Computable Functions on Final Coalgebras

Abstract

This paper tackles computability issues on final coalgebras and tries to shed light on the following two questions: First, which functions on final coalgebras are computable? Second, which formal system allows us to define all computable functions on final coalgebras?In particular, we give a definition of computability on final coalgebras, deriving from the theory of effective domains. We then establish the admissibility of coinductive definitions and of a generalised μ-operator. This gives rise to a formal system, in which every term denotes a computable function.