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.
Cite
@article{arxiv.1203.0670,
title = {Preservation of Strong Normalisation modulo permutations for the structural lambda-calculus},
author = {Beniamino Accattoli and Delia Kesner},
journal= {arXiv preprint arXiv:1203.0670},
year = {2015}
}