General recursive function

Summary

The general recursive functions, also called $\mu$-recursive functions, are the functions on the natural numbers obtained from the primitive recursive functions by adding unbounded search. The search operator $\mu$ returns the least number at which a given function takes the value $0$, and may run forever. So the class contains partial functions, and the total ones among them are exactly the total computable functions. This class was one of the first precise definitions of computability, and it agrees with computability by Turing machines.