## Programming primitive recursive functions and beyond

The most usual approach to calculative (effectively calculable) functions is done by register machines or similar storage-based computers like the Abacus or Turing machines. Another usual approach to computable functions is to **start** with **primitive recursive functions**. However, one has to find a way to put this into a form that does not rely on a pre-knowledge about functions and higher logic. The concrete calcule LAMBDA of decimal pinitive arithmetic allows for such an access. It is based on a machine that is completely different from the storage-based machines: the PINITOR does not use storages but rather many microprocessors, one for each appearance of a command in the code of primitive recursive functior. the codes are decimal numbers, called **pinons**, where only the characters 0 1 2 8 9 appear. There are just four kind of commands: 0 nullification, 1 succession, 2 straight recursion and 8 composition. The PINITOR is a **calculator** which means that there is no halting problem. Computers have halting problems, per defintion calculators do not.

Appendix C6 gives the **programming** of the codes of most of the usual primitive function and goes even farther, e.g. it introduces **generator** technique that allows for the straight-forward calculation of so-called **processive** function, that are not primitive recursive. The most famous examples of the Ackermann-function and other hyperexponential functions are programmed.

**Download: Appendix C6**