def zero(x) = 0;

def suc(x) = x + 1;

def pred(x) = if x == 0 then x else x - 1;

def add(x, y) = if x == 0 then y else suc(add(x - 1, y));

def mult(x, y) = if x == 0 then 0 else add(y, mult(x - 1, y));

def pow(x, y) = if y == 0 then 1 else mult(x, pow(x, y - 1));

def fib(n) = if n == 0 then 0 

             else if n == 1 then 1 

             else fib(n - 1) + fib(n - 2);

def fact(n) = if n == 0 then 1 else n * fact(n - 1);

def ack(m, n) = if m == 0 then n + 1

                else if n == 0 then ack(m - 1, 1)

                else ack(m - 1, ack(m, n - 1));

def stack_test(x) = x + 1 + 2 + 3 + 4 + 5;

def div(x, y) = x / y;   //integer division

def rem(x, y) = x % y;   //remainder

def gcd(a, b) = if b == 0 then a else gcd(b, a % b);

def is_prime_aux(n, i) = 

  if n % i == 0 then 0

  else if (i * i) <= n then is_prime_aux(n, i + 1)  

  else 1;

def is_prime(n) = if n == 2 then 1 else is_prime_aux(n, 2);

def primes(n) = 

  if n == 0 then 0

  else if is_prime(n) == 1 then (write n; primes(n - 1)) 

  else primes(n - 1);

def is_collatz(n) =

  if n == 1 then 1

  else if n % 2 == 0 then is_collatz(n / 2)

  else is_collatz(3 * n + 1);  

def collatz_aux(n, i) = 

  if i > n then 0

  else if is_collatz(i) == 1 then (write i; collatz_aux(n, i + 1)) 

  else collatz_aux(n, i + 1);

def collatz(n) = collatz_aux(n, 1);

def facT(n, acc) = if n == 0 then acc else facT(n - 1, n * acc);

//zero(3)

//suc(8)

//pred(7)

//add(3, 4)

//mult(4,5)

//pow(2, 3)

//fib(20)

//(write(fact(5)) ; fact(6))

//(write(1) ; 2)

ack(3, 12)   // for tail-rec test

//stack_test(0)

//(write (div(11, 3)); rem(11, 3))

//gcd(54, 24)

//is_prime(2)

//primes(1000000)

//collatz(5000)

//facT(6, 1)