types.ml 40.8 KB
Newer Older
1 2
open Recursive
open Printf
3
open Ident
4

5 6 7 8 9 10 11 12 13 14 15 16 17 18
(* IDEAS for optimizations:

  * optimize lines of dnf for products and record;
    instead of
      (t1,s1) & ... & (tn,sn) \ ....
    use:
      (t1 & ... & tn, s1 & ... & sn) \ ....

    ---> more compact representation, more sharing, ...
 
  * re-consider using BDD-like representation instead of dnf
*)


19 20
let map_sort f l =
  SortedList.from_list (List.map f l)
21

22 23 24 25 26 27
module HashedString = 
struct 
  type t = string 
  let hash = Hashtbl.hash
  let equal = (=)
end
28 29


30 31 32 33
type const = 
  | Integer of Intervals.v
  | Atom of Atoms.v
  | Char of Chars.v
34

35 36
type pair_kind = [ `Normal | `XML ]

37 38 39 40 41 42 43 44 45 46 47 48
type 'a node0 = { id : int; mutable descr : 'a }

module NodePair = struct
  type 'a t = 'a node0 * 'a node0
  let compare (x1,y1) (x2,y2) =
    if x1.id < x2.id then -1
    else if x1.id > x2.id then 1
    else y1.id - y2.id
  let equal (x1,y1) (x2,y2) = (x1==x2) && (y1==y2)
  let hash (x,y) = x.id + 17 * y.id
end 

49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
module RecArg = struct
  type 'a t = bool * 'a node0 label_map
  
  let rec compare_rec r1 r2 =
    if r1 == r2 then 0
    else match (r1,r2) with
      | (l1,x1)::r1,(l2,x2)::r2 ->
	  if ((l1:int) < l2) then -1 
	  else if (l1 > l2) then 1 
	  else if x1.id < x2.id then -1
	  else if x1.id > x2.id then 1
	  else compare_rec r1 r2
      | ([],_) -> -1
      | _ -> 1

  let compare (o1,r1) (o2,r2) =
    if o1 && not o2 then -1 
    else if o2 && not o1 then 1
    else compare_rec (LabelMap.get r1) (LabelMap.get r2)

  let rec equal_rec r1 r2 =
    (r1 == r2) ||
    match (r1,r2) with
      | (l1,x1)::r1,(l2,x2)::r2 ->
	  (x1.id == x2.id) && (l1 == l2) && (equal_rec r1 r2)
      | _ -> false

  let equal (o1,r1) (o2,r2) =
    (o1 == o2) && (equal_rec (LabelMap.get r1) (LabelMap.get r2))

  let rec hash_rec accu = function
    | (l,x)::rem -> hash_rec (257 * accu + 17 * l + x.id) rem
    | [] -> accu + 5
      
  let hash (o,r) = hash_rec (if o then 2 else 1) (LabelMap.get r)
end

86
module BoolPair = Boolean.Make(NodePair)
87
module BoolRec = Boolean.Make(RecArg)
88

89
type descr = {
90
  atoms : Atoms.t;
91 92
  ints  : Intervals.t;
  chars : Chars.t;
93 94 95
  times : descr BoolPair.t;
  xml   : descr BoolPair.t;
  arrow : descr BoolPair.t;
96
  record: descr BoolRec.t;
97
  absent: bool
98
} and node = descr node0
99

100
	       
101
let empty = { 
102 103 104
  times = BoolPair.empty; 
  xml   = BoolPair.empty; 
  arrow = BoolPair.empty; 
105
  record= BoolRec.empty;
106 107 108
  ints  = Intervals.empty;
  atoms = Atoms.empty;
  chars = Chars.empty;
109
  absent= false;
110 111 112
}
	      
let any =  {
113 114 115
  times = BoolPair.full; 
  xml   = BoolPair.full; 
  arrow = BoolPair.full; 
116
  record= BoolRec.full; 
117 118 119
  ints  = Intervals.any;
  atoms = Atoms.any;
  chars = Chars.any;
120
  absent= false;
121 122 123 124
}
	     
	     
let interval i = { empty with ints = i }
125 126 127
let times x y = { empty with times = BoolPair.atom (x,y) }
let xml x y = { empty with xml = BoolPair.atom (x,y) }
let arrow x y = { empty with arrow = BoolPair.atom (x,y) }
128
let record label t = 
129 130 131
  { empty with record = BoolRec.atom (true,LabelMap.singleton label t) }
let record' (x : bool * node Ident.label_map) =
  { empty with record = BoolRec.atom x }
132 133 134 135 136 137
let atom a = { empty with atoms = a }
let char c = { empty with chars = c }
let constant = function
  | Integer i -> interval (Intervals.atom i)
  | Atom a -> atom (Atoms.atom a)
  | Char c -> char (Chars.atom c)
138
      
139 140
let cup x y = 
  if x == y then x else {
141 142 143
    times = BoolPair.cup x.times y.times;
    xml   = BoolPair.cup x.xml y.xml;
    arrow = BoolPair.cup x.arrow y.arrow;
144
    record= BoolRec.cup x.record y.record;
145 146 147
    ints  = Intervals.cup x.ints  y.ints;
    atoms = Atoms.cup x.atoms y.atoms;
    chars = Chars.cup x.chars y.chars;
148
    absent= x.absent || y.absent;
149 150 151 152
  }
    
let cap x y = 
  if x == y then x else {
153 154
    times = BoolPair.cap x.times y.times;
    xml   = BoolPair.cap x.xml y.xml;
155
    record= BoolRec.cap x.record y.record;
156
    arrow = BoolPair.cap x.arrow y.arrow;
157 158 159
    ints  = Intervals.cap x.ints  y.ints;
    atoms = Atoms.cap x.atoms y.atoms;
    chars = Chars.cap x.chars y.chars;
160
    absent= x.absent && y.absent;
161 162 163 164
  }
    
let diff x y = 
  if x == y then empty else {
165 166 167
    times = BoolPair.diff x.times y.times;
    xml   = BoolPair.diff x.xml y.xml;
    arrow = BoolPair.diff x.arrow y.arrow;
168
    record= BoolRec.diff x.record y.record;
169 170 171
    ints  = Intervals.diff x.ints  y.ints;
    atoms = Atoms.diff x.atoms y.atoms;
    chars = Chars.diff x.chars y.chars;
172
    absent= x.absent && not y.absent;
173 174
  }
    
175 176 177 178

let rec compare_rec r1 r2 =
  if r1 == r2 then 0
  else match (r1,r2) with
179
    | (l1,x1)::r1,(l2,x2)::r2 ->
180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229
	if ((l1:int) < l2) then -1 
	else if (l1 > l2) then 1 
	else if x1.id < x2.id then -1
	else if x1.id > x2.id then 1
	else compare_rec r1 r2
    | ([],_) -> -1
    | _ -> 1

let rec compare_rec_list l1 l2  =
  if l1 == l2 then 0 
  else match (l1,l2) with
    | (o1,r1)::l1, (o2,r2)::l2 ->
	if o2 && not o1 then -1
	else if o1 && not o2 then 1
	else let c = compare_rec r1 r2 in if c <> 0 then c 
	else compare_rec_list l1 l2
    | ([],_) -> -1
    | _ -> 1

let rec compare_rec_bool l1 l2  =
  if l1 == l2 then 0 
  else match (l1,l2) with
    | (p1,n1)::l1, (p2,n2)::l2 ->
	let c = compare_rec_list p1 p2 in if c <> 0 then c 
	else let c = compare_rec_list n1 n2 in if c <> 0 then c 
	else compare_rec_bool l1 l2
    | ([],_) -> -1
    | _ -> 1

let rec compare_times_list l1 l2  =
  if l1 == l2 then 0 
  else match (l1,l2) with
    | (x1,y1)::l1, (x2,y2)::l2 ->
	if (x1.id < x2.id) then -1
	else if (x1.id > x2.id) then 1 
	else if (y1.id < y2.id) then -1
	else if (y1.id > y2.id) then 1 
	else compare_times_list l1 l2
    | ([],_) -> -1
    | _ -> 1

let rec compare_times_bool l1 l2  =
  if l1 == l2 then 0 
  else match (l1,l2) with
    | (p1,n1)::l1, (p2,n2)::l2 ->
	let c = compare_times_list p1 p2 in if c <> 0 then c 
	else let c = compare_times_list n1 n2 in if c <> 0 then c 
	else compare_times_bool l1 l2
    | ([],_) -> -1
    | _ -> 1
230 231 232 233
	     
let rec equal_rec r1 r2 =
  (r1 == r2) ||
  match (r1,r2) with
234 235
    | (l1,x1)::r1,(l2,x2)::r2 ->
	(x1.id = x2.id) && (l1 == l2) && (equal_rec r1 r2)
236
    | _ -> false
237 238 239 240 241
	
let rec equal_rec_list l1 l2  =
  (l1 == l2) ||
  match (l1,l2) with
    | (o1,r1)::l1, (o2,r2)::l2 ->
242 243
	(o1 == o2) &&
	(equal_rec r1 r2) && (equal_rec_list l1 l2)
244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273
    | _ -> false
	
let rec equal_rec_bool l1 l2 =
  (l1 == l2) ||
  match (l1,l2) with
    | (p1,n1)::l1, (p2,n2)::l2 -> 
	(equal_rec_list p1 p2) &&
	(equal_rec_list n1 n2) &&
        (equal_rec_bool l1 l2)
    | _ -> false
	
let rec equal_times_list l1 l2  =
  (l1 == l2) ||
  match (l1,l2) with
    | (x1,y1)::l1, (x2,y2)::l2 -> 
	(x1.id = x2.id) &&
	(y1.id = y2.id) &&
	(equal_times_list l1 l2)
    | _ -> false
	
let rec equal_times_bool l1 l2 =
  (l1 == l2) ||
  match (l1,l2) with
    | (p1,n1)::l1, (p2,n2)::l2 -> 
	(equal_times_list p1 p2) &&
	(equal_times_list n1 n2) &&
        (equal_times_bool l1 l2)
    | _ -> false
	
let equal_descr a b =
274 275 276
  (Atoms.equal a.atoms b.atoms) &&
  (Chars.equal a.chars b.chars) &&
  (Intervals.equal a.ints  b.ints) &&
277 278 279
  (BoolPair.equal a.times b.times) &&
  (BoolPair.equal a.xml b.xml) &&
  (BoolPair.equal a.arrow b.arrow) &&
280
  (BoolRec.equal a.record b.record) &&
281
  (a.absent == b.absent)
282 283

let compare_descr a b =
284 285
  if a == b then 0 
  else let c = Atoms.compare a.atoms b.atoms in if c <> 0 then c
286 287
  else let c = compare a.chars b.chars in if c <> 0 then c
  else let c = compare a.ints b.ints in if c <> 0 then c
288 289 290
  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
291
  else let c = BoolRec.compare a.record b.record in if c <> 0 then c
292 293
  else if a.absent && not b.absent then -1
  else if b.absent && not a.absent then 1
294 295 296 297 298 299 300 301 302 303
  else 0

(*
let compare_descr a b =
  let c = compare_descr a b in
  assert (c = compare a b);
  c
*)


304 305 306 307 308 309 310 311 312 313 314
let rec hash_times_list accu = function
  | (x,y)::l ->
      hash_times_list (accu * 257 + x.id * 17 + y.id) l
  | [] -> accu + 17
      
let rec hash_times_bool accu = function
  | (p,n)::l -> 
      hash_times_bool (hash_times_list (hash_times_list accu p) n) l
  | [] -> accu + 3
      
let rec hash_rec accu = function
315
  | (l,x)::rem ->
316 317 318 319 320
      hash_rec (257 * accu + 17 * (LabelPool.hash l) + x.id) rem
  | [] -> accu + 5
      
let rec hash_rec_list accu = function
  | (o,r)::l ->
321
      hash_rec_list (hash_rec (if o then accu*3 else accu) r) l
322 323 324 325 326 327 328 329 330
  | [] -> accu + 17
      
let rec hash_rec_bool accu = function
  | (p,n)::l -> 
      hash_rec_bool (hash_rec_list (hash_rec_list accu p) n) l
  | [] -> accu + 3
      
      
let hash_descr a =
331 332 333
  let accu = Chars.hash 1 a.chars in
  let accu = Intervals.hash accu a.ints in
  let accu = Atoms.hash accu a.atoms in
334 335 336
  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
337
  let accu = 17 * accu + BoolRec.hash a.record in
338
  let accu = if a.absent then accu+5 else accu in
339
  accu
340

341

342 343 344 345 346 347 348 349 350
module DescrHash = 
  Hashtbl.Make(
    struct 
      type t = descr
      let hash = hash_descr
      let equal = equal_descr
    end
  )

351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369
let hash_cons = DescrHash.create 17000

let count = ref 0
let make () = incr count; { id = !count; descr = empty }
let define n d = 
(*  DescrHash.add hash_cons d n; *)
  n.descr <- d
let cons d = 
  (* try DescrHash.find hash_cons d with Not_found ->
  incr count; let n = { id = !count; descr = d } in
  DescrHash.add hash_cons d n; n *)
  incr count; { id = !count; descr = d }
let descr n = n.descr
let internalize n = n
let id n = n.id




370 371
let print_descr = ref (fun _ _  -> assert false)

372 373
let neg x = diff any x

374 375
let any_node = cons any

376
module LabelS = Set.Make(LabelPool)
377 378 379

let get_record r =
  let labs accu (_,r) = 
380 381
    List.fold_left 
      (fun accu (l,_) -> LabelS.add l accu) accu (LabelMap.get r) in
382
  let extend descrs labs (o,r) =
383 384 385 386 387
    let rec aux i labs r =
      match labs with
	| [] -> ()
	| l1::labs ->
	    match r with
388
	      | (l2,x)::r when l1 == l2 -> 
389 390 391
		  descrs.(i) <- cap descrs.(i) (descr x);
		  aux (i+1) labs r
	      | r ->
392 393
		  if not o then descrs.(i) <- 
		    cap descrs.(i) { empty with absent = true };
394 395
		  aux (i+1) labs r
    in
396
    aux 0 labs (LabelMap.get r);
397 398 399 400
    o
  in
  let line (p,n) =
    let labels = 
401 402
      List.fold_left labs (List.fold_left labs LabelS.empty p) n in
    let labels = LabelS.elements labels in
403
    let nlab = List.length labels in
404
    let mk () = Array.create nlab { any with absent = true } in
405 406 407 408 409 410 411 412 413 414 415 416 417 418 419

    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
420
  List.map line (BoolRec.get r)
421
   
422

423
module DescrMap = Map.Make(struct type t = descr let compare = compare end)
424

425
let check d =
426 427 428
  BoolPair.check d.times;
  BoolPair.check d.xml;
  BoolPair.check d.arrow;
429
  BoolRec.check d.record;
430
  ()
431

432 433 434 435 436 437 438 439 440 441 442 443 444


(* 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)
let cap_product l =
  List.fold_left 
    (fun (d1,d2) (t1,t2) -> (cap_t d1 t1, cap_t d2 t2))
    (any,any)
    l

445 446 447
let rec exists max f =
  (max > 0) && (f (max - 1) || exists (max - 1) f)

448
let trivially_empty d = equal_descr d empty
449

450
exception NotEmpty
451

452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477
type slot = { mutable status : status; 
	       mutable notify : notify;
	       mutable active : bool }
and status = Empty | NEmpty | Maybe
and notify = Nothing | Do of slot * (slot -> unit) * notify

let memo = DescrHash.create 33000

let marks = ref [] 
let slot_empty = { status = Empty; active = false; notify = Nothing }
let slot_not_empty = { status = NEmpty; active = false; notify = Nothing }

let rec notify = function
  | Nothing -> ()
  | Do (n,f,rem) -> 
      if n.status = Maybe then (try f n with NotEmpty -> ());
      notify rem

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


let set s =
  s.status <- NEmpty;
  notify s.notify;
478
  s.notify <- Nothing; 
479 480 481 482 483 484 485 486 487 488 489 490 491
  raise NotEmpty

let rec big_conj f l n =
  match l with
    | [] -> set n
    | [arg] -> f arg n
    | arg::rem ->
	let s = { status = Maybe; active = false; notify = Do (n,(big_conj f rem), Nothing) } in
	try 
	  f arg s;
	  if s.active then n.active <- true
	with NotEmpty -> if n.status = NEmpty then raise NotEmpty

492

493
let rec guard a f n =
494 495
  match slot a with
    | { status = Empty } -> ()
496
    | { status = Maybe } as s -> n.active <- true; s.notify <- Do (n,f,s.notify)
497
    | { status = NEmpty } -> f n
498 499 500 501

and slot d =
  if not ((Intervals.is_empty d.ints) && 
	  (Atoms.is_empty d.atoms) &&
502 503
	  (Chars.is_empty d.chars) &&
	  (not d.absent)) then slot_not_empty 
504 505 506 507 508
  else try DescrHash.find memo d
  with Not_found ->
    let s = { status = Maybe; active = false; notify = Nothing } in
    DescrHash.add memo d s;
    (try
509 510 511
       iter_s s check_times (BoolPair.get d.times);
       iter_s s check_times (BoolPair.get d.xml);
       iter_s s check_arrow (BoolPair.get d.arrow);
512 513 514 515 516 517 518
       iter_s s check_record (get_record d.record);
       if s.active then marks := s :: !marks else s.status <- Empty;
     with
	 NotEmpty -> ());
    s

and check_times (left,right) s =
519 520
(*  Printf.eprintf "[%i]" (List.length right);
  flush stderr; *)
521 522 523
  let rec aux accu1 accu2 right s = match right with
    | (t1,t2)::right ->
	if trivially_empty (cap_t accu1 t1) || 
524 525 526
	   trivially_empty (cap_t accu2 t2) then (
	     aux accu1 accu2 right s )
	else (
527
          let accu1' = diff_t accu1 t1 in guard accu1' (aux accu1' accu2 right) s;
528
          let accu2' = diff_t accu2 t2 in guard accu2' (aux accu1 accu2' right) s 
529
	)
530 531 532 533
    | [] -> set s
  in
  let (accu1,accu2) = cap_product left in
  guard accu1 (guard accu2 (aux accu1 accu2 right)) s
534

535 536 537 538 539 540 541 542 543 544 545 546
and check_arrow (left,right) s =
  let single_right (s1,s2) s =
    let rec aux accu1 accu2 left s = match left with
      | (t1,t2)::left ->
          let accu1' = diff_t accu1 t1 in guard accu1' (aux accu1' accu2 left) s;
          let accu2' = cap_t  accu2 t2 in guard accu2' (aux accu1 accu2' left) s
      | [] -> set s
    in
    let accu1 = descr s1 in
    guard accu1 (aux accu1 (neg (descr s2)) left) s
  in
  big_conj single_right right s
547

548
and check_record (labels,(oleft,left),rights) s =
549 550
  let rec aux rights s = match rights with
    | [] -> set s
551
    | (oright,right)::rights ->
552
	let next =
553
	  (oleft && (not oright)) || (* ggg... why ???  check this line *)
554 555
	  exists (Array.length left)
	    (fun i ->
556
	       trivially_empty (cap left.(i) right.(i)))
557 558 559 560 561 562
	in
	if next then aux rights s
	else
	  for i = 0 to Array.length left - 1 do
	    let back = left.(i) in
	    let di = diff back right.(i) in
563 564 565 566 567
	    guard di (fun s ->
			left.(i) <- diff back right.(i);
			aux rights s;
			left.(i) <- back;
		     ) s
568 569 570 571 572
	  done
  in
  let rec start i s =
    if (i < 0) then aux rights s
    else
573
      guard left.(i) (start (i - 1)) s
574 575 576 577 578
  in
  start (Array.length left - 1) s


let is_empty d =
579
(*  Printf.eprintf "is_empty: start\n"; flush stderr; *)
580 581 582 583 584
  let s = slot d in
  List.iter 
    (fun s' -> if s'.status = Maybe then s'.status <- Empty; s'.notify <- Nothing) 
    !marks;
  marks := [];
585
(*  Printf.eprintf "is_empty: done\n"; flush stderr; *)
586 587 588
  s.status = Empty
  

589
module Assumptions = Set.Make(struct type t = descr let compare = compare_descr end)
590 591
let memo = ref Assumptions.empty
let cache_false = DescrHash.create 33000
592

593
let rec empty_rec d =
594
  if not (Intervals.is_empty d.ints) then false
595 596
  else if not (Atoms.is_empty d.atoms) then false
  else if not (Chars.is_empty d.chars) then false
597
  else if d.absent then false
598 599
  else if DescrHash.mem cache_false d then false 
  else if Assumptions.mem d !memo then true
600 601
  else (
    let backup = !memo in
602
    memo := Assumptions.add d backup;
603
    if 
604 605 606
      (empty_rec_times (BoolPair.get d.times)) &&
      (empty_rec_times (BoolPair.get d.xml)) &&
      (empty_rec_arrow (BoolPair.get d.arrow)) &&
607 608 609 610
      (empty_rec_record d.record) 
    then true
    else (
      memo := backup;
611
      DescrHash.add cache_false d ();
612 613 614 615 616 617 618 619 620 621
      false
    )
  )

and empty_rec_times c =
  List.for_all empty_rec_times_aux c

and empty_rec_times_aux (left,right) =
  let rec aux accu1 accu2 = function
    | (t1,t2)::right ->
622 623
	if trivially_empty (cap_t accu1 t1) || 
	   trivially_empty (cap_t accu2 t2) then
624 625 626 627 628
	  aux accu1 accu2 right
	else
          let accu1' = diff_t accu1 t1 in
          if not (empty_rec accu1') then aux accu1' accu2 right;
          let accu2' = diff_t accu2 t2 in
629
	  if not (empty_rec accu2') then aux accu1 accu2' right
630 631 632 633 634
    | [] -> raise NotEmpty
  in
  let (accu1,accu2) = cap_product left in
  (empty_rec accu1) || (empty_rec accu2) ||
    (try aux accu1 accu2 right; true with NotEmpty -> false)
635

636 637 638 639 640 641 642 643 644

and empty_rec_arrow c =
  List.for_all empty_rec_arrow_aux c

and empty_rec_arrow_aux (left,right) =
  let single_right (s1,s2) =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff_t accu1 t1 in
645
          if not (empty_rec accu1') then aux accu1' accu2 left;
646
          let accu2' = cap_t accu2 t2 in
647
          if not (empty_rec accu2') then aux accu1 accu2' left
648 649 650 651 652 653 654 655
      | [] -> raise NotEmpty
    in
    let accu1 = descr s1 in
    (empty_rec accu1) ||
    (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)
  in
  List.exists single_right right

656
and empty_rec_record_aux (labels,(oleft,left),rights) =
657 658
  let rec aux = function
    | [] -> raise NotEmpty
659
    | (oright,right)::rights ->
660 661 662 663
	let next =
	  (oleft && (not oright)) ||
	  exists (Array.length left)
	    (fun i ->
664
	       trivially_empty (cap left.(i) right.(i)))
665 666 667 668 669 670
	in
	if next then aux rights 
	else
	  for i = 0 to Array.length left - 1 do
	    let back = left.(i) in
	    let di = diff back right.(i) in
671
	    if not (empty_rec di) then (
672 673 674 675 676 677 678
	      left.(i) <- diff back right.(i);
	      aux rights;
	      left.(i) <- back;
	    )
	  done
  in
  exists (Array.length left) 
679
    (fun i -> empty_rec left.(i))
680 681 682 683
  ||
  (try aux rights; true with NotEmpty -> false)
	    

684
and empty_rec_record c =
685
  List.for_all empty_rec_record_aux (get_record c)
686

687 688
(*
let is_empty d =
689
  empty_rec d
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

let non_empty d = 
  not (is_empty d)

let subtype d1 d2 =
  is_empty (diff d1 d2)

module Product =
struct
  type t = (descr * descr) list

  let other ?(kind=`Normal) d = 
    match kind with
      | `Normal -> { d with times = empty.times }
      | `XML -> { d with xml = empty.xml }

  let is_product ?kind d = is_empty (other ?kind d)

  let need_second = function _::_::_ -> true | _ -> false

  let normal_aux d =
    let res = ref [] in

    let add (t1,t2) =
      let rec loop t1 t2 = function
	| [] -> res := (ref (t1,t2)) :: !res
	| ({contents = (d1,d2)} as r)::l ->
	    (*OPT*) 
719
(*	    if equal_descr d1 t1 then r := (d1,cup d2 t2) else*)
720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736
	      
	      let i = cap t1 d1 in
	      if is_empty i then loop t1 t2 l
	      else (
		r := (i, cup t2 d2);
		let k = diff d1 t1 in 
		if non_empty k then res := (ref (k,d2)) :: !res;
		
		let j = diff t1 d1 in 
		if non_empty j then loop j t2 l
	      )
      in
      loop t1 t2 !res
    in
    List.iter add d;
    List.map (!) !res

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
This version explodes when dealing with
   Any - [ t1? t2? t3? ... tn? ]
==> need partitioning 
*)
  let get_aux d =
    let line accu (left,right) =
      let rec aux accu d1 d2 = function
	| (t1,t2)::right ->
	    let accu = 
	      let d1 = diff_t d1 t1 in
              if is_empty d1 then accu else aux accu d1 d2 right in
	    let accu =
              let d2 = diff_t d2 t2 in
              if is_empty d2 then accu else aux accu d1 d2 right in
	    accu
	| [] -> (d1,d2) :: accu
      in
      let (d1,d2) = cap_product left in
      if (is_empty d1) || (is_empty d2) then accu else aux accu d1 d2 right
    in
    List.fold_left line [] d

(* Partitioning:

(t,s) - ((t1,s1) | (t2,s2) | ... | (tn,sn))
=
(t & t1, s - s1) | ... | (t & tn, s - sn) | (t - (t1|...|tn), s)

766
*)
767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785
  let get_aux d =
    let accu = ref [] in
    let line (left,right) =
      let (d1,d2) = cap_product left in
      if (non_empty d1) && (non_empty d2) then
	let right = List.map (fun (t1,t2) -> descr t1, descr t2) right in
	let right = normal_aux right in
	let resid1 = ref d1 in
	let () = 
	  List.iter
	    (fun (t1,t2) ->
	       let t1 = cap d1 t1 in
	       if (non_empty t1) then
		 let () = resid1 := diff !resid1 t1 in
		 let t2 = diff d2 t2 in
		 if (non_empty t2) then accu := (t1,t2) :: !accu
	    ) right in
	if non_empty !resid1 then accu := (!resid1, d2) :: !accu 
    in
786
    List.iter line (BoolPair.get d);
787
    !accu
788 789 790
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
791

792

793 794
  let get ?(kind=`Normal) d = 
    match kind with
795 796
      | `Normal -> get_aux d.times
      | `XML -> get_aux d.xml
797 798 799

  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty
800 801 802 803
  let pi2_restricted restr = 
    List.fold_left (fun acc (t1,t2) -> 
		      if is_empty (cap t1 restr) then acc
		      else cup acc t2) empty
804 805

  let restrict_1 rects pi1 =
806 807
    let aux acc (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then acc else (t1,t2)::acc in
808 809 810 811
    List.fold_left aux [] rects
  
  type normal = t

812
  module Memo = Map.Make(struct type t = descr BoolPair.t let compare = BoolPair.compare end)
813 814 815 816 817 818 819 820


  let memo = ref Memo.empty
  let normal ?(kind=`Normal) d = 
    let d = match kind with `Normal -> d.times | `XML -> d.xml in
    try Memo.find d !memo 
    with
	Not_found ->
821
	  let gd = get_aux d in
822
	  let n = normal_aux gd in
823 824
(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
825 826
	  memo := Memo.add d n !memo;
	  n
827

828 829 830 831
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
832

833 834
module Print = 
struct
835 836 837 838 839 840 841
  let rec print_union ppf = function
    | [] -> Format.fprintf ppf "Empty"
    | [h] -> h ppf
    | h::t -> Format.fprintf ppf "@[%t |@ %a@]" h print_union t

  let print_tag ppf a =
    match Atoms.is_atom a with
842 843
      | Some a -> Format.fprintf ppf "%s" (Atoms.value a)
      | None -> Format.fprintf ppf "(%a)" print_union (Atoms.print a)
844

845
  let print_const ppf = function
846 847 848
    | Integer i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
849

850 851 852
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
853 854 855 856 857 858 859 860 861 862

  let marks = DescrHash.create 63
  let wh = ref []
  let count_name = ref 0
  let name () =
    incr count_name;
    "X" ^ (string_of_int !count_name)
(* TODO: 
   check that these generated names does not conflict with declared types *)

863
  let trivial_rec b = b = BoolRec.empty || b = BoolRec.full
864
  let trivial_pair b = b = BoolPair.empty || b = BoolPair.full
865 866

  let worth_abbrev d = 
867 868
    not (trivial_pair d.times && trivial_pair d.xml && 
	 trivial_pair d.arrow && trivial_rec d.record) 
869 870 871

  let rec mark n = mark_descr (descr n)
  and mark_descr d =
872
    if not (DescrMap.mem d !named) then
873 874 875 876 877 878 879 880
      try 
	let r = DescrHash.find marks d in
	if (!r = None) && (worth_abbrev d) then 
	  let na = name () in 
	  r := Some na;
	  wh := (na,d) :: !wh
      with Not_found -> 
	DescrHash.add marks d (ref None);
881 882
    	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.times;
    	BoolPair.iter 
883 884
	  (fun (n1,n2) -> mark n1; mark n2
(*
885 886 887
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
888 889 890
    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
891
		  let l = get_record d1.record in
892 893 894 895 896
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
897 898
	       )
	       (Product.normal (descr n2))
899
*)
900
	  ) d.xml;
901
	BoolPair.iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
902 903 904
    	BoolRec.iter 
	  (fun (o,l) -> List.iter (fun (l,n) -> mark n) (LabelMap.get l)) 
	  d.record
905 906 907 908 909

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
910
      let name = DescrMap.find d !named in
911 912 913 914 915 916 917
      Format.fprintf ppf "%s" name
    with Not_found ->
      try
      	match !(DescrHash.find marks d) with
      	  | Some n -> Format.fprintf ppf "%s" n
      	  | None -> real_print_descr ppf d
      with
918
	  Not_found -> assert false
919 920
  and real_print_descr ppf d = 
    if d = any then Format.fprintf ppf "Any" else
921 922 923 924 925 926 927 928 929
      (
	if d.absent then Format.fprintf ppf "?";
	print_union ppf 
	  (Intervals.print d.ints @
	   Chars.print d.chars @
	   Atoms.print d.atoms @
	   BoolPair.print "Pair" print_times d.times @
	   BoolPair.print "XML" print_xml d.xml @
	   BoolPair.print "Arrow" print_arrow d.arrow @
930
	   BoolRec.print "Record" print_record d.record
931 932
	  )
      )
933 934
  and print_times ppf (t1,t2) =
    Format.fprintf ppf "@[(%a,%a)@]" print t1 print t2
935
  and print_xml ppf (t1,t2) =
936 937
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
938 939 940 941 942 943 944 945 946
    let l = Product.normal (descr t2) in
    let l = List.map
	      (fun (d1,d2) ppf ->
		 Format.fprintf ppf "@[<><%a%a>%a@]" 
		   print_tag (descr t1).atoms
		   print_attribs d1.record 
		   print_descr d2) l
    in
    print_union ppf l
947
*)
948 949
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
950 951 952 953
  and print_record ppf (o,r) =
    let o = if o then "" else "|" in
    Format.fprintf ppf "@[{%s" o;
    let first = ref true in
954
    List.iter (fun (l,t) ->
955
		 let sep = if !first then (first := false; "") else ";" in
956 957
		 Format.fprintf ppf "%s@ @[%s =@] %a" sep
		   (LabelPool.value l) print t
958
	      ) (LabelMap.get r);
959 960
    Format.fprintf ppf " %s}@]" o
(*
961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977
  and print_attribs ppf r =
    let l = get_record r in
    if l <> [ [] ] then 
    let l = List.map 
      (fun att ppf ->
	 let first = ref true in
	 Format.fprintf ppf "{" ;
	 List.iter (fun (l,(o,d)) ->
		      Format.fprintf ppf "%s%s=%s%a" 
		        (if !first then "" else " ")
		        (LabelPool.value l) (if o then "?" else "")
		        print_descr d; 
		      first := false
		   ) att;
	   Format.fprintf ppf "}"
      ) l in
    print_union ppf l
978
*)
979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005

	  
  let end_print ppf =
    (match List.rev !wh with
       | [] -> ()
       | (na,d)::t ->
	   Format.fprintf ppf " where@ @[%s = %a" na real_print_descr d;
	   List.iter 
	     (fun (na,d) -> 
		Format.fprintf ppf " and@ %s = %a" na real_print_descr d)
	     t;
	   Format.fprintf ppf "@]"
    );
    Format.fprintf ppf "@]";
    count_name := 0;
    wh := [];
    DescrHash.clear marks

  let print_descr ppf d =
    mark_descr d;
    Format.fprintf ppf "@[%a" print_descr d;
    end_print ppf

   let print ppf n = print_descr ppf (descr n)

end

1006
let () = print_descr := Print.print_descr
1007

1008 1009
module Positive =
struct
1010
  type rhs = [ `Type of descr | `Cup of v list | `Times of v * v | `Xml of v * v ]
1011
  and v = { mutable def : rhs; mutable node : node option }
1012 1013


1014 1015 1016 1017 1018 1019 1020 1021 1022
  let rec make_descr seen v =
    if List.memq v seen then empty
    else
      let seen = v :: seen in
      match v.def with
	| `Type d -> d
	| `Cup vl -> 
	    List.fold_left (fun acc v -> cup acc (make_descr seen v)) empty vl
	| `Times (v1,v2) -> times (make_node v1) (make_node v2)
1023
	| `Xml (v1,v2)