Recursive coalgebras from comonads

Authors:
Venanzio Capretta;Tarmo Uustalu;Varmo Vene
Affiliations:
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave., Ottawa, Ont., Canada K1N 6N5;Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, EE-12618 Tallinn, Estonia;Department of Computer Science, University of Tartu, J. Liivi 2, EE-50409 Tartu, Estonia
Venue:
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Year:
2006

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Abstract

The concept of recursive coalgebra of a functor was introduced in the 1970s by Osius in his work on categorical set theory to discuss the relationship between wellfounded induction and recursively specified functions. In this paper, we motivate the use of recursive coalgebras as a paradigm of structured recursion in programming semantics, list some basic facts about recursive coalgebras and, centrally, give new conditions for the recursiveness of a coalgebra based on comonads, comonad-coalgebras and distributive laws of functors over comonads. We also present an alternative construction using countable products instead of cofree comonads.