Problem Statement

The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.

The Ackermann function is usually defined as follows:

Its arguments are never negative and it always terminates.

Write a function which returns the value of

A ( m , n )

{\displaystyle A(m,n)}

. Arbitrary precision is preferred (since the function grows so quickly), but not required.

Let's start with the solution:

(
  :n :m
  (
    ((m 0 ==) (n 1 +))
    ((n 0 ==) (m 1 - 1 ackermann))
    ((true) (m 1 - m n 1 - ackermann ackermann))
  ) case
) :ackermann