λCalculi with Explicit Substitutions Preserving Strong Normalization
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This paper studies preservation of β-strong normalization by two different confluent λ-calculi with explicit substitutions defined in ; 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 . 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  to that of λ f .
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