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Non-linear Pattern Matching with Backtracking for Non-free Data Types

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Programming Languages and Systems (APLAS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11275))

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Abstract

Non-free data types are data types whose data have no canonical forms. For example, multisets are non-free data types because the multiset \(\{a,b,b\}\) has two other equivalent but literally different forms \(\{b,a,b\}\) and \(\{b,b,a\}\). Pattern matching is known to provide a handy tool set to treat such data types. Although many studies on pattern matching and implementations for practical programming languages have been proposed so far, we observe that none of these studies satisfy all the criteria of practical pattern matching, which are as follows: (i) efficiency of the backtracking algorithm for non-linear patterns, (ii) extensibility of matching process, and (iii) polymorphism in patterns.

This paper aims to design a new pattern-matching-oriented programming language that satisfies all the above three criteria. The proposed language features clean Scheme-like syntax and efficient and extensible pattern matching semantics. This programming language is especially useful for the processing of complex non-free data types that not only include multisets and sets but also graphs and symbolic mathematical expressions. We discuss the importance of our criteria of practical pattern matching and how our language design naturally arises from the criteria. The proposed language has been already implemented and open-sourced as the Egison programming language.

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Notes

  1. 1.

    In fact, this phenomenon that “pattern matching against a single value yields multiple results” does not occur for free data types. This is the unique characteristic of non-free data types.

  2. 2.

    We will explain the meaning of the value pattern ,(+ p 2) and the cons pattern constructor in Sects. 4.2 and 4.3, respectively.

  3. 3.

    Here, we suppose that the number of decompositions by each pattern constructor can be approximated by the size of the target object.

References

  1. Attributes::attnf - Wolfram Language Documentation. http://reference.wolfram.com/language/ref/message/Attributes/attnf.html. Accessed 14 June 2018

  2. Introduction to Patterns - Wolfram Language Documentation. http://reference.wolfram.com/language/tutorial/Introduction-Patterns.html. Accessed 14 June 2018

  3. Orderless - Wolfram Language Documentation. http://reference.wolfram.com/language/ref/Orderless.html. Accessed 14 June 2018

  4. PAKCS. https://www.informatik.uni-kiel.de/~pakcs/. Accessed 14 June 2018

  5. ViewPatterns - GHC. https://ghc.haskell.org/trac/ghc/wiki/ViewPatterns. Accessed 14 June 2018

  6. The Egison programming language (2011). https://www.egison.org. Accessed 14 June 2018

  7. Egison Mathematics Notebook (2016). https://www.egison.org/math. Accessed 14 June 2018

  8. Antoy, S.: Programming with narrowing: a tutorial. J. Symb. Comput. 45(5), 501–522 (2010)

    Article  MathSciNet  Google Scholar 

  9. Antoy, S.: Constructor-based conditional narrowing. In: Proceedings of the 3rd ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming (2001)

    Google Scholar 

  10. Antoy, S., Hanus, M.: Functional logic programming. Commun. ACM 53(4), 74–85 (2010)

    Article  Google Scholar 

  11. Braßel, B., Hanus, M., Peemöller, B., Reck, F.: KiCS2: a new compiler from Curry to Haskell. In: Kuchen, H. (ed.) WFLP 2011. LNCS, vol. 6816, pp. 1–18. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22531-4_1

    Chapter  Google Scholar 

  12. Egi, S.: Non-linear pattern matching against non-free data types with lexical scoping. arXiv preprint arXiv:1407.0729 (2014)

  13. Egi, S.: Scalar and tensor parameters for importing tensor index notation including Einstein summation notation. In: The Scheme and Functional Programming Workshop (2017)

    Google Scholar 

  14. Egi, S.: Scalar and tensor parameters for importing the notation in differential geometry into programming. arXiv preprint arXiv:1804.03140 (2018)

  15. Erwig, M.: Active patterns. In: Kluge, W. (ed.) IFL 1996. LNCS, vol. 1268, pp. 21–40. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-63237-9_17

    Chapter  Google Scholar 

  16. Erwig, M.: Functional programming with graphs. In: ACM SIGPLAN Notices, vol. 32 (1997)

    Article  Google Scholar 

  17. Fischer, S., Kiselyov, O., Shan, C.: Purely functional lazy non-deterministic programming. In: ACM Sigplan Notices, vol. 44 (2009)

    Article  Google Scholar 

  18. Hanus, M.: Multi-paradigm declarative languages. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 45–75. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74610-2_5

    Chapter  Google Scholar 

  19. Hinze, R., Paterson, R.: Finger trees: a simple general-purpose data structure. J. Funct. Program. 16(2), 197–217 (2006)

    Article  MathSciNet  Google Scholar 

  20. Krebber, M.: Non-linear associative-commutative many-to-one pattern matching with sequence variables. arXiv preprint arXiv:1705.00907 (2017)

  21. McBride, F., Morrison, D., Pengelly, R.: A symbol manipulation system. Mach. Intell. 5, 337–347 (1969)

    Google Scholar 

  22. Okasaki, C.: Views for standard ML. In: SIGPLAN Workshop on ML (1998)

    Google Scholar 

  23. Syme, D., Neverov, G., Margetson, J.: Extensible pattern matching via a lightweight language extension. In: ACM SIGPLAN Notices, vol. 42 (2007)

    Article  Google Scholar 

  24. Thompson, S.: Lawful functions and program verification in Miranda. Sci. Comput. Program. 13(2–3), 181–218 (1990)

    Article  MathSciNet  Google Scholar 

  25. Thompson, S.: Laws in Miranda. In: Proceedings of the 1986 ACM Conference on LISP and Functional Programming (1986)

    Google Scholar 

  26. Tullsen, M.: First class patterns? In: Pontelli, E., Santos Costa, V. (eds.) PADL 2000. LNCS, vol. 1753, pp. 1–15. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-46584-7_1

    Chapter  Google Scholar 

  27. Turner, D.A.: Miranda: a non-strict functional language with polymorphic types. In: Jouannaud, J.-P. (ed.) FPCA 1985. LNCS, vol. 201, pp. 1–16. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-15975-4_26

    Chapter  Google Scholar 

  28. Wadler, P.: Views: a way for pattern matching to cohabit with data abstraction. In: Proceedings of the 14th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages (1987)

    Google Scholar 

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Acknowledgments

We thank Ryo Tanaka, Takahisa Watanabe, Kentaro Honda, Takuya Kuwahara, Mayuko Kori, and Akira Kawata for their important contributions to implement the interpreter. We thank Michal J. Gajda, Yi Dai, Hiromi Hirano, Kimio Kuramitsu, and Pierre Imai for their helpful feedback on the earlier versions of the paper. We thank Masami Hagiya, Yoshihiko Kakutani, Yoichi Hirai, Ibuki Kawamata, Takahiro Kubota, Takasuke Nakamura, Yasunori Harada, Ikuo Takeuchi, Yukihiro Matsumoto, Hidehiko Masuhara, and Yasuhiro Yamada for constructive discussion and their continuing encouragement.

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Authors and Affiliations

  1. Rakuten Institute of Technology, Tokyo, Japan

    Satoshi Egi

  2. University of Tokyo, Tokyo, Japan

    Yuichi Nishiwaki

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  1. Satoshi Egi
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  2. Yuichi Nishiwaki
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Correspondence to Satoshi Egi .

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Editors and Affiliations

  1. Korea Advanced Institute of Science and Technology, Daejeon, Korea (Republic of)

    Sukyoung Ryu

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Egi, S., Nishiwaki, Y. (2018). Non-linear Pattern Matching with Backtracking for Non-free Data Types. In: Ryu, S. (eds) Programming Languages and Systems. APLAS 2018. Lecture Notes in Computer Science(), vol 11275. Springer, Cham. https://doi.org/10.1007/978-3-030-02768-1_1

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  • DOI: https://doi.org/10.1007/978-3-030-02768-1_1

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  • Online ISBN: 978-3-030-02768-1

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