boolVar.ml 15.1 KB
Newer Older
1 2 3 4
let (<) : int -> int -> bool = (<)
let (>) : int -> int -> bool = (>)
let (=) : int -> int -> bool = (=)

5
(* this is the the of the Constructor container *)
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
module type E =
sig
  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

module type S =
sig
22 23 24 25 26 27 28
  type s
  type elem = s Custom.pairvar
  type 'a bdd =
    [ `True
    | `False
    | `Split of int * 'a * ('a bdd) * ('a bdd) * ('a bdd) ]

29
  include Custom.T with type t = elem bdd
30

31
  (* returns the union of all leaves in the BDD *)
32
  val leafconj: t -> s
33

34
  val get: t -> (elem list * elem list) list
35 36 37

  val empty : t
  val full  : t
Pietro Abate's avatar
Pietro Abate committed
38 39 40
  (* same as full, but we keep it for the moment to avoid chaging 
   * the code everywhere *)
  val any  : t
41 42 43 44
  val cup   : t -> t -> t
  val cap   : t -> t -> t
  val diff  : t -> t -> t
  val atom  : elem -> t
45
  val vars  : Custom.var -> t
46 47 48 49 50 51 52 53 54 55 56 57

  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

  val print: string -> t -> (Format.formatter -> unit) list

  val trivially_disjoint: t -> t -> bool
58

59 60
  val extractvars : t -> [> `Var of Custom.String.t ] bdd * t 

61 62
end

63 64 65 66
(*
module type MAKE = functor (T : E) -> S with type elem = T.t Custom.pairvar 
*)

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
(* 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
 *
 * *)

85
module Make(T : E) : S with type s = T.t =
86 87 88
struct
  (* ternary decision trees . cf section 11.3.3 Frish PhD *)
  (* plus variables *)
89 90
  (* `Atm are containers (Atoms, Chars, Intervals, Pairs ... )
   * `Var are String
91
   *)
92
  type s = T.t
93
  module X = Custom.Var(T)
94 95 96 97 98 99 100 101
  type elem = s Custom.pairvar
  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 =
102 103
    (a == b) ||
    match (a,b) with
104
      | `Split (h1,x1,p1,i1,n1), `Split (h2,x2,p2,i2,n2) ->
105
	  (h1 == h2) &&
106 107
	  (equal_aux eq p1 p2) && (equal_aux eq i1 i2) &&
	  (equal_aux eq n1 n2) && (eq x1 x2)
108 109
      | _ -> false

110 111
  let equal = equal_aux X.equal

112 113 114 115 116 117
(* 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
118
      | `Split (h1,x1, p1,i1,n1), `Split (h2,x2, p2,i2,n2) ->
119 120 121 122 123
	  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
124 125 126 127
      | `True,_  -> -1
      | _, `True -> 1
      | `False,_ -> -1
      | _,`False -> 1
128 129

  let rec hash = function
130 131 132
    | `True -> 1
    | `False -> 0
    | `Split(h, _,_,_,_) -> h
133 134

  let compute_hash x p i n = 
135
	(Hashtbl.hash x) + 17 * (hash p) + 257 * (hash i) + 16637 * (hash n)
136 137

  let rec check = function
138 139 140
    | `True -> assert false;
    | `False -> ()
    | `Split (h,x,p,i,n) ->
141
	assert (h = compute_hash x p i n);
142 143 144
	(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) | _ -> ());
145 146 147 148
	X.check x; check p; check i; check n

  let atom x =
    let h = X.hash x + 17 in (* partial evaluation of compute_hash... *)
149
    `Split (h, x,`True,`False,`False)
150 151 152
 
  let neg_atom x =
    let h = X.hash x + 16637 in (* partial evaluation of compute_hash... *)
153 154 155 156 157 158
    `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 )
159 160

  let rec iter f = function
161
    | `Split (_, x, p,i,n) -> f x; iter f p; iter f i; iter f n
162 163 164
    | _ -> ()

  let rec dump ppf = function
165 166 167 168 169
    | `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
170 171

  let rec print f ppf = function
172 173 174
    | `True -> Format.fprintf ppf "Any"
    | `False -> Format.fprintf ppf "Empty"
    | `Split (_, x, p,i, n) ->
175 176 177
	let flag = ref false in
	let b () = if !flag then Format.fprintf ppf " | " else flag := true in
	(match p with 
178 179
	   | `True -> b(); Format.fprintf ppf "%a" f x
	   | `False -> ()
180 181
	   | _ -> b (); Format.fprintf ppf "%a & @[(%a)@]" f x (print f) p );
	(match i with 
182 183
	   | `True -> assert false;
	   | `False -> ()
184 185
	   | _ -> b(); print f ppf i);
	(match n with 
186 187
	   | `True -> b (); Format.fprintf ppf "@[~%a@]" f x
	   | `False -> ()
188 189 190
	   | _ -> b (); Format.fprintf ppf "@[~%a@] & @[(%a)@]" f x (print f) n)
	
  let print a = function
191 192
    | `True -> [ fun ppf -> Format.fprintf ppf "%s" a ]
    | `False -> []
193 194
    | c -> [ fun ppf -> print X.dump ppf c ]

195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221
  (* 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
      | `True -> (pos,neg) :: accu
      | `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)
222

223
(*      
224
  let rec get' accu pos neg = function
225 226 227
    | `True -> (pos,neg) :: accu
    | `False -> accu
    | `Split (_,x,p,i,n) ->
228 229
	let accu = get' accu (x::pos) neg p in
	let rec aux l = function
230
	  | `Split (_,x,`False,i,n') when equal n n' ->
231 232 233 234 235 236 237 238
	      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
239
  *)
240 241 242

  let compute ~empty ~full ~cup ~cap ~diff ~atom b =
    let rec aux = function
243 244 245
      | `True -> full
      | `False -> empty
      | `Split(_,x, p,i,n) ->
246 247 248 249 250 251 252 253 254 255
	  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 =
256
    `Split (compute_hash x pos ign neg, x, pos, ign, neg)
257

258 259 260
  let empty = `False
  let full = split0 (`Atm T.full) `True `False `False
  let any = full
261 262 263 264

  let is_empty t = (t == empty)

(* Invariants:
265
     `Split (x, pos,ign,neg) ==>  (ign <> `True), (pos <> neg)
266 267 268 269
*)

  let rec has_true = function
    | [] -> false
270
    | `True :: _ -> true
271 272
    | _ :: l -> has_true l

273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357
  (* 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)
358 359 360 361 362 363

(* 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
364 365
    | `True, a | a, `True -> a
    | `False, _ | _, `False -> `False
366

367 368
    | `Split (_,`Atm x1, `True,`False,`False), `Split (_,`Atm x2, `True,`False,`False) ->
        split (`Atm(T.cap x1 x2)) `True `False `False
369

370 371
    | `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
372

373 374
    | `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
375

376 377
    | `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
378

379
    | `Split (_,x1, p1,i1,n1), `Split (_,x2, p2,i2,n2) ->
380 381 382 383 384 385 386 387 388 389
	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 =
390
    if a == b then a == `False
391
    else match (a,b) with
392 393 394
      | `True, a | a, `True -> a == `False
      | `False, _ | _, `False -> true
      | `Split (_,x1, p1,i1,n1), `Split (_,x2, p2,i2,n2) ->
395 396 397 398 399 400 401 402 403 404 405 406 407 408 409
	  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
410 411 412 413 414 415 416 417
    | `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))
418 419 420
	      
  let rec ( // ) a b =
    let negatm = T.diff T.full in
421
    if a == b then `False 
422
    else match (a,b) with
423 424 425
      | `False,_ | _, `True -> `False
      | a, `False -> a
      | `True, b -> neg b
426

427 428
      | `Split (_,`Atm x1, `True,`False,`False), `Split (_,`Atm x2, `True,`False,`False) ->
          split (`Atm(T.diff x1 x2)) `True `False `False
429

430 431
      | `Split (_,`Atm x1, `False,`False,`True), `Split (_,`Atm x2, `False,`False,`True) ->
          split (`Atm(T.diff (negatm x1) (negatm x2))) `True `False `False
432

433 434
      | `Split (_,`Atm x1, `True,`False,`False), `Split (_,`Atm x2, `False,`False,`True) ->
          split (`Atm(T.diff x1 (negatm x2))) `True `False `False
435

436 437
      | `Split (_,`Atm x1, `False,`False,`True), `Split (_,`Atm x2, `True,`False,`False) ->
          split (`Atm(T.diff (negatm x1) x2)) `True `False `False
438

439
      | `Split (_,x1, p1,i1,n1), `Split (_,x2, p2,i2,n2) ->
440 441
	  let c = X.compare x1 x2 in
	  if c = 0 then
442
	    if (i2 == `False) && (n2 == `False) 
443 444
	    then split x1 (p1 // p2) (i1 // p2) (n1 ++ i1)
	    else 
445
	      split x1 ((p1++i1) // (p2 ++ i2)) `False ((n1++i1) // (n2 ++ i2))
446 447 448
	  else if c < 0 then
	    split x1 (p1 // b) (i1 // b) (n1 // b) 
	  else
449
	    split x2 (a // (i2 ++ p2)) `False (a // (i2 ++ n2))
450 451 452 453 454 455 456 457 458
	      
  let cup = ( ++ )
  let cap = ( ** )
  let diff = ( // )

  (* return a couple of trees (v,a), the second where all variables
   * v = only variables as leaves
   * a = only atoms as leaves
   *)
459 460 461 462 463 464 465 466 467 468 469 470 471 472 473
  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)
Pietro Abate's avatar
Pietro Abate committed
474

475
end
476 477 478 479 480 481 482

module Vars = struct
  module V = struct include Custom.String end
  include Bool.Make(V)
end

module BoolVars = Make(Vars)