3 - Programs and Machines

Abstract

This chapter discusses another way of formalizing the concept of effective calculability, namely register-machine programs. The main aim is to show that all general recursive partial functions are also computable by register machines. It provides half of a significant fact that formalizing the effective calculability concept by means of general recursiveness and formalizing the effective calculability concept by means of register machines lead to exactly the same class of partial functions. The register machines are capable of doing much more than might have been apparent initially from their very simple definition. The methods used here to obtain the equivalence of general recursiveness to register-machine computability are adaptable to obtaining equivalence between other formalizations of effective calculability.