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Modularity of strong normalization in the algebraic-λ-cube

Published online by Cambridge University Press:  01 November 1997

FRANCO BARBANERA ,
MARIBEL FERNÁNDEZ  and
HERMAN GEUVERS
FRANCO BARBANERA
Affiliation:
Dipartimento di Informatica, Universitá di Torino, Corso Svizzera 185, 10149 Torino, Italy (e-mail: barba@di.unito.it)
MARIBEL FERNÁNDEZ
Affiliation:
DMI - LIENS (CNRS URA 1327), École Normale Supérieure, 45, rue d'Ulm, 75005 Paris, France (e-mail: maribel@dmi.ens.fr)
HERMAN GEUVERS
Affiliation:
Faculty of Mathematics and Informatics, Catholic University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands (e-mail: herman@cs.kun.nl)
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Abstract

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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.

Type
Research Article
Information
Journal of Functional Programming , Volume 7 , Issue 6 , November 1997 , pp. 613 - 660
Copyright
© 1997 Cambridge University Press
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