View difference between Paste ID: XhPabW2g and SpfB0jZX

-type pure =
+module Op = struct
-	| Binary of expression * Ops.t * expression
+  type t =
-	| Atom of int
+    | Plus
-	and bracketed = pure
+    | Minus
-	and expression =
+    | Mult
-	| Bracketed of bracketed
+    | Div
-	| Pure of pure
+  [@@deriving enumerate]
 end
 ;;
-type pure = Binary of expression * Ops.t * expression | Atom of int
+
-and bracketed = pure
+type node =
-and expression = Bracketed of bracketed | Pure of pure
+  { left : expression
   ; right : expression
-let rec enum' i =
+  ; op : Op.t
-if i = 0 then [(Atom 0)]
+  ; is_bracketed : bool
-else (
+  }
-  let children = enum (i - 1) in
+and expression =
-  List.cartesian_product children children |> List.map ~f:(fun (child1, child2) ->
+  | Node of node
-    List.concat_map Ops.all ~f:(fun op ->
+  | Leaf of int
-      [(Binary (child1, op, child2))]
+
-))) |> List.concat
+
-and enum i = let children = enum' i in
+(* enum functions to generate all possible expression of depth i *)
-[List.map children ~f:(fun child -> Pure(child));
+let rec enum i =
-List.map children ~f:(fun child -> Bracketed(child))
+  if i = 0 then [(Leaf 0)]
-] |> List.concat
+  else (
     let possible_children = enum (i - 1) in
-let ops_to_str = function
+    List.bind possible_children ~f:(fun left ->
-| Ops.Plus -> "+"
+      List.bind possible_children ~f:(fun right ->
-| Minus -> "-"
+        List.bind Op.all ~f:(fun op ->
-| Mult -> "*"
+          List.bind Bool.all ~f:(fun is_bracketed ->
-| Div -> "/"
+          [Node { left; right; op; is_bracketed }])))))
 ;;
-let rec pure_to_str = function
+
-| Binary (e1, op, e2) -> (expr_to_str e1) ^ (ops_to_str op) ^ (expr_to_str e2)
+(* to_str functions *)
-| Atom x -> Int.to_string x
+let op_to_str = function
-and bracket_to_str e = "(" ^ (pure_to_str e) ^ ")"
+  | Op.Plus -> "+"
-and expr_to_str = function
+  | Minus -> "-"
-| Bracketed x-> bracket_to_str x
+  | Mult -> "*"
-| Pure x -> pure_to_str x
+  | Div -> "/"
 ;;
-enum 2 |> List.map ~f:expr_to_str;;
+
 let rec expression_to_str = function
-["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";
+  | Leaf x -> Int.to_string x
- "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";
+  | Node { left; right; op; is_bracketed } ->
- "0+0*0/0"; "0+0/0/0"; "0+0+0+(0)"; "0+0-0+(0)"; "0+0*0+(0)"; "0+0/0+(0)"; ...
+    let inside = (expression_to_str left) ^ (op_to_str op) ^ (expression_to_str right) in
     if is_bracketed then
       "(" ^ inside ^ ")"
     else inside
 ;;
 
 (* finally running *)
 utop # enum 2 |> List.map ~f:expression_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)"; "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)"; "0+0+(0*0)"; "(0+0+(0*0))"; "0+0-(0*0)"; ...