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International Conference on Relational and Algebraic Methods in Computer Science

RAMiCS 2018: Relational and Algebraic Methods in Computer Science pp 97–112Cite as

Composition of Different-Type Relations via the Kleisli Category for the Continuation Monad

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11194))

Abstract

We give the way of composing different types of relational notions under certain condition, for example, ordinary binary relations, up-closed multirelations, ordinary (possibly non-up-closed) multirelations, quantale-valued relations, and probabilistic relations. Our key idea is to represent a relational notion as a generalized predicate transformer based on some truth value in some category and to represent it as a Kleisli arrow for some continuation monad. The way of composing those relational notions is given via identity-on-object faithful functors between different Kleisli categories. We give a necessary and sufficient condition to have such identity-on-object faithful functor.

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Acknowledgements

The authors thank Tatsuya Abe, Hitoshi Furusawa, Walter Guttmann, Masahito Hasegawa, Shinya Katsumata, and Georg Struth for valuable comments. The second author would like to thank Ichiro Hasuo and members of his group at the University of Tokyo for their generous support. This work was supported by JSPS KAKENHI Grant Numbers JP24700017, JP16K21557.

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Authors and Affiliations

  1. Department of Information Systems Creation, Faculty of Engineering, Kanagawa University, Yokohama, Japan

    Koki Nishizawa

  2. Center for Education and Innovation, Sojo University, Kumamoto, Japan

    Norihiro Tsumagari

Authors
  1. Koki Nishizawa
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  2. Norihiro Tsumagari
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Correspondence to Koki Nishizawa .

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Editors and Affiliations

  1. Université Laval, Québec, QC, Canada

    Jules Desharnais

  2. University of Canterbury, Christchurch, New Zealand

    Walter Guttmann

  3. Open Universiteit, Heerlen, The Netherlands

    Stef Joosten

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Nishizawa, K., Tsumagari, N. (2018). Composition of Different-Type Relations via the Kleisli Category for the Continuation Monad. In: Desharnais, J., Guttmann, W., Joosten, S. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2018. Lecture Notes in Computer Science(), vol 11194. Springer, Cham. https://doi.org/10.1007/978-3-030-02149-8_7

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  • DOI: https://doi.org/10.1007/978-3-030-02149-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-02148-1

  • Online ISBN: 978-3-030-02149-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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