A lambda-calculus à la de Bruijn with explicit substitutions
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Department of Computing Science, University of Glasgow
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The aim of this paper is to present the s-calculus which is a very simple -calculus with explicit substitutions and to prove its confluence 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 oe-calculus [ACCL91], and therefore the relation between both calculi will be made explicit. The confluence 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 AE-calculus (cf. [BBLRD95]). The relation between s and AE is also studied.