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A Categorical Model for the Geometry of Interaction

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Automata, Languages and Programming (ICALP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3142))

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Abstract

We consider the multiplicative and exponential fragment of linear logic (MELL) and give a Geometry of Interaction (GoI) semantics for it based on unique decomposition categories. We prove a Soundness and Finiteness Theorem for this interpretation. We show that Girard’s original approach to GoI 1 via operator algebras is exactly captured in this categorical framework.

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References

  1. Abramsky, S.: Retracing Some Paths in Process Algebra. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 1–17. Springer, Heidelberg (1996)

    Google Scholar 

  2. Abramsky, S.: Interaction, Combinators and Complexity. Lecture Notes, Siena, Italy (1997)

    Google Scholar 

  3. Abramsky, S., Haghverdi, E., Scott, P.J.: Geometry of Interaction and Linear Combinatory Algebras. MSCS 12(5), 625–665 (2002)

    MATH  MathSciNet  Google Scholar 

  4. Abramsky, S., Jagadeesan, R.: New Foundations for the Geometry of Interaction. Information and Computation 111(1), 53–119 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Abramsky, S., Lenisa, M.: A Fully-complete PER Model for ML Polymorphic Types. In: Clote, P.G., Schwichtenberg, H. (eds.) CSL 2000. LNCS, vol. 1862, pp. 140–155. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Barr, M.: Algebraically Compact Functors. JPAA 82, 211–231 (1992)

    MATH  MathSciNet  Google Scholar 

  7. Danos, V.: La logique linéaire appliquée à l’étude de divers processus de normalisation et principalement du λ-calcul. PhD thesis, Université Paris VII (1990)

    Google Scholar 

  8. Danos, V., Regnier, L.: Proof-nets and the Hilbert Space. In: Advances in Linear Logic. London Math. Soc. Notes, vol. 222, pp. 307–328. CUP (1995)

    Google Scholar 

  9. Girard, J.-Y.: Geometry of Interaction II: Deadlock-free Algorithms. In: Martin-Löf, P., Mints, G. (eds.) COLOG 1988. LNCS, vol. 417, pp. 76–93. Springer, Heidelberg (1990)

    Google Scholar 

  10. Girard, J.-Y.: Geometry of Interaction I: Interpretation of System F. In: Proc. Logic Colloquium 1988, pp. 221–260. North Holland, Amsterdam (1989a)

    Google Scholar 

  11. Girard, J.-Y.: Geometry of Interaction III: Accommodating the Additives. In: Advances in Linear Logic. LNS, vol. 222, pp. 329–389. CUP (1995)

    Google Scholar 

  12. Haghverdi, E.: A Categorical Approach to Linear Logic, Geometry of Proofs and Full Completeness, PhD Thesis, University of Ottawa, Canada (2000)

    Google Scholar 

  13. Haghverdi, E.: Unique Decomposition Categories, Geometry of Interaction and combinatory logic. Math. Struct. in Comp. Science, vol. 10, pp. 205–231 (2000)

    Google Scholar 

  14. Hasegawa, M.: Recursion from Cyclic Sharing: Traced Monoidal Categories and Models of Cyclic Lambda Calculus. In: de Groote, P., Hindley, J.R. (eds.) TLCA 1997. LNCS, vol. 1210, pp. 196–213. Springer, Heidelberg (1997)

    Google Scholar 

  15. Hildebrandt, T., Panangaden, P., Winskel, G.: A Relational Model of Nondeterministic Dataflow. To appear in Math. Struct. in Comp. Science (2004)

    Google Scholar 

  16. Hines, P.: A categorical framework for finite state machines. Math. Struct Comp. Science, vol. 13, pp. 451–480 (2003)

    Google Scholar 

  17. Joyal, A., Street, R., Verity, D.: Traced Monoidal Categories. Math. Proc. Camb. Phil. Soc., vol. 119, pp. 447–468 (1996)

    Google Scholar 

  18. Manes, E.G., Arbib, M.A.: Algebraic Approaches to Program Semantics. Springer, Heidelberg (1986)

    MATH  Google Scholar 

  19. Selinger, P.: Categorical Structure of Asynchrony. Electronic Notes in Theoretical Computer Science, vol. 20. Elsevier Science B.V., Amsterdam (1999)

    Google Scholar 

  20. Stefanescu, G.: Network Algebra. Springer, Heidelberg (2000)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Informatics & Department of Mathematics, Indiana University, Bloomington, Indiana, USA

    Esfandiar Haghverdi

  2. Department of Mathematics & Statistics, University of Ottawa, Ottawa, Ontario, K1N 6N5, CANADA

    Philip Scott

Authors
  1. Esfandiar Haghverdi
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  2. Philip Scott
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega, 240 Jordi Girona Salgado, 1-3 E-08034, Barcelona

    Josep Díaz

  2. Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. Department of Mathematics, University of Turku, Turku, Finland

    Arto Lepistö

  4. Laboratory for Foundations of Computer Science, University of Edinburgh,  

    Donald Sannella

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Haghverdi, E., Scott, P. (2004). A Categorical Model for the Geometry of Interaction. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_60

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  • DOI: https://doi.org/10.1007/978-3-540-27836-8_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22849-3

  • Online ISBN: 978-3-540-27836-8

  • eBook Packages: Springer Book Archive

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