Ackermann function is defined as follows for nonnegative integers m and n:

    A(m, n) =   n+1                 if  m = 0 
                A(m-1, 1)           if  m > 0 and n = 0 
                A(m-1, A(m, n-1))   if  m > 0 and  n > 0. 
 
/***************************************************************************/
 
 Pseudo-code list functions

empty(list)   if list is empty, return true
              else return false
              
head(list)    return first element of list

tail(list)    return list with first element removed

cons(element, list) return list that has element inserted as new first element of list

Example:

list = [2, 4, 6]

empty(list)  --> false
head(list)   --> 2
tail(list)   --> [4, 6]
tail( [6] )  --> [ ]
cons ('a', list) --> [ 'a', 2, 4, 6 ]

/***************************************************************************/
                                       
--- reverse a list ---                

reverse (list) {
  return rev (list, []);
  }
  
rev (list, acc) {
  if ( empty( list ) )  return acc;
  return ( rev ( tail( list ), cons( head( list ), acc ) ) );
  }
  
  
 --- return a list with element x repeated n times ---
 
replicate ( n, x ) {
  if ( n == 0 ) return [ ];
  return cons( x, replicate (n-1, x) );
  }
  
  
  --- return true if element a is contained in list ---

elem ( a, list ) {
  if ( empty( list )) return false;
  if ( a == head( list ) ) return true;
  return elem( a, tail (list ) );
  }
  
 
 --- count elements in a linked list ---
 
 count (head) {
   if (head == null) return 0;
   return 1 + count (head.next);
   }
   
 // count on generic list
 
 count (list) {
   if (empty (list) ) return 0;
   return 1 + count (tail(list));
   }
   

 --- print elements of linked list ---
 
printList(head) {
  if (head == null) return;
  print head.value;
  printList(head.next);
  }
  
  
--- insert new element at end of linked list
   
insertAtEnd (head, n) {
     if (head == null) return n;
     head.next = insertAtEnd(head.next, n);
     return head;
     }
     
main() {
  head = null;
  head = insertAtEnd(head, 1);
  head = insertAtEnd(head, 10);
  }
  
  
/******************************************************************************/
/*  Functions in Python
 */

def ackermann(m, n):
   if m == 0:
      return n + 1
   if n == 0:
      return ackermann(m - 1, 1)
   return ackermann( m - 1, ackermann( m, n - 1 ) )