Brazilian Symposium on Formal Methods

SBMF 2009: Formal Methods: Foundations and Applications pp 84-100

Corecursive Algebras: A Study of General Structured Corecursion

  • Venanzio Capretta
  • Tarmo Uustalu
  • Varmo Vene
Conference paper

DOI: 10.1007/978-3-642-10452-7_7

Volume 5902 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Venanzio Capretta
    • 1
  • Tarmo Uustalu
    • 2
  • Varmo Vene
    • 3
  1. 1.School of Computer ScienceUniversity of NottinghamUnited Kingdom
  2. 2.Institute of Cybernetics at Tallinn University of TechnologyEstonia
  3. 3.Department of Computer ScienceUniversity of TartuEstonia