trying to write polymorphic type generators in ocaml

a_gen.ml

type exp =
  | Int of int
  | Succ of exp
  | Plus of exp * exp

(* realistically we would want to specify depth and/or the bias of
choosing a certain expression *)
let rec gen_exp () : exp =
  match Random.int 3 with
  | 0 -> Int (Random.int 42)
  | 1 -> Succ (gen_exp ())
  | 2 -> Plus (gen_exp (), gen_exp ())
  | _ -> raise (Failure "ocaml again doesn't know whats going on")

(* but we'd like to write a polymorphic function *)
let rec gen_typ (typs : ((unit -> 'a) -> 'a) list) : 'a =
  let n = Random.int (List.length typs) in
  let g = List.nth typs n in
  (g (fun () -> gen_typ typs))

(* and we can create a generator like this *)
let gen_exp = fun () -> gen_typ [(fun _ -> Int (Random.int 42));
                                 (fun g -> Succ (g ()));
                                 (fun g -> Plus (g (), g()))]

(* but then we have to write a list of generators every time we have a new type *)
(* Some something like this would be nice (totally made up) *)

(* let rec gen_typ () : 'a = *)
(*   let typ = Typ.nth 'a (Random.int (Typ.size 'a)) in *)
(*   Typ.create typ (List.map gen_typ (Typ.members typ)) *)

(* but we can't do this because types aren't values *)