type a_exp =
    Aval of int
  | Plus of a_exp * a_exp
  | Minus of a_exp * a_exp
  | Times of a_exp * a_exp
  | Of_bool of b_exp
and b_exp =
    Bval of bool
  | And of b_exp * b_exp
  | Or of b_exp * b_exp
  | Not of b_exp
  | Minor of a_exp * a_exp


let rec eval_a_exp node =
  match node with
    Aval (i) -> i
  | Plus (i, j) -> (eval_a_exp i) + (eval_a_exp j)
  | Minus (i, j) -> (eval_a_exp i) - (eval_a_exp j)
  | Times (i, j) -> (eval_a_exp i) * (eval_a_exp j)
  | Of_bool b -> if (eval_b_exp b) then 1 else 0
and eval_b_exp node =
  match node with
    Bval (b) -> b
  | And (a, b) -> (eval_b_exp a) && (eval_b_exp b)
  | Or (a, b) -> (eval_b_exp a) || (eval_b_exp b)
  | Not b -> not (eval_b_exp b)
  | Minor (i, j) -> (eval_a_exp i) < (eval_a_exp j)

type 'a my_tree =
    Leaf of 'a
  | Node of ('a my_tree) list

let mod_list y =
  (List.fold_left
     (fun acc x ->
        match acc with
        | [a] when ((List.hd a) = x) -> [x :: a]
        | a :: tl when ((List.hd a) = x) -> (x :: a) :: tl
        | _ -> [x] :: acc)
     []
     y)
  |> List.rev

(* -------------------------------------------------------------------------- *)

let to_tup f g =
  fun x -> match x with
      (a, b) -> (f a, g b)

let partialsum l =
  snd (List.fold_left_map (fun acc x -> (acc+x, acc+x)) 0 l)

type label =
  string

type 'a finite_state_automata = {
  l: label;
  next: ('a finite_state_automata *  'a list) list;
  final: bool;
}

let rec check_included input fsa =
  match input with
    [] -> fsa.final
  | a::rest -> (
      match List.find_opt (fun x -> List.mem a (snd x)) fsa.next with
        None -> false
      | Some x -> check_included rest (fst x)
    )


(* -------------------------------------------------------------------------- *)

module StringMap = Map.Make(String)

type fsa = {
  vertices: bool StringMap.t;
  edges: (string * char) StringMap.t;
  state: string;
}

let ex8 (instr: char list) (infsa: fsa) =
  let rec helper_ex8 (i: char list) (ifsa: fsa) (current: string) =
    match i with
      [] -> (
        match StringMap.find_opt current ifsa.vertices with
          None -> false
        | Some b -> b
      )
    | a::rest -> (
        match StringMap.find_first_opt (fun _ -> true) (StringMap.filter (fun x (_, y) -> x = current && y = a) ifsa.edges) with
          None -> false
        | Some (_, (outedge, _)) -> helper_ex8 rest ifsa outedge
      )
  in helper_ex8 instr infsa infsa.state

type binary_tree =
    Node of binary_tree * binary_tree
  | Leaf of int

let ex9 b =
  let rec helper_ex9 b' n =
    match b' with
      Leaf a -> a + n
    | Node (r, l) -> (helper_ex9 r (helper_ex9 l n))
  in helper_ex9 b 0

(* -------------------------------------------------------------------------- *)