The structural lambda-calculus

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 action at a distance with exponential rules decomposing the substitution by means of weakening, contraction and dereliction. Firstly, we prove fundamental properties such as confluence and preservation of beta-strong normalisation. Secondly, we use lambda_j to describe known notions of developments and superdevelopments, and introduce a more general one called XL-development. Then we show how to reformulate Regnier's sigma-equivalence in lambda_j so that it becomes a strong bisimulation. Finally, we prove that explicit composition or de-composition of substitutions can be added to lambda_j while still preserving beta-strong normalisation

Weak orthogonality implies confluence : the higher-order case

In this paper we prove confluence for weakly orthogonal Higher-Order Rewriting Systems. This generalises all the known `confluence by orthogonality' results