Abstract
Higher-order patterns, together with higher-order matching, enable concise specification of program transformation, and have been implemented in several program transformation systems. However,higher-order matching in general is nondeterministic, and the matching algorithm is so expensive that even second-order matching is NP-complete. It is orthodox to impose constraint on the form of patterns to obtain the desirable matches satisfying certain properties such as decidability and finiteness. In the context of unification, Miller’s higher-order patterns have a single most general unifier. We relax the restrictions in his patterns without changing determinism within the context of matching instead of unification. As a consequence, the new class of patterns covers a wide class of useful patterns for program transformation. The time-complexity of the matching algorithm is linear for the size of a term for a fixed pattern.
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
Huet, G.P., Lang, B.: Proving and applying program transformations expressed with second-order patterns. Acta Informatica 11, 31–55 (1978)
de Moor, O., Sittampalam, G.: Higher-order matching for program transformation. Theoretical Computer Science 269, 135–162 (2001)
Krieg-Brückner, B., Liu, J., Shi, H., Wolff, B.: Towards correct, efficient and reusable transformational developments. In: Broy, M., Jähnichen, S. (eds.) KORSO 1995. LNCS, vol. 1009, pp. 270–284. Springer, Heidelberg (1995)
Gill, A., Launchbury, J., Jones, S.L.P.: A short cut to deforestation. In: Proceedings of the 6th International Conference on Functional Programming Languages and Computer Architecture (FPCA 1993), Copenhagen, Denmark, pp. 223–232. ACM Press, New York (1993)
Sheard, T., Launchbury, J.: Warm fusion: Deriving build-catas from recursive definitions. In: Conference on Functional Programming Languages and Computer Architecture, La Jolla, CA, USA, ACM, pp. 314–323. ACM, New York (1995)
Bird, R.: Introduction to Functional Programming using Haskell, 2nd edn. Prentice-Hall, Englewood Cliffs (1998)
Baxter, L.: The complexity of unification. PhD thesis, Department of Computer Science, University of Waterloo (1977)
Schubert, A.: Linear interpolation for the higher-order matching problem. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214, pp. 441–452. Springer, Heidelberg (1997)
Miller, D.: A logic programming language with lambda-abstraction, function variables, and simple unification. Journal of Logic and Computation 1, 497–536 (1991)
Nipkow, T.: Functional unification of higher-order patterns. In: 8th IEEE Symposium on Logic in Computer Science, pp. 64–74. IEEE Computer Society Press, Los Alamitos (1993)
Meijer, E., Fokkinga, M., Paterson, R.: Functional programming with bananas, lenses, envelopes and barbed wire. In: Hughes, J. (ed.) FPCA 1991. LNCS, vol. 523, pp. 124–144. Springer, Heidelberg (1991)
Sheard, T., Fegaras, L.: A fold for all seasons. In: Conference on Functional Programming Languages and Computer Architecture, pp. 233–242 (1993)
Heckmann, R.: A functional language for the specification of complex tree transformation. In: Ganzinger, H. (ed.) ESOP 1988. LNCS, vol. 300, pp. 175–190. Springer, Heidelberg (1988)
Sheard, T., Peyton Jones, S.L.: Template metaprogramming for Haskell. In: Haskell Workshop, Pittsburgh, Pennsylvania, pp. 1–16 (2002)
Hu, Z., Iwasaki, H., Takeichi, M., Takano, A.: Tupling calculation eliminates multiple data traversals. In: Proceedings of the 2nd ACM SIGPLAN International Conference on Functional Programming (ICFP 1997), Amsterdam, The Netherlands, pp. 164–175. ACM Press, New York (1997)
Curien, R., Qian, Z., Shi, H.: Efficient second-order matching. In: Ganzinger, H. (ed.) RTA 1996. LNCS, vol. 1103, pp. 317–331. Springer, Heidelberg (1996)
Wierzbicki, T.: Complexity of the higher order matching. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 82–96. Springer, Heidelberg (1999)
Hirata, K., Yamada, K., Harao, M.: Tractable and intractable second-order matching problems. In: Asano, T., Imai, H., Lee, D.T., Nakano, S.-i., Tokuyama, T. (eds.) COCOON 1999. LNCS, vol. 1627, pp. 432–441. Springer, Heidelberg (1999)
Schmidt-Schauß, M., Stuber, J.: On the complexity of linear and stratified context matching problems. Rapport de Recherche RR-4923, Institut National de Recherche en Informatique et en Automatique (2003)
Guttmann, W., Partsch, H., Schulte, W., Vullinghs, T.: Tool support for the interactive derivation of formally correct functional programs. Journal of Universal Computer Science 9, 173–188 (2003)
Peyton Jones, S.L., Tolmach, A., Hoare, T.: Playing by the rules: rewriting as a practical optimisation technique in ghc. In: Haskell Workshop (2001)
Visser, E.: Stratego: A language for program transformation based on rewriting strategies. system description of stratego 0.5. In Middeldorp. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 357–362. Springer, Heidelberg (2001)
Bauer, F., Ehler, H., Horsch, B., Möller, B., Partsch, H., Paukner, O., Pepper, P. (eds.): The Munich Project CIP. LNCS, vol. 292. Springer, Heidelberg (1988)
Taha, W., Sheard, T.: Multi-stage programming with explicit annotations. In: Proc. Conference on Partial Evaluation and Program Manipulation, Amsterdam, Amsterdam, pp. 203–217. ACM Press, New York (1997)
Tullsen, M., Hudak, P.: An intermediate meta-language for program transformation. Research report yaleu/dcs/rr-1154, Department of Computer Science, Yale University (1998)
de Moor, O., Sittampalam, G.: Generic program transformation. In: Swierstra, S.D., Oliveira, J.N. (eds.) AFP 1998. LNCS, vol. 1608, pp. 116–149. Springer, Heidelberg (1999)
Sittampalam, G.: Higher-order matching for program transformation. PhD thesis, University of Oxford (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yokoyama, T., Hu, Z., Takeichi, M. (2004). Deterministic Higher-Order Patterns for Program Transformation. In: Bruynooghe, M. (eds) Logic Based Program Synthesis and Transformation. LOPSTR 2003. Lecture Notes in Computer Science, vol 3018. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25938-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-25938-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22174-6
Online ISBN: 978-3-540-25938-1
eBook Packages: Springer Book Archive