Concurrent processes as wireless proof nets

Emmanuel Beffara (1) , Virgile Mogbil (2)

1 IML - Institut de mathématiques de Luminy
2 LIPN - Laboratoire d'Informatique de Paris-Nord

We present a proofs-as-programs correspondence between linear logic and process calculi that permits non-deterministic behaviours. Processes are translated into wireless proof nets, i.e. proof nets of multiplicative linear logic without cut wires. Typing a term using them consists in typing some of its possible determinisations in standard sequent calculus. Generalized cut-elimination steps in wireless proof nets is shown to correspond to executions that avoid deadlocks.

Mots clés: Pi-calculus; Linear Logic; Proof Nets; Non-deterministic Cut-elimination

Domaines: Logique en informatique [cs.LO]; Calcul parallèle, distribué et partagé [cs.DC]

Emmanuel Beffara, Virgile Mogbil. Concurrent processes as wireless proof nets. 2010. ⟨hal-00462484⟩