Proofs as Executions

Emmanuel Beffara (1) , Virgile Mogbil (2)

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

This paper proposes a new interpretation of the logical contents of programs in the context of concurrent interaction, wherein proofs correspond to successful executions of a processes. A type system based on linear logic is used, in which a given process may have several different types, each typing corresponding to a particular way of interacting with its environment, and cut elimination corresponds to executing the process in a given scenario. We prove that, for any process, the set of lock-avoiding executions precisely corresponds to the set of typings of the process. Particularly important is the role played by the axiom rule, which allows typings to make assumptions on the events of the environment. In this interpretation, logic appears as a way of making explicit the flow of causality between interacting processes.

Mots clés: CCS; Process determinisation; Deadlock-free execution; Linear logic; Proof nets; Cut-elimination

Domaines: Logique en informatique [cs.LO]

Emmanuel Beffara, Virgile Mogbil. Proofs as Executions. 2011. ⟨hal-00586459v1⟩