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Simulating expansions without expansions

Published online by Cambridge University Press:  04 March 2009

Roberto Di Cosmo  and
Delia Kesner
Roberto Di Cosmo
Affiliation:
DMI-LIENS (CNRS URA 1347) Ecole Normale Supérieure - 45, Rue d'Ulm 75230 Paris France email: dicosmo@dmi.ens.fr
Delia Kesner
Affiliation:
INRIA Rocquencourt - Domaine de Voluceau, BP 105 - 78153 Le Chesnay Cedex, France and CNRS and LRI - Bât 490, Université de Paris-Sud - 91405 Orsay Cedex, France email: kesner@lri.lri.fr
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Abstract

We add extensional equalities for the functional and product types to the typed λ-calculus with, in addition to products and terminal object, sums and bounded recursion (a version of recursion that does not allow recursive calls of infinite length). We provide a confluent and strongly normalizing (thus decidable) rewriting system for the calculus that stays confluent when allowing unbounded recursion. To do this, we turn the extensional equalities into expansion rules, and not into contractions as is done traditionally. We first prove the calculus to be weakly confluent, which is a more complex and interesting task than for the usual λ-calculus. Then we provide an effective mechanism to simulate expansions without expansion rules, so that the strong normalization of the calculus can be derived from that of the underlying, traditional, non-extensional system. These results give us the confluence of the full calculus, but we also show how to deduce confluence directly form our simulation technique without using the weak confluence property.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 4 , Issue 3 , September 1994 , pp. 315 - 362
Copyright
Copyright © Cambridge University Press 1994

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