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 recursive function definition. In this talk, I will motivate the use of recursive coalgebras as a paradigm of structured recursion in programming semantics, list some basic facts about recursive coalgebras and give new conditions for the recursiveness of a coalgebra based on comonads, comonad-coalgebras and distributive laws of functors over comonads.
Time permitting, I will also touch upon related concepts such as Taylor's wellfounded coalgebras and Adámek, Lücke and Milius's coalgebras with a map to the initial algebra.
Joint work with Venanzio Capretta, University of Ottawa, Varmo Vene, University of Tartu. |