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αProlog: A Logic Programming Language with Names, Binding and α-Equivalence

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Logic Programming (ICLP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3132))

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Abstract

There are two well-known approaches to programming with names, binding, and equivalence up to consistent renaming: representing names and bindings as concrete identifiers in a first-order language (such as Prolog), or encoding names and bindings as variables and abstractions in a higher-order language (such as λProlog). However, both approaches have drawbacks: the former often involves stateful name-generation and requires manual definitions for α-equivalence and capture-avoiding substitution, and the latter is semantically very complicated, so reasoning about programs written using either approach can be very difficult. Gabbay and Pitts have developed a new approach to encoding abstract syntax with binding based on primitive operations of name-swapping and freshness. This paper presents αProlog, a logic programming language that uses this approach, along with several illustrative example programs and an operational semantics.

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References

  1. Andreas, A.: A third-order representation of the λμ-calculus. In: MERLIN 2001: Mechanized Reasoning about Languages with Variable Binding. Electronic Notes in Theoretical Computer Science, vol. 58(1), Elsevier, Amsterdam (2001)

    Google Scholar 

  2. 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)

    Chapter  Google Scholar 

  3. de Bruijn, N.G.: Lambda-calculus notation with nameless dummies, a tool for automatic formula manipulation. Indag. Mat. 34(5), 381–392 (1972)

    Google Scholar 

  4. Despeyroux, J., Felty, A., Hirschowitz, A.: Higher-order abstract syntax in Coq. In: Dezani-Ciancaglini, M., Plotkin, G. (eds.) TLCA 1995. LNCS, vol. 902, pp. 124–138. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  5. Fiore, M.P., Plotkin, G.D., Turi, D.: Abstract syntax and variable binding. In: Proc. 14th Symp. on Logic in Computer Science (LICS 1999), pp. 193–202. IEEE, Los Alamitos (1999)

    Google Scholar 

  6. Gabbay, M.J.: The π-calculus in FM. In: Kamareddine, F. (ed.) Thirty-five years of Automath, Kluwer, Dordrecht (2003)

    Google Scholar 

  7. Gabbay, M.J., Cheney, J.: A proof theory for nominal logic. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, LICS 2004 (2004) (to appear)

    Google Scholar 

  8. Gabbay, M.J., Pitts, A.M.: A new approach to abstract syntax with variable binding. Formal Aspects of Computing 13, 341–363 (2002)

    Article  MATH  Google Scholar 

  9. Hamana, M.: A logic programming language based on binding algebras. In: Kobayashi, N., Pierce, B.C. (eds.) TACS 2001. LNCS, vol. 2215, pp. 243–262. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Hofmann, M.: Semantical analysis of higher-order abstract syntax. In: Proc. 14th Symp. on Logic in Computer Science, July 1999, pp. 204–213. IEEE, Los Alamitos (1999)

    Google Scholar 

  11. Jaffar, J., Maher, M.J., Marriott, K., Stuckey, P.J.: The semantics of constraint logic programs. Journal of Logic Programming 37(1-3), 1–46 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Miller, D.: A logic programming language with lambda-abstraction, function variables, and simple unification. J. Logic and Computation 1(4), 497–536 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  13. Miller, D., Nadathur, G., Pfenning, F., Scedrov, A.: Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic 51, 125–157 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  14. Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, I-II. Information and Computation 100(1), 1–77 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  15. Momigliano, A., Ambler, S.J., Crole, R.L.: A comparison of formalizations of the meta-theory of a language with variable bindings in Isabelle. In: Informatics Research Report EDI-INF-RR-0046, Supplemental Proceedings of TPHOLs 2001, pp. 267–282. University of Edinburgh, Edinburgh (2001)

    Google Scholar 

  16. Nadathur, G., Miller, D.: Higher-order logic programming. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 5, ch. 8, pp. 499–590. Oxford University Press, Oxford (1998)

    Google Scholar 

  17. Parigot, M.: Lambda-mu-calculus: An algorithmic interpretation of classical natural deduction. In: Voronkov, A. (ed.) LPAR 1992. LNCS, vol. 624, pp. 190–201. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  18. Pfenning, F., Elliott, C.: Higher-order abstract syntax. In: Proc. ACM SIGPLAN Conf. on Programming Language Design and Implementation (PLDI 1989), pp. 199–208. ACM Press, New York (1989)

    Google Scholar 

  19. Pitts, A.M.: Nominal logic, a first order theory of names and binding. Information and Computation 183, 165–193 (2003)

    Article  MathSciNet  Google Scholar 

  20. Röckl, C.: A first-order syntax for the pi-calculus in isabelle/hol using permutations. In: Ambler, S.J., Crole, R.L., Momigliano, A. (eds.) MERLIN 2001: Mechanized Reasoning about Languages with Variable Binding. Electronic Notes in Theoretical Computer Science, vol. 58(1), Elsevier, Amsterdam (2001)

    Google Scholar 

  21. Schürmann, C., Fontana, R., Liao, Y.: Delphin: Functional programming with deductive systems (2002), Available at http://cs-www.cs.yale.edu/homes/carsten/

  22. 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)

    Chapter  Google Scholar 

  23. Somogyi, Z., Henderson, F., Conway, T.: The execution algorithm of Mercury: an efficient purely declarative logic programming language. J. Logic Programming 29(1-3), 17–64 (1996)

    Article  MATH  Google Scholar 

  24. Staples, J., Robinson, P.J., Paterson, R.A., Hagen, R.A., Craddock, A.J., Wallis, P.C.: Qu-prolog: An extended prolog for meta level programming. In: Abramson, H., Rogers, M.H. (eds.) Meta-Programming in Logic Programming, ch. 23, MIT Press, Cambridge (1996)

    Google Scholar 

  25. Urban, C., Pitts, A.M., Gabbay, M.J.: Nominal unification. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 513–527. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  26. Urban, C., Cheney, J.: Avoiding equivariant unification (submitted)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Cornell University,  

    James Cheney

  2. University of Cambridge,  

    Christian Urban

Authors
  1. James Cheney
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  2. Christian Urban
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Editor information

Editors and Affiliations

  1. Katholieke Universiteit Leuven, Belgium

    Bart Demoen

  2. Department of Computer Sciences, University of Texas at Austin, USA

    Vladimir Lifschitz

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Cheney, J., Urban, C. (2004). αProlog: A Logic Programming Language with Names, Binding and α-Equivalence. In: Demoen, B., Lifschitz, V. (eds) Logic Programming. ICLP 2004. Lecture Notes in Computer Science, vol 3132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27775-0_19

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  • DOI: https://doi.org/10.1007/978-3-540-27775-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22671-0

  • Online ISBN: 978-3-540-27775-0

  • eBook Packages: Springer Book Archive

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