(***********************************************************************)
(*                                                                     *)
(*                               TAToo                                 *)
(*                                                                     *)
(*                     Kim Nguyen, LRI UMR8623                         *)
(*                   Université Paris-Sud & CNRS                       *)
(*                                                                     *)
(*  Copyright 2010-2012 Université Paris-Sud and Centre National de la *)
(*  Recherche Scientifique. All rights reserved.  This file is         *)
(*  distributed under the terms of the GNU Lesser General Public       *)
(*  License, with the special exception on linking described in file   *)
(*  ../LICENSE.                                                        *)
(*                                                                     *)
(***********************************************************************)
INCLUDE "utils.ml"

open Format
type move = [ `Left | `Right | `Epsilon | `Up1 | `Up2 ]
type 'formula expr =
  | False
  | True
  | Or of 'formula * 'formula
  | And of 'formula * 'formula
  | Move of move * bool * State.t

type 'hcons node = {
  pos : 'hcons expr;
  mutable neg : 'hcons;
}

external hash_const_variant : [> ] -> int = "%identity"
external vb : bool -> int = "%identity"

module rec Node : Hcons.S
  with type data = Data.t = Hcons.Make (Data)
  and Data : Hashtbl.HashedType  with type t = Node.t node =
  struct
    type t =  Node.t node
    let equal x y = (*x.size == y.size &&*)
      match x.pos, y.pos with
      | a,b when a == b -> true
      | Or(xf1, xf2), Or(yf1, yf2)
      | And(xf1, xf2), And(yf1,yf2)  -> (xf1 == yf1) && (xf2 == yf2)
      | Move(d1, p1, s1), Move(d2 ,p2 ,s2) -> d1 == d2 && p1 == p2 && s1 == s2
      | _ -> false

    let hash f =
      match f.pos with
      | False -> 0
      | True -> 1
      | Or (f1, f2) ->
        HASHINT3 (PRIME1, Uid.to_int f1.Node.id, Uid.to_int f2.Node.id)
      | And (f1, f2) ->
        HASHINT3(PRIME3, Uid.to_int f1.Node.id, Uid.to_int f2.Node.id)

      | Move(d, p, s) -> HASHINT4(PRIME5, hash_const_variant d,vb p,s)
  end

type t = Node.t
let hash x = x.Node.hash
let uid x = x.Node.id
let equal = Node.equal
let expr f = f.Node.node.pos

let compare f1 f2 = compare f1.Node.id  f2.Node.id
let prio f =
  match expr f with
    | True | False -> 10
    | Move _ -> 8
    | And _ -> 6
    | Or _ -> 1

let rec print ?(parent=false) ppf f =
  if parent then fprintf ppf "(";
  let _ = match expr f with
    | True -> fprintf ppf "%s" Pretty.top
    | False -> fprintf ppf "%s" Pretty.bottom
    | And(f1,f2) ->
      print ~parent:(prio f > prio f1) ppf f1;
      fprintf ppf " %s "  Pretty.wedge;
      print ~parent:(prio f > prio f2) ppf f2;
    | Or(f1,f2) ->
      (print ppf f1);
      fprintf ppf " %s " Pretty.vee;
      (print ppf f2);
    | Move(dir, b, s) ->
      let _ = flush_str_formatter() in
      let fmt = str_formatter in
        let a_str, d_str =
          match  dir with
          | `Left ->  Pretty.down_arrow, Pretty.subscript 1
          | `Right -> Pretty.down_arrow, Pretty.subscript 2
          | `Epsilon -> Pretty.epsilon, ""
          | `Up1 -> Pretty.up_arrow, Pretty.subscript 1
          | `Up2 -> Pretty.up_arrow, Pretty.subscript 2
        in
        fprintf fmt "%s%s" a_str d_str;
        State.print fmt s;
        let str = flush_str_formatter() in
        if b then fprintf ppf "%s" str
        else Pretty.pp_overline ppf str
  in
    if parent then fprintf ppf ")"

let print ppf f =  print ~parent:false ppf f

let is_true f = (expr f) == True
let is_false f = (expr f) == False


let cons pos neg =
  let nnode = Node.make { pos = neg; neg = (Obj.magic 0); } in
  let pnode = Node.make { pos = pos; neg = nnode } in
    (Node.node nnode).neg <- pnode; (* works because the neg field isn't taken into
                                       account for hashing ! *)
    pnode,nnode


let true_,false_ = cons True False
let atom_ d p s =
  fst (cons (Move(d,p,s)) (Move(d,not p,s)))

let not_ f = f.Node.node.neg


let order f1 f2 = if uid f1  < uid f2 then f2,f1 else f1,f2

let or_ f1 f2 =
  (* Tautologies: x|x, x|not(x) *)

  if equal f1 f2 then f1
  else if equal f1 (not_ f2) then true_

  (* simplification *)
  else if is_true f1 || is_true f2 then true_
  else if is_false f1 && is_false f2 then false_
  else if is_false f1 then f2
  else if is_false f2 then f1

  (* commutativity of | *)
  else
    let f1, f2 = order f1 f2 in
      fst (cons (Or(f1,f2)) (And(not_ f1, not_ f2)))


let and_ f1 f2 =
  not_ (or_ (not_ f1) (not_ f2))


let of_bool = function true -> true_ | false -> false_