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Local States in String Diagrams

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Rewriting and Typed Lambda Calculi (RTA 2014, TLCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8560))

Abstract

We establish that the local state monad introduced by Plotkin and Power is a monad with graded arities in the category [Inj,Set]. From this, we deduce that the local state monad is associated to a graded Lawvere theory which is presented by generators and relations, depicted in the graphical language of string diagrams.

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References

  1. Beck, J.: Distributive laws. Lecture Notes in Mathematics, vol. 80, pp. 119–140 (1969)

    Google Scholar 

  2. Clouston, R.A., Pitts, A.M.: Nominal equational logic. In: Computation, Meaning, and Logic. Elsevier (2007)

    Google Scholar 

  3. Fiore, M.P., Hur, C.-K.: Term equational systems and logics. In: Proc. MFPS 2008, pp. 171–192 (2008)

    Google Scholar 

  4. Gabbay, M.J., Mathijssen, A.: Nominal (universal) algebra: Equational logic with names and binding. J. Log. Comput. 19 (2009)

    Google Scholar 

  5. Hyland, J.M.E., Plotkin, G., Power, A.J.: Combining effects: sum and tensor. Theoretical Computer Science 357(1), 70–99 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hyland, J.M.E., Levy, P.B., Plotkin, G., Power, A.J.: Combining algebraic effects with continuations. Theoretical Computer Science 375 (2007)

    Google Scholar 

  7. Hyland, J.M.E., Power, A.J.: Discrete lawvere theories and computational effects. Theoretical Computer Science 366, 144–162 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kurz, A., Petrisan, D.: Presenting functors on many-sorted varieties and applications. Inform. Comput. 208, 1421–1446 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  9. Mellies, P.-A.: Segal condition meets computational monads. In: Proc. of LICS 2010 (2010)

    Google Scholar 

  10. Moggi, E.: Notions of computation and monads. Information and Computation 93(1) (1991)

    Google Scholar 

  11. O’Hearn, P.W., Tennent, R.D.: Algol-like Languages. Progress in Theoretical Computer Science. Birkhauser, Boston (1997)

    Book  Google Scholar 

  12. Plotkin, G., Power, J.: Notions of computation determine monads. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, p. 342. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Power, J.: Enriched lawvere theories. Theory and Applications of Categories 6(7), 83–93 (1999)

    MATH  MathSciNet  Google Scholar 

  14. Power, J.: Semantics for Local Computational Effects. In: Proc. MFPS 2006. ENTCS, vol. 158, pp. 355–371 (2006)

    Google Scholar 

  15. Power, J.: Indexed Lawvere theories for local state. Models, Logics and Higher-Dimensional Categories: A Tribute to the Work of Mihály Makkai, pp. 213–229. American Mathematical Society

    Google Scholar 

  16. Pretnar, M.: The Logic and Handling of Algebraic Effects. PhD thesis, University of Edinburgh (2010)

    Google Scholar 

  17. Staton, S.: Two cotensors in one: Presentations of algebraic theories for local state and fresh names. In: Proc. of MFPS XXV (2009)

    Google Scholar 

  18. Staton, S.: Completeness for algebraic theories of local state. In: Ong, L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 48–63. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Staton, S.: Instances of computational effects. In: Proceedings of Twenty-Eighth Annual ACM/IEEE Symposium on Logic in Computer Science (2013)

    Google Scholar 

  20. Weber, M.: Familial 2-functors and parametric right adjoints. Theory and Applications of Categories 18, 665–732 (2007)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Laboratoire Preuves, Programmes, Systèmes CNRS, Université Paris Diderot, Paris, France

    Paul-André Melliès

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  1. Paul-André Melliès
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Editors and Affiliations

  1. Inria, 23 avenue d’Italie, CS 81321, 75214, Paris Cedex 13, France

    Gilles Dowek

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© 2014 Springer International Publishing Switzerland

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Melliès, PA. (2014). Local States in String Diagrams. In: Dowek, G. (eds) Rewriting and Typed Lambda Calculi. RTA TLCA 2014 2014. Lecture Notes in Computer Science, vol 8560. Springer, Cham. https://doi.org/10.1007/978-3-319-08918-8_23

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  • DOI: https://doi.org/10.1007/978-3-319-08918-8_23

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08917-1

  • Online ISBN: 978-3-319-08918-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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