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Corecursive Algebras: A Study of General Structured Corecursion

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Formal Methods: Foundations and Applications (SBMF 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5902))

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Abstract

Motivated by issues in designing practical total functional programming languages, we are interested in structured recursive equations that uniquely describe a function not because of the properties of the coalgebra marshalling the recursive call arguments but thanks to the algebra assembling their results. Dualizing the known notions of recursive and wellfounded coalgebras, we call an algebra of a functor corecursive, if from any coalgebra of the same functor there is a unique map to this algebra, and antifounded, if it admits a bisimilarity principle. Differently from recursiveness and wellfoundedness, which are equivalent conditions under mild assumptions, corecursiveness and antifoundedness turn out to be generally inequivalent.

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Nottingham, United Kingdom

    Venanzio Capretta

  2. Institute of Cybernetics at Tallinn University of Technology, Estonia

    Tarmo Uustalu

  3. Department of Computer Science, University of Tartu, Estonia

    Varmo Vene

Authors
  1. Venanzio Capretta
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  2. Tarmo Uustalu
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  3. Varmo Vene
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Editor information

Editors and Affiliations

  1. Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Campus Universitário, CEP: 59078-900, Lagoa Nova Natal, RN, Brasil

    Marcel Vinícius Medeiros Oliveira

  2. Department of Computer Science, University of York, Heslington, YO1 7BZ, York, UK

    Jim Woodcock

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© 2009 Springer-Verlag Berlin Heidelberg

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Capretta, V., Uustalu, T., Vene, V. (2009). Corecursive Algebras: A Study of General Structured Corecursion. In: Oliveira, M.V.M., Woodcock, J. (eds) Formal Methods: Foundations and Applications. SBMF 2009. Lecture Notes in Computer Science, vol 5902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10452-7_7

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  • DOI: https://doi.org/10.1007/978-3-642-10452-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10451-0

  • Online ISBN: 978-3-642-10452-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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