Attempting fixed list in Elm

FixedList.elm

module FixedList exposing (..)

type Nil a = Nil
type Cons fa a = Cons a fa

type alias FixedList0 a = Nil a
type alias FixedList1 a = Cons (FixedList0 a) a
type alias FixedList2 a = Cons (FixedList1 a) a

fl1 : FixedList1 Int
fl1 = Cons 1 Nil 

fl2 : FixedList2 Int
fl2 = Cons 2 fl1
fl2_1 : FixedList2 Int
fl2_1 = Cons 2 (Cons 1 Nil )

map : (a -> b) -> Cons fa a -> Cons fa b
map f (Cons x xs) =
  Cons (f x) xs
 
map0 : (a -> b) -> FixedList0 a -> FixedList0 b 
map0 f Nil = Nil 

map1 : (a -> b) -> FixedList1 a -> FixedList1 b
map1 f (Cons x xs) =
  Cons (f x) (map0 f xs)

map2 : (a -> b) -> FixedList2 a -> FixedList2 b
map2 f (Cons x xs) =
  Cons (f x) (map1 f xs)

fl2_mapped = map2 ((+) 2) fl2