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IFIP International Conference on Theoretical Computer Science

TCS 2012: Theoretical Computer Science pp 280–294Cite as

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Proofs as Executions

Proofs as Executions

  • Emmanuel Beffara18 &
  • Virgile Mogbil19 
  • Conference paper
  • 810 Accesses

  • 3 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7604)

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 a 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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Author information

Authors and Affiliations

  1. IML – FRE3529, CNRS – Université d’Aix-Marseille, France

    Emmanuel Beffara

  2. LIPN – UMR7030, CNRS – Université Paris 13, France

    Virgile Mogbil

Authors
  1. Emmanuel Beffara
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  2. Virgile Mogbil
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Editor information

Editors and Affiliations

  1. Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG, Amsterdam, The Netherlands

    Jos C. M. Baeten & Frank S. de Boer & 

  2. Microsoft Research, One Microsoft Way, 98052, Redmond, WA, USA

    Tom Ball

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© 2012 IFIP International Federation for Information Processing

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Cite this paper

Beffara, E., Mogbil, V. (2012). Proofs as Executions. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds) Theoretical Computer Science. TCS 2012. Lecture Notes in Computer Science, vol 7604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33475-7_20

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  • DOI: https://doi.org/10.1007/978-3-642-33475-7_20

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  • Print ISBN: 978-3-642-33474-0

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