fun brackets(s,i,j) =

if (size s)=i

then

if j=0

then true

else false

else

if String.sub(s,i) = #"("

then brackets(s,i+1,j+1)

else

if String.sub(s,i) = #")"

then

if j=0

then false

else brackets(s,i+1,j-1)

else brackets(s,i+1,j);

fun balance s = brackets(s,0,0);

fun ten n =

if n<=1

then 1

else 10 * ten(n-1);

fun numbers(s,i) =

if (size s)=i

then

0

else

(ord (String.sub(s,i)) - 48) * (ten ((size s) - i)) + numbers(s,i+1);;

fun atoi s = numbers(s,0);

fun backwards(s,n) =

if n=0

then ""

else str (String.sub(s,n-1)) ^ backwards(s,n-1);

fun reverseString s = backwards(s,(size s));

fun helper ((d1:int,s1:int,t1:int),m:int,n:int) =

if d1>=0 then (d1,t1,(s1-(m div n)*t1))

else (~d1,~t1,~(s1-(m div n)*t1));

fun extended (m,n) =

if n=0 then (m,1,0)

else helper(extended(n,m mod n),m,n);