λCalculi with Explicit Substitutions Preserving Strong Normalization

Abstract

This paper studies preservation of β-strong normalization by two different confluent λ-calculi with explicit substitutions defined in [96]; the particularity of these calculi, called λ _d and λ _dn respectively, is that both have a (weak) composition operator for substitutions. We apply an abstract simulation technique to reduce preservation of β-strong normalization of λ _d and λ _dn to that of another calculus, called λ _f having no composition operator. Then, preservation of β-strong normalization of λ _f is shown using the same technique as in [2]. As a consequence, λ _d and λ _dn become the first λ-calculi with explicit substitutions having (weak) composition and preserving β-strong normalization. As an aside, we also show how to apply our technique to reduce preservation of β-strong normalization of the calculus λ _v in [20] to that of λ _f .