Proofs as Executions

Abstract : 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.
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Communication dans un congrès
Jos C. M. Baeten; Tom Ball; Frank S. Boer. 7th International Conference on Theoretical Computer Science (TCS), Sep 2012, Amsterdam, Netherlands. Springer, Lecture Notes in Computer Science, LNCS-7604, pp.280-294, 2012, Lecture Notes in Computer Science. 〈10.1007/978-3-642-33475-7_20〉
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Emmanuel Beffara, Virgile Mogbil. Proofs as Executions. Jos C. M. Baeten; Tom Ball; Frank S. Boer. 7th International Conference on Theoretical Computer Science (TCS), Sep 2012, Amsterdam, Netherlands. Springer, Lecture Notes in Computer Science, LNCS-7604, pp.280-294, 2012, Lecture Notes in Computer Science. 〈10.1007/978-3-642-33475-7_20〉. 〈hal-00586459v2〉

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