-- Eq

class Eq a where {
  eq :: a -> a -> Bool;
}

instance Eq Int where {
  eq x y = x == y;
}

-- Float

data Float = MkFloat Int;

instance Eq Float where {
  eq (MkFloat x) (MkFloat y) = eq x y;
}

-- Num

class Num a where {
  zero :: a;
  add  :: a -> a -> a;
}

instance Num Int where {
  zero    = 0;
  add x y =  x + y;
}

instance Num Float where {
  zero                        = MkFloat 0;
  add (MkFloat x) (MkFloat y) = MkFloat (x + y);
}

sum :: Num a => List a -> a;
sum l = case l of 
          Nil       -> zero;
	  Cons x xs -> add x (sum xs);
        ;

--

class Collects c where {
  type Elem c;
  empty  :: c;
  insert :: Elem c -> c -> c;
  toList :: c -> List (Elem c);
}

instance Eq e => Collects (List e) where {
  type Elem (List e) = e;
  empty    = Nil;
  insert   = Cons;
  toList c = c;
}

data BitSet = MkBitSet;

instance Collects BitSet where {
  type Elem BitSet = Char;
  empty = MkBitSet;
  insert = insert;
  toList = toList;
}

--sumColl :: Collects c, Elem c = Int => c -> Int;  -- ERROR (now ok)
--sumColl :: Collects c, Elem c = Int => c -> Elem c;  -- ERROR (now ok)
--sumColl :: Collects c, Num (Elem c) => c -> Elem c;  -- ok (still ok)
--sumColl :: List Int -> Int;  -- ok (still ok)
sumColl c = sum (toList c);
--sumColl = sumColl;

main = 42;