kunishi

fun duplicate(L) =
    if L=nil then nil
    else hd(L)::hd(L)::duplicate(tl(L));

kunishi

fun divide nil  = (nil, nil)
  | divide (x::nil) = ([x], nil)
  | divide (x::y::xs) = 
    let
	val (ys, zs) = divide xs
    in
	(x::ys, y::zs)
    end;

kunishi

fun count (x, nil) = 0
  | count (x, y::ys) = if x = y then 1 + count(x, ys) else count(x, ys);

kunishi

fun concat(s, t) = s ^ t;
fun concatList(L) = reduce(concat,
			   map(Char.toString, L);

kunishi

fun combine(nil) = nil
|   combine([x]) = [(x, 0)]
|   combine(x::y::zs) = (x,y)::combine(zs);

kunishi

exception BadN;
exception BadM;

fun comb(n,m) =
    if n<0 then raise BadN
    else if m<0 orelse m>n then raise BadM
    else if m=0 orelse m=n then 1
    else comb(n-1, m) + comb(n-1, m-1);

kunishi

fun comb(n,m) =
    if m=0 orelse m=n then 1
    else comb(n-1, m) + comb(n-1, m-1);

kunishi

fun collatz(n:int) =
    if n = 1 then 1
    else if n mod 2 = 0 then collatz(n div 2)
    else collatz(n * 3 + 1);

kunishi

fun carlist(nil) = nil
|   carlist(nil::xs) = carlist(xs)
|   carlist((x::xs)::ys) = x::carlist(ys);

kunishi

fun area1 1 = 1
 |  area1 n = n * n + area1 (n-1);

fun area n = real (area1 n) / real (n * n * n);