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Embedding Non-linear Pattern Matching with Backtracking for Non-free Data Types into Haskell

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Abstract

Pattern matching is an important language construct for data abstraction. Many pattern-match extensions have been developed for extending the range of data types to which pattern matching is applicable. Among them, the pattern-match system proposed by Egi and Nishiwaki features practical pattern matching for non-free data types by providing a user-customizable non-linear pattern-match facility with backtracking. However, they implemented their proposal only in dynamically typed programming languages, and there were no proposals that allow programmers to benefit from both static type systems and expressive pattern matching. This paper proposes a method for implementing this pattern-match facility by meta-programming in Haskell. There are two technical challenges: (i) we need to design a set of typing rules for the pattern-match facility; (ii) we need to embed these typing rules in Haskell to make types of the pattern-match expressions inferable by the Haskell type system. We propose a set of typing rules and show that several GHC extensions, such as multi-parameter type classes, datatype promotion, GADTs, existential types, and view patterns, play essential roles for embedding these typing rules into Haskell. The implementation has already been distributed as a Haskell library miniEgison via Hackage.

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Notes

  1. We borrow this notation from [8].

  2. The definitions of the nil and join patterns are omitted.

References

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Acknowledgements

We thank Yuichi Nishiwaki for constructive discussion while implementing the proposed library.

Author information

Author notes

  1. Akira Kawata

    Present address: Preferred Networks, Inc., Tokyo, Japan

  2. Mayuko Kori

    Present address: National Institute of Informatics, Tokyo, Japan

  3. Hiromi Ogawa

    Present address: University of Tsukuba, Tsukuba, Japan

Authors and Affiliations

  1. Rakuten, Inc., Tokyo, Japan

    Satoshi Egi

  2. Kyoto University, Kyoto, Japan

    Akira Kawata

  3. The University of Tokyo, Tokyo, Japan

    Mayuko Kori

  4. Koishikawa Secondary Education School, Tokyo, Japan

    Hiromi Ogawa

Authors
  1. Satoshi Egi
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  2. Akira Kawata
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  3. Mayuko Kori
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  4. Hiromi Ogawa
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Corresponding author

Correspondence to Satoshi Egi.

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Egi, S., Kawata, A., Kori, M. et al. Embedding Non-linear Pattern Matching with Backtracking for Non-free Data Types into Haskell. New Gener. Comput. 40, 481–506 (2022). https://doi.org/10.1007/s00354-022-00177-z

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