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:

ack := function(m, n)
  if m = 0 then
    return n + 1;
  elif (m > 0) and (n = 0) then
    return ack(m - 1, 1);
  elif (m > 0) and (n > 0) then
    return ack(m - 1, ack(m, n - 1));
  else
    return fail;
  fi;
end;