Computability on dI-Domains

AbstractIn this paper we investigate a subset of the class of Scott-computable stable functions called Berry-computable. Furthermore we introduce a corresponding notion of an effectively given dI-domain. We obtain the result that the category with these domains as objects and Berry-computable functions as morphisms has all the important attributes of recursive domains and Scott-computable continuous functions, e.g., Cartesian closedness. Moreover, we investigate the relationship between stable functions and sequential algorithms. We show that any Berry-computable function can be computed in a sequential way by a relative algorithm. Additionally, if the codomain of the considered stable function is an atomic dI-domain, we obtain the result that the reverse holds as well