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VOLUME 8, ISSUE 1, PAPER 28
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Preservation of Strong Normalisation modulo permutations for the structural lambda-calculus
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©Beniamino Accattoli, LIPN (CNRS and Universite Paris-Nord) and INRIA and LIX (Ecole Polytechnique)
©Delia Kesner, PPS, Universite Paris-Diderot and CNRS
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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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Publication date: March 27, 2012
Full Text: PDF | PostScript
DOI: 10.2168/LMCS-8(1:28)2012
Hit Counts: 833 |
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