-- Class Declarations
class {- variant -} List xs x => List2 xs x | xs -> x where {
  cons2 :: x -> x -> xs -> xs;
};

class {- variant -} List xs x => AppendList xs x | xs -> x where {
  append :: xs -> xs -> xs;
};

class {- variant -} List xs x | xs -> x where {
  cons :: x -> xs -> xs;
  nil :: xs;
};

class {- record -}  ListAcceptor xs x | xs -> x where {
  toListView :: xs -> Either (x, xs) ();
};

-- Data Declarations
data Data''1 a = C''cons''1 a (Data''1 a) | 
                 C''nil''1 | 
                 C''append''1 (Data''1 a) (Data''1 a) | 
                 C''cons2''1 a a (Data''1 a) ;
{-
-- using GADT-style declaration
data Data''1 a where {
  C''cons''1 :: a -> Data''1 a -> Data''1 a;
  C''nil''1 :: Data''1 a;
  C''append''1 :: Data''1 a -> Data''1 a -> Data''1 a;
  C''cons2''1 :: a -> a -> Data''1 a -> Data''1 a;
};

-}

data Data''0 a = C''cons''0 a (Data''0 a) | 
                 C''nil''0 | 
                 C''append''0 (Data''0 a) (Data''0 a) | 
                 C''cons2''0 a a (Data''0 a) ;
{-
-- using GADT-style declaration
data Data''0 a where {
  C''cons''0 :: a -> Data''0 a -> Data''0 a;
  C''nil''0 :: Data''0 a;
  C''append''0 :: Data''0 a -> Data''0 a -> Data''0 a;
  C''cons2''0 :: a -> a -> Data''0 a -> Data''0 a;
};
-}

-- Instance Declarations
instance ListAcceptor (Data''1 a) a where {
  toListView (C''cons''1 x xs) = Left (x, xs);
  toListView (C''nil''1) = Right ();
  toListView (C''append''1 xs ys) = toListView (if isNull xs then ys else cons (hd xs) (append (tl xs) ys));
  toListView (C''cons2''1 x1 x2 xs) = toListView (cons x1 (cons x2 xs));
};

instance List (Data''1 a) a where {
  cons = C''cons''1;
  nil = C''nil''1;
};

instance AppendList (Data''1 a) a where {
  append = C''append''1;
};

instance List2 (Data''1 a) a where {
  cons2 = C''cons2''1;
};

instance ListAcceptor (Data''0 a) a where {
  toListView (C''cons''0 x xs) = Left (x, xs);
  toListView (C''nil''0) = Right ();
  toListView (C''append''0 xs ys) = toListView (if isNull xs then ys else cons (hd xs) (append (tl xs) ys));
  toListView (C''cons2''0 x1 x2 xs) = toListView (cons x1 (cons x2 xs));
};

instance List (Data''0 a) a where {
  cons = C''cons''0;
  nil = C''nil''0;
};

instance AppendList (Data''0 a) a where {
  append = C''append''0;
};

instance List2 (Data''0 a) a where {
  cons2 = C''cons2''0;
};

-- Cast(?) Declarations
id''1 :: Data''1 a -> Data''1 a;
id''1 x = x;
id''0 :: Data''0 a -> Data''0 a;
id''0 x = x;

-- BindGroups
isNull = (.) isNullView toListView;
isNullView (Left (x, xs)) = False;
isNullView (Right ()) = True;
hd = (.) hdView toListView;
hdView (Left (x, xs)) = x;
tl =  (.) tlView toListView;
tlView (Left (x, xs)) = xs;
baz = myLength (id''1 ys);
ys = append xs xs;
xs = cons2 ((*) 2 1) ((+) x 1) nil;
x = 1;
qux a = myLength (id''0 (append (cons2 a a nil) nil));
myLength = (.) myLengthView toListView;
myLengthView (Left (x, xs)) = (+) 1 (myLength xs);
myLengthView (Right ()) = 0;