(* This code extends 'mini_prelude'. *)

type ('a) queue = 
    Queue of ('a) list * int * ('a) list * int * ('a) list ;;

let empty = (Queue (Nil, 0, Nil, 0, Nil)) ;;

let is_empty = 
  (fun v6 -> 
    (match v6 with 
        (Queue (v5, v4, v3, v2, v1)) -> (v4 <= 0))) ;;

let checkw = 
  (fun v8 -> 
    (match v8 with 
        (Queue (v7, v6, v5, v4, v3)) -> 
          (match v7 with 
              Nil -> (Queue (v5, v6, v5, v4, v3)) 
            | (Cons (v2, v1)) -> (Queue ((Cons (v2, v1)), v6, v5, v4, v3))))) ;;

let check = 
  (fun v6 -> 
    (match v6 with 
        (Queue (v5, v4, v3, v2, v1)) -> 
          (if (v2 <= v4) 
          then (checkw (Queue (v5, v4, v3, v2, v1))) 
          else (checkw (Queue (v3, (v4 + v2), ((APPEND v3) (REVERSE v1)), 0, Nil)))))) ;;

let snoc = 
  (fun v6 -> 
    (fun v7 -> 
      (match v6 with 
          (Queue (v5, v4, v3, v2, v1)) -> (check (Queue (v5, v4, v3, (v2 + 1), (Cons (v7, v1)))))))) ;;

let head = 
  (fun x -> 
    (match x with 
        (Queue (v7, v6, v5, v4, v3)) -> 
          (match v7 with 
              Nil -> (raise (Match_failure (string_of_bool true, 0, 0))) 
            | (Cons (v2, v1)) -> v2))) ;;

let tail = 
  (fun x -> 
    (match x with 
        (Queue (v7, v6, v5, v4, v3)) -> 
          (match v7 with 
              Nil -> (raise (Match_failure (string_of_bool true, 0, 0))) 
            | (Cons (v2, v1)) -> (check (Queue (v1, 
                (let k = (v6 - 1) 
                in 
                  (if (k < 0) 
                  then 0 
                  else k)), (TL v5), v4, v3)))))) ;;