-calculi with Explicit Substitutions and Composition Which Preserve -strong Normalization (extended Abstract)

We study preservation of-strong normalization by d and dn, two connuent-calculi with explicit substitutions deened in 10]; the par-ticularity of these calculi is that both have a composition operator for substitutions. We develop an abstract simulation technique allowing to reduce preservation of-strong normalization of one calculus to that of another one, and apply said technique to reduce preservation of-strong normaliza-tion of d and dn to that of f, another calculus having no composition operator. Then, preservation of-strong normalization of f is shown using the same technique as in 2]. As a consequence, d and dn become the rst-calculi with explicit substitutions having composition and preserving-strong normalization. We also apply our technique to reduce preservation of-strong normalization of the calculus in 14] to that of f.