In the following simplified program I'm trying to use phantom
types to express read / write / read_write permissions.
This program fails at runtime in the call to Io.write.
Is it possible to adjust the phantom types so that it fails at
compilation time?
I'd like to express a typing like
val dup : 'a perm -> [< `Read | `Write > 'a] desc -> 'a desc
but a type variable inside the polymorphic variant type is not allowed.

module Io : sig
  type 'a perm  constraint 'a = [< `Read | `Write ]
  val ro : [ `Read ] perm
  val rw : [ `Read | `Write ] perm

  type 'a desc constraint 'a = [< `Read | `Write ]

  val open_file : 'a perm -> string -> 'a desc
  val dup : 'a perm -> [< `Read | `Write] desc -> 'a desc
  val read : [> `Read ] desc -> string
  val write : [> `Read | `Write ] desc -> string -> unit
end
= struct
  type 'a perm = [ `Ro | `Rw ] constraint 'a = [< `Read | `Write ]
  type 'a desc = Unix.file_descr constraint 'a = [< `Read | `Write ]
  let ro : [ `Read ] perm = `Ro
  let rw : [ `Read | `Write ] perm = `Rw

  let open_file perm file =
    Unix.(openfile
            file
            [match perm with |`Ro -> O_RDONLY |`Rw -> O_RDWR]
            0o000
         )
  let read desc =
    let buf = Bytes.create 10 in
    assert (Unix.read desc buf 0 10 = 10);
    Bytes.unsafe_to_string buf
  let write desc buf =
    let buf = Bytes.unsafe_of_string buf in
    assert (Unix.write desc buf 0 (Bytes.length buf) = Bytes.length buf)

  let dup desc = Unix.dup ?cloexec:None
end

let () =
  let fd_ro = Io.(open_file ro "/tmp/test") in
  let fd_rw = Io.(dup rw fd_ro) in
  Io.write fd_rw "Hello, World";
  print_endline (Io.read fd_ro);


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