  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.
