boolVar.ml 15.1 KB
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let (<) : int -> int -> bool = (<)
let (>) : int -> int -> bool = (>)
let (=) : int -> int -> bool = (=)

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(* this is the the of the Constructor container *)
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module type E = sig
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  type elem
  include Custom.T

  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

end

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module type S = sig
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  type s
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  type elem = s Var.pairvar
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  type 'a bdd =
    [ `True
    | `False
    | `Split of int * 'a * ('a bdd) * ('a bdd) * ('a bdd) ]

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  include Custom.T with type t = elem bdd
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  (* returns the union of all leaves in the BDD *)
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  val leafconj: t -> s
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  val get: t -> (elem list * elem list) list
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  val empty : t
  val full  : t
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  (* same as full, but we keep it for the moment to avoid chaging 
   * the code everywhere *)
  val any  : t
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  val cup   : t -> t -> t
  val cap   : t -> t -> t
  val diff  : t -> t -> t
  val atom  : elem -> t
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  val neg_atom  : elem -> t
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  (* vars a : return a bdd that is ( Any ^ Var a ) *)
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  val vars  : Var.var -> t
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  val iter: (elem-> unit) -> t -> unit

  val compute: empty:'b -> full:'b -> cup:('b -> 'b -> 'b) 
    -> cap:('b -> 'b -> 'b) -> diff:('b -> 'b -> 'b) ->
    atom:(elem -> 'b) -> t -> 'b

  val is_empty : t -> bool

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  val print: ?f:(Format.formatter -> elem -> unit) -> t -> (Format.formatter -> unit) list
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  val trivially_disjoint: t -> t -> bool
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  val extractvars : t -> [> `Var of Var.t ] bdd * t 
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end

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

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(* ternary BDD
 * where the nodes are Atm of X.t | Var of String.t
 * Variables are always before Values
 * All the leaves are then base types 
 *
 * we add a third case when two leaves of the bdd are of the same
 * kind, that's it Val of t1 , Val of t2
 *
 * This representation can be used for all kinds.
 * Intervals, Atoms and Chars can be always merged (for union and intersection)
 * Products can be merged for intersections
 * Arrows can be never merged
 *
 * extract_var : copy the orginal tree and on one copy put to zero all 
 * leaves that have an Atm on the other all leaves that have a Var
 *
 * *)

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module Make(T : E) : S with type s = T.t =
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struct
  (* ternary decision trees . cf section 11.3.3 Frish PhD *)
  (* plus variables *)
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  (* `Atm are containers (Atoms, Chars, Intervals, Pairs ... )
   * `Var are String
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   *)
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  type s = T.t
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  module X = Var.Make(T)
  type elem = s Var.pairvar
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  type 'a bdd =
    [ `True
    | `False
    | `Split of int * 'a * ('a bdd) * ('a bdd) * ('a bdd) ]
  type t = elem bdd

  let rec equal_aux eq a b =
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    (a == b) ||
    match (a,b) with
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      | `Split (h1,x1,p1,i1,n1), `Split (h2,x2,p2,i2,n2) ->
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	  (h1 == h2) &&
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	  (equal_aux eq p1 p2) && (equal_aux eq i1 i2) &&
	  (equal_aux eq n1 n2) && (eq x1 x2)
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      | _ -> false

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  let equal = equal_aux X.equal

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

  let rec compare a b =
    if (a == b) then 0 
    else match (a,b) with
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      | `Split (h1,x1, p1,i1,n1), `Split (h2,x2, p2,i2,n2) ->
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	  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
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      | `True,_  -> -1
      | _, `True -> 1
      | `False,_ -> -1
      | _,`False -> 1
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  let rec hash = function
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    | `True -> 1
    | `False -> 0
    | `Split(h, _,_,_,_) -> h
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  let compute_hash x p i n = 
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	(Hashtbl.hash x) + 17 * (hash p) + 257 * (hash i) + 16637 * (hash n)
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  let rec check = function
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    | `True -> assert false;
    | `False -> ()
    | `Split (h,x,p,i,n) ->
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	assert (h = compute_hash x p i n);
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	(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

  let atom x =
    let h = X.hash x + 17 in (* partial evaluation of compute_hash... *)
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    `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... *)
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    `Split (h, x,`False,`False,`True)

  let vars v =
    let a = atom (`Atm T.full) in 
    let h = compute_hash v a `False `False in 
    ( `Split (h,v,a,`False,`False) :> t )
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  let rec iter f = function
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    | `Split (_, x, p,i,n) -> f x; iter f p; iter f i; iter f n
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    | _ -> ()

  let rec dump ppf = function
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    | `True -> Format.fprintf ppf "+"
    | `False -> Format.fprintf ppf "-"
    | `Split (_,x, p,i,n) -> 
	Format.fprintf ppf "%a(@[%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
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    | `True -> Format.fprintf ppf "Any"
    | `False -> Format.fprintf ppf "Empty"
    | `Split (_, x, p,i, n) ->
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	let flag = ref false in
	let b () = if !flag then Format.fprintf ppf " | " else flag := true in
	(match p with 
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	   | `True -> b(); Format.fprintf ppf "%a" f x
	   | `False -> ()
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	   | _ -> b (); Format.fprintf ppf "%a & @[(%a)@]" f x (print f) p );
	(match i with 
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	   | `True -> assert false;
	   | `False -> ()
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	   | _ -> b(); print f ppf i);
	(match n with 
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	   | `True -> b (); Format.fprintf ppf "@[~%a@]" f x
	   | `False -> ()
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	   | _ -> b (); Format.fprintf ppf "@[~%a@] & @[(%a)@]" f x (print f) n)
	
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  let print ?(f=X.dump) = function
    | `True -> [] (* [] a bdd cannot be of this type *)
    | `False -> [ fun ppf -> Format.fprintf ppf "Empty" ]
    | c -> [ fun ppf -> print f ppf c ]
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  (* return a list of pairs, where each pair holds the list
   * of positive and negative elements on a branch *)
  let get x =
    let rec aux accu pos neg = function
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      | `True -> (List.rev pos, List.rev neg) :: accu
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      | `False -> accu
      | `Split (_,x, p,i,n) ->
        (*OPT: can avoid creating this list cell when pos or neg =`False *)
        let accu = aux accu (x::pos) neg p in
        let accu = aux accu pos (x::neg) n in
        let accu = aux accu pos neg i in
        accu
    in aux [] [] [] x

  let leafconj x = 
    let rec aux accu = function
      | `True -> accu
      | `False -> accu
      | `Split (_,`Atm x, `True,`False,`False) -> x :: accu
      | `Split (_,`Atm x, _,_,_) -> assert false
      | `Split (_,`Var x, p,i,n) ->
        let accu = aux accu p in
        let accu = aux accu n in
        let accu = aux accu i in
        accu
    in
    List.fold_left T.cup T.empty (aux [] x)
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(*      
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  let rec get' accu pos neg = function
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    | `True -> (pos,neg) :: accu
    | `False -> accu
    | `Split (_,x,p,i,n) ->
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	let accu = get' accu (x::pos) neg p in
	let rec aux l = function
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	  | `Split (_,x,`False,i,n') when equal n n' ->
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	      aux (x :: l) i
	  | i ->
	      let accu = get' accu pos (l :: neg) n in
	      get' accu pos neg i
	in
	aux [x] i

  let get' x = get' [] [] [] x
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  *)
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  let compute ~empty ~full ~cup ~cap ~diff ~atom b =
    let rec aux = function
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      | `True -> full
      | `False -> empty
      | `Split(_,x, p,i,n) ->
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	  let p = cap (atom x) (aux p)
	  and i = aux i
	  and n = diff (aux n) (atom x) in
	  cup (cup p i) n
    in
    aux b
      
(* Invariant: correct hash value *)

  let split0 x pos ign neg =
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    `Split (compute_hash x pos ign neg, x, pos, ign, neg)
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  let empty = `False
  let full = split0 (`Atm T.full) `True `False `False
  let any = full
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  let is_empty t = (t == empty)

(* Invariants:
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     `Split (x, pos,ign,neg) ==>  (ign <> `True), (pos <> neg)
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*)

  let rec has_true = function
    | [] -> false
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    | `True :: _ -> true
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    | _ :: l -> has_true l

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  (* split removes redundant subtrees from the positive and negative
   * branch if they are present in the lazy union branch *)
  let gensplit compare normalize normunion is_empty =
    let equal = equal_aux (fun a b -> compare a b = 0) in
    let rec has_same a = function
      | [] -> false
      | b :: l -> (equal a b) || (has_same a l)
    in
    let rec split x p i n =
      if is_empty x  then `False
      (* 0?p:i:n -> 0 *)
      else if i == `True then `True 
      (* x?p:1:n -> 1 *)
      else if equal p n then p ++ i
      else let p = simplify p [i] and n = simplify n [i] in
      (* x?p:i:n when p = n -> bdd of (p ++ i) *)
      if equal p n then p ++ i
      else split0 x p i n

    (* simplify t l -> bdd of ( t // l ) *)
    and simplify a l =
      match normalize a with
        | `False -> `False
        | `True -> if has_true l then `False else `True
        | `Split (_,x,p,i,n) ->
          if (has_true l) || (has_same a l) then `False
          else s_aux2 a x p i n [] [] [] l
    and s_aux2 a x p i n ap ai an = function
      | [] -> 
        let p = simplify p ap 
        and n = simplify n an
        and i = simplify i ai in
        if equal p n then p ++ i else split0 x p i n
      | b :: l -> s_aux3 a x p i n ap ai an l b 
    and s_aux3 a x p i n ap ai an l = function
      | `False -> s_aux2 a x p i n ap ai an l
      | `True -> assert false
      | `Split (_,x2,p2,i2,n2) as b ->
        if equal a b then `False 
        else let c = compare x2 x in
        if c < 0 then s_aux3 a x p i n ap ai an l i2
        else if c > 0 then s_aux2 a x p i n (b :: ap) (b :: ai) (b :: an) l
        else s_aux2 a x p i n (p2 :: i2 :: ap) (i2 :: ai) (n2 :: i2 :: an) l

    (* Inv : all leafs are of type Atm and they are always merged *)
    (* union *)
    and ( ++ ) a b = if a == b then a
    else match normunion (a,b) with
      | `True, _ | _, `True -> `True
      | `False, a | a, `False -> a
      
      | `Split (_,x1, p1,i1,n1), `Split (_,x2, p2,i2,n2) ->
        let c = 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

    in split,(++)

    (*
  let splitvar,_ = gensplit Pervasives.compare (fun x -> x) (fun x -> x) (fun _ -> false)
*)


  let split,(++) = 
    let norm = function 
      | `Split (_,`Atm x, `False,`False,`True) -> split0 (`Atm(T.diff T.full x)) `True `False `False 
      | x -> x
    in
    let normunion = function
        | `Split (_,`Atm x1, `True,`False,`False), `Split (_,`Atm x2, `True,`False,`False) ->
            split0 (`Atm (T.cup x1 x2)) `True `False `False,`False

        | `Split (_,`Atm x1, `False,`False,`True), `Split (_,`Atm x2, `False,`False,`True) ->
            split0 (`Atm (T.cup (T.diff T.full x1) (T.diff T.full x2))) `True `False `False,`False

        | `Split (_,`Atm x1, `True,`False,`False), `Split (_,`Atm x2, `False,`False,`True) ->
            split0 (`Atm (T.cup x1 (T.diff T.full x2))) `True `False `False,`False

        | `Split (_,`Atm x1, `False,`False,`True), `Split (_,`Atm x2, `True,`False,`False) ->
            split0 (`Atm (T.cup (T.diff T.full x1) x2)) `True `False `False,`False

        |a,b -> a,b
    in
      gensplit X.compare norm normunion (fun x -> X.equal (`Atm T.empty) x)
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(* seems better not to make ++ and this split mutually recursive;
   is the invariant still inforced ? *)

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

  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
      | `False, _ | _, `False -> true
      | `Split (_,x1, p1,i1,n1), `Split (_,x2, p2,i2,n2) ->
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	  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

  let rec neg = function
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    | `True -> `False
    | `False -> `True
    | `Split (_,`Atm x, `True,`False,`False) -> split0 (`Atm(T.diff T.full x)) `True `False `False
    | `Split (_,`Atm x, `False,`False,`True) -> split0 (`Atm(T.diff T.full x)) `True `False `False
    | `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))
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  let rec ( // ) a b =
    let negatm = T.diff T.full in
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    if a == b then `False 
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    else match (a,b) with
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      | `False,_ | _, `True -> `False
      | a, `False -> a
      | `True, b -> neg b
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      | `Split (_,`Atm x1, `True,`False,`False), `Split (_,`Atm x2, `True,`False,`False) ->
          split (`Atm(T.diff x1 x2)) `True `False `False
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      | `Split (_,`Atm x1, `False,`False,`True), `Split (_,`Atm x2, `False,`False,`True) ->
          split (`Atm(T.diff (negatm x1) (negatm x2))) `True `False `False
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      | `Split (_,`Atm x1, `True,`False,`False), `Split (_,`Atm x2, `False,`False,`True) ->
          split (`Atm(T.diff x1 (negatm x2))) `True `False `False
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      | `Split (_,`Atm x1, `False,`False,`True), `Split (_,`Atm x2, `True,`False,`False) ->
          split (`Atm(T.diff (negatm x1) x2)) `True `False `False
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      | `Split (_,x1, p1,i1,n1), `Split (_,x2, p2,i2,n2) ->
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	  let c = X.compare x1 x2 in
	  if c = 0 then
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	    if (i2 == `False) && (n2 == `False) 
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	    then split x1 (p1 // p2) (i1 // p2) (n1 ++ i1)
	    else 
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	      split x1 ((p1++i1) // (p2 ++ i2)) `False ((n1++i1) // (n2 ++ i2))
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	  else if c < 0 then
	    split x1 (p1 // b) (i1 // b) (n1 // b) 
	  else
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	    split x2 (a // (i2 ++ p2)) `False (a // (i2 ++ n2))
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  let cup = ( ++ )
  let cap = ( ** )
  let diff = ( // )

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  (* return a couple of trees (v,a)
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   * v = only variables as leaves
   * a = only atoms as leaves
   *)
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  let rec extractvars = function
    (* `True or `False can only be under a variable *)
    | `True -> `True,`False
    | `False -> `False,`False
    | `Split (_,`Atm _, `True,`False,`False) as x -> `False, x
    | `Split (_,`Atm _, _,_,_) -> assert false
    | `Split (_,((`Var y) as x),p,i,n) ->
        let p1,p2 = extractvars p in
        let i1,i2 = extractvars i in
        let n1,n2 = extractvars n in
        (* let v = `Split (compute_hash x p1 i1 n1,x,p1,i1,n1) in   *)
        let v = (fst(gensplit Pervasives.compare (fun x -> x) (fun x -> x) (fun _ -> false)) x p1 i1 n1) in
        let t = split x p2 i2 n2 in
        assert(v <> `True);
        (v,t)
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end