Rudimentary, case insensitive grep in OCaml

ogrep.ml

let pattern = Sys.argv.(1);;
let filename = Sys.argv.(2);;

let string_contains s1 s2 =
  try
    let len = String.length s2 in
    for i = 0 to String.length s1 - len do
      let lowercase_s1 = String.lowercase s1 in
        let lowercase_s2 = String.lowercase s2 in
        if String.sub lowercase_s1 i len = lowercase_s2 then raise Exit
    done;
    false
  with Exit -> true

let output s =
  Printf.printf "%s\n" s;;

let chan = open_in filename in
try
  while true; do
    let line = input_line chan in
    if string_contains line pattern then output line
  done;
with End_of_file ->
  close_in chan;