A Calculus of Explicit Substitutions Which Preserves Strong Normalisation , 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. is simple and preserves strong normalisation. Apparently that important property cannot stay with another important one, namely connuence on open terms. The spirit of 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 normalization of-reduction. , un calcul de substitutions explicites qui preserve la forte normalisation RRsumm : Les calculs de substitutions explicites ont tt proposss par Abadi, Cardelli, Curien, Hardin et LLvy dans le but d'inclure les substitutions l'inttrieur du-calcul et de proposer un mmcanisme pour les valuer. est une autre approche qui permet d'expliquer le processus de substitution en ddcomposant celle-ci en plusieures petites oprations ll-mentaires. Le calcul est simple et prrserve la forte normalisation de la-reduction. NNanmoins, ce calcul n'est pas connuent sur les termes ouverts. L'esprit du est lii un autre calcul proposs par de Bruijn, appell C. Dans ce rapport, on introduira et C puis on comparera ces deux calculs. De plus, on prouvera plusieures propriitts sur ,