A Calculus of Explicit Substitutions Which Preserves Strong Normalisation

Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and LLvy to internalise substitutions into-calculus and to propose a mechanism for computing on substitutions. is another view of the same concept which aims to explain the process of substitution and to decompose it in small steps. It favours simplicity and preservation of strong normalisation. This way, another important property is missed, namely connuence on open terms. In spirit, is closely related to another calculus of explicit substitutions proposed by de Bruijn and called C. In this paper, we introduce , we present C in the same framework as and we compare both calculi. Moreover, we prove properties of ; namely correctly implements reduction, is connuent on closed terms, i.e., on terms of classical-calculus and on all terms that are derived from those terms, and nally preserves strong normalisation in the following sense: strongly normalising terms are strongly normalising.