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Presenting Distributive Laws

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Algebra and Coalgebra in Computer Science (CALCO 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8089))

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Abstract

Distributive laws of a monad \(\mathcal{T}\) over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If \(\mathcal{T}\) is a free monad, then such distributive laws correspond to simple natural transformations. However, when \(\mathcal{T}\) is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of context-free languages.

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Author information

Authors and Affiliations

  1. LIACS – Leiden University, Netherlands

    Marcello M. Bonsangue & Jurriaan Rot

  2. ICIS/IS – Radboud University Nijmegen, Netherlands

    Helle Hvid Hansen

  3. Formal Methods – Centrum Wiskunde & Informatica, Amsterdam, Netherlands

    Marcello M. Bonsangue, Helle Hvid Hansen & Jurriaan Rot

  4. Dep. of Computer Science, University of Leicester, United Kingdom

    Alexander Kurz

Authors
  1. Marcello M. Bonsangue
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  2. Helle Hvid Hansen
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  3. Alexander Kurz
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  4. Jurriaan Rot
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, LE1 7RH, Leicester, UK

    Reiko Heckel

  2. Lehrstuhl für Theoretische Informatik, Friedrich-Alexander Universität, 91058, Erlangen-Nürnberg, Germany

    Stefan Milius

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Bonsangue, M.M., Hansen, H.H., Kurz, A., Rot, J. (2013). Presenting Distributive Laws. In: Heckel, R., Milius, S. (eds) Algebra and Coalgebra in Computer Science. CALCO 2013. Lecture Notes in Computer Science, vol 8089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40206-7_9

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  • DOI: https://doi.org/10.1007/978-3-642-40206-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40205-0

  • Online ISBN: 978-3-642-40206-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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