church_encoding_list

let nil = fun f -> fun g -> f
;;
let cons = fun x -> fun xs -> fun f -> fun g -> g x (xs f g)
;;
let map = fun f -> fun lst ->
  lst
    nil
    (fun x -> fun xs -> cons (f x) xs)
;;
let sample = cons 1 (cons 2 (cons 3 nil))
;;
let show_list = fun lst ->
  lst
    ""
    (fun x -> fun s -> show x ^ s)
;;
show_list sample
;;
show_list (map (fun x -> x * 2) sample)
;;