The point of ADT syntax is to allow deriving many functions on different data structures automatically. For example, lists and some functions can be defined as:

The point of ADT syntax is to allow deriving many functions on different data structures automatically. For example, lists and some functions can be defined as: cons = (x list cons nil -> (cons x (list cons nil))) nil = (cons nil -> (id nil)) map = (f list cons -> (list (comp cons f))) head = (list -> (list (a b -> a) nil)) tail = (list cons nil -> (list (h t g -> (g h (t cons))) (const nil) (h t -> t))) zip_with = (f a b -> ((left a) (right f b))) left = (foldr (x xs cont -> (cont x xs)) (const [])) right = (f -> (foldr (y ys x cont -> (cons (f x y) (cont ys))) (const (const [])))) length = (flip comp const) The very same definitions could be written more tersely as just: List = #{Cons Type * | Nil} cons = (Ctor 0 List) nil = (Ctor 1 List) head = (Getter 0 0 List) tail = (Getter 0 1 List) zip_with = (ZipWith List) length = (Size List) Where Ctor/Getter/ZipWith/Size are proper derivers. It is possible because all the information you need is there, but it is very hard to come up with those derivers and I currently only have some very bloated derivers for Scott encoded structures, and none for Church encoded structures yet.