  We define a class of computable functions over real numbers using functional
schemes similar to the class of primitive and partial recursive functions
defined by G\"odel and Kleene. We show that this class of functions can also be
characterized by master-slave machines, which are Turing machine like devices.
The proof of the characterization gives a normal form theorem in the style of
Kleene. Furthermore, this characterization is a natural combination of two most
influential theories of computation over real numbers, namely, the type-two
theory of effectivity (TTE) (see, for example, Weihrauch) and the
Blum-Shub-Smale model of computation (BSS). Under this notion of computability,
the recursive (or computable) subsets of real numbers are exactly effective
$\Delta^0_2$ sets.
