types.ml 62.8 KB
Newer Older
1
open Ident
2
open Encodings
3

4
let count = ref 0
5 6 7 8 9
		
let () =
  Stats.register Stats.Summary
    (fun ppf -> Format.fprintf ppf "Allocated type nodes:%i@\n" !count)

Jérôme Maloberti's avatar
Jérôme Maloberti committed
10
(* 
11 12 13 14 15 16 17 18
To be sure not to use generic comparison ...
*)
let (=) : int -> int -> bool = (==)
let (<) : int -> int -> bool = (<)
let (<=) : int -> int -> bool = (<=)
let (<>) : int -> int -> bool = (<>)
let compare = 1

19
type const = 
20
  | Integer of Intervals.V.t
21
  | Atom of Atoms.V.t
22
  | Var of BoolVar.Vars.V.t
23
  | Char of Chars.V.t
24 25 26 27
  | Pair of const * const
  | Xml of const * const
  | Record of const label_map
  | String of U.uindex * U.uindex * U.t * const
28

Jérôme Maloberti's avatar
Jérôme Maloberti committed
29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
type service_params =
  | TProd of service_params * service_params
  | TOption of service_params 
  | TList of string * service_params
  | TSet of service_params
  | TSum of service_params * service_params
  | TString of string
  | TInt of string
  | TInt32 of string
  | TInt64 of string
  | TFloat of string 
  | TBool of string
  | TFile of string
      (* | TUserType of string * (string -> 'a) * ('a -> string) *)
  | TCoord of string 
  | TCoordv of service_params * string
  | TESuffix of string 
  | TESuffixs of string
      (*  | TESuffixu of (string * (string -> 'a) * ('a -> string)) *)
  | TSuffix of (bool * service_params)
  | TUnit 
  | TAny
  | TConst of string;;

53 54 55
module Const = struct
  type t = const

56 57
  let check _ = ()
  let dump ppf _ = Format.fprintf ppf "<Types.Const.t>"
58 59

  let rec compare c1 c2 = match (c1,c2) with
60
    | Integer x, Integer y -> Intervals.V.compare x y
61 62
    | Integer _, _ -> -1
    | _, Integer _ -> 1
63
    | Atom x, Atom y -> Atoms.V.compare x y
64 65
    | Atom _, _ -> -1
    | _, Atom _ -> 1
66
    | Var x, Var y -> BoolVar.Vars.V.compare x y
67 68 69
    | Var _, _ -> -1
    | _, Var _ -> 1

70
    | Char x, Char y -> Chars.V.compare x y
71 72 73
    | Char _, _ -> -1
    | _, Char _ -> 1
    | Pair (x1,x2), Pair (y1,y2) ->
74 75
	let c = compare x1 y1 in
	if c <> 0 then c else compare x2 y2
76 77 78
    | Pair (_,_), _ -> -1
    | _, Pair (_,_) -> 1
    | Xml (x1,x2), Xml (y1,y2) ->
79 80
	let c = compare x1 y1 in
	if c <> 0 then c else compare x2 y2
81 82 83
    | Xml (_,_), _ -> -1
    | _, Xml (_,_) -> 1
    | Record x, Record y ->
84
	LabelMap.compare compare x y
85 86 87 88 89 90 91
    | Record _, _ -> -1
    | _, Record _ -> 1
    | String (i1,j1,s1,r1), String (i2,j2,s2,r2) ->
	let c = Pervasives.compare i1 i2 in if c <> 0 then c 
	else let c = Pervasives.compare j1 j2 in if c <> 0 then c
	else let c = U.compare s1 s2 in if c <> 0 then c (* Should compare
							    only the substring *)
92 93 94 95 96 97 98 99 100 101
	else compare r1 r2

  let rec hash = function
    | Integer x -> 1 + 17 * (Intervals.V.hash x)
    | Atom x -> 2 + 17 * (Atoms.V.hash x)
    | Char x -> 3 + 17 * (Chars.V.hash x)
    | Pair (x,y) -> 4 + 17 * (hash x) + 257 * (hash y)
    | Xml (x,y) -> 5 + 17 * (hash x) + 257 * (hash y)
    | Record x -> 6 + 17 * (LabelMap.hash hash x)
    | String (i,j,s,r) -> 7 + 17 * (U.hash s) + 257 * hash r
102
    | Var x -> 7 + 17 * (BoolVar.Vars.V.hash x)
103
      (* Note: improve hash for String *)
104

105 106
  let equal c1 c2 = compare c1 c2 = 0
end
107

108 109
module Abstract =
struct
110
  module T = Custom.String
111 112 113 114 115 116 117 118 119 120
  type abs = T.t

  module V =
  struct
    type t = abs * Obj.t
  end

  include SortedList.FiniteCofinite(T)

  let print = function
121
    | Finite l -> List.map (fun x ppf -> Format.fprintf ppf "!%s" x) l
122 123 124 125 126
    | Cofinite l ->       
	[ fun ppf ->
	  Format.fprintf ppf "@[Abstract";
	  List.iter (fun x -> Format.fprintf ppf " \\@ !%s" x) l;
	  Format.fprintf ppf "@]" ]
127

128 129 130 131 132
  let contains_sample s t = match s,t with
    | None, Cofinite _ -> true
    | None, Finite _ -> false
    | Some s, t -> contains s t
    
133 134
end

135 136
type pair_kind = [ `Normal | `XML ]

137
module BoolAtoms : BoolVar.S with 
138
  type s = Atoms.t = BoolVar.Make(Atoms)
139
module BoolIntervals : BoolVar.S with 
140
  type s = Intervals.t = BoolVar.Make(Intervals)
141
module BoolChars : BoolVar.S with 
142
  type s = Chars.t = BoolVar.Make(Chars)
143

144 145
module rec Descr : 
sig
146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
  (* each kind is represented as a union of itersection of types 
   * the type is a union of all kinds
   *
   * we add a new field that contains only variables.
   * Inv : 
     * if the bdd of ANY kind is composed only of variables,
       the we move it in vars:
     * From a bdd we move all variables to vars: that belong to
     * to a path in the bdd that contains only variables and end in
     * true
     * A bdd never contains a path that ends in 1 and contains only variables
     *
     * (t1 v a ) ^ ( t2 v b )
     * we need to distribute variables for the intersection
     * (t1 ^ t2) v (t1 ^ b) v (t2 ^ a) v (a ^ b)
     * before we were doing only t1 ^ t2
   *)
163
  type s = {
164 165 166
    atoms : BoolAtoms.t;
    ints  : BoolIntervals.t;
    chars : BoolChars.t;
167 168 169 170
    times : BoolPair.t;
    xml   : BoolPair.t;
    arrow : BoolPair.t;
    record: BoolRec.t;
171
    abstract: Abstract.t;
172 173 174
    (* this is used in record to flag the fact that the type of a label is
     * absent . It is used for optional arguments in functions as ?Int
     * is the union of Int ^ undef where undef is a type with absent : true *)
175 176
    absent: bool
  }
177
  include Custom.T with type t = s
178
  val empty: t
179 180
end =
struct
181
  type s = {
182 183 184
    atoms : BoolAtoms.t;
    ints  : BoolIntervals.t;
    chars : BoolChars.t;
185 186 187 188
    times : BoolPair.t;
    xml   : BoolPair.t;
    arrow : BoolPair.t;
    record: BoolRec.t;
189
    abstract: Abstract.t;
190 191
    absent: bool
  }
192
  type t = s
193

194 195 196 197
  let print_lst ppf =
    List.iter (fun f -> f ppf; Format.fprintf ppf " |")

  let dump ppf d =
198
    Format.fprintf ppf "<types atoms(%a) ints(%a) chars(%a) times(%a) record(%a) xml(%a)>"
199
      BoolAtoms.dump d.atoms
200 201
      BoolIntervals.dump d.ints
      BoolChars.dump d.chars
202 203 204
      BoolPair.dump d.times
      BoolRec.dump d.record
      BoolPair.dump d.xml
205

206 207 208 209 210
  let empty = { 
    times = BoolPair.empty; 
    xml   = BoolPair.empty; 
    arrow = BoolPair.empty; 
    record= BoolRec.empty;
211 212 213
    ints  = BoolIntervals.empty;
    atoms = BoolAtoms.empty;
    chars = BoolChars.empty;
214
    abstract = Abstract.empty;
215 216 217
    absent= false;
  }

218
  let equal a b =
219
    (a == b) || (
220 221 222
      (BoolAtoms.equal a.atoms b.atoms) &&
      (BoolChars.equal a.chars b.chars) &&
      (BoolIntervals.equal a.ints  b.ints) &&
223 224 225 226
      (BoolPair.equal a.times b.times) &&
      (BoolPair.equal a.xml b.xml) &&
      (BoolPair.equal a.arrow b.arrow) &&
      (BoolRec.equal a.record b.record) &&
227
      (Abstract.equal a.abstract b.abstract) &&
228 229
      (a.absent == b.absent)
    )
230 231 232

  let compare a b =
    if a == b then 0 
233 234 235
    else let c = BoolAtoms.compare a.atoms b.atoms in if c <> 0 then c
    else let c = BoolChars.compare a.chars b.chars in if c <> 0 then c
    else let c = BoolIntervals.compare a.ints b.ints in if c <> 0 then c
236 237 238 239
    else let c = BoolPair.compare a.times b.times in if c <> 0 then c
    else let c = BoolPair.compare a.xml b.xml in if c <> 0 then c
    else let c = BoolPair.compare a.arrow b.arrow in if c <> 0 then c
    else let c = BoolRec.compare a.record b.record in if c <> 0 then c
240
    else let c = Abstract.compare a.abstract b.abstract in if c <> 0 then c
241 242 243
    else if a.absent && not b.absent then -1
    else if b.absent && not a.absent then 1
    else 0
244
      
245
  let hash a =
246 247 248
    let accu = BoolChars.hash a.chars in
    let accu = 17 * accu + BoolIntervals.hash a.ints in
    let accu = 17 * accu + BoolAtoms.hash a.atoms in
249 250 251 252 253 254 255
    let accu = 17 * accu + BoolPair.hash a.times in
    let accu = 17 * accu + BoolPair.hash a.xml in
    let accu = 17 * accu + BoolPair.hash a.arrow in
    let accu = 17 * accu + BoolRec.hash a.record in
    let accu = 17 * accu + Abstract.hash a.abstract in
    let accu = if a.absent then accu+5 else accu in
    accu
256

257
  let check a =
258 259 260
    BoolChars.check a.chars;
    BoolIntervals.check a.ints;
    BoolAtoms.check a.atoms;
261 262 263 264
    BoolPair.check a.times;
    BoolPair.check a.xml;
    BoolPair.check a.arrow;
    BoolRec.check a.record;
265
    Abstract.check a.abstract;
266 267
    ()

268 269 270
end
and Node :
sig
271
  type t = { id : int; cu: Compunit.t; mutable descr : Descr.t }
272 273 274 275 276
  val dump: Format.formatter -> t -> unit
  val check: t -> unit
  val equal: t -> t -> bool
  val hash: t -> int
  val compare:t -> t -> int
277
  val mk: int -> Descr.t -> t
278
end =
279

280
struct
281
  type t = { id : int; cu: Compunit.t; mutable descr : Descr.t }
282
  let check n = ()
283
  let dump ppf n = Format.fprintf ppf "X%i" n.id
284
  let hash x = x.id + Compunit.hash x.cu
285
  let compare x y = 
286 287 288
    let c = x.id - y.id in if c = 0 then Compunit.compare x.cu y.cu else c
  let equal x y = x==y || (x.id == y.id && (Compunit.equal x.cu y.cu))
  let mk id d = { id = id; cu = Compunit.current (); descr = d }
289 290
end

291 292
and Pair : Bool.S with type elem = (Node.t * Node.t) =
  Bool.Make(Custom.Pair(Node)(Node))
293 294
and BoolPair : BoolVar.S with 
  type s = Pair.t = BoolVar.Make(Pair)
295

296 297 298 299 300
(* bool = true means that the record is open that is, that
 * the labels that are not in the domain of the map are
 * equal to "any" *)
and Rec : Bool.S with type elem = bool * Node.t Ident.label_map =
  Bool.Make(Custom.Pair(Custom.Bool)(LabelSet.MakeMap(Node)))
301 302
and BoolRec : BoolVar.S with
  type s = Rec.t = BoolVar.Make(Rec)
303

304 305
module DescrHash = Hashtbl.Make(Descr)
module DescrMap = Map.Make(Descr)
306 307
module DescrSet = Set.Make(Descr)
module DescrSList = SortedList.Make(Descr)
308

309 310 311
type descr = Descr.t
type node = Node.t
include Descr
312

313 314
let forward_print = ref (fun _ _ -> assert false)

315 316 317 318
let make () = 
  incr count; 
  Node.mk !count empty

319 320 321 322 323 324 325
let define n d = 
  n.Node.descr <- d

let cons d = 
  incr count; 
  Node.mk !count d

326 327 328
(* two representation possible. either all fields (except vars) are full, OR
 * the field vars is full.
 *)
329
let any =  {
330 331 332
  times = BoolPair.full; 
  xml   = BoolPair.full; 
  arrow = BoolPair.full; 
333
  record= BoolRec.full; 
334 335 336
  ints  = BoolIntervals.full;
  atoms = BoolAtoms.full;
  chars = BoolChars.full;
337
  abstract = Abstract.any;
338
  absent= false;
339
}
340 341

let non_constructed =
342 343
  { any with  
      times = empty.times; xml = empty.xml; record = empty.record }
344
     
345
let non_constructed_or_absent = 
346
  { non_constructed with absent = true }
347 348 349 350 351

(* Descr.t type constructors *)	     
let times x y = { empty with times = BoolPair.atom (`Atm (Pair.atom (x,y))) }
let xml x y = { empty with xml = BoolPair.atom (`Atm (Pair.atom (x,y))) }
let arrow x y = { empty with arrow = BoolPair.atom (`Atm (Pair.atom (x,y))) }
352
let record label t = 
353
  { empty with 
354
      record = BoolRec.atom (`Atm (Rec.atom (true,LabelMap.singleton label t))) }
355
let record_fields x =
356
  { empty with record = BoolRec.atom (`Atm (Rec.atom x)) }
357
let atom a = { empty with atoms = a }
358 359 360 361 362 363 364 365 366 367 368 369 370
let vars a =  {
  (* Atm = Any ^ a *)
  times = BoolPair.vars a;
  xml   = BoolPair.vars a; 
  arrow = BoolPair.vars a; 
  record= BoolRec.vars a; 
  ints  = BoolIntervals.vars a;
  atoms = BoolAtoms.vars a;
  chars = BoolChars.vars a;
  abstract = Abstract.any;
  absent= false;
}

371
let char c = { empty with chars = c }
372
let interval i = { empty with ints = i }
373
let abstract a = { empty with abstract = a }
374 375

let get_abstract t = t.abstract
376 377 378 379

(* union is component wise + a pass to extract variables
 * Var = ( t1.Var v t2.Var ) v ( extracted variables )
 *)
380 381
let cup x y = 
  if x == y then x else {
382 383 384
    times = BoolPair.cup x.times y.times;
    xml   = BoolPair.cup x.xml y.xml;
    arrow = BoolPair.cup x.arrow y.arrow;
385
    record= BoolRec.cup x.record y.record;
386 387 388
    ints  = BoolIntervals.cup x.ints  y.ints;
    atoms = BoolAtoms.cup x.atoms y.atoms;
    chars = BoolChars.cup x.chars y.chars;
389
    abstract = Abstract.cup x.abstract y.abstract;
390
    absent= x.absent || y.absent;
391
  }
392 393 394

(* intersection 
 *)
395 396
let cap x y = 
  if x == y then x else {
397
    ints  = BoolIntervals.cap x.ints y.ints;
398 399
    times = BoolPair.cap x.times y.times;
    xml   = BoolPair.cap x.xml y.xml;
400
    record= BoolRec.cap x.record y.record;
401
    arrow = BoolPair.cap x.arrow y.arrow;
402 403
    atoms = BoolAtoms.cap x.atoms y.atoms;
    chars = BoolChars.cap x.chars y.chars;
404
    abstract = Abstract.cap x.abstract y.abstract;
405
    absent= x.absent && y.absent;
406
  }
407 408 409 410 411 412 413 414 415

(* 
 *
 * t1 // t2 = ( t1.Atm ^ - t2.Atm ^ t2.Var ) v
 *            ( t1.Var ^ t2.Var )
 *
 * Atm t1.Atm // ( t2.Atm v t2.Var )
 * Var ( t1.Var // t2.Var ) v ( extracted variables )
 *)    
416 417
let diff x y = 
  if x == y then empty else {
418 419 420
    times = BoolPair.diff x.times y.times;
    xml   = BoolPair.diff x.xml y.xml;
    arrow = BoolPair.diff x.arrow y.arrow;
421
    record= BoolRec.diff x.record y.record;
422
    ints  = BoolIntervals.diff x.ints y.ints;
423 424
    atoms = BoolAtoms.diff x.atoms y.atoms;
    chars = BoolChars.diff x.chars y.chars;
425
    abstract = Abstract.diff x.abstract y.abstract;
426
    absent= x.absent && not y.absent;
427 428
  }
    
429 430
(* TODO: optimize disjoint check for boolean combinations *)
let trivially_disjoint a b =
431 432 433
  (BoolChars.trivially_disjoint a.chars b.chars) &&
  (BoolIntervals.trivially_disjoint a.ints b.ints) &&
  (BoolAtoms.trivially_disjoint a.atoms b.atoms) &&
434 435 436
  (BoolPair.trivially_disjoint a.times b.times) &&
  (BoolPair.trivially_disjoint a.xml b.xml) &&
  (BoolPair.trivially_disjoint a.arrow b.arrow) &&
437
  (BoolRec.trivially_disjoint a.record b.record) &&
438
  (Abstract.disjoint a.abstract b.abstract) &&
439
  (not (a.absent && b.absent))
440

441
let descr n = n.Node.descr
442
let internalize n = n
443
let id n = n.Node.id
444

445
let rec constant = function
446 447 448 449
  | Integer i -> interval (BoolIntervals.atom (`Atm (Intervals.atom i)))
  | Atom a -> atom (BoolAtoms.atom (`Atm (Atoms.atom a)))
  | Var a -> vars (`Var a)
  | Char c -> char (BoolChars.atom (`Atm (Chars.atom c)))
450
  | Pair (x,y) -> times (const_node x) (const_node y)
451
  | Xml (x,y) -> xml (const_node x) (const_node y)
452
  | Record x -> record_fields (false ,LabelMap.map const_node x)
453 454 455 456 457 458
  | String (i,j,s,c) ->
      if U.equal_index i j then constant c
      else 
	let (ch,i') = U.next s i in
	constant (Pair (Char (Chars.V.mk_int ch), String (i',j,s,c)))
and const_node c = cons (constant c)
459

460 461
let neg x = diff any x

462
let any_node = cons any
463
let empty_node = cons empty
464

465
module LabelS = Set.Make(Label)
466

467 468
let any_or_absent = { any with absent = true } 
let only_absent = { empty with absent = true }
469

470 471
let get_record r =
  let labs accu (_,r) = 
472 473
    List.fold_left 
      (fun accu (l,_) -> LabelS.add l accu) accu (LabelMap.get r) in
474
  let extend descrs labs (o,r) =
475 476 477 478 479
    let rec aux i labs r =
      match labs with
	| [] -> ()
	| l1::labs ->
	    match r with
480
	      | (l2,x)::r when l1 == l2 -> 
481 482 483
		  descrs.(i) <- cap descrs.(i) (descr x);
		  aux (i+1) labs r
	      | r ->
484 485
		  if not o then 
		    descrs.(i) <- cap descrs.(i) only_absent; (* TODO:OPT *)
486 487
		  aux (i+1) labs r
    in
488
    aux 0 labs (LabelMap.get r);
489 490 491 492
    o
  in
  let line (p,n) =
    let labels = 
493 494
      List.fold_left labs (List.fold_left labs LabelS.empty p) n in
    let labels = LabelS.elements labels in
495
    let nlab = List.length labels in
496
    let mk () = Array.create nlab any_or_absent in
497 498 499 500 501 502 503 504 505 506 507 508 509 510 511

    let pos = mk () in
    let opos = List.fold_left 
		 (fun accu x -> 
		    (extend pos labels x) && accu)
		 true p in
    let p = (opos, pos) in

    let n = List.map (fun x ->
			let neg = mk () in
			let o = extend neg labels x in
			(o,neg)
		     ) n in
    (labels,p,n)
  in
512
  List.map line (Rec.get r)
513
   
514 515 516 517 518
(* Subtyping algorithm *)

let diff_t d t = diff d (descr t)
let cap_t d t = cap d (descr t)
let cup_t d t = cup d (descr t)
519
let cap_product any_left any_right l =
520 521
  List.fold_left 
    (fun (d1,d2) (t1,t2) -> (cap_t d1 t1, cap_t d2 t2))
522
    (any_left,any_right)
523
    l
524
let any_pair = { empty with times = any.times }
525

526 527 528
let rec exists max f =
  (max > 0) && (f (max - 1) || exists (max - 1) f)

529
exception NotEmpty
530

531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599
module Witness = struct

  module NodeSet = Set.Make(Node)

  type witness =
    | WInt of Intervals.V.t
    | WAtom of Atoms.sample
    | WChar of Chars.V.t
    | WAbsent
    | WAbstract of Abstract.elem option

    | WPair of witness * witness * witness_slot
    | WXml of witness * witness * witness_slot
    | WRecord of witness label_map * bool * witness_slot
	(* Invariant: WAbsent cannot actually appear *)

    | WFun of (witness * witness option) list * witness_slot
  and witness_slot = 
      { mutable wnodes_in: NodeSet.t;
	mutable wnodes_out: NodeSet.t;
	mutable wuid: int }

  module WHash = Hashtbl.Make(
    struct
      type t = witness
      let hash_small = function
	| WInt i -> 17 * Intervals.V.hash i
	| WChar c -> 1 + 17 * Chars.V.hash c
	| WAtom None -> 2
	| WAtom (Some (ns,None)) -> 3 + 17 * Ns.Uri.hash ns
	| WAtom (Some (_,Some t)) -> 4 + 17 * Ns.Label.hash t
	| WAbsent -> 5
	| WAbstract None -> 6
	| WAbstract (Some t) -> 7 + 17 * Abstract.T.hash t
	| WPair (_,_,s) 
	| WXml (_,_,s)
	| WRecord (_,_,s)
	| WFun (_,s) -> 8 + 17 * s.wuid
      let hash = function
	| WPair (p1,p2,_) -> 257 * hash_small p1 + 65537 * hash_small p2
	| WXml (p1,p2,_) -> 1 + 257 * hash_small p1 + 65537 * hash_small p2
	| WRecord (r,o,_) -> 
	    (if o then 2 else 3) + 257 * LabelMap.hash hash_small r
	| WFun (f,_) ->
	    4 + 257 *
	      (Hashtbl.hash 
		 (List.map 
		    (function (x,None) -> 17 * hash_small x
		       | (x,Some y) -> 
			   1 + 17 * hash_small x + 257 * hash_small y)
		    f)
	      )
	| _ -> assert false

      let equal_small w1 w2 = match w1,w2 with
	| WInt i1, WInt i2 -> Intervals.V.equal i1 i2
	| WChar c1, WChar c2 -> Chars.V.equal c1 c2
	| WAtom None, WAtom None -> true
	| WAtom (Some (ns1,None)), WAtom (Some (ns2,None)) ->
	    Ns.Uri.equal ns1 ns2
	| WAtom (Some (_,Some t1)), WAtom (Some (_,Some t2)) ->
	    Ns.Label.equal t1 t2
	| WAbsent, WAbsent -> true
	| WAbstract None, WAbstract None -> false
	| WAbstract (Some t1), WAbstract (Some t2) -> Abstract.T.equal t1 t2
	| _ -> w1 == w2

      let equal w1 w2 = match w1,w2 with
	| WPair (p1,q1,_), WPair (p2,q2,_) 
600
	| WXml (p1,q1,_), WXml (p2,q2,_) -> 
601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621
	    equal_small p1 p2 && equal_small q1 q2
	| WRecord (r1,o1,_), WRecord (r2,o2,_) ->
	    o1 == o2 && (LabelMap.equal equal_small r1 r2)
	| WFun (f1,_), WFun (f2,_) ->
	    List.length f1 = List.length f2 &&
		List.for_all2
		(fun (x1,y1) (x2,y2) ->
		   equal_small x1 x2 && (match y1,y2 with
					   | Some y1, Some y2 -> 
					       equal_small y1 y2
					   | None, None -> true
					   | _ -> false)
		) f1 f2
	| _ -> false
    end)

  let wmemo = WHash.create 1024
  let wuid = ref 0
  let wslot () = { wuid = !wuid; wnodes_in = NodeSet.empty; 
		   wnodes_out = NodeSet.empty }

622 623 624 625
  let () =
    Stats.register Stats.Summary
      (fun ppf -> Format.fprintf ppf "Allocated witnesses:%i@\n" !wuid)

626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663
  let rec print_witness ppf = function
    | WInt i ->
	Format.fprintf ppf "%a" Intervals.V.print i
    | WChar c ->
	Format.fprintf ppf "%a" Chars.V.print c
    | WAtom None ->
	Format.fprintf ppf "`#:#"
    | WAtom (Some (ns,None)) ->
	Format.fprintf ppf "`%a" Ns.InternalPrinter.print_any_ns ns
    | WAtom (Some (_,Some t)) ->
	Format.fprintf ppf "`%a" Ns.Label.print_attr t
    | WPair (w1,w2,_) -> 
	Format.fprintf ppf "(%a,%a)" print_witness w1 print_witness w2
    | WXml (w1,w2,_) -> 
	Format.fprintf ppf "XML(%a,%a)" print_witness w1 print_witness w2
    | WRecord (ws,o,_) ->
	Format.fprintf ppf "{";
	LabelMap.iteri
	  (fun l w -> Format.fprintf ppf " %a=%a" 
	     Label.print_attr l print_witness w)
	  ws;
	if o then Format.fprintf ppf " ..";
	Format.fprintf ppf " }"
    | WFun (f,_) ->
	Format.fprintf ppf "FUN{";
	List.iter (fun (x,y) ->
		     Format.fprintf ppf " %a->" print_witness x;
		     match y with
		       | None -> Format.fprintf ppf "#"
		       | Some y -> print_witness ppf y) f;
	Format.fprintf ppf " }"
    | WAbstract None ->
	Format.fprintf ppf "Abstract(..)"
    | WAbstract (Some s) ->
	Format.fprintf ppf "Abstract(%s)" s
    | WAbsent ->
	Format.fprintf ppf "Absent"
	  
664 665 666 667 668 669 670 671 672 673 674 675 676 677
  let wmk w =  (* incr wuid; w *)  (* hash-consing disabled *)
    try WHash.find wmemo w
    with Not_found -> 
      incr wuid; 
      WHash.add wmemo w w;
(*      Format.fprintf Format.std_formatter "W:%a@." 
	print_witness w; *)
      w

  let wpair p1 p2 = wmk (WPair (p1,p2, wslot()))
  let wxml p1 p2 = wmk (WXml (p1,p2, wslot()))
  let wrecord r o = wmk (WRecord (r,o, wslot()))
  let wfun f = wmk (WFun (f, wslot()))

678
  let bool_pair f =
679
    Pair.compute 
680 681 682 683 684
      ~empty:false ~full:true 
      ~cup:(||) ~cap:(&&) ~diff:(fun x y -> x && not y) 
      ~atom:f

  let bool_rec f =
685
    Rec.compute 
686 687 688 689 690 691 692 693 694 695 696 697 698 699 700
      ~empty:false ~full:true 
      ~cup:(||) ~cap:(&&) ~diff:(fun x y -> x && not y) 
      ~atom:f

  let rec node_has n = function
    | WXml (_,_,s) | WPair (_,_,s) | WFun (_,s) | WRecord (_,_,s) as w ->
	if NodeSet.mem n s.wnodes_in then true
	else if NodeSet.mem n s.wnodes_out then false
	else (let r = type_has (descr n) w in
	      if r then s.wnodes_in <- NodeSet.add n s.wnodes_in
	      else s.wnodes_out <- NodeSet.add n s.wnodes_out;
	      r)
    | w -> type_has (descr n) w

  and type_has t = function
701 702 703
    | WInt i -> Intervals.contains i (BoolIntervals.get t.ints)
    | WChar c -> Chars.contains c (BoolChars.get t.chars)
    | WAtom a -> Atoms.contains_sample a (BoolAtoms.get t.atoms)
704 705 706
    | WPair (w1,w2,_) -> 
	bool_pair 
	  (fun (n1,n2) -> node_has n1 w1 && node_has n2 w2) 
707
	  (BoolPair.get t.times)
708 709 710
    | WXml (w1,w2,_) ->
	bool_pair 
	  (fun (n1,n2) -> node_has n1 w1 && node_has n2 w2)
711
	  (BoolPair.get t.xml)
712 713 714 715 716 717 718 719 720
    | WFun (f,_) ->
	bool_pair 
	  (fun (n1,n2) ->
	     List.for_all
	       (fun (x,y) ->
		  not (node_has n1 x) ||
		    (match y with None -> false
		       | Some y -> node_has n2 y))
	       f) 
721
	  (BoolPair.get t.arrow)
722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739
    | WRecord (f,o,_) ->
	bool_rec 
	  (fun (o',f') ->
	     ((not o) || o') && (
	       let checked = ref 0 in
	       try 
		 LabelMap.iteri 
		   (fun l n ->
		      let w = 
			try let w = LabelMap.assoc l f in incr checked; w
			with Not_found -> WAbsent in
		      if not (node_has n w) then raise Exit
		   ) f'; 
		 o' || (LabelMap.length f == !checked)
		   (* All the remaining fields cannot be WAbsent
		      because of an invariant. Otherwise, we must
		      check that all are WAbsent here. *)
	       with Exit -> false))
740
	  (BoolRec.get t.record)
741 742 743 744
    | WAbsent -> t.absent
    | WAbstract a -> Abstract.contains_sample a t.abstract
end

745 746 747
type slot = { mutable status : status; 
	       mutable notify : notify;
	       mutable active : bool }
748 749
and status = Empty | NEmpty of Witness.witness | Maybe
and notify = Nothing | Do of slot * (Witness.witness -> unit) * notify
750 751

let slot_empty = { status = Empty; active = false; notify = Nothing }
752 753
let slot_nempty w = { status = NEmpty w;
		     active = false; notify = Nothing }
754

755
let rec notify w = function
756 757
  | Nothing -> ()
  | Do (n,f,rem) -> 
758 759
      if n.status == Maybe then (try f w with NotEmpty -> ());
      notify w rem
760 761 762 763 764

let rec iter_s s f = function
  | [] -> ()
  | arg::rem -> f arg s; iter_s s f rem

765 766 767
let set s w =
  s.status <- NEmpty w;
  notify w s.notify;
768
  s.notify <- Nothing; 
769 770
  raise NotEmpty

771
let rec big_conj f l n w =
772
  match l with
773 774
    | [] -> set n w
    | [arg] -> f w arg n
775
    | arg::rem ->
776 777
	let s = 
	  { status = Maybe; active = false; 
778
	    notify = Do (n,(big_conj f rem n), Nothing) } in
779
	try 
780
	  f w arg s;
781
	  if s.active then n.active <- true
782
	with NotEmpty when n.status == Empty || n.status == Maybe -> ()
783

784
let memo = DescrHash.create 8191
785 786
let marks = ref [] 

787 788
let count_subtype = Stats.Counter.create "Subtyping internal loop" 

789 790
let complex = ref 0

791
let rec slot d =
792
  incr complex;
793
  Stats.Counter.incr count_subtype; 
794
  if d.absent then slot_nempty Witness.WAbsent
795 796 797 798 799 800
  else if not (Intervals.is_empty (BoolIntervals.get d.ints)) 
  then slot_nempty (Witness.WInt (Intervals.sample (BoolIntervals.get d.ints)))
  else if not (Atoms.is_empty (BoolAtoms.get d.atoms)) 
  then slot_nempty (Witness.WAtom (Atoms.sample (BoolAtoms.get d.atoms)))
  else if not (Chars.is_empty (BoolChars.get d.chars)) 
  then slot_nempty (Witness.WChar (Chars.sample (BoolChars.get d.chars)))
801
  else if not (Abstract.is_empty d.abstract) 
802
  then slot_nempty (Witness.WAbstract (Abstract.sample d.abstract))
803 804 805 806 807
  else try DescrHash.find memo d
  with Not_found ->
    let s = { status = Maybe; active = false; notify = Nothing } in
    DescrHash.add memo d s;
    (try
808 809 810 811
       iter_s s check_times (Pair.get (BoolPair.get d.times));
       iter_s s check_xml (Pair.get (BoolPair.get d.xml)); 
       iter_s s check_arrow (Pair.get (BoolPair.get d.arrow));
       iter_s s check_record (get_record (BoolRec.get d.record));
812
       if s.active then marks := s :: !marks else s.status <- Empty;
813
     with NotEmpty -> ());
814 815
    s

816 817 818 819 820
and guard n t f = match (slot t) with
  | { status = Empty } -> ()
  | { status = Maybe } as s -> n.active <- true; s.notify <- Do (n,f,s.notify)
  | { status = NEmpty v } -> f v

821
and check_times (left,right) s =
822 823 824 825 826 827 828 829
  let rec aux w1 w2 accu1 accu2 seen = function
    (* Find a product in right which contains (w1,w2) *)
    | [] -> (* no such product: the current witness is in the difference. *)
	set s (Witness.wpair w1 w2)
    | (n1,n2) :: rest 
	when (Witness.node_has n1 w1) && (Witness.node_has n2 w2) ->
	let right = seen @ rest in
	let accu2' = diff accu2 (descr n2) in 
830 831 832
	guard s accu2' (fun w2 -> aux w1 w2 accu1 accu2' [] right);
	let accu1' = diff accu1 (descr n1) in
	guard s accu1' (fun w1 -> aux w1 w2 accu1' accu2 [] right)
833
    | k :: rest -> aux w1 w2 accu1 accu2 (k::seen) rest
834
  in
835 836
  let (t1,t2) = cap_product any any left in
  guard s t1 (fun w1 -> guard s t2 (fun w2 -> aux w1 w2 t1 t2 [] right))
837 838

and check_xml (left,right) s =
839 840 841 842 843 844 845 846
  let rec aux w1 w2 accu1 accu2 seen = function
    (* Find a product in right which contains (w1,w2) *)
    | [] -> (* no such product: the current witness is in the difference. *)
	set s (Witness.wxml w1 w2)
    | (n1,n2) :: rest 
	when (Witness.node_has n1 w1) && (Witness.node_has n2 w2) ->
	let right = seen @ rest in
	let accu2' = diff accu2 (descr n2) in 
847 848 849
	guard s accu2' (fun w2 -> aux w1 w2 accu1 accu2' [] right);
	let accu1' = diff accu1 (descr n1) in
	guard s accu1' (fun w1 -> aux w1 w2 accu1' accu2 [] right)
850
    | k :: rest -> aux w1 w2 accu1 accu2 (k::seen) rest
851
  in
852 853
  let (t1,t2) = cap_product any any_pair left in
  guard s t1 (fun w1 -> guard s t2 (fun w2 -> aux w1 w2 t1 t2 [] right))
854

855
and check_arrow (left,right) s =
856 857
  let single_right f (s1,s2) s =
    let rec aux w1 w2 accu1 accu2 left = match left with
858
      | (t1,t2)::left ->
859
          let accu1' = diff_t accu1 t1 in 
860
	  guard s accu1' (fun w1 -> aux w1 w2 accu1' accu2 left);
861 862

          let accu2' = cap_t  accu2 t2 in 
863
	  guard s accu2' (fun w2 -> aux w1 (Some w2) accu1 accu2' left)
864 865 866
      | [] -> 
	  let f = match f with Witness.WFun (f,_) -> f | _ -> assert false in
	  set s (Witness.wfun ((w1,w2)::f))
867 868
    in
    let accu1 = descr s1 in
869
    guard s accu1 (fun w1 -> aux w1 None accu1 (neg (descr s2)) left)
870
  in
871
  big_conj single_right right s (Witness.wfun [])
872

873
and check_record (labels,(oleft,left),rights) s =