Abstract
Nominal logic is a variant of first-order logic with special facilities for reasoning about names and binding based on the underlying concepts of swapping and freshness. It serves as the basis of logic programming and term rewriting techniques that provide similar advantages to, but remain simpler than, higher-order logic programming or term rewriting systems. Previous work on nominal rewriting and logic programming has relied on nominal unification, that is, unification up to equality in nominal logic. However, because of nominal logic’s equivariance property, these applications require a stronger form of unification, which we call equivariant unification. Unfortunately, equivariant unification and matching are NP-hard decision problems. This paper presents an algorithm for equivariant unification that produces a complete set of finitely many solutions, as well as NP decision procedure and a version that enumerates solutions one at a time. In addition, we present a polynomial time algorithm for swapping-free equivariant matching, that is, for matching problems in which the swapping operation does not appear.
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References
Cheney, J., Urban, C.: Alpha-Prolog: A logic programming language with names, binding and alpha-equivalence. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 269–283. Springer, Heidelberg (2004)
Cheney, J.: The complexity of equivariant unification. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 332–344. Springer, Heidelberg (2004)
Cheney, J.R.: Nominal Logic Programming. PhD thesis, Cornell University, Ithaca, NY (August 2004)
Fernández, M., Gabbay, M., Mackie, I.: Nominal rewriting systems. In: Proceedings of the 6th Conference on Principles and Practice of Declarative Programming (PPDP 2004) (to appear)
Frühwirth, T.: Theory and practice of constraint handling rules. Journal of Logic Programming 37(1-3), 95–138 (1998)
Gabbay, M.J., Pitts, A.M.: A new approach to abstract syntax with variable binding. Formal Aspects of Computing 13, 341–363 (2002)
Pitts, A.M.: Nominal logic, a first order theory of names and binding. Information and Computation 183, 165–193 (2003)
Shinwell, M.R., Pitts, A.M., Gabbay, M.J.: FreshML: Programmming with binders made simple. In: Proc. 8th ACM SIGPLAN Int. Conf. on Functional Programming (ICFP 2003), Uppsala, Sweden, pp. 263–274. ACM Press, New York (2003)
Snyder, W.: A Proof Theory for General Unification. Progress in Computer Science and Applied Logic, vol. 11. Birkhäuser, Basel (1991)
Urban, C., Cheney, J.: Avoiding equivariance in alpha-Prolog (2004)
Urban, C., Pitts, A.M., Gabbay, M.J.: Nominal unification. Theoretical Computer Science 323(1-3), 473–497 (2004)
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Cheney, J. (2005). Equivariant Unification. In: Giesl, J. (eds) Term Rewriting and Applications. RTA 2005. Lecture Notes in Computer Science, vol 3467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32033-3_7
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DOI: https://doi.org/10.1007/978-3-540-32033-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25596-3
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