bool.ml 40.5 KB
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let (<) : int -> int -> bool = (<)
let (>) : int -> int -> bool = (>)
let (=) : int -> int -> bool = (=)

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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 =
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    if ign == True then True 
    else if (pos == False) && (neg == False) then ign
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    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 =
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    if (a == False) then False else simpl_aux1 a [] l
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  and simpl_aux1 a accu = function
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    | [] -> 
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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 =
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    if a == b then a == False
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    else match (a,b) with
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      | True, a | a, True -> a == False
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      | 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 -> 
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	Serialize.Put.bool t true; Serialize.Put.bool t (b == True)
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    | 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 = Weak(*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 -> 
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	Serialize.Put.bool t true; Serialize.Put.bool t (b == One)
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    | 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

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

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  module V = SortedList.Make(X)

  type f = {
    pos: V.t;
    neg: V.t;
    subs: fset;
    mutable id: int  (* unique id for hash consing *)
  }
  and fset =
    | Empty
    | Leaf of f
    | Branch of int * int * fset * fset

  type t = PosF of f | NegF of f | PosV of X.t | NegV of X.t | Zero | One

  let id k = k.id

  module F = struct
    let empty = Empty
    let is_empty = function Empty -> true | _ -> false
    let singleton k = Leaf k
    let zero_bit k m = (k land m) == 0
    let rec mem k = function
      | Empty -> false
      | Leaf j -> k == j
      | Branch (_, m, l, r) -> mem k (if zero_bit (id k) m then l else r)
    let lowest_bit x = x land (-x)
    let branching_bit p0 p1 = lowest_bit (p0 lxor p1)
    let mask p m = p land (m-1)
    let join (p0,t0,p1,t1) = 
      let m = branching_bit p0 p1 in
      if zero_bit p0 m then Branch (mask p0 m, m, t0, t1)
      else Branch (mask p0 m, m, t1, t0)
    let match_prefix k p m = (mask k m) == p
    let add k t =
      let rec ins = function
	| Empty -> Leaf k
640
	| Leaf j as t -> if j == k then t else join (id k, Leaf k, id j, t)
641 642 643 644 645 646 647
	| Branch (p,m,t0,t1) as t ->
            if match_prefix (id k) p m then
              if zero_bit (id k) m then Branch (p, m, ins t0, t1)
              else Branch (p, m, t0, ins t1)
            else join (id k, Leaf k, p, t)
      in
      ins t
648
	
649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790
    let rec union s t = match s,t with
      | Empty, t  -> t
      | t, Empty  -> t
      | Leaf k, t -> add k t
      | t, Leaf k -> add k t
      | (Branch (p,m,s0,s1) as s), (Branch (q,n,t0,t1) as t) ->
	  if m == n && match_prefix q p m then 
	    Branch (p, m, union s0 t0, union s1 t1)
	  else if m < n && match_prefix q p m then
            if zero_bit q m then Branch (p, m, union s0 t, s1)
            else Branch (p, m, s0, union s1 t)
	  else if m > n && match_prefix p q n then
            if zero_bit p n then Branch (q, n, union s t0, t1)
            else Branch (q, n, t0, union s t1)
	  else join (p, s, q, t)
	    
    let rec subset s1 s2 = match s1,s2 with
      | Empty, _ -> true
      | _, Empty -> false
      | Leaf k1, _ -> mem k1 s2
      | Branch _, Leaf _ -> false
      | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
	  if m1 == m2 && p1 == p2 then subset l1 l2 && subset r1 r2
	  else if m1 > m2 && match_prefix p1 p2 m2 then
            if zero_bit p1 m2 then subset l1 l2 && subset r1 l2
            else subset l1 r2 && subset r1 r2
	  else
            false
	      
    let branch = function
      | (_,_,Empty,t) -> t
      | (_,_,t,Empty) -> t
      | (p,m,t0,t1)   -> Branch (p,m,t0,t1)
	  
    let rec remove k = function
      | Empty -> Empty
      | Leaf j as t -> if k == j then Empty else t
      | Branch (p,m,t0,t1) as t ->
          if match_prefix (id k) p m then 
	    if zero_bit (id k) m then branch (p, m, remove k t0, t1)
            else branch (p, m, t0, remove k t1)
          else t
	    
    let rec inter s1 s2 = match s1,s2 with
      | Empty, _ -> Empty
      | _, Empty -> Empty
      | Leaf k1, _ -> if mem k1 s2 then s1 else Empty
      | _, Leaf k2 -> if mem k2 s1 then s2 else Empty
      | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
	  if m1 == m2 && p1 == p2 then union (inter l1 l2) (inter r1 r2)
	  else if m1 < m2 && match_prefix p2 p1 m1 then
            inter (if zero_bit p2 m1 then l1 else r1) s2
	  else if m1 > m2 && match_prefix p1 p2 m2 then
            inter s1 (if zero_bit p1 m2 then l2 else r2)
	  else Empty
	    
    let rec split s1 s2 = match s1,s2 with
      | Empty, _ -> Empty,Empty,s2
      | _, Empty -> s1,Empty,Empty
      | Leaf k1, _ -> if mem k1 s2 then Empty,s1,(remove k1 s2) else s1,Empty,s2
      | _, Leaf k2 -> if mem k2 s1 then (remove k2 s1),s2,Empty else s1,Empty,s2
      | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
	  if m1 == m2 && p1 == p2 then 
	    let x1,x12,x2 = split l1 l2
	    and y1,y12,y2 = split r1 r2 in
	    union x1 y1, union x12 y12, union x2 y2
	  else if m1 < m2 && match_prefix p2 p1 m1 then
	    if zero_bit p2 m1 
	    then let x1,x12,x2 = split l1 s2 in union x1 r1, x12, x2
	    else let x1,x12,x2 = split r1 s2 in union l1 x1, x12, x2
	  else if m2 < m1 && match_prefix p1 p2 m1 then
	    if zero_bit p1 m2 
	    then let x1,x12,x2 = split l2 s1 in x1, x12, union x2 r2
	    else let x1,x12,x2 = split r1 s2 in x1, x12, union l2 x2
	  else (s1,Empty,s2)

    let rec diff s1 s2 = match s1,s2 with
      | Empty, _ -> Empty
      | _, Empty -> s1
      | Leaf k1, _ -> if mem k1 s2 then Empty else s1
      | _, Leaf k2 -> remove k2 s1
      | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
	  if m1 == m2 && p1 == p2 then union (diff l1 l2) (diff r1 r2)
	  else if m1 < m2 && match_prefix p2 p1 m1 then
            if zero_bit p2 m1 then union (diff l1 s2) r1
            else union l1 (diff r1 s2)
	  else if m1 > m2 && match_prefix p1 p2 m2 then
            if zero_bit p1 m2 then diff s1 l2 else diff s1 r2
	  else s1

    let rec intersect s1 s2 = match s1,s2 with
      | Empty, _ -> false
      | _, Empty -> false
      | Leaf k1, _ -> mem k1 s2
      | _, Leaf k2 -> mem k2 s1
      | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
	  if m1 == m2 && p1 == p2 then intersect l1 l2 || intersect r1 r2
	  else if m1 < m2 && match_prefix p2 p1 m1 then
            intersect (if zero_bit p2 m1 then l1 else r1) s2
	  else if m1 > m2 && match_prefix p1 p2 m2 then
            intersect s1 (if zero_bit p1 m2 then l2 else r2)
	  else false

    let disjoint s1 s2 = not (intersect s1 s2)

    let rec equal x y = x == y || match x,y with
      | Leaf k1, Leaf k2 -> k1 == k2
      | Branch (p1,m1,l1,r1), Branch (p2,m2,l2,r2) ->
          p1 == p2 && m1 == m2 && (equal l1 l2) && (equal r1 r2)
      | _ -> false

    let rec hash = function
      | Empty -> 0
      | Leaf k -> 1 + 3 * (id k)
      | Branch (p,m,l,r) -> 
	  2 + 3 * p + 257 * m + 16387 * (hash l) + 1048577 * (hash r)

    let rec iter f = function
      | Empty -> ()
      | Leaf k -> f k
      | Branch (_,_,t0,t1) -> iter f t0; iter f t1

    let rec fold f s accu = match s with
      | Empty -> accu
      | Leaf k -> f k accu
      | Branch (_,_,t0,t1) -> fold f t0 (fold f t1 accu)

    let rec card f s accu = match s with
      | Empty -> accu
      | Leaf k -> f k accu
      | Branch (_,_,t0,t1) -> fold f t0 (fold f t1 accu)

    let rec cardinal = function
      | Empty -> 0
      | Leaf _ -> 1
      | Branch (_,_,t0,t1) -> cardinal t0 + cardinal t1

  end



  let print_f px =
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    let rec aux ppf f =
      let first = ref true in
      let sep () = if !first then first := false else Format.fprintf ppf "|" in
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      V.iter (fun x -> sep (); Format.fprintf ppf "%a" px x) f.pos;
      V.iter (fun x -> sep (); Format.fprintf ppf "~%a" px x) f.neg;
      F.iter (fun f -> sep (); Format.fprintf ppf "~(@[%a@])" aux f) f.subs;
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      if !first then Format.fprintf ppf "."
    in
    fun ppf f -> (*allvars ppf f; *) aux ppf f

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  let print_t px ppf = function
    | PosV f -> Format.fprintf ppf "%a" px f
    | NegV f -> Format.fprintf ppf "~%a" px f
    | PosF f -> Format.fprintf ppf "%a" (print_f px) f
    | NegF f -> Format.fprintf ppf "~(%a)" (print_f px) f
    | Zero -> Format.fprintf ppf "0"
    | One -> Format.fprintf ppf "1"

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

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  let dump_vars ppf v =
    let first = ref true in
    let sep () = if !first then first := false else Format.fprintf ppf "|" in
    V.iter (fun x -> sep (); Format.fprintf ppf "%i" (X.hash x)) v
    
  let dump_subs ppf v =
    let first = ref true in
    let sep () = if !first then first := false else Format.fprintf ppf "|" in
    F.iter (fun f -> sep (); Format.fprintf ppf "#%i:%a" f.id dump f) v
    
822 823

(*
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  let rec form f =
    let rec aux1 accu = function
      | x::l -> aux1 (B.cup accu (B.atom x)) l
      | [] -> accu in
    let rec aux2 accu = function
      | x::l -> aux2 (B.cup accu (B.diff B.full (B.atom x))) l
      | [] -> accu in
    let accu = aux2 (aux1 B.empty f.pos) f.neg in
    F.fold (fun f accu -> B.cup accu (B.diff B.full (form f))) f.subs accu
833
      
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  let get f = match f.get with Some x -> x | None ->
    let r = B.get (form f) in
    f.get <- Some r;
    r
*)
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  (* Hash-consing *)
  module W = Weak.Make(
    struct
      type t = f
      let hash f = 
	(V.hash f.pos) 
	+ 257 * (V.hash f.neg) 
	+ 65537 * (F.hash f.subs)

      let equal f1 f2 =
	V.equal f1.pos f2.pos 
	&& V.equal f1.neg f2.neg 
	&& F.equal f1.subs f2.subs
    end
  )

  let tmpl = { pos = V.empty; neg = V.empty; subs = F.empty; id = 0 }

  let mk_f = let id = ref 0 and tbl = W.create 16387 in
  fun pos neg subs ->
860
    assert (V.length pos + V.length neg + F.cardinal subs >= 2);
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    let f = W.merge tbl { pos = pos; neg = neg; subs = subs; id = 0 } in
    if f.id = 0 then f.id <- (incr id; !id);
    f
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  let neg = function
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    | PosF x -> NegF x
    | NegF x -> PosF x
    | PosV x -> NegV x
    | NegV x -> PosV x
    | Zero -> One
    | One -> Zero

  let only_vars pos neg = match pos,neg with
    | [x],[] -> PosV x
    | [],[x] -> NegV x
    | [], [] -> Zero
    | _ -> PosF (mk_f pos neg Empty)

  let mk pos neg subs = match pos,neg,subs with
    | [],[],Empty  -> Zero
    | [x],[],Empty -> PosV x
    | [],[x],Empty -> NegV x
    | [],[],Leaf f -> NegF f
    | _ -> PosF (mk_f pos neg subs)

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  let trivially_disjoint f g =
    F.mem f g.subs || F.mem g f.subs ||
      not (V.disjoint f.pos g.neg) || not (V.disjoint f.neg g.pos)

  let cap_f f g =
    if trivially_disjoint f g then Zero
    else
      PosF 
	(mk_f (V.cup f.pos g.pos) (V.cup f.neg g.neg) (F.union f.subs g.subs))

  let diff_f f g =
    if trivially_disjoint f g then PosF f
    else
      PosF (mk_f f.pos f.neg (F.union (Leaf g) f.subs))

  let nor_f f g =
    (* TODO: factorize *)
    PosF (mk_f [] [] (F.union (Leaf f) (Leaf g)))

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  let cap t1 t2 = match t1,t2 with 
    | Zero, t | t, Zero -> Zero
    | One, t | t, One -> t
    | PosV x, PosV y -> 
	let c = X.compare x y in
	if c = 0 then t1 
	else PosF (mk_f (if c <0 then [x;y] else [y;x]) [] Empty)
    | NegV x, NegV y ->
	let c = X.compare x y in
	if c = 0 then t1 
	else PosF (mk_f [] (if c <0 then [x;y] else [y;x]) Empty)
    | PosV x, NegV y 
    | NegV y, PosV x -> if X.equal x y then Zero else PosF (mk_f [x] [y] Empty)
    | PosF f, PosF g -> cap_f f g
    | PosF f, NegF g
    | NegF g, PosF f -> diff_f f g
    | NegF f, NegF g -> nor_f f g
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    | (PosF f as t), PosV x | PosV x, (PosF f as t) -> 
	if V.mem f.pos x then t
	else if V.mem f.neg x then Zero
	else PosF (mk_f (V.add x f.pos) f.neg f.subs)
    | (PosF f as t), NegV x | NegV x, (PosF f as t) -> 
	if V.mem f.neg x then t
	else if V.mem f.pos x then Zero
	else PosF (mk_f f.pos (V.add x f.neg) f.subs)
    | (PosV x as t), NegF f | NegF f, (PosV x as t) ->
	if V.mem f.pos x then 
	  match mk (V.remove x f.pos) f.neg f.subs with
	    | PosF g -> PosF (mk_f [x] [] (Leaf g))
	    | NegF g -> PosF (mk_f (V.add x f.pos) f.neg f.subs)
	    | PosV y -> if X.equal x y then Zero else PosF (mk_f [x] [y] Empty)
	    | NegV y -> 	
		let c = X.compare x y in
		if c = 0 then t
		else PosF (mk_f (if c <0 then [x;y] else [y;x]) [] Empty)
	    | Zero | One -> assert false
	else if V.mem f.neg x then t
	else PosF (mk_f [x] [] (Leaf f))
    | (NegV x as t), NegF f | NegF f, (NegV x as t) ->
	if V.mem f.neg x then 
	  match mk f.pos (V.remove x f.neg) f.subs with
	    | PosF g -> PosF (mk_f [] [x] (Leaf g))
	    | NegF g -> PosF (mk_f f.pos (V.add x f.neg) f.subs)
	    | NegV y -> if X.equal x y then Zero else PosF (mk_f [y] [x] Empty)
	    | PosV y -> 	
		let c = X.compare x y in
		if c = 0 then t
		else PosF (mk_f [] (if c <0 then [x;y] else [y;x]) Empty)
	    | Zero | One -> assert false
	else if V.mem f.pos x then t
	else PosF (mk_f [] [x] (Leaf f))

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(*



		     PosF { tmpl with pos = [x]; neg = [y]; 
963
		   allvars = if c <0 then [x;y] else [y;x] }
964
	| PosV x, (PosF f as t)| (PosF f as t), PosV x ->
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	if V.mem f.pos x then t 
	else if V.mem f.neg x then One
	else if V.mem f.allvars x
	then zero_var_mk x (V.add x f.pos) f.neg f.subs
	else
	  PosF { tmpl with pos = V.add x f.pos; neg = f.neg;
	      allvars = V.add x f.allvars; subs = f.subs }
    | PosV x, NegF f | NegF f, PosV x ->
	if V.mem f.neg x then One
	else if V.mem f.allvars x 
	then match zero_var_mk x f.pos f.neg f.subs with
	  | NegF f -> PosF { tmpl with pos = V.add x f.pos; neg = f.neg;
			       allvars = V.add x f.allvars; subs = f.subs }
	  | PosF f -> PosF { tmpl with pos = [x];
			       allvars = V.add x f.allvars; subs = Leaf f }
	  | One -> PosV x
	  | Zero -> One
	  | PosV y -> 
	      PosF { tmpl with pos = [x]; neg = [y];
		       allvars = if X.compare x y <0 then [x;y] else [y;x] }
	  | NegV y -> 
	      let vs = if X.compare x y < 0 then [x;y] else [y;x] in
	      PosF { tmpl with pos = vs; allvars = vs }
	else PosF { tmpl with pos = V.add x f.pos; neg = f.neg;
		      allvars = V.add x f.allvars; subs = f.subs }
    | NegF x, _ -> assert false
    | PosF x, _ -> assert false
	
(*
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995 996
  (* Memoization *)
  type memo = { key1 : int array; key2 : int array; res  : f array }
997

998 999
  let new_memo n = { key1 = Array.create n (-1); key2 = Array.create n (-1);
		     res = Array.create n tmpl }
1000 1001 1002 1003 1004 1005 1006 1007

  let memo_cup = new_memo 16383

  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
1008
      let r = g f1 f2 in
1009 1010 1011 1012 1013 1014
      tbl.key1.(h) <- f1.id;
      tbl.key2.(h) <- f2.id;
      tbl.res.(h) <- r;
      r


1015 1016
  let empty = mk V.empty V.empty F.empty
  let full = mk V.empty V.empty (F.singleton empty)
1017

1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029
  let rec check f =
    F.iter 
      (fun g -> 
	 let n1 = V.length g.pos and n2 = V.length g.neg and n3 =
	   F.fold (fun _ x -> succ x) g.subs 0 in
	 if (n1 + n2 + n3 < 2) && f != full then
	   (Format.fprintf Format.std_formatter "BUG f=%a g=%a pos=%i neg=%i subs=%i@." dump f dump g n1 n2 n3; 
	    assert false);
	 check g;
	 assert(V.disjoint f.pos g.allvars);
	 assert(V.disjoint f.neg g.allvars)) f.subs;
    assert (V.disjoint f.pos f.neg)
1030

1031 1032
  let posvar x = mk (V.singleton x) V.empty F.empty
  let negvar x = mk V.empty (V.singleton x) F.empty
1033

1034 1035 1036 1037 1038
  let neg = function
    | { pos = [x]; neg = []; subs = Empty } -> negvar x
    | { pos = []; neg = [x]; subs = Empty } -> posvar x
    | { pos = []; neg = []; subs = Leaf f } -> f
    | f -> mk V.empty V.empty (F.singleton f)
1039

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(*
  let neg f =
    let r = neg f in
    Format.fprintf Format.std_formatter
      "NEG %a ===>%a@." dump f dump r; 
    check f; check r;
    r 
*)

  let trivially_disjoint f1 f2 =
    f1 == empty || f2 == empty || 
      match f1,f2 with
	| { pos=[x]; neg=[]; subs=Empty }, { pos=[]; neg=[y]; subs=Empty }
	| { pos=[]; neg=[x]; subs=Empty }, { pos=[y]; neg=[]; subs=Empty } ->
	    X.equal x y
	| { pos=[]; neg=[]; subs=Leaf f }, _ when f == f2 -> true
	| _, { pos=[]; neg=[]; subs=Leaf f } when f == f1 -> true
	| _ -> false
	    

  let rec mk_subs pos neg vpos vneg (spos:fset) (sneg:fset) subs =
    (* pos and neg cannot appears in subs *)
    (* invariant: pos <= vneg, neg <= vpos *)

    let loop = ref true and subs = ref subs and pos = ref pos and neg = ref neg and
	vpos = ref vpos and vneg = ref vneg and spos = ref spos and sneg = ref sneg
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    in

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    (* let check_inv () = 
       Format.fprintf Format.std_formatter
	"mk_subs pos=%a neg=%a vpos=%a vneg=%a spos=%a sneg=%a subs=%a:@."
	dump_vars !pos dump_vars !neg dump_vars !vpos dump_vars !vneg
	dump_subs !spos	dump_subs !sneg	dump_subs !subs;
      assert(V.disjoint !pos !neg); assert(V.subset !pos !vneg);
      assert(V.subset !neg !vpos); assert(V.disjoint !vpos !vneg);
      assert(F.disjoint !spos !sneg); assert(F.disjoint !spos !subs);
      assert(F.disjoint !sneg !subs) in check_inv (); *)

    (* OPT TODO: maintain (union subs spos) ? *)
    let aux f = 
      if F.mem f !sneg then raise Exit 
      else if F.mem f !spos then ()
      else let f' = filter_sub !vpos !vneg (F.union !subs !spos) !sneg f in
      if f == f' then ()
      else let () = subs := F.remove f !subs; spos := F.add f !spos in 
      if f' == empty then raise Exit
      else if f' == full then ()
      else loop := true; match f' with
	| { pos = []; neg = [v]; subs = Empty } -> 
	    pos := V.add v !pos; vneg := V.add v !vneg
	| { pos = [v]; neg = []; subs = Empty } -> 
	    neg := V.add v !neg; vpos := V.add v !vpos
	| { pos = []; neg = []; subs = Leaf f'' } ->
(*	    assert(F.disjoint f''.subs !spos); *)
	    subs := F.union f''.subs !subs;
	    pos := V.cup !pos f''.pos;
	    vneg := V.cup !vneg f''.pos;
	    neg := V.cup !neg f''.neg;
	    vpos := V.cup !vpos f''.neg;
	    sneg := F.add f'' !sneg;
	| _ ->
(*	    assert (not (F.mem f' !spos)); *)
	    subs := F.add f' !subs
1103
    in
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    if (try while !loop do loop := false; F.iter aux !subs done; false 
	with Exit -> true) then full
    else let f = mk !pos !neg !subs in
    if F.mem f !sneg then empty
    else if F.mem f !spos then full
    else f

      
  and filter_sub vpos vneg spos sneg f =
    if V.disjoint f.allvars vpos && V.disjoint f.allvars vneg &&
      F.disjoint f.allsubs spos && F.disjoint f.allsubs sneg
    then f
    else if not (V.disjoint vpos f.pos) || not (V.disjoint vneg f.neg)
      || F.intersect sneg f.subs then full
1118
    else
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      let pos = V.diff f.pos vneg in
      let neg = V.diff f.neg vpos in
      mk_subs pos neg (V.cup neg vpos) (V.cup pos vneg) spos sneg 
	(F.diff f.subs spos)

  let real_cup f1 f2 =
    let pos = V.cup f1.pos f2.pos in
    let neg = V.cup f1.neg f2.neg in
    let subs = F.union f1.subs f2.subs in
    mk_subs pos neg neg pos F.empty F.empty subs

  let trivially_subset f1 f2 =
    V.subset f1.pos f2.pos && V.subset f1.neg f2.neg && F.subset f1.subs f2.subs

  let trivially_cover f1 f2 =
    F.mem f1 f2.subs || F.mem f2 f2.subs 
    || not (V.disjoint f1.pos f2.neg)
    || not (V.disjoint f1.neg f2.pos)

  let no_overlap f1 f2 =
    V.disjoint f1.pos f2.pos && V.disjoint f1.neg f2.neg 
    && F.disjoint f1.subs f2.subs

  let remove_overlap f1 f2 = 
    let pos1 = V.diff f1.pos f2.pos in
    let neg1 = V.diff f1.neg f2.neg in
    let subs1 = F.diff f1.subs f2.subs in
    mk pos1 neg1 subs1

  let split_overlap f1 f2 =
    let pos1,pos,pos2 = V.split f1.pos f2.pos in
    let neg1,ne,neg2 = V.split f1.neg f2.neg in
    let sub1,sub,sub2 = F.split f1.subs f2.subs in
    let f1 = mk pos1 neg1 sub1 in
    let f2 = mk pos2 neg2 sub2 in
    let f  = mk pos  ne  sub in
    f1,f,f2

  let rec cup f1 f2 = 
    if (f1 == f2) then f1 else if (f1 == full) || (f2 == full)
    then full else if (f1 == empty) then f2 else if (f2 == empty) then f1 
    else match f1,f2 with
      | { pos=[];neg=[];subs=Leaf f1' }, { pos=[];neg=[];subs=Leaf f2' } -> 
	  if trivially_subset f1' f2' then f1
	  else if trivially_subset f2' f1' then f2
	  else if no_overlap f1' f2' 
	  then mk [] [] (F.union (F.singleton f1') (F.singleton f2'))
	  else 
	    let f1,f,f2 = split_overlap f1' f2' in
	    neg (cup f (cap f1 f2))
(* TODO: special cases with variables *)
      |  f1, ({ pos=[];neg=[];subs=Leaf f2 } as f0)
      | ({ pos=[];neg=[];subs=Leaf f2 } as f0), f1 ->
	  if f1 == f2 then full else
	    if trivially_cover f1 f2 then f1
	    else if trivially_subset f2 f1 then full
	    else if no_overlap f1 f2 then 
	      mk_subs f1.pos f1.neg f1.neg f1.pos F.empty F.empty (F.add f2 f1.subs)
	    else cup f1 (neg (remove_overlap f2 f1)) 
      | f1,f2 ->
	  if trivially_subset f1 f2 then f2
	  else if trivially_subset f2 f1 then f1
	  else if trivially_cover f1 f2 then full
	  else if f1.id < f2.id then memo_bin memo_cup real_cup f1 f2
	  else memo_bin memo_cup real_cup f2 f1

  and cap f1 f2 = neg (cup (neg f1) (neg f2))
(*
    if (f1 == f2) then f1 else if (f1 == empty) || (f2 == empty)
    then empty else if (f1 == full) then f2 else if (f2 == full) then f1 
    else match f1,f2 with
      | { pos=[x]; neg=[]; subs=Empty }, { pos=[y]; neg=[]; subs=Empty } ->
	  mk [] [] (Leaf (mk (if X.compare x y < 0 then [x;y] else [y;x]) [] Empty))
      | { pos=[x]; neg=[]; subs=Empty }, { pos=[]; neg=[y]; subs=Empty }
      | { pos=[]; neg=[y]; subs=Empty }, { pos=[x]; neg=[]; subs=Empty } ->
	  if X.equal x y then empty
	  else mk [] [] (Leaf (mk [x] [y] Empty))
      | ({ pos=[x]; neg=[]; subs=Empty } as fx), f
      | f, ({ pos=[x]; neg=[]; subs=Empty } as fx) ->
	  Format.fprintf Format.std_formatter
	    "%!!! %a AND %a ===> %b,%b,%b,%a@." dump f1 dump f2
	    (V.mem f.allvars x) (V.mem f.pos x ) (V.mem f.neg x)
	    dump (neg (mk_subs [x] [] [] [x] F.empty F.empty (Leaf f)));
	  if V.mem f.allvars x then
	    if V.mem f.pos x then fx
	    else if V.mem f.neg x then cap fx (mk f.pos (V.remove x f.neg) f.subs)
	    else neg (mk_subs [] [x] [x] [] F.empty F.empty (Leaf f))
	  else mk [] [] (Leaf (mk [] [x] (Leaf f)))
      | ({ pos=[]; neg=[x]; subs=Empty } as fx), f
      | f, ({ pos=[]; neg=[x]; subs=Empty } as fx) ->
	  if V.mem f.allvars x then
	    if V.mem f.neg x then fx
	    else if V.mem f.pos x then cap fx (mk (V.remove x f.pos) f.neg f.subs)
	    else neg (mk_subs [x] [] [] [x] F.empty F.empty (Leaf f))
	  else mk [] [] (Leaf (mk [x] [] (Leaf f)))

      | { pos=[];neg=[];subs=Leaf f1' }, { pos=[];neg=[];subs=Leaf f2' } -> 
	  if trivially_subset f1' f2' then f2
	  else if trivially_subset f2' f1' then f1
	  else if trivially_cover f1' f2' then empty
	  else if f1'.id < f2'.id then neg (memo_bin memo_cup real_cup f1' f2')
	  else neg (memo_bin memo_cup real_cup f2' f1')
      |  f1, ({ pos=[];neg=[];subs=Leaf f2 } as f0)
      | ({ pos=[];neg=[];subs=Leaf f2 } as f0), f1 ->
	  if f1 == f2 then empty else
	    if trivially_cover f1 f2 then f0
	    else if trivially_subset f1 f2 then empty
	    else if no_overlap f1 f2 then 
	      neg (mk_subs f2.pos f2.neg f2.neg f2.pos F.empty F.empty 
		     (F.add f1 f2.subs))
	    else cap (remove_overlap f1 f2) f0
      | f1,f2 ->
	  if trivially_subset f1 f2 then f1
	  else if trivially_subset f2 f1 then f2
	  else if no_overlap f1 f2
	  then mk [] [] (F.singleton 
			   (mk [] [] (F.union (F.singleton f1) (F.singleton f2))))
	  else 
	    let f1,f,f2 = split_overlap f1 f2 in
	    cup f (cap f1 f2)
*)
1240

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(*
  let cap f1 f2 =
    let r = cap f1 f2 in
    if (f1 != full) && (f2 != full) && ((f1.subs != Empty) || (f2.subs != Empty)) then
      Format.fprintf Format.std_formatter
	"%a AND %a ===>%a@." dump f1 dump f2 dump r;
    check r;
    r
*)	 
(*   
  let cup f1 f2 =
    let r = cup f1 f2 in
    if (f1 != empty) && (f1 != full) && (f2 != empty) && (f2 != full)
    then Format.fprintf Format.std_formatter
      "%a \\/ %a ===>%a@." dump f1 dump f2 dump r;
    check f1; check f2; check r;
    r 
*)
(*  let cap f1 f2 = 
    if (f1 == empty) || (f2 == empty) then empty
    else if f1 == f2 then f1
    else if trivially_subset f1 f2 then f1
    else if trivially_subset f2 f1 then f2
    else 
    neg (cup (neg f1) (neg f2)) *)

  let diff f1 f2 = neg (cup (neg f1) f2)
    
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1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284
    
(*
  let cap f1 f2 =
    let r = cap f1 f2 in
    Format.fprintf Format.std_formatter
      "%a /\\ %a ===>%a@." dump f1 dump f2 dump r;
    check f1; check f2; check r;
    r
  let diff f1 f2 =
    let r = diff f1 f2 in
    Format.fprintf Format.std_formatter
      "%a \\  %a ===>%a@." dump f1 dump f2 dump r;
    check f1; check f2; check r;
    r
*)
1285

1286
(*
1287
  let simplify f =
1288 1289 1290 1291 1292
    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))
1293
      else
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	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
1300
    with Not_found -> f
1301
*)
1302 1303 1304 1305

  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) *)
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(*
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  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)
*)

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  let rec iter g =
    let rec aux f =
      V.iter g f.pos;
      V.iter g f.neg;
      F.iter aux f.subs
    in
    aux

  let compute ~empty ~full ~cup ~cap ~diff ~atom =
    let rec aux f =
      let rec aux1 accu = function
	| x::l -> aux1 (cup accu (atom x)) l
	| [] -> accu in
      let rec aux2 accu = function
	| x::l -> aux2 (cup accu (diff full (atom x))) l
	| [] -> accu in
      let accu = aux2 (aux1 empty f.pos) f.neg in
      F.fold (fun f accu -> cup accu (diff full (aux f))) f.subs accu
    in aux
  (*    B.compute ~empty ~full ~cup ~cap ~diff ~atom (form f) *)
1333 1334

  let rec serialize s f =
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    V.serialize s f.pos;
    V.serialize s f.neg;
    Serialize.Put.list serialize s (F.fold (fun x accu -> x::accu) f.subs [])
1338 1339

  let rec deserialize s =
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    let pos = V.deserialize s in
    let neg = V.deserialize s in
1342
    let subs = Serialize.Get.list deserialize s in
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    let f = mk pos neg (List.fold_left (fun accu x -> F.add x accu) F.empty subs) in
(*    check f; *)
    f

  let atom = posvar

  type t = f
*)
1351
*)
1352 1353
end

1354