// Bubble sort with the same algorithm as others

/*
// length
length_(r,n) >< [] => r~n;
length_(r,int n) >< (int x):xs => length_(r,n+1)~xs;

length(r) >< [] => r~0;
length(r) >< x:xs => length_(r,0) ~ x:xs;
*/


// stream length
len_stream_(len, list, int ct) >< [] => len~ct, list~(*R)[];
len_stream_(len, list, int ct) >< x:xs => 
	list~(*R)(x:cnt), 
	len_stream_(len, cnt, ct+1) ~ xs; 


len_stream(len, list) >< [] => len~0, list~(*R)[];
len_stream(len, list) >< x:xs => 
	list~(x:cnt), 
	len_stream_(len, cnt, 1)~xs;


// bubble sort
bs(r, xs) >< (int n)
| n == 0 => r~xs
| _ => (*L)bs_Cons(r, n)~xs;

bs_Cons(r, int n)>< x:xs => (*L)bs_ConsCons(r, n, x) ~ xs;
bs_Cons(r, int n)>< [] => r~(*R)[];

bs_ConsCons(r, int n, int x) >< (int y):ys
| x < y => r~x:cnt, (*L)bs(cnt, y:ys) ~(n-1)
| _ => r~y:cnt, (*L)bs(cnt, x:ys)~(n-1);
bs_ConsCons(r, int n, int x) >< [] => r~(*R)[x];

go(r,xs) >< (int n)
| n==0 => r~xs
| _ => bs(cnt, xs)~n, (*L)go(r, cnt)~(n-1);

bsort(r) >< [] => r~[];
bsort(r) >< x:xs => 
	(*L)len_stream(len, alist) ~ (*R)(x:xs),
	go(r, alist)~lengthDec1, 
        Sub(lengthDec1,len)~1;


// Creates a random list
make_RandList(ret) >< (int n)
| n>0 => ret~(rd:cnt), (*L)make_RandList(cnt)~(n-1) 
  where rd=rand(10000)
| _ => ret~[];


// validation checks
valid(ret) >< [] => ret~True;
valid(ret) >< x:xs => (*L)valid_Cons(ret,x)~xs;

valid_Cons(ret, int x) >< [] => ret~True;
valid_Cons(ret, int x) >< (int y):ys
| x<=y => (*L)valid_Cons(ret,y)~ys
| _ => ret~False, Eraser~ys;

// The `Eraser' is a built-in agent defined for any agents as follows:
//Eraser >< Alpha(a1, ..., a5) => Eraser~a1, ..., Eraser~a5;


// Main
const LIST_ELEM=20000;

make_RandList(rndlist)~(LIST_ELEM),
bsort(sorted)~rndlist,
valid(ret)~sorted;

ret;