Proving Strong Normalisation via Non-deterministic Translations into Klop's Extended lambda-Calculus

In this paper we present strong normalisation proofs using a technique of non-deterministic translations into Klop's extended lambda-calculus. We first illustrate the technique by showing strong normalisation of a typed calculus that corresponds to natural deduction with general elimination rules. Then we study its explicit substitution version, the type-free calculus of which does not satisfy PSN with respect to reduction of the original calculus; nevertheless it is shown that typed terms are strongly normalising with respect to reduction of the explicit substitution calculus. In the same framework we prove strong normalisation of Sørensen and Urzyczyn's cut-elimination system in intuitionistic sequent calculus.