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Towards nominal computation

Published:25 January 2012Publication History
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Abstract

Nominal sets are a different kind of set theory, with a more relaxed notion of finiteness. They offer an elegant formalism for describing lambda-terms modulo alpha-conversion, or automata on data words. This paper is an attempt at defining computation in nominal sets. We present a rudimentary programming language, called Nlambda. The key idea is that it includes a native type for finite sets in the nominal sense. To illustrate the power of our language, we write short programs that process automata on data words.

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References

  1. P. Aziz Abdulla, J. Deneux, J. Ouaknine, and J. Worrell. Decidability and complexity results for timed automata via channel machines. In ICALP, pages 1089--1101, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. M. Bojanczyk. Data monoids. In STACS, 2011.Google ScholarGoogle Scholar
  3. M. Bojanczyk, B. Klin, and S. Lasota. Languages with group actions. In LICS, 2011.Google ScholarGoogle Scholar
  4. J. A. Brzozowski and E. L. Leiss. On equations for regular languages, finite automata, and sequential networks. Theor. Comput. Sci., 10:19--35, 1980.Google ScholarGoogle ScholarCross RefCross Ref
  5. A. K. Chandra, D. Kozen, and L. J. Stockmeyer. Alternation. J. ACM, 28(1):114--133, 1981. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. S. Demri and R. Lazic. LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log., 10(3), 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. G. L. Ferrari, U. Montanari, and M. Pistore. Minimizing transition systems for name passing calculi: A co-algebraic formulation. In FoSSaCS, volume 2303 of LNCS, pages 129--158, 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. D. Figueira, P. Hofman, and S. Lasota. Relating timed and register automata. In Proc. EXPRESS'10, volume 41 of EPTCS, pages 61--75, 2010.Google ScholarGoogle Scholar
  9. R. Fraïssé. Theory of relations. North-Holland, 1953.Google ScholarGoogle Scholar
  10. N. Francez and M. Kaminski. Finite-memory automata. Theor. Comput. Sci., 134(2):329--363, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. M. Gabbay and A. M. Pitts. A new approach to abstract syntax with variable binding. Formal Asp. Comput., 13(3--5):341--363, 2002.Google ScholarGoogle Scholar
  12. S. Lasota and I. Walukiewicz. Alternating timed automata. In FoSSaCS, pages 250--265, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. S. Lasota and I. Walukiewicz. Alternating timed automata. ACM Trans. Comput. Log., 9(2), 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. U. Montanari and M. Pistore. History-dependent automata: An introduction. In SFM, pages 1--28, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. J. Ouaknine and J. Worrell. On the decidability of metric temporal logic. In LICS, pages 188--197, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. M. Pistore. History Dependent Automata. PhD thesis, University of Pisa, 1999.Google ScholarGoogle Scholar
  17. M. R. Shinwell. The Fresh Approach: functional programming with names and binders. Technical Report UCAM-CL-TR-618, University of Cambridge, Computer Laboratory, February 2005.Google ScholarGoogle Scholar
  18. M. R. Shinwell and A. M. Pitts. Fresh Objective Caml user manual. Technical Report UCAM-CL-TR-621, University of Cambridge Computer Laboratory, February 2005.Google ScholarGoogle Scholar

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      • Published in

        cover image ACM SIGPLAN Notices
        ACM SIGPLAN Notices  Volume 47, Issue 1
        POPL '12
        January 2012
        569 pages
        ISSN:0362-1340
        EISSN:1558-1160
        DOI:10.1145/2103621
        Issue’s Table of Contents
        • cover image ACM Conferences
          POPL '12: Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
          January 2012
          602 pages
          ISBN:9781450310833
          DOI:10.1145/2103656

        Copyright © 2012 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 25 January 2012

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