Advertisement

Lightweight Higher-Order Rewriting in Haskell

  • Emil Axelsson
  • Andrea Vezzosi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9547)

Abstract

We present a generic Haskell library for expressing rewrite rules with a safe treatment of variables and binders. Both sides of the rules are written as typed EDSL expressions, which leads to syntactically appealing rules and hides the underlying term representation. Matching is defined as an instance of Miller’s higher-order pattern unification and has the same complexity as first-order matching. The restrictions of pattern unification are captured in the types of the library, and we show by example that the library is capable of expressing useful simplifications that might be used in a compiler.

Notes

Acknowledgements

This research was funded by the Swedish Foundation for Strategic Research (in the RAWFP project). The anonymous referees provided useful input.

References

  1. 1.
    Antoy, S., Hanus, M.: Declarative programming with function patterns. In: Hill, P.M. (ed.) LOPSTR 2005. LNCS, vol. 3901, pp. 6–22. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Axelsson, E., Claessen, K.: Using circular programs for higher-order syntax: functional pearl. In: Proceedings of the 18th ACM SIGPLAN International Conference on Functional Programming, pp. 257–262. ACM, New York (2013)Google Scholar
  3. 3.
    Axelsson, E., Claessen, K., Dévai, G., Horváth, Z., Keijzer, K., Lyckegård, B., Persson, A., Sheeran, M., Svenningsson, J., Vajda, A.: Feldspar: a domain specific language for digital signal processing algorithms. In: 8th IEEE/ACM International Conference on Formal Methods and Models for Codesign, pp. 169–178. IEEE (2010)Google Scholar
  4. 4.
    Bahr, P., Hvitved, T.: Compositional data types. In: Proceedings of the Seventh ACM SIGPLAN Workshop on Generic Programming, pp. 83–94. ACM, New York (2011)Google Scholar
  5. 5.
    Brown, N.C., Sampson, A.T.: Matching and modifying with generics. In: Draft Proceedings of Trends in Functional Programming, pp. 304–318 (2008)Google Scholar
  6. 6.
    Carette, J., Kiselyov, O., Shan, C.C.: Finally tagless, partially evaluated: tagless staged interpreters for simpler typed languages. J. Funct. Programm. 19(5), 509–543 (2009)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Cervesato, I., Pfenning, F.: A linear spine calculus. J. Logic Comput. 13(5), 639–688 (2003)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Dévai, G.: Extended pattern matching for embedded languages. Annales Univ. Sci. Budapestiensis de Rolando Eötvös Nominatae, Sectio Comutatorica 36, 277–297 (2012)MATHGoogle Scholar
  9. 9.
    Felgenhauer, B., Avanzini, M., Sternagel, C.: A Haskell library for term rewriting. CoRR abs/1307.2328 (2013). http://arxiv.org/abs/1307.2328
  10. 10.
    Goldfarb, W.D.: The undecidability of the second-order unification problem. Theoret. Comput. Sci. 13(2), 225–230 (1981)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Huet, G.: Résolution d’équations dans les langages d’ordre 1, 2,.., \(\omega \). Ph.D. thesis, Université Paris VII (1976)Google Scholar
  12. 12.
    Miller, D.: A logic programming language with lambda-abstraction, function variables, and simple unification. J. logic Comput. 1(4), 497–536 (1991)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Mohnen, M.: Context patterns in Haskell. In: Kluge, W. (ed.) IFL’96. LNCS, vol. 1268, pp. 41–57. Springer, Berlin, Heidelberg (1997)CrossRefGoogle Scholar
  14. 14.
    Nadathur, G., Miller, D.: An overview of Lambda-Prolog. Technical report MS-CIS-88-40, University of Pennsylvania, Department of Computer and Information Science (1988)Google Scholar
  15. 15.
    van Noort, T., Yakushev, A.R., Holdermans, S., Jeuring, J., Heeren, B., Magalhães, J.P.: A lightweight approach to datatype-generic rewriting. J. Funct. Programm. 20, 375–413 (2010)CrossRefMATHGoogle Scholar
  16. 16.
    Norell, U.: Towards a practical programming language based on dependent type theory. Ph.D. thesis, Department of Computer Science and Engineering, Chalmers University of Technology, SE-412 96 Göteborg, Sweden, September 2007Google Scholar
  17. 17.
    Oosterhof, N., Hölzenspies, P., Kuper, J.: Application patterns. In: van Eekelen, M. (ed.) Trends in Functional Programming, pp. 370–382. Tartu University Press, Tallinn (2005)Google Scholar
  18. 18.
    Pfenning, F., Schürmann, C.: System description: twelf - a meta-logical framework for deductive systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 202–206. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  19. 19.
    Sculthorpe, N., Frisby, N., Gill, A.: The kansas university rewrite engine. J. Funct. Programm. 24, 434–473 (2014)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Serrano, A., Hage, J.: Feedback upon feedback. Presented at Trends in Functional Programming (2015). ftp://ftp-sop.inria.fr/indes/TFP15/TFP2015_submission_22.pdf
  21. 21.
    Swierstra, W.: Data types à la carte. J. Funct. Programm. 18, 423–436 (2008)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Wierzbicki, T.M.: Complexity of the higher order matching. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 82–96. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  23. 23.
    Yokoyama, T., Hu, Z., Takeichi, M.: Design and implementation of deterministic higher-order patterns (2005). http://takeichi.ipl-lab.org/yicho/YoHT05.pdf

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Chalmers University of TechnologyGothenburgSweden

Personalised recommendations