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.

Source : oai:arXiv.org:1203.0670

DOI : 10.2168/LMCS-8(1:28)2012

Volume: Volume 8, Issue 1

Published on: March 27, 2012

Submitted on: October 4, 2011

Keywords: Computer Science - Logic in Computer Science,F.3.2, D.1.1, F.4.1

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