Chapter

Formal Methods: Foundations and Applications

Volume 5902 of the series Lecture Notes in Computer Science pp 84-100

Corecursive Algebras: A Study of General Structured Corecursion

  • Venanzio CaprettaAffiliated withLancaster UniversitySchool of Computer Science, University of Nottingham
  • , Tarmo UustaluAffiliated withLancaster UniversityInstitute of Cybernetics at Tallinn University of Technology
  • , Varmo VeneAffiliated withCarnegie Mellon UniversityDepartment of Computer Science, University of Tartu

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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.