λν, a Calculus of Explicit Substitutions which Preserves Strong Normalisation (1995)
| Citations: | 2 - 0 self |
BibTeX
@MISC{Benaissa95λν,a,
author = {Zine-el-abidine Benaissa and Daniel Briaud and Pierre Lescanne and Jocelyne Rouyer-degli and Projet Eureca},
title = {λν, a Calculus of Explicit Substitutions which Preserves Strong Normalisation},
year = {1995}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and Lévy to internalise substitutions into λ-calculus and to propose a mechanism for computing on substitutions. λν is another view of the same concept which aims to explain the process of substitution and to decompose it in small steps. λν is simple and preserves strong normalisation. Apparently that important property cannot stay with another important one, namely confluence on open terms. The spirit of λν is closely related to another calculus of explicit substitutions proposed by de Bruijn and called Cλξφ. In this paper, we introduce λν, we present Cλξφ in the same framework as λν and we compare both calculi. Moreover, we prove properties of λν; namely λν correctly implements β reduction, λν is confluent on closed terms, i.e., on terms of classical λ-calculus and on all terms that are derived from those terms, and finally λν preserves strong normalization of β-reduction.
