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Strong Normalisation of Cut-Elimination that Simulates β-Reduction

By Kentaro Kikuchi and Stéphane Lengrand


This paper is concerned with strong normalisation of cutelimination for a standard intuitionistic sequent calculus. The cutelimination procedure is based on a rewrite system for proof-terms with cut-permutation rules allowing the simulation of β-reduction. Strong normalisation of the typed terms is inferred from that of the simply-typed λ-calculus, using the notions of safe and minimal reductions as well as a simulation in Nederpelt-Klop’s λI-calculus. It is also shown that the type-free terms enjoy the preservation of strong normalisation (PSN) property with respect to β-reduction in an isomorphic image of the typefree λ-calculus

Year: 2008
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