open Ast

let or_else (type a) (l : a option) (r : a option Lazy.t) : a option =
  match l with Some x -> Some x | None -> Lazy.force r

let is_redex (ast : expr ast) (i : expr index) : bool =
  match get_subexpr ast i with
  | App (f, _) -> (
      match get_subexpr ast f with Lam (_, _) -> true | _ -> false)
  | Int _ -> false
  | Lam (_, _) -> false
  | Prim (Add, (l, r)) | Prim (Sub, (l, r)) | Prim (Mul, (l, r)) -> (
      match (get_subexpr ast l, get_subexpr ast r) with
      | Int _, Int _ -> true
      | _ -> false)
  | Var _ -> false

let find_redex_cbv_in (_ast : expr ast) (_i : expr index) : expr index option =
  None

let find_redex_cbn_in (ast : expr ast) : expr index -> expr index option =
  let rec loop (i : expr index) : expr index option =
    if is_redex ast i then Some i
    else
      match get_subexpr ast i with
      | App (f, x) -> or_else (loop f) (lazy (loop x))
      | Int _ -> None
      | Lam (_, _) -> None
      | Prim (Add, (l, r)) | Prim (Sub, (l, r)) | Prim (Mul, (l, r)) ->
          or_else (loop l) (lazy (loop r))
      | Var _ -> None
  in
  loop

let find_redex_cbv (ast : expr ast) : expr index option =
  find_redex_cbv_in ast ast.root

let find_redex_cbn (ast : expr ast) : expr index option =
  find_redex_cbn_in ast ast.root

let reduce (ast : expr ast) (_i : expr index) : expr ast =
  let ast = copy ast in
  ast