Abstract
αProlog is a logic programming language which is well-suited for rapid prototyping of type systems and operational semantics of typed λ-calculi and many other languages involving bound names. In αProlog, the nominal unification algorithm of Urban, Pitts and Gabbay is used instead of first-order unification. However, although αProlog can be viewed as Horn-clause logic programming in Pitts’ nominal logic, proof search using nominal unification is incomplete in nominal logic. Because of nominal logic’s equivariance principle, complete proof search would require solving NP-hard equivariant unification problems. Nevertheless, the αProlog programs we studied run correctly without equivariant unification. In this paper, we give several examples of αProlog programs that do not require equivariant unification, develop a test for identifying such programs, and prove the correctness of this test via a proof-theoretic argument.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.: Nominal Logic Programming. PhD thesis, Cornell University, Ithaca, NY (2004)
Cheney, J., Urban, C.: aProlog: A logic programming language with names, binding and a-equivalence. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 269–283. Springer, Heidelberg (2004)
Dyckhoff, R., Pinto, L.: Proof Search in Constructive Logic. In: Cooper, S.B., Truss, J.K. (eds.) Proc. of the Logic Colloquium 1997. London Mathematical Society Lecture Note Series, vol. 258, pp. 53–65. Cambridge University Press, Cambridge (1997)
Gabbay, M.J., Cheney, J.: A proof theory for nominal logic. In: Proc. of Annual IEEE Symposium on Logic in Computer Science, pp. 139–148 (2004)
Nadathur, G., Miller, D.: Higher-order logic programming. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logics for Artificial Intelligence and Logic Programming, vol. 5, pp. 499–590. Clarendon Press, Oxford (1998)
Pitts, A.M.: Nominal logic, a first order theory of names and binding. Information and Computation 186, 165–193 (2003)
Urban, C., Pitts, A.M., Gabbay, M.J.: Nominal unification. Theoretical Computer Science 323(1-2), 473–497 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Urban, C., Cheney, J. (2005). Avoiding Equivariance in Alpha-Prolog. In: Urzyczyn, P. (eds) Typed Lambda Calculi and Applications. TLCA 2005. Lecture Notes in Computer Science, vol 3461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11417170_29
Download citation
DOI: https://doi.org/10.1007/11417170_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25593-2
Online ISBN: 978-3-540-32014-2
eBook Packages: Computer ScienceComputer Science (R0)