Table of Contents - 20.43.22.14. Primitive recursive functions

According to Wikipedia ("Primitive recursive function", 19-May-2024,
https://en.wikipedia.org/wiki/Primitive_recursive_function): "In
computability theory, a primitive recursive function is, roughly speaking, a
function that can be computed by a computer program whose loops are all "for"
loops (that is, an upper bound of the number of iterations of every loop is
fixed before entering the loop). Primitive recursive functions form a strict
subset of those general recursive functions that are also total functions."

Furthermore: "A primitive recursive function takes a fixed number of
arguments, each a natural number (nonnegative integer: {0, 1, 2, ...}), and
returns a natural number. If it takes n arguments it is called n-ary.

The basic primitive recursive functions are given by ... axioms:

1. Constant functions

2. Successor function

3. Projection functions

More complex primitive recursive functions can be obtained by applying the
operations given by ... axioms:

4. Composition operator

5. Primitive recursion operator

The primitive recursive functions are the basic functions and those obtained
from the basic functions by applying these operations a finite number of
times."