(***********************************************************************)
(*                                                                     *)
(*                               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 ]
type 'hcons expr =
  | False | True
  | Or of 'hcons * 'hcons
  | And of 'hcons * 'hcons
  | Atom of (move * bool * State.t)

type 'hcons node = {
  pos : 'hcons expr;
  mutable neg : 'hcons;
  st : StateSet.t * StateSet.t;
  size: int; (* Todo check if this is needed *)
}

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)
      | Atom(d1, p1, s1), Atom(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)

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

type t = Node.t
let hash x = x.Node.key
let uid x = x.Node.id
let equal = Node.equal
let expr f = f.Node.node.pos
let st f = f.Node.node.st
let size f = f.Node.node.size
let compare f1 f2 = compare f1.Node.id  f2.Node.id
let prio f =
  match expr f with
    | True | False -> 10
    | Atom _ -> 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);
    | Atom(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
        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 s1 s2 size1 size2 =
  let nnode = Node.make { pos = neg; neg = (Obj.magic 0); st = s2; size = size2 } in
  let pnode = Node.make { pos = pos; neg = nnode ; st = s1; size = size1 } in
    (Node.node nnode).neg <- pnode; (* works because the neg field isn't taken into
                                       account for hashing ! *)
    pnode,nnode


let empty_pair = StateSet.empty, StateSet.empty
let true_,false_ = cons True False empty_pair empty_pair 0 0
let atom_ d p s =
  let si = StateSet.singleton s in
  let ss = match d with
    | `Left -> si, StateSet.empty
    | `Right -> StateSet.empty, si
  in fst (cons (Atom(d,p,s)) (Atom(d,not p,s)) ss ss 1 1)

let not_ f = f.Node.node.neg

let union_pair (l1,r1) (l2, r2) =
  StateSet.union l1 l2,
  StateSet.union r1 r2

let merge_states f1 f2 =
  let sp =
    union_pair (st f1) (st f2)
  and sn =
    union_pair (st (not_ f1)) (st (not_ f2))
  in
    sp,sn

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
    let psize = (size f1) + (size f2) in
    let nsize = (size (not_ f1)) + (size (not_ f2)) in
    let sp, sn = merge_states f1 f2 in
      fst (cons (Or(f1,f2)) (And(not_ f1, not_ f2)) sp sn psize nsize)


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


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


module Infix = struct
  let ( +| ) f1 f2 = or_ f1 f2

  let ( *& ) f1 f2 = and_ f1 f2

  let ( *+ ) d s = atom_ d true s
  let ( *- ) d s = atom_ d false s
end