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λν, a calculus of explicit substitutions which preserves strong normalisation

Identifieur interne : 00BF26 ( Main/Exploration ); précédent : 00BF25; suivant : 00BF27

λν, a calculus of explicit substitutions which preserves strong normalisation

Auteurs : Zine-El-Abidine Benaissa [France] ; Daniel Briaud [France] ; Pierre Lescanne [France] ; Jocelyne Rouyer-Degli [France]

Source :

Journal of Functional Programming [ 0956-7968 ] ; 1996-09.

RBID : ISTEX:4C55CE437CD1FEBA5991D822B39BA53FAA0D522B

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. It favours simplicity and preservation of strong normalisation. This way, another important property is missed, namely confluence on open terms. In spirit, 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 normalisation in the following sense: strongly β normalising terms are strongly λν normalising.

Url:

https://api.istex.fr/ark:/67375/6GQ-Z6MJ7TC5-0/fulltext.pdf

DOI: 10.1017/S0956796800001945

Affiliations:

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Le document en format XML

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<front><div type="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. It favours simplicity and preservation of strong normalisation. This way, another important property is missed, namely confluence on open terms. In spirit, 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 normalisation in the following sense: strongly β normalising terms are strongly λν normalising.</div>
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λν, a calculus of explicit substitutions which preserves strong normalisation

λν, a calculus of explicit substitutions which preserves strong normalisation

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