Type-2 Computability and Moore's Recursive Functions

Regarding effectivity of functions on the reals, there have been several proposed models of analog, continuous-time computation, as opposed to the digital, discrete nature of the type-2 computability. We study one of them, Moore's real (primitive) recursive functions, whose definition mimics the classical characterization of recursive functions on N by the closure properties. We show that the class of type-2 computable real functions falls between Moore's classes of primitive recursive and recursive functions.