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Double Applicative Functors

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Book cover Theoretical Aspects of Computing – ICTAC 2018 (ICTAC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11187))

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Abstract

Writing easily readable parser code is a classic application of monads in functional programming. For simpler cases, the Applicative and Alternative type classes in Haskell can be used for this purpose instead of the more powerful Monad and MonadPlus classes. Counterparts of all parsing expression grammar constructs except lookaheads are expressible via the Applicative and Alternative class methods. Yet their error handling capabilities are unsatisfactory even for simple applications. This paper proposes double applicative functors for increasing the flexibility of error handling without full monadic power, along with an extended set of operations, and studies relationships between mathematical laws that these operations are assumed to fulfill. Many properties of these operations are generalizations of semantic equivalences previously known for parsing expression grammars.

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Notes

  1. 1.

    Not to be confused with the standard notion of idempotent monads defined as those whose multiplication is an isomorphism.

  2. 2.

    For similar reasons, of [1] is not a monad morphism though is (the paper incorrectly claims both to be monad morphisms).

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Acknowledgement

The work was partially supported by the Estonian Research Council under R&D project No. IUT2-1.

The author thanks Tarmo Uustalu for fruitful discussions and also the anonymous reviewers for valuable feedback.

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Authors and Affiliations

  1. University of Tartu, Institute of Computer Science, J. Liivi 2, 50409, Tartu, Estonia

    Härmel Nestra

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  1. Härmel Nestra
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Correspondence to Härmel Nestra .

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Editors and Affiliations

  1. Stellenbosch University, Stellenbosch, South Africa

    Bernd Fischer

  2. Reykjavík University, Reykjavik, Iceland

    Tarmo Uustalu

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Nestra, H. (2018). Double Applicative Functors. In: Fischer, B., Uustalu, T. (eds) Theoretical Aspects of Computing – ICTAC 2018. ICTAC 2018. Lecture Notes in Computer Science(), vol 11187. Springer, Cham. https://doi.org/10.1007/978-3-030-02508-3_18

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  • DOI: https://doi.org/10.1007/978-3-030-02508-3_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-02507-6

  • Online ISBN: 978-3-030-02508-3

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