 Note finally that if \(f(\vec{x})\) is recursive it may be defined via some finite number of applications of composition, primitive recursion, and unbounded minimization in a manner which preserves the totality of intermediate functions in its definition. Thus although the specification of \(f(\vec{x})\) may involve one or more applications of unbounded search, each search required to compute its value is guaranteed to terminate in a finite number of steps. It thus follows that all of functions in \(\mathbf{REC}\) are computable by an algorithm (despite the fact that we will soon see that this class contains functions which are not primitive recursive). This constitutes part of the evidence for Church’s Thesis—i.e., the claim that \(\mathbf{REC}\) coincides with the class of effectively computable functions—which was surveyed in  Section 1.6.