fun inside(k,l)=
if l=nil then false
else if k=hd(l) then true
else inside(k,tl(l));

fun union(l1,l2)=
 if l1=nil then l2
else if inside(hd(l1),l2)=false then hd(l1)::union(tl(l1),l2)
else union(tl(l1),l2); 

 fun intersection(l1,l2)=
if l1=nil then nil
else if inside(hd(l1),l2)=true then hd(l1)::intersection(tl(l1),l2)
else intersection(tl(l1),l2);

fun cart(l1,l2)=
let
fun nxs(k,l)=
if l=nil then nil
else [k,hd(l)]::nxs(k,tl(l))
in
if l1= nil then nil
else nxs(hd(l1),l2)@cart(tl(l1),l2)
end;


fun subtract(a,b)=
let fun rem1ele(l1,k)=
	if l1=nil then nil else
	if hd(l1)=k then tl(l1)	
	else hd(l1)::rem1ele(tl(l1),k)
in
if b=nil then a
else subtract(rem1ele(a,hd(b)),tl(b)) end; 


 fun add(a,b)=if b=nil then a
else if inside(hd(b),a)=false then add(hd(b)::a,tl(b))
else add(a,tl(b));

fun equalto(a,b)=
let fun rem1ele(l1,k)=
	if l1 = nil then nil 
	else
        if hd(l1)=k then tl(l1)
        else hd(l1)::rem1ele(tl(l1),k)
in
if (a=nil) andalso (b=nil) then true
else if (a=nil) orelse (b=nil) then false 
else 
if inside(hd(a),b)=false then false
else 
equalto(tl(a),rem1ele(b,hd(a))) end;


fun disjoint(a,b)=
if intersection(a,b)=nil then true else false;

fun symdiff(a,b)=subtract(union(a,b),intersection(a,b));

fun subset(a,b)=
if a=nil then true else
if b=nil then false
else if inside(hd(a),b)=true then subset(tl(a),b)
else false;

fun card(a)=if a=nil then 0 else 1+card(tl(a));

fun max(a)=
let fun max_iter(a,v)=
if a=nil then v 
else 
if v<hd(a) then max_iter(tl(a),hd(a))
else max_iter(tl(a),v)
in max_iter(a,~99999999) end; 

fun min(a)=
let fun min_iter(a,v)=
if a=nil then v
else 
if v>hd(a) then min_iter(tl(a),hd(a))
else min_iter(tl(a),v)
in min_iter(a,99999999) end;


fun P(L)=
 let fun rem1ele(l1,k)=
                if l1 = nil then nil
                else
                if hd(l1)=k then tl(l1)
                else hd(l1)::rem1ele(tl(l1),k)  
fun P1(A,B,x)=

	hd(B)::P(rem1ele(A,hd(B)))@P(x::tl(A));
in 
if L=nil then nil else
P1(L,L,hd(L)) end;