Modularity of strong normalization in the algebraic-λ-cube

Authors:
Franco Barbanera;Maribel Fernández;Herman Geuvers
Affiliations:
Dipartimento di Informatica, Universitá di Torino, Corso Svizzera 185, 10149 Torino, Italy (e-mail: barba@di.unito.it);DMI - LIENS (CNRS URA 1327), École Normale Supérieure, 45, rue d'Ulm, 75005 Paris, France (e-mail: maribel@dmi.ens.fr);Faculty of Mathematics and Informatics, Catholic University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands (e-mail: herman@cs.kun.nl)
Venue:
Journal of Functional Programming
Year:
1997

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Abstract

In this paper we present the algebraic-λ-cube, an extension of Barendregt's λ-cube with first- and higher-order algebraic rewriting. We show that strong normalization is a modular property of all the systems in the algebraic-λ-cube, provided that the first-order rewrite rules are non-duplicating and the higher-order rules satisfy the general schema of Jouannaud and Okada. We also prove that local confluence is a modular property of all the systems in the algebraic-λ-cube, provided that the higher-order rules do not introduce critical pairs. This property and the strong normalization result imply the modularity of confluence.