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:

ackermann = { m, n |
	when { m == 0 } { n + 1 }
		{ m > 0 && n == 0 } { ackermann(m - 1, 1) }
		{ m > 0 && n > 0 } { ackermann(m - 1, ackermann(m, n - 1)) }
}

p ackermann 3, 4  #Prints 125