ocaml

type pure =
    | Binary of expression * Ops.t * expression
    | Atom of int
    and bracketed = pure
    and expression =
    | Bracketed of bracketed
    | Pure of pure
;;

type pure = Binary of expression * Ops.t * expression | Atom of int
and bracketed = pure
and expression = Bracketed of bracketed | Pure of pure

let rec enum' i =
if i = 0 then [(Atom 0)]
else (
  let children = enum (i - 1) in
  List.cartesian_product children children |> List.map ~f:(fun (child1, child2) ->
    List.concat_map Ops.all ~f:(fun op ->
      [(Binary (child1, op, child2))]
))) |> List.concat
and enum i = let children = enum' i in
[List.map children ~f:(fun child -> Pure(child));
List.map children ~f:(fun child -> Bracketed(child))
] |> List.concat
;;
let ops_to_str = function
| Ops.Plus -> "+"
| Minus -> "-"
| Mult -> "*"
| Div -> "/"
;;
let rec pure_to_str = function
| Binary (e1, op, e2) -> (expr_to_str e1) ^ (ops_to_str op) ^ (expr_to_str e2)
| Atom x -> Int.to_string x
and bracket_to_str e = "(" ^ (pure_to_str e) ^ ")"
and expr_to_str = function
| Bracketed x-> bracket_to_str x
| Pure x -> pure_to_str x
;;
enum 2 |> List.map ~f:expr_to_str;;
- : string list =
["0+0+0+0"; "0+0-0+0"; "0+0*0+0"; "0+0/0+0"; "0+0+0-0"; "0+0-0-0"; "0+0*0-0";
 "0+0/0-0"; "0+0+0*0"; "0+0-0*0"; "0+0*0*0"; "0+0/0*0"; "0+0+0/0"; "0+0-0/0";
 "0+0*0/0"; "0+0/0/0"; "0+0+0+(0)"; "0+0-0+(0)"; "0+0*0+(0)"; "0+0/0+(0)"; ...