bool.ml 31.1 KB
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module type S =
sig
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  type elem
  include Custom.T
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  val get: t -> (elem list * elem list) list
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  val empty : t
  val full  : t
  val cup   : t -> t -> t
  val cap   : t -> t -> t
  val diff  : t -> t -> t
  val atom  : elem -> t
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  val iter: (elem-> unit) -> t -> unit
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  val compute: empty:'b -> full:'b -> cup:('b -> 'b -> 'b) 
    -> cap:('b -> 'b -> 'b) -> diff:('b -> 'b -> 'b) ->
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    atom:(elem -> 'b) -> t -> 'b
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(*
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  val print: string -> (Format.formatter -> elem -> unit) -> t ->
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    (Format.formatter -> unit) list
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*)
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  val trivially_disjoint: t -> t -> bool
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end

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module type MAKE = functor (X : Custom.T) -> S with type elem = X.t

module Make(X : Custom.T) =
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struct
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  type elem = X.t
  type t =
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    | True
    | False
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    | Split of int * elem * t * t * t
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  let rec equal a b =
    (a == b) ||
    match (a,b) with
      | Split (h1,x1, p1,i1,n1), Split (h2,x2, p2,i2,n2) ->
	  (h1 == h2) &&
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	  (equal p1 p2) && (equal i1 i2) &&
	  (equal n1 n2) && (X.equal x1 x2)
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      | _ -> false

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(* Idea: add a mutable "unique" identifier and set it to
   the minimum of the two when egality ... *)


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  let rec compare a b =
    if (a == b) then 0 
    else match (a,b) with
      | Split (h1,x1, p1,i1,n1), Split (h2,x2, p2,i2,n2) ->
	  if h1 < h2 then -1 else if h1 > h2 then 1 
	  else let c = X.compare x1 x2 in if c <> 0 then c
	  else let c = compare p1 p2 in if c <> 0 then c
	  else let c = compare i1 i2 in if c <> 0 then c 
	  else compare n1 n2
      | True,_  -> -1
      | _, True -> 1
      | False,_ -> -1
      | _,False -> 1
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  let rec hash = function
    | True -> 1
    | False -> 0
    | Split(h, _,_,_,_) -> h

  let compute_hash x p i n = 
	(X.hash x) + 17 * (hash p) + 257 * (hash i) + 16637 * (hash n)

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  let rec check = function
    | True | False -> ()
    | Split (h,x,p,i,n) ->
	assert (h = compute_hash x p i n);
	(match p with Split (_,y,_,_,_) -> assert (X.compare x y < 0) | _ -> ());
	(match i with Split (_,y,_,_,_) -> assert (X.compare x y < 0) | _ -> ());
	(match n with Split (_,y,_,_,_) -> assert (X.compare x y < 0) | _ -> ());
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	X.check x; check p; check i; check n
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  let atom x =
    let h = X.hash x + 17 in (* partial evaluation of compute_hash... *)
    Split (h, x,True,False,False)
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  let neg_atom x =
    let h = X.hash x + 16637 in (* partial evaluation of compute_hash... *)
    Split (h, x,False,False,True)
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  let rec iter f = function
    | Split (_, x, p,i,n) -> f x; iter f p; iter f i; iter f n
    | _ -> ()

  let rec dump ppf = function
    | True -> Format.fprintf ppf "+"
    | False -> Format.fprintf ppf "-"
    | Split (_,x, p,i,n) -> 
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	Format.fprintf ppf "%i(@[%a,%a,%a@])" 
	(* X.dump x *) (X.hash x) dump p dump i dump n
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  let rec print f ppf = function
    | True -> Format.fprintf ppf "Any"
    | False -> Format.fprintf ppf "Empty"
    | Split (_, x, p,i, n) ->
	let flag = ref false in
	let b () = if !flag then Format.fprintf ppf " | " else flag := true in
	(match p with 
	   | True -> b(); Format.fprintf ppf "%a" f x
	   | False -> ()
	   | _ -> b (); Format.fprintf ppf "%a & @[(%a)@]" f x (print f) p );
	(match i with 
	   | True -> assert false;
	   | False -> ()
	   | _ -> b(); print f ppf i);
	(match n with 
	   | True -> b (); Format.fprintf ppf "@[~%a@]" f x
	   | False -> ()
	   | _ -> b (); Format.fprintf ppf "@[~%a@] & @[(%a)@]" f x (print f) n)
	
  let print a f = function
    | True -> [ fun ppf -> Format.fprintf ppf "%s" a ]
    | False -> []
    | c -> [ fun ppf -> print f ppf c ]
	
	
  let rec get accu pos neg = function
    | True -> (pos,neg) :: accu
    | False -> accu
    | Split (_,x, p,i,n) ->
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	(*OPT: can avoid creating this list cell when pos or neg =False *)
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	let accu = get accu (x::pos) neg p in
	let accu = get accu pos (x::neg) n in
	let accu = get accu pos neg i in
	accu
	  
  let get x = get [] [] [] x
		
  let compute ~empty ~full ~cup ~cap ~diff ~atom b =
    let rec aux = function
      | True -> full
      | False -> empty
      | Split(_,x, p,i,n) ->
	  let p = cap (atom x) (aux p)
	  and i = aux i
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	  and n = diff (aux n) (atom x) in
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	  cup (cup p i) n
    in
    aux b
      
(* Invariant: correct hash value *)

  let split x pos ign neg =
    Split (compute_hash x pos ign neg, x, pos, ign, neg)

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  let empty = False
  let full = True
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(* Invariants:
     Split (x, pos,ign,neg) ==>  (ign <> True);   
     (pos <> False or neg <> False)
*)

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  let split x pos ign neg =
    if ign = True then True 
    else if (pos = False) && (neg = False) then ign
    else split x pos ign neg
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(* Invariant:
   - no ``subsumption'
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*)
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(*
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  let rec simplify a b =
    if equal a b then False 
    else match (a,b) with
      | False,_ | _, True -> False
      | a, False -> a
      | True, _ -> True
      | Split (_,x1,p1,i1,n1), Split (_,x2,p2,i2,n2) ->
	  let c = X.compare x1 x2 in
	  if c = 0 then
	    let p1' = simplify (simplify p1 i2) p2 
	    and i1' = simplify i1 i2
	    and n1' = simplify (simplify n1 i2) n2 in
	    if (p1 != p1') || (n1 != n1') || (i1 != i1') 
	    then split x1 p1' i1' n1'
	    else a
	  else if c > 0 then
	    simplify a i2
	  else
	    let p1' = simplify p1 b 
	    and i1' = simplify i1 b
	    and n1' = simplify n1 b in
	    if (p1 != p1') || (n1 != n1') || (i1 != i1') 
	    then split x1 p1' i1' n1'
	    else a
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*)


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  let rec simplify a l =
    if (a = False) then False else simpl_aux1 a [] l
  and simpl_aux1 a accu = function
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    | [] -> 
	if accu = [] then a else
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	  (match a with
	     | True -> True
	     | False -> assert false
	     | Split (_,x,p,i,n) -> simpl_aux2 x p i n [] [] [] accu)
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    | False :: l -> simpl_aux1 a accu l
    | True :: l -> False
    | b :: l -> if a == b then False else simpl_aux1 a (b::accu) l
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  and simpl_aux2 x p i n ap ai an = function
    | [] -> split x (simplify p ap) (simplify i ai) (simplify n an)
    | (Split (_,x2,p2,i2,n2) as b) :: l ->
	let c = X.compare x2 x in
	if c < 0 then 
	  simpl_aux3 x p i n ap ai an l i2
	else if c > 0 then 
	  simpl_aux2 x p i n (b :: ap) (b :: ai) (b :: an) l
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	else
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	  simpl_aux2 x p i n (p2 :: i2 :: ap) (i2 :: ai) (n2 :: i2 :: an) l
    | _ -> assert false
  and simpl_aux3 x p i n ap ai an l = function
    | False -> simpl_aux2 x p i n ap ai an l
    | True -> assert false
    | Split (_,x2,p2,i2,n2) as b ->
	let c = X.compare x2 x in
	if c < 0 then 
	  simpl_aux3 x p i n ap ai an l i2
	else if c > 0 then 
	  simpl_aux2 x p i n (b :: ap) (b :: ai) (b :: an) l
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	else
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	  simpl_aux2 x p i n (p2 :: i2 :: ap) (i2 :: ai) (n2 :: i2 :: an) l
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  let split x p i n = 
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    split x (simplify p [i]) i (simplify n [i])

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  let rec ( ++ ) a b =
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(*    if equal a b then a *)
    if a == b then a  
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    else match (a,b) with
      | True, _ | _, True -> True
      | False, a | a, False -> a
      | Split (_,x1, p1,i1,n1), Split (_,x2, p2,i2,n2) ->
	  let c = X.compare x1 x2 in
	  if c = 0 then
	    split x1 (p1 ++ p2) (i1 ++ i2) (n1 ++ n2)
	  else if c < 0 then
	    split x1 p1 (i1 ++ b) n1
	  else
	    split x2 p2 (i2 ++ a) n2

(* Pseudo-Invariant:
   - pos <> neg
*)

  let split x pos ign neg =
    if equal pos neg then (neg ++ ign) else split x pos ign neg

(* seems better not to make ++ and this split mutually recursive;
   is the invariant still inforced ? *)

  let rec ( ** ) a b =
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    (*    if equal a b then a *)
    if a == b then a
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    else match (a,b) with
      | True, a | a, True -> a
      | False, _ | _, False -> False
      | Split (_,x1, p1,i1,n1), Split (_,x2, p2,i2,n2) ->
	  let c = X.compare x1 x2 in
	  if c = 0 then
(*	    split x1 
	      (p1 ** (p2 ++ i2) ++ (p2 ** i1))
	      (i1 ** i2)
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	      (n1 ** (n2 ++ i2) ++ (n2 ** i1))  *)
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	    split x1 
	      ((p1 ++ i1) ** (p2 ++ i2))
	      False
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	      ((n1 ++ i1) ** (n2 ++ i2)) 
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	  else if c < 0 then
	    split x1 (p1 ** b) (i1 ** b) (n1 ** b)
	  else
	    split x2 (p2 ** a) (i2 ** a) (n2 ** a)

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  let rec trivially_disjoint a b =
    if a == b then a = False
    else match (a,b) with
      | True, a | a, True -> a = False
      | False, _ | _, False -> true
      | Split (_,x1, p1,i1,n1), Split (_,x2, p2,i2,n2) ->
	  let c = X.compare x1 x2 in
	  if c = 0 then
(* try expanding -> p1 p2; p1 i2; i1 p2; i1 i2 ... *)
	    trivially_disjoint (p1 ++ i1) (p2 ++ i2) &&
	    trivially_disjoint (n1 ++ i1) (n2 ++ i2)
	  else if c < 0 then
	    trivially_disjoint p1 b &&
	    trivially_disjoint i1 b &&
	    trivially_disjoint n1 b
	  else
	    trivially_disjoint p2 a &&
	    trivially_disjoint i2 a &&
	    trivially_disjoint n2 a

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  let rec neg = function
    | True -> False
    | False -> True
(*    | Split (_,x, p,i,False) -> split x False (neg (i ++ p)) (neg i)
    | Split (_,x, False,i,n) -> split x (neg i) (neg (i ++ n)) False 
    | Split (_,x, p,False,n) -> split x (neg p) (neg (p ++ n)) (neg n)  *)
    | Split (_,x, p,i,n) -> split x (neg (i ++ p)) False (neg (i ++ n))
	      
  let rec ( // ) a b =  
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(*    if equal a b then False  *)
    if a == b then False 
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    else match (a,b) with
      | False,_ | _, True -> False
      | a, False -> a
      | True, b -> neg b
      | Split (_,x1, p1,i1,n1), Split (_,x2, p2,i2,n2) ->
	  let c = X.compare x1 x2 in
	  if c = 0 then
	    split x1
	      ((p1 ++ i1) // (p2 ++ i2))
	      False
	      ((n1 ++ i1) // (n2 ++ i2))
	  else if c < 0 then
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	    split x1 (p1 // b) (i1 // b) (n1 // b) 
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(*	    split x1 ((p1 ++ i1)// b) False ((n1 ++i1) // b)  *)
	  else
	    split x2 (a // (i2 ++ p2)) False (a // (i2 ++ n2))
	      

  let cup = ( ++ )
  let cap = ( ** )
  let diff = ( // )

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 let rec serialize t = function
    | (True | False) as b -> 
	Serialize.Put.bool t true; Serialize.Put.bool t (b = True)
    | Split (_,x,p,i,n) ->
	Serialize.Put.bool t false;
	X.serialize t x;
	serialize t p;
	serialize t i;
	serialize t n

  let rec cap_atom x pos a = (* Assume that x does not appear in a *)
    match a with
      | False -> False
      | True -> if pos then atom x else neg_atom x
      | Split (_,y,p,i,n) ->
	  let c = X.compare x y in
	  assert (c <> 0);
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	  if (c < 0) then 
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	    if pos then split x a False False
	    else split x False False a
	  else split y (cap_atom x pos p) (cap_atom x pos i) (cap_atom x pos n)


    
  let rec deserialize t =
    if Serialize.Get.bool t then
      if Serialize.Get.bool t then True else False
    else
      let x = X.deserialize t in
      let p = deserialize t in
      let i = deserialize t in
      let n = deserialize t in
      (cap_atom x true p) ++ i ++ (cap_atom x false n)
      (* split x p i n is not ok, because order of keys might have changed! *)
  
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(*
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  let diff x y =
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    let d = diff x y in
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    Format.fprintf Format.std_formatter "X = %a@\nY = %a@\nX\\Z = %a@\n"
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      dump x dump y dump d;  
    d

  let cap x y =
    let d = cap x y in
    Format.fprintf Format.std_formatter "X = %a@\nY = %a@\nX**Z = %a@\n"
      dump x dump y dump d;  
    d
*)
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end
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module type S' = sig
  include S
  type bdd = False | True | Br of elem * t * t
  val br: t -> bdd
end
module MakeBdd(X : Custom.T) =
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struct
  type elem = X.t
  type t =
    | Zero
    | One
    | Branch of elem * t * t * int * t
  type node = t

  let neg = function
    | Zero -> One | One -> Zero
    | Branch (_,_,_,_,neg) -> neg

  let id = function
    | Zero -> 0
    | One -> 1
    | Branch (_,_,_,id,_) -> id

(* Internalization + detection of useless branching *)
  let max_id = ref 2 (* Must be >= 2 *)
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  module W = Myweak.Make(
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    struct
      type t = node
	  
      let hash = function
	| Zero | One -> assert false
	| Branch (v,yes,no,_,_) -> 
	    1 + 17*X.hash v + 257*(id yes) + 65537*(id no)

      let equal x y = (x == y) || match x,y with
	| Branch (v1,yes1,no1,id1,_), Branch (v2,yes2,no2,id2,_) ->
	    (id1 == 0 || id2 == 0) && X.equal v1 v2 && 
	      (yes1 == yes2) && (no1 == no2)
	| _ -> assert false
    end)
  let table = W.create 16383
  type branch = 
      { v : X.t; yes : node; no : node; mutable id : int; neg : branch }
  let mk v yes no =
    if yes == no then yes
    else
      let rec pos = Branch (v,yes,no,0,Branch (v,neg yes,neg no,0,pos)) in
      let x = W.merge table pos in
      let pos : branch = Obj.magic x in
      if (pos.id == 0) 
      then (let n = !max_id in
	    max_id := succ n;
	    pos.id <- n;
	    pos.neg.id <- (-n));
      x

  let atom v = mk v One Zero

  let dummy = Obj.magic (ref 0)
  let memo_size = 16383
  let memo_keys = Array.make memo_size (Obj.magic dummy)
  let memo_vals = Array.make memo_size (Obj.magic dummy)
  let memo_occ = Array.make memo_size 0

  let eg2 (x1,y1) (x2,y2) = x1 == x2 && y1 == y2
  let rec cup x1 x2 = if (x1 == x2) then x1 else match x1,x2 with
    | One, x | x, One -> One
    | Zero, x | x, Zero -> x
    | Branch (v1,yes1,no1,id1,neg1), Branch (v2,yes2,no2,id2,neg2) ->
	if (x1 == neg2) then One
	else
	  let k,h = 
	    if id1<id2 then (x1,x2),id1+65537*id2 else (x2,x1),id2+65537*id1 in
	  let h = (h land max_int) mod memo_size in
	  let i = memo_occ.(h) in
	  let k' = memo_keys.(h) in
	  if (k' != dummy) && (eg2 k k') 
	  then (memo_occ.(h) <- succ i; memo_vals.(h))
	  else 
	    let r = 
              let c = X.compare v1 v2 in
	      if (c = 0) then mk v1 (cup yes1 yes2) (cup no1 no2)
	      else if (c < 0) then mk v1 (cup yes1 x2) (cup no1 x2)
	      else mk v2 (cup yes2 x1) (cup no2 x1) in
	    if (i = 0) then (memo_keys.(h) <- k; memo_vals.(h) <- r;
			     memo_occ.(h) <- 1)
	    else memo_occ.(h) <- pred i;
	    r
  
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  let rec dump ppf = function
    | One -> Format.fprintf ppf "+"
    | Zero -> Format.fprintf ppf "-"
    | Branch (x,p,n,id,_) -> 
	Format.fprintf ppf "%i:%a(@[%a,%a@])" 
	  id
	  X.dump x dump p dump n

(*
  let cup x y =
    let d = cup x y in
    Format.fprintf Format.std_formatter "X = %a@\nY = %a@\nX+Z = %a@\n"
      dump x dump y dump d;  
    d
*)
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  let cap x1 x2 = neg (cup (neg x1) (neg x2))
  let diff x1 x2 = neg (cup (neg x1) x2)


  let rec iter f = function
    | Branch (x,p,n,_,_) -> f x; iter f p; iter f n
    | _ -> ()



  let rec print f ppf = function
    | One -> Format.fprintf ppf "Any"
    | Zero -> Format.fprintf ppf "Empty"
    | Branch (x,p,n,_,_) ->
	let flag = ref false in
	let b () = if !flag then Format.fprintf ppf " | " else flag := true in
	(match p with 
	   | One -> b(); Format.fprintf ppf "%a" f x
	   | Zero -> ()
	   | _ -> b (); Format.fprintf ppf "%a & @[(%a)@]" f x (print f) p );
	(match n with 
	   | One -> b (); Format.fprintf ppf "@[~%a@]" f x
	   | Zero -> ()
	   | _ -> b (); Format.fprintf ppf "@[~%a@] & @[(%a)@]" f x (print f) n)
	
  let print a f = function
    | One -> [ fun ppf -> Format.fprintf ppf "%s" a ]
    | Zero -> []
    | c -> [ fun ppf -> print f ppf c ]
	
  let rec get accu pos neg = function
    | One -> (pos,neg) :: accu
    | Zero -> accu
    | Branch (x,p,n,_,_) ->
	(*OPT: can avoid creating this list cell when pos or neg =False *)
	let accu = get accu (x::pos) neg p in
	let accu = get accu pos (x::neg) n in
	accu
	  
  let get x = get [] [] [] x
		
  let compute ~empty ~full ~cup ~cap ~diff ~atom b =
    let rec aux = function
      | One -> full
      | Zero -> empty
      | Branch(x,p,n,_,_) ->
	  let p = cap (atom x) (aux p)
	  and n = diff (aux n) (atom x) in
	  cup p n
    in
    aux b
      
  let empty = Zero
  let full = One

  let rec serialize t = function
    | (Zero | One) as b -> 
	Serialize.Put.bool t true; Serialize.Put.bool t (b = One)
    | Branch (x,p,n,_,_) ->
	Serialize.Put.bool t false;
	X.serialize t x;
	serialize t p;
	serialize t n

  let rec deserialize t =
    if Serialize.Get.bool t then
      if Serialize.Get.bool t then One else Zero
    else
      let x = X.deserialize t in
      let p = deserialize t in
      let n = deserialize t in

      let x = atom x in
      cup (cap x p) (cap (neg x) n)

      (* mk x p n is not ok, because order of keys might have changed!
	 OPT TODO: detect when this is ok *)

  let trivially_disjoint x y = neg x == y  
  let compare x y = compare (id x) (id y)
  let equal x y = x == y
  let hash x = id x
  let check x = ()
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  type bdd = False | True | Br of elem * t * t 
  let br = function
    | Zero -> False | One -> True | Branch (x,p,n,_,_) -> Br (x,p,n)
end

module Simplify(M : MAKE)(X : Custom.T) = struct
  module B = M(X)
  type elem = X.t

  type f = { vars: (X.t * bool) list; (* toplevel vars and their polarity *)
	     subs: f list; (* subformulas *)
	     allvars: (X.t * int * int) list; (* # of pos,neg occurences *)
	     mutable form: B.t option;
	     mutable id: int  (* unique id for hash consing *)
	   }
  type t = f

  let tmpl = { vars = []; subs = []; allvars = []; form = None; id = 0 }
	
  let print px =
    let allvars ppf f = 
      List.iter (fun (x,p,n) -> Format.fprintf ppf "[%a:%i,%i]" px x p n) 
	f.allvars
    in
    let rec aux ppf f =
(*      Format.fprintf ppf "{%i}" f.id; *)
(*      (match f.form with Some _ ->  Format.fprintf ppf "*" | _ -> ());  *)
(*      allvars ppf f; *)
      let first = ref true in
      let sep () = if !first then first := false else Format.fprintf ppf "|" in
      List.iter (function 
		   | (x,true) -> sep (); Format.fprintf ppf "%a" px x
		   | (x,false) -> sep (); Format.fprintf ppf "~%a" px x) f.vars;
      List.iter (fun f -> sep (); Format.fprintf ppf "~(@[%a@])" aux f) f.subs;
      if !first then Format.fprintf ppf "."
    in
    fun ppf f -> (*allvars ppf f; *) aux ppf f

  let dump = print (*X.dump*)
    (fun ppf i -> Format.fprintf ppf "%i" (X.hash i))

  let rec cup_vars vars1 vars2 = match (vars1,vars2) with
    | ((x1,p1,n1) as z1)::vars1', ((x2,p2,n2) as z2)::vars2' ->
	let c = X.compare x1 x2 in
	if c = 0 then (x1,p1+p2,n1+n2)::(cup_vars vars1' vars2')
	else if c < 0 then z1::(cup_vars vars1' vars2)
	else z2::(cup_vars vars1 vars2')
    | vars, [] | [], vars -> vars

  let occ (x1,x1v) = if x1v then (x1,1,0) else (x1,0,1)

  let rec cup_vars' vars1 vars2 = match (vars1,vars2) with
    | (x1,x1v)::vars1', (x2,p2,n2)::vars2' ->
	let c = X.compare x1 x2 in
	if c = 0 then assert false (* x1::(cup_vars' vars1' vars2') *)
	else if c < 0 then 
	  (if x1v then (x1,1,0) else (x1,0,1))::(cup_vars' vars1' vars2)
	else (x2,n2,p2)::(cup_vars' vars1 vars2')
    | vars, [] -> List.map occ vars
    | [], vars -> List.map (fun (x,p,n) -> (x,n,p)) vars

  let compute_allvars subs vars =
    cup_vars' vars 
      (List.fold_left (fun accu f -> cup_vars accu f.allvars) [] subs)


  let rec cap_vars vars1 vars2 = match (vars1,vars2) with
    | ((x1,xv1) as z1)::vars1', (x2,_,_)::vars2' ->
	let c = X.compare x1 x2 in
	if c = 0 then z1::(cap_vars vars1' vars2')
	else if c < 0 then cap_vars vars1' vars2
	else cap_vars vars1 vars2'
    | _ -> []

  let rec csubs s1 s2 = match s1,s2 with
    | f1::s1', f2::s2' ->
	if f1 == f2 then f1::(csubs s1' s2')
	else if f1.id < f2.id then f1::(csubs s1' s2)
	else f2::(csubs s1 s2')
    | [], [] -> []
    | s, [] | [], s -> s

  let print_vars v = 
    List.iter (fun (x,b) -> Printf.printf "[%i:%b]" (X.hash x) b) v;
    print_newline ()


  module H = struct
    type t = f
    let rec hash_vars accu = function
      | (x,v)::r -> 
	  hash_vars (65537 * accu + 257 * X.hash x + (if v then 1 else 0)) r
      | [] -> accu

    let rec hash_subs accu = function
      | f::r -> hash_subs (257 * accu + f.id) r
      | [] -> accu

    let hash f = hash_vars (hash_subs 1 f.subs) f.vars

(*
    let rec equal_vars vars1 vars2 = vars1 == vars2 || match vars1,vars2 with
      | (x1,xv1)::(x1',xv1')::vars1,(x2,xv2)::(x2',xv2')::vars2 ->
	 xv1 == xv2 && xv1' == xv2' && X.equal x1 x2 && 
	   X.equal x1' x2' && equal_vars vars1 vars2
      | [(x1,xv1)],[(x2,xv2)] ->
	 xv1 == xv2 &&  X.equal x1 x2
      | _ -> false *)

    let rec equal_vars vars1 vars2 = vars1 == vars2 || match vars1,vars2 with
      | (x1,xv1)::vars1,(x2,xv2)::vars2 ->
	 xv1 == xv2 && X.equal x1 x2 && equal_vars vars1 vars2
      | _ -> false

    let rec equal_subs s1 s2 = s1 == s2 || match s1,s2 with
      | f1::s1, f2::s2 -> f1 == f2 && equal_subs s1 s2
      | _ -> false

    let equal f1 f2 =
      (f1 == f2) || ((f1.id = 0 || f2.id = 0) &&
		       equal_vars f1.vars f2.vars &&
		       equal_subs f1.subs f2.subs)
  end
  module W = Myweak.Make(H)

  let mk =
    let tbl = W.create 16387 in
    let id = ref 0 in
    fun f ->
      if (f.id != 0) then f 
      else
	let f = W.merge tbl f in
	if (f.id = 0) then f.id <- (incr id; !id);
	f
      
  let empty = mk { tmpl with subs = [] }
  let full = mk { tmpl with subs = [ empty ] }

  let check f = ()

  let posvar x = mk { tmpl with vars = [x,true]; allvars = [x,1,0] }
  let negvar x = mk { tmpl with vars = [x,false]; allvars = [x,0,1] }

  let neg = function
    | { vars = [x,true]; subs = [] } -> negvar x
    | { vars = [x,false]; subs = [] } -> posvar x
    | { vars = []; subs = [ f ] } -> f
    | f -> mk { tmpl with
		allvars = List.map (fun (x,p,n) -> (x,n,p)) f.allvars; 
		subs = [ f ] }

  let has_complement f1 f2 = List.memq f2 f1.subs

  let is_complement f1 f2 =
    match f1 with
      | { vars = []; subs = [f] } -> f == f2
      | _ -> match f2 with
	  | { vars = []; subs = [f] } -> f == f1
	  | _ -> false

  exception One

  type memo = { key1 : int array;
		key2 : int array;
		res  : t array }

  let new_memo n = { key1 = Array.create n (-1);
		     key2 = Array.create n (-1);
		     res = Array.create n empty }

  let memo_cup = new_memo 16383
  let memo_cap = new_memo 16383

  let filrat tbl =
    let o = ref 0 in
    Array.iter (fun i -> if i >= 0 then incr o) tbl.key1;
    !o
    
  let memo_bin tbl g f1 f2 =
    let h = ((f1.id + 1027 * f2.id) land max_int) mod (Array.length tbl.res) in
    if (tbl.key1.(h) == f1.id) && (tbl.key2.(h) == f2.id) then
      tbl.res.(h)
    else
      let r = g (f1,f2) in
      tbl.key1.(h) <- f1.id;
      tbl.key2.(h) <- f2.id;
      tbl.res.(h) <- r;
      r


  let rec cvars vars1 vars2 = match (vars1,vars2) with
    | ((x1,xv1) as z1)::vars1', ((x2,xv2) as z2)::vars2' ->
	let c = X.compare x1 x2 in
	if c = 0 then 
	  if xv1 == xv2 then z1::(cvars vars1' vars2') else raise One
	else if c < 0 then z1::(cvars vars1' vars2)
	else z2::(cvars vars1 vars2')
    | vars,[] | [],vars -> vars

  let mk_vs vars subs =
    mk { tmpl with 
	   vars = vars; allvars = compute_allvars subs vars;
	   subs = subs }

  let rec split_vars vars1 vars2 = match vars1,vars2 with
    | ((x1,xv1) as z1)::vars1', ((x2,xv2) as z2)::vars2' ->
	let c = X.compare x1 x2 in
	if c = 0 then
	  let (vars1,common,vars2) = split_vars vars1' vars2' in
	  if xv1 == xv2 then (vars1,z1::common,vars2)
	  else (z1::vars1,common,z2::vars2)
	else if c < 0 then
	  let (vars1,common,vars2) = split_vars vars1' vars2 in
	  z1::vars1,common,vars2
	else
	  let (vars1,common,vars2) = split_vars vars1 vars2' in
	  vars1,common,z2::vars2
    | vars1,vars2 -> vars1,[],vars2
  let rec split_subs s1 s2 = match s1,s2 with
    | f1::s1',f2::s2' ->
	if f1 == f2 then	  
	  let (s1,common,s2) = split_subs s1' s2' in (s1,f1::common,s2)
	else if f1.id < f2.id then
	  let (s1,common,s2) = split_subs s1' s2 in f1::s1,common,s2
	else
	  let (s1,common,s2) = split_subs s1 s2' in s1,common,f2::s2
    | s1,s2 -> s1,[],s2

  let order_subs subs =
    let rec clean = function
      | f1::(f2::_ as z) -> if f1 == f2 then clean z else f1::(clean z)
      | z -> z
    in
    clean (List.sort (fun f1 f2 -> f1.id - f2.id) subs)

  let rec remove_complement f c =
    let rec aux = function
      | c'::r -> if (c == c') then r else c'::(aux r)
      | _ -> assert false
    in
    vars_subs f.vars (aux f.subs)

  and simplify_subs subs =
    (* TODO: avoid quadratic behavior by pre-detecting collisions in one pass *)
    let rec aux f1 = function
      | [] -> [f1]
      | f2::s ->
	  let (vars1,vars,vars2) = split_vars f1.vars f2.vars in
	  let (subs1,subs,subs2) = split_subs f1.subs f2.subs in
	  if vars = [] && subs = [] then 
	    if has_complement f2 f1 then (remove_complement f2 f1)::(aux f1 s)
	    else if has_complement f1 f2 then f2::(aux (remove_complement f1 f2) s)
	    else f2::(aux f1 s)
	  else (
	    let f1' = mk_vs vars1 subs1 in
	    let f2' = mk_vs vars2 subs2 in
	    let f   = mk_vs vars subs in
	    let f' = cup f (cap f1' f2') in
(*	    Format.fprintf Format.std_formatter
	      "MERGE %a+%a==>%a@." dump f1 dump f2 dump f'; *)
	    if f' == full then s
	    else aux f' s)
    in
    if subs = [] then [] else
      let subs = List.fold_left (fun accu f -> aux f accu) [] subs in
      order_subs subs

  and vars_subs vars subs =
    let subs = simplify_subs subs in

    let extra = ref [] in
    let rec aux = function
      | [] -> []
      | { vars = [x,v]; subs = [] } :: s -> extra:=(x, not v)::!extra; aux s
      | f :: s -> f :: (aux s) in
    let subs = aux subs in
    let rec aux = function
      | ((x1,v1) as z)::((x2,v2)::_ as r) -> 
	  if X.equal x1 x2 then if v1 == v2 then aux r else raise One
	  else z::(aux r)
      | r -> r in
    let extra = 
      aux (List.sort (fun (x1,_) (x2,_) -> X.compare x1 x2) !extra) in
    let vars = cvars vars extra
    and subs = elim_subs_opt (List.map (fun (x,v) -> (x,not v)) extra) subs 
    in

    let hoist = ref [] in
    let rec aux = function
      | [] -> []
      | { vars = []; subs = [ f ] } :: s -> hoist := f :: !hoist; aux s
      | f :: s -> f :: (aux s) in
    let subs = aux subs in

    let f = mk_vs vars subs in
    List.fold_left cup f !hoist

  and elim_real elv f =
    let vars = cap_vars elv f.allvars in
    if vars = [] then f
    else (
      let el = ref [] in
      let rec evars vars1 vars2 = match (vars1,vars2) with
	| ((x1,xv1) as z1)::vars1', ((x2,xv2) as z2)::vars2' ->
	    let c = X.compare x1 x2 in
	    if c = 0 then 
	      if xv1 == xv2 then raise One else evars vars1' vars2' 
	    else if c < 0 then z1::(evars vars1' vars2)
	    else (el := z2::!el; evars vars1 vars2')
	| vars1, [] -> el := List.rev !el; vars1
	| [], vars2 -> el := List.rev_append !el vars2; []
      in
      try
	let vars = evars f.vars elv in
	let subs = elim_subs_opt !el f.subs in
	vars_subs vars subs
      with One -> full
    )

  and elim elv f =
    let f' = elim_real elv f in
(*    print_string "elim vars="; print_vars elv;
    Format.fprintf Format.std_formatter "<= %a@." dump f;
    Format.fprintf Format.std_formatter "=> %a@." dump f'; *)
    f'

  and elim_subs_opt el subs =
    if el = [] then subs else order_subs (elim_subs el subs)

  and elim_subs vars = function
    | [] -> []
    | f::s ->
	let f = elim vars f in
	if f == empty then raise One
	else if f == full then elim_subs vars s
	else f :: (elim_subs vars s)


  and cup f1 f2 =
    if (f1 == f2) then f1
    else if (f1 == empty) then f2
    else if (f2 == empty) then f1
    else if (f1 == full) || (f2 == full) || (has_complement f1 f2) 
      || (has_complement f2 f1) then full
    else memo_bin memo_cup real_cup f1 f2

  and real_cup (f1,f2) =
    let elim1 = ref [] and elim2 = ref [] in
    let rec cvars vars1 vars2 = match (vars1,vars2) with
      | ((x1,xv1) as z1)::vars1', ((x2,xv2) as z2)::vars2' ->
	  let c = X.compare x1 x2 in
	  if c = 0 then 
	    if xv1 == xv2 then z1::(cvars vars1' vars2') else raise One
	  else if c < 0 then (elim2 := (x1, not xv1)::!elim2; 
			      z1::(cvars vars1' vars2))
	  else (elim1 := (x2,not xv2)::!elim1; z2::(cvars vars1 vars2'))
      | vars, [] -> List.iter (fun (x,v) -> elim2 := (x,not v) :: !elim2) vars; vars
      | [], vars -> List.iter (fun (x,v) -> elim1 := (x,not v) :: !elim1) vars; vars
    in
    try
      let vars = cvars f1.vars f2.vars in
      let elim1 = cap_vars (List.rev !elim1) f1.allvars in
      let subs1 = elim_subs_opt elim1 f1.subs in
      let elim2 = cap_vars (List.rev !elim2) f2.allvars in
      let subs2 = elim_subs_opt elim2 f2.subs in
      let subs = csubs subs1 subs2 in
      vars_subs vars subs
    with One -> full



  and real_cap (f1,f2) = 
    let (vars1,vars,vars2) = split_vars f1.vars f2.vars in
    let (subs1,subs,subs2) = split_subs f1.subs f2.subs in
    if vars = [] && subs = [] then
      neg (cup (neg f1) (neg f2))
    else
      let f1 = mk_vs vars1 subs1 in
      let f2 = mk_vs vars2 subs2 in
      let f  = mk_vs vars subs in
(*      print_int (List.length vars); print_char ':';
      print_int (List.length subs); print_char ' '; *)
      cup f (cap f1 f2)

  and cap t1 t2 =     
    if t1 == t2 then t1
    else if t1 == empty || t2 == empty then empty
    else if t1 == full then t2 else if t2 == full then t1 
    else if is_complement t1 t2 then empty
    else memo_bin memo_cap real_cap t1 t2

  let rec diff t1 t2 = 
    if t1 == t2 then empty
    else if t2 == empty then t1 else if t2 == full then empty
    else if is_complement t1 t2 then t1
    else real_diff t1 t2

  and real_diff f1 f2 =
    (* Need only to compute vars1,subs1 *)
    let (vars1,vars,vars2) = split_vars f1.vars f2.vars in
    let (subs1,subs,subs2) = split_subs f1.subs f2.subs in
    if vars = [] && subs = [] then
      neg (cup (neg f1) f2)
    else
      let f1 = mk_vs vars1 subs1 in
(*      print_int (List.length vars); print_char '!';
      print_int (List.length subs); print_char ' '; *)
      diff f1 f2


  let find_max f l =
    let aux m z = if f m z < 0 then z else m in
    match l with [] -> raise Not_found | m::z -> List.fold_left aux m z

  let simplify f =
    try
      let (x,p,n) = 
	find_max
	  (fun (x1,p1,n1) (x2,p2,n2) ->
	     Pervasives.compare (p1+n1) (p2+n2))
	  f.allvars in
(*      Printf.printf "x=%i;  p=%i,n=%i\n"  (X.hash x) p n;  *)
      if (p + n) > 2 then (
	let g =
	  if (n = 0) then
	    cup (elim [x,false] f) (cap (posvar x) (elim [x,true] f))
	  else if (p = 0) then
	    cup (elim [x,true] f) (cap (negvar x) (elim [x,false] f))
	  else
	    cup (cap (negvar x) (elim [x,false] f)) 
	      (cap (posvar x) (elim [x,true] f))
	in
	Format.fprintf Format.std_formatter
	  "Simplify %a ==> %a@." dump f dump g;
	g
      )
      else
	f
    with Not_found -> f
  let elim_simplify e f =
    simplify (elim e f)

(* TODO: cache neg of form as well ? *)
  let rec form f =
(*    print_char '*'; flush stdout; *)
    match f.form with
      | Some x -> x
      | None -> 
	  (* TODO: simplify before computing ? *)
	  let accu = 
	    List.fold_left
	      (fun accu (x,v) -> 
		 B.cup accu (if v then B.atom x else B.diff B.full (B.atom x)))
	      B.empty
	      f.vars in 
	  let accu =
	    List.fold_left (fun accu s -> B.cup accu (B.diff B.full (form s))) 
	      accu f.subs in
(*	  Format.fprintf Format.std_formatter "FORM: %a ==> %a@." dump f B.dump accu; *)
	  f.form <- Some accu;
	  accu

  let atom x = posvar x
	  
  let trivially_disjoint f1 f2 =
    (f1 == empty) || (f2 == empty) 
    || is_complement f1 f2

(*
  let hash f = f.id (* B.hash (form f) *)
  let equal f1 f2 = (f1 == f2) (* || B.equal (form f1) (form f2) *)
  let compare f1 f2 = f1.id - f2.id (* B.compare (form f1) (form f2) *)
*)
  let hash f = B.hash (form f)
  let equal f1 f2 = (f1 == f2) || B.equal (form f1) (form f2)
  let compare f1 f2 = B.compare (form f1) (form f2)

  let iter g f = B.iter g (form f)

  let compute ~empty ~full ~cup ~cap ~diff ~atom f =
(*
  let rec aux f = 
      let accu = 
	List.fold_left
	  (fun accu (x,v) -> 
	     cup accu (if v then atom x else diff full (atom x)))
	  empty
	  f.vars in 
      let accu =
	List.fold_left (fun accu s -> cup accu (diff full (aux s))) 
	  accu f.subs in
      accu
    in
    aux f
*)
    B.compute ~empty ~full ~cup ~cap ~diff ~atom (form f)

  let get f = 
    B.get (form (simplify f))


  module V = Custom.List(Custom.Pair(X)(Custom.Bool))
  let rec serialize s f =
    V.serialize s f.vars;
    Serialize.Put.list serialize s f.subs

  let rec deserialize s =
    let vars = V.deserialize s in
    let vars = List.sort (fun (x1,v1) (x2,v2) -> X.compare x1 x2) vars in
    let subs = Serialize.Get.list deserialize s in
    let subs = List.sort (fun f1 f2 -> f1.id - f2.id) subs in
    mk_vs vars subs
   
1104
end