(* requires: y >= 0 *)
(* requires: d >= 0 *)
let valid_date (y: int) (m: string) (d: int) = 
  if y < 0 || d < 0 then false
  else match m with
  | "Jan" | "Mar" | "May" | "Jul" | "Aug" | "Oct" | "Dec" -> d < 32
  | "Feb" -> if (y mod 4 == 0) && (y mod 100 <> 0) then d < 30 else d < 29
  | "Apr" | "Jun" | "Sep" | "Nov" -> d < 31
  | _ -> false

(* Test leap day in a non-century leap year. *)
let () = assert (valid_date 2020 "Feb" 29)
(* Test invalid day. *)
let () = assert (not (valid_date 2010 "Jun" 50))


(* requires: n > 0 *)
let syr n =
  let rec collatz n res =
    if n == 1 then res
    else if n mod 2 == 0 then collatz (n/2) (res+1)
    else collatz ((n*3)+1) (res+1) in collatz n 0

(* Test syr *)
let () = assert (syr 1 = 0)
let () = assert (syr 2 = 1)
let () = assert (syr 10 = 6)
let () = assert (syr 3 = 7)


let rec next_nacci n l sum =
  if n = 0 then sum
  else match l with
       | [] -> next_nacci (n - 1) [] sum
       | h :: t -> next_nacci (n - 1) t (sum + h)

let nacci n k =
  let rec tail_nacci n k res =
    if k = 0 then res
    else tail_nacci n (k - 1) ((next_nacci n res 0) :: res)
  in if k = 1 || k = 0 then [1] else List.rev (tail_nacci n (k - 2) [1; 1])


let () = assert (nacci 2 6 = [1; 1; 2; 3; 5; 8])
let () = assert (nacci 4 9 = [1; 1; 2; 4; 8; 15; 29; 56; 108])
let () = assert (nacci 5 9 = [1; 1; 2; 4; 8; 16; 31; 61; 120])
let () = assert (nacci 7 9 = [1; 1; 2; 4; 8; 16; 32; 64; 127])