A -calculus a La De Bruijn with Explicit Substitutions 7th International Conference on Programming Languages: Implementations, Logics and Programs, Plilp95, Lncs 982, Pages 45-62

The aim of this paper is to present the s-calculus which is a very simple-calculus with explicit substitutions and to prove its connuence on closed terms and the preservation of strong normalisation of-terms. We shall prove strong normalisation of the corresponding calculus of substitution by translating it into the-calculus ACCL91], and therefore the relation between both calculi will be made explicit. The connuence of the s-calculus is obtained by the \interpretation method" ((Har89], CHL92]). The proof of the preservation of normalisation follows the lines of an analogous result for the-calculus (cf. BBLRD95]). The relation between s and is also studied.