let test = true
;;

(* Remember scope, shadowing *)
let x = 1 in
  (x + x) * (let x = 2 in x + x);;
(* A. 4 *)
(* B. 8 *)
(* C. 16 *)

let x = 1 in
  (x * 2) + (let x = 2 in x + 5)
  + 4 * x;;
(* A. 12 *)
(* B. 13 *)
(* C. 17 *)
(* D. 19 *)

let x = (let y = 3 in y * 2) + 5
in
  let y = 1 in x + y;;
(* A. 8 *)
(* B. 12 *)
(* C. 14 *)

(* Side effects (* Still a comment*)
   NOTE (after lecture):
   this is still a comment; they can have arbitrary line breaks
 *)
42 / 0;;
Printf.printf "The answer is %d\n" 42;;

(* Won't typecheck *)
(*
let x : int = "Hello";;
 *)

let square x = x * x;;
let square (x : int) : int = x * x;;
let x = square 3;;
let y = square 4;;
let z = square 5;;

let x = 1 in (let x = 2 in x) + x;;

let x = ();;

let square = fun x -> x * x
in
  (square 3) + (square 4);;

(* + operator as a function *)
(+) 1 2;;
(-) 4 3;;
( * ) 1 2;;

(* Partial application *)
let add1 = (+) 1;;
add1 41;;
(* add1 41 2 won't typecheck -- too many arguments *)
add1 99;;

let my_add x y = x + y;;
(* is syntactic sugar for *)
let my_add =
  fun x -> fun y -> x + y;;

let rec fact (n: int) : int =
  if n <= 0 then 1
  else n * fact (n - 1);;

let one = fact 0 in
  one + one;;

let rec sum (min: int) (max: int) : int =
  if max < min then raise (Invalid_argument "sum")
  else
    if max = min then min
    else
      max + sum min (max - 1)
    ;;
    
sum 1 5;;
sum 5 1;;