1 

     2 def zero(x) = 0;

     3 

     4 def suc(x) = x + 1;

     5 

     6 def pred(x) =

     7   if x == 0 then x else x - 1;

     8 

     9 def add(x, y) =

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

    11 

    12 def mult(x, y) =

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

    14 

    15 def pow(x, y) =

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

    17 

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

    19              else if n == 1 then 1 

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

    21 

    22 def fact(n) =

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

    24 

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

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

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

    28 

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

    30 

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

    32 

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

    34 

    35 def gcd(a, b) =

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

    37 

    38 def is_prime_aux(n, i) = 

    39   if n % i == 0 then 0

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

    41   else 1;

    42 

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

    44 

    45 def primes(n) = 

    46   if n == 0 then 0

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

    48   else primes(n - 1);

    49 

    50 def is_collatz(n) =

    51   if n == 1 then 1

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

    53   else is_collatz(3 * n + 1);  

    54 

    55 def collatz_aux(n, i) = 

    56   if i > n then 0

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

    58   else collatz_aux(n, i + 1);

    59 

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

    61 

    62 def facT(n, acc) =

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

    64 

    65 

    66 //zero(3)

    67 //suc(8)

    68 //pred(7)

    69 //write(add(3, 4))

    70 //mult(4,5)

    71 //pow(2, 3)

    72 //fib(20)

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

    74 //(write(1) ; 2)

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

    76 //stack_test(0)

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

    78 //gcd(54, 24)

    79 //is_prime(2)

    80 primes(1000)

    81 //primes(1000000)

    82 //collatz(4000)

    83 //collatz(5000)

    84 //facT(6, 1)

    85