1 

     2 def zero(x) = 0;

     3 

     4 def suc(x) = x + 1;

     5 

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

     7 

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

     9 

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

    11 

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

    13 

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

    15              else if n == 1 then 1 

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

    17 

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

    19 

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

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

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

    23 

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

    25 

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

    27 

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

    29 

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

    31 

    32 def is_prime_aux(n, i) = 

    33   if n % i == 0 then 0

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

    35   else 1;

    36 

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

    38 

    39 def primes(n) = 

    40   if n == 0 then 0

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

    42   else primes(n - 1);

    43 

    44 def is_collatz(n) =

    45   if n == 1 then 1

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

    47   else is_collatz(3 * n + 1);  

    48 

    49 def collatz_aux(n, i) = 

    50   if i > n then 0

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

    52   else collatz_aux(n, i + 1);

    53 

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

    55 

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

    57 

    58 

    59 //zero(3)

    60 //suc(8)

    61 //pred(7)

    62 //add(3, 4)

    63 //mult(4,5)

    64 //pow(2, 3)

    65 //fib(20)

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

    67 //(write(1) ; 2)

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

    69 //stack_test(0)

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

    71 //gcd(54, 24)

    72 //is_prime(2)

    73 //primes(1000000)

    74 //collatz(5000)

    75 //facT(6, 1)

    76