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:

on ackermann(m, n)
    if m is equal to 0 then return n + 1
    if n is equal to 0 then return ackermann(m - 1, 1)
    return ackermann(m - 1, ackermann(m, n - 1))
end ackermann