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Nominal rewriting with name generation: abstraction vs. locality

Published: 11 July 2005 Publication History

Abstract

Nominal rewriting extends first-order rewriting with Gabbay-Pitts abstractors: bound entities are named, matching respects α-conversion and can be directly implemented thanks to the use of freshness constraints. In this paper we study two extensions to nominal rewriting. First we introduce a NEW quantifier for modelling name generation and restriction. This allows us to model higher-order functions involving local state, and has also applications in concurrency theory. The second extension introduces new constraints in freshness contexts. This allows us to express strategies of reduction and has applications in programming language design and implementation. Finally, we study confluence properties of nominal rewriting and its extensions.

References

[1]
F. Baader and T. Nipkow, Term rewriting and all that, Cambridge University Press, 1998.]]
[2]
H. P. Barendregt, The Lambda Calculus: its Syntax and Semantics (revised ed.), Studies in Logic and the Foundations of Mathematics, Vol. 103, North-Holland, 1984.]]
[3]
H. Cirstea and C. Kirchner, The Rewriting Calculus - Part I, Logic Journal of the Interest Group in Pure and Applied Logics 9 (2001), 363--399.]]
[4]
H. Cirstea and C. Kirchner, The Rewriting Calculus - Part II, Logic Journal of the Interest Group in Pure and Applied Logics 9 (2001), 401--434.]]
[5]
N. Dershowitz and J.-P. Jouannaud, Rewrite Systems, Handbook of Theoretical Computer Science: Formal Methods and Semantics, vol. B, 1989.]]
[6]
M. Fernández, M. J. Gabbay and I. Mackie,Nominal Rewriting Systems, ACM Symposium on Principles and Practice of Declarative Programming (PPDP'04), ACM Press, 2004.]]
[7]
M. Fernández and J-P. Jouannaud. Modular Termination of Term Rewriting Systems Revisited. ADT'94, LNCS 906, Springer-Verlag, 1994.]]
[8]
M. Fernández, I. Mackie and F-R. Sinot, Closed Reduction: Explicit Substitutions without alpha-conversion, Mathematical Structures in Computer Science 15:2, 2005.]]
[9]
M. J. Gabbay and J. Cheney, A Sequent Calculus for Nominal Logic, Proc. 19th IEEE Symposium on Logic in Computer Science (LICS'04), pages 139--148, 2004.]]
[10]
M. J. Gabbay and A. M. Pitts, A New Approach to Abstract Syntax with Variable Binding. Formal Aspects of Computing, vol. 13, pp. 341--363, 2002.]]
[11]
Z. Khasidashvili, Expression reduction systems, Proceedings of I.Vekua Institute of Applied Mathematics (Tbisili), vol. 36, 1990, pp. 200--220.]]
[12]
J.-W. Klop, Term Rewriting Systems, Handbook of Logic in Computer Science, Oxford University Press, 1992.]]
[13]
J.-W. Klop, V. van Oostrom, and F. van Raamsdonk, Combinatory reduction systems, introduction and survey, Theoretical Computer Science 121 (1993), 279--308.]]
[14]
J-W. Klop, Combinatory reduction systems, Mathematical Centre Tracts, vol. 127, Amsterdam, 1980.]]
[15]
R. Mayr and T. Nipkow, Higher-order rewrite systems and their confluence, TCS 192 (1998), 3--29.]]
[16]
D. Miller and A. Tiu, A proof theory for generic judgments: An extended abstract, LICS 2003, 118--127.]]
[17]
Milner, Parrow, and Walker, A Calculus of Mobile Processes, II, Inf. and Comp. 100:1 1992, 41--77.]]
[18]
A. Momigliano and F. Pfenning, Higher-order Pattern Complement and the Strict λ-calculus, ACM Trans. Comput. Logic 4:4, 493--529, ACM Press, 2003.]]
[19]
M.H.A. Newman, On theories with a combinatorial definition of equivalence, Annals of Mathematics 43 (1942), no. 2, 223--243.]]
[20]
A. M. Pitts, Nominal logic, a first order theory of names and binding, Information and Computation 186 (2003), 165--193.]]
[21]
A. M. Pitts and I. D. B. Stark, Observable Properties of Higher Order Functions That Dynamically Create Local Names, or: What's new?. LNCS 711, 1993.]]
[22]
A. M. Pitts and M. J. Gabbay, A metalanguage for programming with bound names modulo renaming, MPC2000, LNCS 1837, 2000.]]
[23]
C. Urban, A. M. Pitts, and M. J. Gabbay, Nominal unification, CSL'03 & KGC. LNCS 2803, 2003.]]

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  1. Nominal rewriting with name generation: abstraction vs. locality

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      cover image ACM Conferences
      PPDP '05: Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming
      July 2005
      260 pages
      ISBN:1595930906
      DOI:10.1145/1069774
      • General Chair:
      • Pedro Barahona,
      • Program Chair:
      • Amy Felty
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      Published: 11 July 2005

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      Author Tags

      1. α-conversion
      2. binders
      3. confluence
      4. first and higher-order rewriting
      5. locality
      6. name generation

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      • (2015)Completeness and Incompleteness in Nominal Kleene AlgebraRelational and Algebraic Methods in Computer Science10.1007/978-3-319-24704-5_4(51-66)Online publication date: 8-Nov-2015
      • (2012)Nominal Unification from a Higher-Order PerspectiveACM Transactions on Computational Logic10.1145/2159531.215953213:2(1-31)Online publication date: 1-Apr-2012
      • (2012)A Higher-Order Distributed Calculus with Name CreationProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.63(531-540)Online publication date: 25-Jun-2012
      • (2011)Stone duality for nominal Boolean algebras with ИProceedings of the 4th international conference on Algebra and coalgebra in computer science10.5555/2040096.2040112(192-207)Online publication date: 30-Aug-2011
      • (2011)Freshness and name-restriction in sets of traces with namesProceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software10.5555/1987171.1987202(365-380)Online publication date: 26-Mar-2011
      • (2008)Nominal Unification from a Higher-Order PerspectiveProceedings of the 19th international conference on Rewriting Techniques and Applications10.1007/978-3-540-70590-1_17(246-260)Online publication date: 15-Jul-2008
      • (2007)Mechanized metatheory model-checkingProceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming10.1145/1273920.1273931(75-86)Online publication date: 14-Jul-2007
      • (2007)Language Primitives and Type Discipline for Structured Communication-Based Programming RevisitedElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2007.02.056171:4(73-93)Online publication date: 1-Jul-2007
      • (2006)Curry-style types for nominal termsProceedings of the 2006 international conference on Types for proofs and programs10.5555/1789277.1789286(125-139)Online publication date: 18-Apr-2006
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