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.
*)