Preservation of Strong Normalisation modulo permutations for the structural lambda-calculus

Beniamino Accattoli 1, 2 Delia Kesner 3
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7161
Abstract : Inspired by a recent graphical formalism for lambda-calculus based on linear logic technology, we introduce an untyped structural lambda-calculus, called lambda j, which combines actions at a distance with exponential rules decomposing the substitution by means of weakening, contraction and derelicition. First, we prove some fundamental properties of lambda j such as confluence and preservation of beta-strong normalisation. Second, we add a strong bisimulation to lambda j by means of an equational theory which captures in particular Regnier's sigma-equivalence. We then complete this bisimulation with two more equations for (de)composition of substitutions and we prove that the resulting calculus still preserves beta-strong normalization. Finally, we discuss some consequences of our results.
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Article dans une revue
Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2012, Logical Methods in Computer Science, 8 (1), pp.44. 〈10.2168/LMCS-8(1:28)2012〉
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https://hal.inria.fr/hal-00780319
Contributeur : Beniamino Accattoli <>
Soumis le : mercredi 23 janvier 2013 - 16:59:15
Dernière modification le : jeudi 11 janvier 2018 - 06:22:14

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Beniamino Accattoli, Delia Kesner. Preservation of Strong Normalisation modulo permutations for the structural lambda-calculus. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2012, Logical Methods in Computer Science, 8 (1), pp.44. 〈10.2168/LMCS-8(1:28)2012〉. 〈hal-00780319〉

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