Abstract

We use the Recursive Path Ordering (RPO) technique of semantic labelling to show the Preservation of Strong Normalization (PSN) property for several calculi of explicit substitution. Preservation of Strong Normalization states that if a term M is strongly normalizing under ordinary fi-reduction (using `global' substitutions), then it is strongly normalizing if the substitution is made explicit (`local'). There are different ways of making global substitution explicit and PSN is a quite natural and desirable property for the explicit substitution calculus. Our method for proving PSN is very general and applies to several known systems of explicit substitutions, both with named variables and with De Bruijn indices: AE of Lescanne et al., s of Kamareddine and R'ios and x of Rose and Bloo. We also look at two small extensions of the explicit substitution calculus that allow to permute substitutions. For one of these extensions PSN fails (using the counterexample in [Melli`es 95]). For the...

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