Lambda-Calculi with Explicit Substitutions and Composition Which Preserve Beta-Strong Normalization

We study preservation of β-strong normalization by λ d and λ dn , two confluent λ-calculi with explicit substitutions defined in [10]; the particularity of these calculi is that both have a composition operator for substitutions. We develop an abstract simulation technique allowing to reduce preservation of β-strong normalization of one calculus to that of another one, and apply said technique to reduce preservation of β-strong normalization of λ d and λ dn to that of λ f , another calculus 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 composition and preserving β- strong normalization. We also apply our technique to reduce preservation of β-strong normalization of the calculus λ v in [14] to that of λ f .