The Recursion Scheme from the Cofree Recursive Comonad

  • Authors:

  • Tarmo Uustalu;Varmo Vene

  • Affiliations:

  • Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, EE-12618 Tallinn, Estonia;Dept. of Computer Science, University of Tartu, J. Liivi 2, EE-50409 Tartu, Estonia

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2011

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Abstract

We instantiate the general comonad-based construction of recursion schemes for the initial algebra of a functor F to the cofree recursive comonad on F. Differently from the scheme based on the cofree comonad on F in a similar fashion, this scheme allows not only recursive calls on elements structurally smaller than the given argument, but also subsidiary recursions. We develop a Mendler formulation of the scheme via a generalized Yoneda lemma for initial algebras involving strong dinaturality and hint a relation to circular proofs a la Cockett, Santocanale.