+type num = int -> int
+type contents = Num of num | Op of (num -> num) | Op2 of (num -> num -> num)
+type tree = Leaf of contents | Branch of tree * tree | Error
+
+let mid a = fun _ -> a;; (* K *)
+
+let map2 f u v x = f (u x) (v x);; (* S *)
+
+let rec eval (t:tree) = match t with
+ | Leaf _ -> t
+ | Branch (Leaf (Op f), b2) -> (match (eval b2) with
+ | Leaf (Num n) -> Leaf (Num (f n))
+ | _ -> Error)
+ | Branch (Leaf (Op2 f), b2) -> (match (eval b2) with
+ | Leaf (Num n) -> Leaf (Op (f n))
+ | _ -> Error)
+ | Branch (b1, b2) -> eval (Branch (eval b1, eval b2))
+ | _ -> Error
+
+
+(* to get an arithmetic function, type, e.g., "(+)".
+ to get times instead of comment, type "( * )". *)
+
+(* Encoding of (+ 1 (* (/ 6 x) 4)) *)
+let t1 = Branch ((Branch ((Leaf (Op2 (map2 (+)))),
+ (Leaf (Num (mid 1))))),
+ (Branch ((Branch ((Leaf (Op2 (map2 ( * ))),
+ (Branch ((Branch ((Leaf (Op2 (map2 (/)))),
+ (Leaf (Num (mid 6))))),
+ (Leaf (Num (fun x -> x)))))))),
+ (Leaf (Num (mid 4))))));;
+
+
+(* try
+
+match eval t1 with Leaf (Num f) -> f 2;;
+
+The answer should be 13.
+*)