization for Atomic F.Fernando Ferreira & Gilda Ferreira - 2016 - Bulletin of the Section of Logic 45 (1):1-15.
Herbrand's theorem as higher order recursion.Bahareh Afshari, Stefan Hetzl & Graham E. Leigh - 2020 - Annals of Pure and Applied Logic 171 (6):102792.
Analyzing Godel's T Via Expanded Head Reduction Trees.Arnold Beckmann & Andreas Weiermann - 2000 - Mathematical Logic Quarterly 46 (4):517-536.
A decidable theory of type assignment.William R. Stirton - 2013 - Archive for Mathematical Logic 52 (5-6):631-658.
References found in this work
The Lambda Calculus. Its Syntax and Semantics.E. Engeler - 1984 - Journal of Symbolic Logic 49 (1):301-303.
An upper bound for reduction sequences in the typed λ-calculus.Helmut Schwichtenberg - 1991 - Archive for Mathematical Logic 30 (5-6):405-408.
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