let rec ackermann x y = match (x,y) with
    | (0, _) -> y + 1
    | (_ , 0) -> ackermann (x - 1) 1
    | (_, _) -> ackermann (x - 1) (ackermann x (y - 1));;
</ocaml>
 
 
====== Python ======
 
<code python>
def ackermann(m, n):
    if m == 0:
        return n + 1
    elif n == 0:
        return ackermann(m - 1, 1)
    else:
        return ackermann(m - 1, ackermann(m, n - 1))

def ackermann(m, n):
    while m >= 4:
        if n == 0:
            n = 1
        else:
            n = ackermann(m, n - 1)
        m -= 1
    if m == 3:
        return (1 << n + 3) - 3
    elif m == 2:
        return (n << 1) + 3
    elif m == 1:
        return n + 2
    else:
        return n + 1