Logspace computability and regressive machines

We consider the function class E generated by the constant functions, the projection functions, the predecessor function, the substitution operator, and the recursion on notation operator. Furthermore, we introduce regressive machines, i.e. register machines which have the division by 2 and the predecessor as basic operations. We show that E is the class of functions computable by regressive machines and that the sharply bounded functions of E coincide with the sharply bounded logspace computable functions.