The structural lambda-calculus

Beniamino Accattoli (1) , Delia Kesner (1)

1 PPS - Preuves, Programmes et Systèmes

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.

Domaines: Langage de programmation [cs.PL]

Beniamino Accattoli, Delia Kesner. The structural lambda-calculus. 2010. ⟨hal-00528228⟩