types.ml 43.1 KB
Newer Older
1 2
open Recursive
open Printf
3

4

5 6
let map_sort f l =
  SortedList.from_list (List.map f l)
7

8 9 10 11 12 13
module HashedString = 
struct 
  type t = string 
  let hash = Hashtbl.hash
  let equal = (=)
end
14

15
module LabelPool = Pool.Make(HashedString)
16

17
type label = LabelPool.t
18

19 20 21 22
type const = 
  | Integer of Intervals.v
  | Atom of Atoms.v
  | Char of Chars.v
23

24 25
type pair_kind = [ `Normal | `XML ]

26
type descr = {
27
  atoms : Atoms.t;
28 29 30 31 32 33 34 35 36 37
  ints  : Intervals.t;
  chars : Chars.t;
  times : (node * node) Boolean.t;
  xml   : (node * node) Boolean.t;
  arrow : (node * node) Boolean.t;
  record: (bool * (label, (bool * node)) SortedMap.t) Boolean.t;
} and node = {
  id : int;
  mutable descr : descr;
}
38

39
	       
40 41 42 43 44 45 46 47 48 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
let empty = { 
  times = Boolean.empty; 
  xml   = Boolean.empty; 
  arrow = Boolean.empty; 
  record= Boolean.empty;
  ints  = Intervals.empty;
  atoms = Atoms.empty;
  chars = Chars.empty;
}
	      
let any =  {
  times = Boolean.full; 
  xml   = Boolean.full; 
  arrow = Boolean.full; 
  record= Boolean.full; 
  ints  = Intervals.any;
  atoms = Atoms.any;
  chars = Chars.any;
}
	     
	     
let interval i = { empty with ints = i }
let times x y = { empty with times = Boolean.atom (x,y) }
let xml x y = { empty with xml = Boolean.atom (x,y) }
let arrow x y = { empty with arrow = Boolean.atom (x,y) }
let record label opt t = 
  { empty with record = Boolean.atom (true,[label,(opt,t)]) }
let record' x =
  { empty with record = Boolean.atom x }
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)
75
      
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115
let cup x y = 
  if x == y then x else {
    times = Boolean.cup x.times y.times;
    xml   = Boolean.cup x.xml y.xml;
    arrow = Boolean.cup x.arrow y.arrow;
    record= Boolean.cup x.record y.record;
    ints  = Intervals.cup x.ints  y.ints;
    atoms = Atoms.cup x.atoms y.atoms;
    chars = Chars.cup x.chars y.chars;
  }
    
let cap x y = 
  if x == y then x else {
    times = Boolean.cap x.times y.times;
    xml   = Boolean.cap x.xml y.xml;
    record= Boolean.cap x.record y.record;
    arrow = Boolean.cap x.arrow y.arrow;
    ints  = Intervals.cap x.ints  y.ints;
    atoms = Atoms.cap x.atoms y.atoms;
    chars = Chars.cap x.chars y.chars;
  }
    
let diff x y = 
  if x == y then empty else {
    times = Boolean.diff x.times y.times;
    xml   = Boolean.diff x.xml y.xml;
    arrow = Boolean.diff x.arrow y.arrow;
    record= Boolean.diff x.record y.record;
    ints  = Intervals.diff x.ints  y.ints;
    atoms = Atoms.diff x.atoms y.atoms;
    chars = Chars.diff x.chars y.chars;
  }
    
let count = ref 0
let make () = incr count; { id = !count; descr = empty }
let define n d = n.descr <- d
let cons d = incr count; { id = !count; descr = d }
let descr n = n.descr
let internalize n = n
let id n = n.id
116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172

let rec compare_rec r1 r2 =
  if r1 == r2 then 0
  else match (r1,r2) with
    | (l1,(o1,x1))::r1,(l2,(o2,x2))::r2 ->
	if ((l1:int) < l2) then -1 
	else if (l1 > l2) then 1 
	else if o2 && not o1 then -1
	else if o1 && not o2 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
173 174 175 176
	     
let rec equal_rec r1 r2 =
  (r1 == r2) ||
  match (r1,r2) with
177
    | (l1,(o1,x1))::r1,(l2,(o2,x2))::r2 ->
178
	(x1.id = x2.id) && (l1 == l2) && (o1 == o2) && (equal_rec r1 r2)
179
    | _ -> false
180 181 182 183 184
	
let rec equal_rec_list l1 l2  =
  (l1 == l2) ||
  match (l1,l2) with
    | (o1,r1)::l1, (o2,r2)::l2 ->
185 186
	(o1 == o2) &&
	(equal_rec r1 r2) && (equal_rec_list l1 l2)
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
    | _ -> 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 =
217 218 219
  (Atoms.equal a.atoms b.atoms) &&
  (Chars.equal a.chars b.chars) &&
  (Intervals.equal a.ints  b.ints) &&
220 221 222 223
  (equal_times_bool a.times b.times) &&
  (equal_times_bool a.xml b.xml) &&
  (equal_times_bool a.arrow b.arrow) &&
  (equal_rec_bool a.record b.record)
224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242

let compare_descr a b =
  let c = compare a.atoms b.atoms in if c <> 0 then c
  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
  else let c = compare_times_bool a.times b.times in if c <> 0 then c
  else let c = compare_times_bool a.xml b.xml in if c <> 0 then c
  else let c = compare_times_bool a.arrow b.arrow in if c <> 0 then c
  else let c = compare_rec_bool a.record b.record in if c <> 0 then c
  else 0

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


243 244 245 246 247 248 249 250 251 252 253 254
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
  | (l,(o,x))::rem ->
255
      let accu = if o then accu else accu + 5 in
256 257 258 259 260
      hash_rec (257 * accu + 17 * (LabelPool.hash l) + x.id) rem
  | [] -> accu + 5
      
let rec hash_rec_list accu = function
  | (o,r)::l ->
261
      hash_rec_list (hash_rec (if o then accu*3 else accu) r) l
262 263 264 265 266 267 268 269 270
  | [] -> 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 =
271 272 273
  let accu = Chars.hash 1 a.chars in
  let accu = Intervals.hash accu a.ints in
  let accu = Atoms.hash accu a.atoms in
274 275 276 277 278
  let accu = hash_times_bool accu a.times in
  let accu = hash_times_bool accu a.xml in
  let accu = hash_times_bool accu a.arrow in
  let accu = hash_rec_bool accu a.record in
  accu
279

280 281 282 283 284 285 286 287 288
module DescrHash = 
  Hashtbl.Make(
    struct 
      type t = descr
      let hash = hash_descr
      let equal = equal_descr
    end
  )

289 290
let print_descr = ref (fun _ _  -> assert false)

291 292
let neg x = diff any x

293 294
let any_node = cons any

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
module LabelSet = Set.Make(LabelPool)

let get_record r =
  let labs accu (_,r) = 
    List.fold_left (fun accu (l,_) -> LabelSet.add l accu) accu r in
  let extend (opts,descrs) labs (o,r) =
    let rec aux i labs r =
      match labs with
	| [] -> ()
	| l1::labs ->
	    match r with
	      | (l2,(o,x))::r when l1 = l2 -> 
		  descrs.(i) <- cap descrs.(i) (descr x);
		  opts.(i) <- opts.(i) && o;
		  aux (i+1) labs r
	      | r ->
		  if not o then descrs.(i) <- empty;
		  aux (i+1) labs r
    in
    aux 0 labs r;
    o
  in
  let line (p,n) =
    let labels = 
      List.fold_left labs (List.fold_left labs LabelSet.empty p) n in
    let labels = LabelSet.elements labels in
    let nlab = List.length labels in
    let mk () = Array.create nlab true, Array.create nlab any in

    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
  List.map line r
   
340

341
module DescrMap = Map.Make(struct type t = descr let compare = compare end)
342

343 344
let check d =
  Boolean.check d.times;
345
  Boolean.check d.xml;
346 347 348
  Boolean.check d.arrow;
  Boolean.check d.record;
  ()
349

350 351 352 353 354 355 356 357 358 359 360 361 362


(* 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

363 364 365
let rec exists max f =
  (max > 0) && (f (max - 1) || exists (max - 1) f)

366
let trivially_empty d = equal_descr d empty
367

368
exception NotEmpty
369

370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446
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;
  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

let rec guard a f n =
  let s = slot a in
  match s.status with
    | Empty -> ()
    | Maybe -> n.active <- true; s.notify <- Do (n,f,s.notify)
    | NEmpty -> f n

and slot d =
  if not ((Intervals.is_empty d.ints) && 
	  (Atoms.is_empty d.atoms) &&
	  (Chars.is_empty d.chars)) then slot_not_empty 
  else try DescrHash.find memo d
  with Not_found ->
    let s = { status = Maybe; active = false; notify = Nothing } in
    DescrHash.add memo d s;
    (try
       iter_s s check_times d.times;
       iter_s s check_times d.xml;
       iter_s s check_arrow d.arrow;
       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 =
  let rec aux accu1 accu2 right s = match right with
    | (t1,t2)::right ->
	if trivially_empty (cap_t accu1 t1) || 
	   trivially_empty (cap_t accu2 t2) then
	     aux accu1 accu2 right s
	else
          let accu1' = diff_t accu1 t1 in guard accu1' (aux accu1' accu2 right) s;
          let accu2' = diff_t accu2 t2 in guard accu2' (aux accu1 accu2' right) s
    | [] -> set s
  in
  let (accu1,accu2) = cap_product left in
  guard accu1 (guard accu2 (aux accu1 accu2 right)) s
447

448 449 450 451 452 453 454 455 456 457 458 459
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
460

461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512
and check_record (labels,(oleft,(left_opt,left)),rights) s =
  let rec aux rights s = match rights with
    | [] -> set s
    | (oright,(right_opt,right))::rights ->
	let next =
	  (oleft && (not oright)) ||
	  exists (Array.length left)
	    (fun i ->
	       (not (left_opt.(i) && right_opt.(i))) &&
	       (trivially_empty (cap left.(i) right.(i))))
	in
	if next then aux rights s
	else
	  for i = 0 to Array.length left - 1 do
	    let back = left.(i) in
	    let oback = left_opt.(i) in
	    let odi = oback && (not right_opt.(i)) in
	    let di = diff back right.(i) in
	    if odi then (
	      left.(i) <- diff back right.(i);
	      left_opt.(i) <- odi;
	      aux rights s;
	      left.(i) <- back;
	      left_opt.(i) <- oback;
	    ) else
	      guard di (fun s ->
			  left.(i) <- diff back right.(i);
			  left_opt.(i) <- odi;
			  aux rights s;
			  left.(i) <- back;
			  left_opt.(i) <- oback;
		       ) s
	  done
  in
  let rec start i s =
    if (i < 0) then aux rights s
    else
      if left_opt.(i) then start (i - 1) s
      else guard left.(i) (start (i - 1)) s
  in
  start (Array.length left - 1) s


let is_empty d =
  let s = slot d in
  List.iter 
    (fun s' -> if s'.status = Maybe then s'.status <- Empty; s'.notify <- Nothing) 
    !marks;
  marks := [];
  s.status = Empty
  

513
module Assumptions = Set.Make(struct type t = descr let compare = compare_descr end)
514 515
let memo = ref Assumptions.empty
let cache_false = DescrHash.create 33000
516

517
let rec empty_rec d =
518
  if not (Intervals.is_empty d.ints) then false
519 520
  else if not (Atoms.is_empty d.atoms) then false
  else if not (Chars.is_empty d.chars) then false
521 522
  else if DescrHash.mem cache_false d then false 
  else if Assumptions.mem d !memo then true
523 524
  else (
    let backup = !memo in
525
    memo := Assumptions.add d backup;
526 527 528 529 530 531 532 533
    if 
      (empty_rec_times d.times) &&
      (empty_rec_times d.xml) &&
      (empty_rec_arrow d.arrow) &&
      (empty_rec_record d.record) 
    then true
    else (
      memo := backup;
534
      DescrHash.add cache_false d ();
535 536 537 538 539 540 541 542 543 544
      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 ->
545 546
	if trivially_empty (cap_t accu1 t1) || 
	   trivially_empty (cap_t accu2 t2) then
547 548 549 550 551
	  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
552
	  if not (empty_rec accu2') then aux accu1 accu2' right
553 554 555 556 557
    | [] -> 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)
558

559 560 561 562 563 564 565 566 567

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
568
          if not (empty_rec accu1') then aux accu1' accu2 left;
569
          let accu2' = cap_t accu2 t2 in
570
          if not (empty_rec accu2') then aux accu1 accu2' left
571 572 573 574 575 576 577 578
      | [] -> 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

579 580 581 582 583 584 585 586 587
and empty_rec_record_aux (labels,(oleft,(left_opt,left)),rights) =
  let rec aux = function
    | [] -> raise NotEmpty
    | (oright,(right_opt,right))::rights ->
	let next =
	  (oleft && (not oright)) ||
	  exists (Array.length left)
	    (fun i ->
	       (not (left_opt.(i) && right_opt.(i))) &&
588
	       (trivially_empty (cap left.(i) right.(i))))
589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611
	in
	if next then aux rights 
	else
	  for i = 0 to Array.length left - 1 do
	    let back = left.(i) in
	    let oback = left_opt.(i) in
	    let odi = oback && (not right_opt.(i)) in
	    let di = diff back right.(i) in
	    if odi || not (empty_rec di) then (
	      left.(i) <- diff back right.(i);
	      left_opt.(i) <- odi;
	      aux rights;
	      left.(i) <- back;
	      left_opt.(i) <- oback;
	    )
	  done
  in
  exists (Array.length left) 
    (fun i -> not left_opt.(i) && (empty_rec left.(i))) 
  ||
  (try aux rights; true with NotEmpty -> false)
	    

612
and empty_rec_record c =
613
  List.for_all empty_rec_record_aux (get_record c)
614

615 616
(*
let is_empty d =
617
  empty_rec d
618
  *)
619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664

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*) 
	    if d1 = t1 then r := (d1,cup d2 t2) else
	      
	      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

665
(*
666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693
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)

694
*)
695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715
  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
    List.iter line d;
    !accu
716 717 718
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
719

720

721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749
  let get ?(kind=`Normal) d = 
    match kind with
      | `Normal -> get_aux d.times
      | `XML -> get_aux d.xml

  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty

  let restrict_1 rects pi1 =
    let aux accu (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then accu else (t1,t2)::accu in
    List.fold_left aux [] rects
  
  type normal = t

  module Memo = Map.Make(struct 
			   type t = (node * node) Boolean.t
			   let compare = compare end)
			   


  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 ->
	  let gd = get_aux d in
	  let n = normal_aux gd in
750 751
(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
752 753
	  memo := Memo.add d n !memo;
	  n
754

755 756 757 758
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
759

760 761
module Print = 
struct
762 763 764 765 766 767 768
  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
769 770
      | Some a -> Format.fprintf ppf "%s" (Atoms.value a)
      | None -> Format.fprintf ppf "(%a)" print_union (Atoms.print a)
771

772
  let print_const ppf = function
773 774 775
    | Integer i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
776

777 778 779
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799

  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 *)

  let bool_iter f b =
    List.iter (fun (p,n) -> List.iter f p; List.iter f n) b

  let trivial b = b = Boolean.empty || b = Boolean.full

  let worth_abbrev d = 
    not (trivial d.times && trivial d.arrow && trivial d.record) 

  let rec mark n = mark_descr (descr n)
  and mark_descr d =
800
    if not (DescrMap.mem d !named) then
801 802 803 804 805 806 807 808 809
      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);
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.times;
810
    	bool_iter 
811 812
	  (fun (n1,n2) -> mark n1; mark n2
(*
813 814 815
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
816 817 818
    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
819
		  let l = get_record d1.record in
820 821 822 823 824
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
825 826
	       )
	       (Product.normal (descr n2))
827
*)
828
	  ) d.xml;
829
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
830
    	bool_iter (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) d.record
831 832 833 834 835

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
836
      let name = DescrMap.find d !named in
837 838 839 840 841 842 843
      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
844
	  Not_found -> assert false
845 846 847 848 849
  and real_print_descr ppf d = 
    if d = any then Format.fprintf ppf "Any" else
      print_union ppf 
	(Intervals.print d.ints @
	 Chars.print d.chars @
850
	 Atoms.print d.atoms @
851
	 Boolean.print "Pair" print_times d.times @
852
	 Boolean.print "XML" print_xml d.xml @
853 854 855 856 857
	 Boolean.print "Arrow" print_arrow d.arrow @
	 Boolean.print "Record" print_record d.record
	)
  and print_times ppf (t1,t2) =
    Format.fprintf ppf "@[(%a,%a)@]" print t1 print t2
858
  and print_xml ppf (t1,t2) =
859 860
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
861 862 863 864 865 866 867 868 869
    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
870
*)
871 872
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
873 874 875 876 877
  and print_record ppf (o,r) =
    let o = if o then "" else "|" in
    Format.fprintf ppf "@[{%s" o;
    let first = ref true in
    List.iter (fun (l,(o,t)) ->
878 879
		 let sep = if !first then (first := false; "") else ";" in
		 Format.fprintf ppf "%s@ @[%s =%s@] %a" sep
880 881 882 883
		   (LabelPool.value l) (if o then "?" else "") print t
	      ) r;
    Format.fprintf ppf " %s}@]" o
(*
884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900
  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
901
*)
902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928

	  
  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

929
let () = print_descr := Print.print_descr
930

931 932 933 934
module Positive =
struct
  type rhs = [ `Type of descr | `Cup of v list | `Times of v * v ]
  and v = { mutable def : rhs; mutable node : node option }
935 936


937 938 939 940 941 942 943 944 945
  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)
946

947 948 949 950 951 952 953 954 955
  and make_node v =
    match v.node with
      | Some n -> n
      | None ->
	  let n = make () in
	  v.node <- Some n;
	  let d = make_descr [] v in
	  define n d;
	  n
956

957 958 959 960 961 962 963
  let forward () = { def = `Cup []; node = None }
  let def v d = v.def <- d
  let cons d = let v = forward () in def v d; v
  let ty d = cons (`Type d)
  let cup vl = cons (`Cup vl)
  let times d1 d2 = cons (`Times (d1,d2))
  let define v1 v2 = def v1 (`Cup [v2]) 
964

965 966
  let solve v = internalize (make_node v)
end
967

968

969

970

971 972 973
(* Sample value *)
module Sample =
struct
974

975

976 977 978 979 980
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
981 982 983
  | Int of Intervals.v
  | Atom of Atoms.v
  | Char of Chars.v
984 985
  | Pair of (t * t)
  | Xml of (t * t)
986 987
  | Record of (label * t) list
  | Fun of (node * node) list
988
  | Other
989
  exception FoundSampleRecord of (label * t) list
990 991 992 993 994

let rec sample_rec memo d =
  if (Assumptions.mem d memo) || (is_empty d) then raise Not_found 
  else 
    try Int (Intervals.sample d.ints) with Not_found ->
995
    try Atom (Atoms.sample d.atoms) with 
996 997
	Not_found ->
(* Here: could create a fresh atom ... *)
998
    try Char (Chars.sample d.chars) with Not_found ->
999 1000 1001
    try sample_rec_arrow d.arrow with Not_found ->

    let memo = Assumptions.add d memo in
1002 1003
    try Pair (sample_rec_times memo d.times) with Not_found ->
    try Xml (sample_rec_times memo d.xml) with Not_found ->
1004 1005 1006 1007 1008 1009 1010 1011 1012 1013
    try sample_rec_record memo d.record with Not_found -> 
    raise Not_found


and sample_rec_times memo c = 
  find (sample_rec_times_aux memo) c

and sample_rec_times_aux memo (left,right) =
  let rec aux accu1 accu2 = function
    | (t1,t2)::right ->
1014 1015
(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
1016 1017 1018 1019 1020
        let accu1' = diff_t accu1 t1 in
        if non_empty accu1' then aux accu1' accu2 right else
          let accu2' = diff_t accu2 t2 in
          if non_empty accu2' then aux accu1 accu2' right else
	    raise Not_found
1021
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
1022 1023 1024 1025
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right
1026

1027 1028
and sample_rec_arrow c =
  find sample_rec_arrow_aux c
1029

1030 1031 1032 1033 1034 1035 1036 1037
and check_empty_simple_arrow_line left (s1,s2) = 
  let rec aux accu1 accu2 = function
    | (t1,t2)::left ->
        let accu1' = diff_t accu1 t1 in
        if non_empty accu1' then aux accu1 accu2 left;
        let accu2' = cap_t accu2 t2 in
        if non_empty accu2' then aux accu1 accu2 left
    | [] -> raise NotEmpty
1038
  in
1039 1040 1041 1042 1043 1044 1045 1046 1047
  let accu1 = descr s1 in
  (is_empty accu1) ||
  (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)

and check_empty_arrow_line left right = 
  List.exists (check_empty_simple_arrow_line left) right

and sample_rec_arrow_aux (left,right) =
  if (check_empty_arrow_line left right) then raise Not_found
1048 1049 1050 1051 1052
  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))
1053

1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089
and sample_rec_record_aux memo (labels,(oleft,(left_opt,left)),rights) =
  let rec aux = function
    | [] -> 
	let l = ref labels and fields = ref [] in
	for i = 0 to Array.length left - 1 do
	  if not left_opt.(i) then
	    fields := (List.hd !l, sample_rec memo left.(i))::!fields;
	  l := List.tl !l
	done;
	raise (FoundSampleRecord (List.rev !fields))
    | (oright,(right_opt,right))::rights ->
	let next = (oleft && (not oright)) in
	if next then aux rights 
	else
	  for i = 0 to Array.length left - 1 do
	    let back = left.(i) in
	    let oback = left_opt.(i) in
	    let odi = oback && (not right_opt.(i)) in
	    let di = diff back right.(i) in
	    if odi || not (is_empty di) then (
	      left.(i) <- diff back right.(i);
	      left_opt.(i) <- odi;
	      aux rights;
	      left.(i) <- back;
	      left_opt.(i) <- oback;
	    )
	  done
  in
  if exists (Array.length left) 
    (fun i -> not left_opt.(i) && (is_empty left.(i))) then raise Not_found;
  try aux rights; raise Not_found
  with FoundSampleRecord r -> r

	    


1090

1091
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
1092

1093 1094 1095 1096 1097 1098 1099
  let rec print_sep f sep ppf = function
    | [] -> ()
    | [x] -> f ppf x
    | x::rem -> f ppf x; Format.fprintf ppf "%s" sep; print_sep f sep ppf rem


  let rec print ppf = function
1100 1101 1102
    | Int i -> Intervals.print_v ppf i
    | Atom a -> Atoms.print_v ppf a
    | Char c -> Chars.print_v ppf c
1103
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
1104
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
1105 1106 1107 1108 1109
    | Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
1110
		(LabelPool.value l)
1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123
		print x
	     )
	     " ; "
	  ) r
    | Fun iface ->
	Format.fprintf ppf "(fun ( %a ) x -> ...)"
	  (print_sep
	     (fun ppf (t1,t2) ->
		Format.fprintf ppf "%a -> %a; "
		Print.print t1 Print.print t2
	     )
	     " ; "
	  ) iface
1124 1125
    | Other ->
	Format.fprintf ppf "[cannot determine value]"
1126 1127
end

1128 1129


1130
module Record = 
1131
struct
1132 1133 1134 1135 1136
  type atom = bool * (label, (bool * node)) SortedMap.t
  type t = atom Boolean.t

  let get d = d.record

1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163
  module T = struct
    type t = descr
    let any = any
    let cap = cap
    let cup = cup
    let diff = diff
    let empty = is_empty
  end
  module R = struct
    (*Note: Boolean.cap,cup,diff would be ok,
      but we add here the simplification rules:
      { } & r --> r    ; { } | r -> { }
      r \ { } --> Empty *)

    type t = atom Boolean.t
    let any = Boolean.full
    let cap =  Boolean.cap
    let cup = Boolean.cup
    let diff = Boolean.diff
    let empty x = is_empty { empty with record = x }
  end
  module TR = Normal.Make(T)(R)

  let atom = function
    | (true,[]) -> Boolean.full
    | (o,l) -> Boolean.atom (o,l)

1164 1165 1166 1167 1168 1169
  let somefield_possible t =
    not (R.empty (R.diff t (Boolean.atom (false,[]))))

  let nofield_possible t =    
    not (R.empty (R.cap t (Boolean.atom (false,[]))))

1170 1171
  let restrict_label_absent t l =
    Boolean.compute_bool
1172
      (fun ((o,r) as x) ->
1173 1174
	 try
	   let (lo,_) = List.assoc l r in
1175
	   if lo then atom (o,SortedMap.diff r [l])
1176 1177 1178 1179 1180 1181 1182 1183 1184
	   else Boolean.empty
	 with Not_found -> Boolean.atom x
      )
      t

  let restrict_field t l d =
    (* Is it correct ?  Do we need to keep track of "first component"
       (value of l) as in label_present, then filter at the end ... ? *)
    Boolean.compute_bool
1185
      (fun ((o,r) as x) ->
1186 1187 1188
	 try
	   let (lo,lt) = List.assoc l r in
	   if (not lo) && (is_empty (cap d (descr lt))) then Boolean.empty
1189
	   else atom (o, SortedMap.diff r [l])
1190 1191 1192 1193 1194 1195 1196 1197 1198 1199
	 with Not_found -> 
	   if o then Boolean.atom x else Boolean.empty
      )
      t



  let label_present (t:t) l : (descr * t) list =
    let x =
      Boolean.compute_bool
1200
	(fun ((o,r) as x) ->
1201 1202
	   try
	     let (_,lt) = List.assoc l r in
1203
	     Boolean.atom (descr lt, atom (o, SortedMap.diff r [l]))
1204 1205 1206 1207 1208 1209 1210 1211
	   with Not_found -> 
	     if o then Boolean.atom (any, Boolean.atom x) else Boolean.empty
	)
	t
    in
    TR.boolean x

  let restrict_label_present t l =
1212
    Boolean.compute_bool
1213
      (fun ((o,r) as x) ->
1214 1215 1216 1217 1218 1219 1220 1221
	 try
	   Boolean.atom (o, SortedMap.change_exists l (fun (_,lt) -> (false,lt)) r)
	 with Not_found -> 
	   if o then Boolean.atom 
	     (true, SortedMap.union_disj [l, (false,any_node)] r)
	   else Boolean.empty
      )
      t