open Ast

exception FoundRedex of expr index

let check_redex (ast : expr ast) (i : expr index) : unit =
  match get_subexpr ast i with
  | App (f, _) -> (
      match get_subexpr ast f with
      | Lam (_, _) -> raise (FoundRedex i)
      | _ -> ())
  | Int _ -> ()
  | Lam (_, _) -> ()
  | Prim (Add, (l, r)) | Prim (Sub, (l, r)) | Prim (Mul, (l, r)) -> (
      match (get_subexpr ast l, get_subexpr ast r) with
      | Int _, Int _ -> raise (FoundRedex i)
      | _ -> ())
  | Var _ -> ()

let find_redex_cbv_in (ast : expr ast) : expr index -> unit =
  let rec loop (i : expr index) : unit =
    (match get_subexpr ast i with
    | App (f, x) ->
        loop f;
        loop x
    | Int _ -> ()
    | Lam (_, _) -> ()
    | Prim (Add, (l, r)) | Prim (Sub, (l, r)) | Prim (Mul, (l, r)) ->
        loop l;
        loop r
    | Var _ -> ());
    check_redex ast i
  in
  loop

let find_redex_cbn_in (ast : expr ast) : expr index -> unit =
  let rec loop (i : expr index) : unit =
    check_redex ast i;
    match get_subexpr ast i with
    | App (f, x) ->
        loop f;
        loop x
    | Int _ -> ()
    | Lam (_, _) -> ()
    | Prim (Add, (l, r)) | Prim (Sub, (l, r)) | Prim (Mul, (l, r)) ->
        loop l;
        loop r
    | Var _ -> ()
  in
  loop

let find_redex_cbv (ast : expr ast) : expr index option =
  try
    find_redex_cbv_in ast ast.root;
    None
  with FoundRedex i -> Some i

let find_redex_cbn (ast : expr ast) : expr index option =
  try
    find_redex_cbn_in ast ast.root;
    None
  with FoundRedex i -> Some i

exception NotARedex of expr ast

let reduce (ast : expr ast) (i : expr index) : expr ast =
  let fail () = raise (NotARedex { ast with root = i }) in
  let ast = copy ast in
  let must_int j = match get_subexpr ast j with Int n -> n | _ -> fail () in
  Arraylist.set ast.subexprs i.index
    (match get_subexpr ast i with
    | App (_f, _x) -> failwith "TODO"
    | Prim (Add, (l, r)) -> Int (must_int l + must_int r)
    | Prim (Sub, (l, r)) -> Int (must_int l - must_int r)
    | Prim (Mul, (l, r)) -> Int (must_int l * must_int r)
    | _ -> fail ());
  ast