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

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11275)


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.



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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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Rakuten Institute of TechnologyTokyoJapan
  2. 2.University of TokyoTokyoJapan

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