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

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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Contributor : Beniamino Accattoli Connect in order to contact the contributor
Submitted on : Wednesday, January 23, 2013 - 4:59:15 PM
Last modification on : Wednesday, January 26, 2022 - 3:41:29 AM

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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, 8 (1), pp.44. ⟨10.2168/LMCS-8(1:28)2012⟩. ⟨hal-00780319⟩



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