Any computable function can be incorporated into a Program using while-loops (i.e., ``while something is true, do something else''). For-loops (which have a fixed iteration limit) are a special case of while-loops, so computable functions could also be coded using a combination of for- and while-loops. The Ackermann Function is the simplest example of a well-defined Total Function which is computable but not Primitive Recursive, providing a counterexample to the belief in the early 1900s that every computable function was also primitive recursive (Dötzel 1991).

**References**

Dötzel, G. ``A Function to End All Functions.'' *Algorithm: Recreational Programming* **2**, 16-17, 1991.

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1999-05-26