Generalized β-reduction and explicit substitutions

Abstract

Extending the λ-calculus with either explicit substitution or generalised reduction has been the subject of extensive research recently which still has many open problems. Due to this reason, the properties of a calculus combining both generalised reduction and explicit substitutions have never been studied. This paper presents such a calculus λsg and shows that it is a desirable extension of the λ-calculus. In particular, we show that λsg preserves strong normalisation, is sound and it simulates classical β-reduction. Furthermore, we study the simply typed λ-calculus extended with both generalised reduction and explicit substitution and show that well-typed terms are strongly normalising and that other properties such as subtyping and subject reduction hold.KeywordsGeneralise ReductionFunctional ProgrammingOpen TermStrong NormalisationLambda CalculusThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.