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 valid executions of a processes. A type system based on linear logic is used, in which a given process has many 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 interaction scenario. A completeness result is established, stating that every lock-avoiding execution of process in some environment corresponds to a particular typing. Besides traces, types contain precise information about the flow of control between a process and its environment, and proofs are interpreted as composable schedulings of processes. 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 as execution

Domaines: Logique en informatique [cs.LO]

Emmanuel Beffara, Virgile Mogbil. Proofs as Executions. 7th International Conference on Theoretical Computer Science (TCS), Sep 2012, Amsterdam, Netherlands. pp.280-294, ⟨10.1007/978-3-642-33475-7_20⟩. ⟨hal-00586459v2⟩