Count the number of newlines in a file (learning OCaml)

count_newlines.ml

(* Fold over a file in chunks *)
let fold_file f x file_name =
  let buffer = String.create 1024 in
  let file = open_in file_name in
  let rec go a =
    let length = input file buffer 0 (String.length buffer) in
    let a' = f a (String.sub buffer 0 length) in
    if length > 0 then go a' else a' in
  let r = go x in
  close_in file;
  r;;

(* Count the number of newlines in a buffer *)
let count_newlines s =
  let rec go n i =
    try
      let i' = String.index_from s i '\n' in
      go (n + 1) (i' + 1)
    with Not_found -> n in
  go 0 0;;

(* Compose the previous two functions to count the lines in a file *)
let newlines = fold_file (fun x s -> x + count_newlines s) 0 Sys.argv.(1);;
print_int newlines;;
print_newline ();;