Computable Function

Any computable function can be incorporated into a Program using while-loops (i.e., ``while something is true, dosomething else''). For-loops (which have a fixed iteration limit) are a special case of while-loops, so computable functionscould also be coded using a combination of for- and while-loops. The Ackermann Function is the simplest example ofa 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 alsoprimitive recursive (Dötzel 1991).

References

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

• Particularly Well-Behaved Functions
• Partisan Game
• Partition
• Partition Function P
• Partition Function Q
• Part Metric
• Party Problem
• Parzen Apodization Function
• Pascal Distribution
• Pascal Line
• Pascal's Formula
• Pascal's Hexagrammum Mysticum
• Pascal's Limaçon
• Pascal's Rule
• Pascal's Theorem
• Pascal's Triangle
• Pascal's Wager
• Pasch's Axiom
• Pasch's Theorem
• Pass Equivalent
• Pass Move
• Patch
• Path
• Path Graph
• Path Integral