types.ml 38.8 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
16
module LabelPool = Pool.Make(HashedString)
module AtomPool  = Pool.Make(HashedString)
17

18
19
type label = LabelPool.t
type atom  = AtomPool.t
20

21
type const = Integer of Big_int.big_int | Atom of atom | Char of Chars.Unichar.t
22

23
24
type pair_kind = [ `Normal | `XML ]

25
26
27
module I = struct
  type 'a t = {
    atoms : atom Atoms.t;
28
29
    ints  : Intervals.t;
    chars : Chars.t;
30
    times : ('a * 'a) Boolean.t;
31
    xml   : ('a * 'a) Boolean.t;
32
    arrow : ('a * 'a) Boolean.t;
33
    record: (bool * (label, (bool * 'a)) SortedMap.t) Boolean.t;
34
  }
35

36
  let empty = { 
37
    times = Boolean.empty; 
38
    xml   = Boolean.empty; 
39
40
    arrow = Boolean.empty; 
    record= Boolean.empty;
41
42
    ints  = Intervals.empty;
    atoms = Atoms.empty;
43
    chars = Chars.empty;
44
  }
45

46
47
  let any =  {
    times = Boolean.full; 
48
    xml   = Boolean.full; 
49
50
    arrow = Boolean.full; 
    record= Boolean.full; 
51
    ints  = Intervals.any;
52
53
    atoms = Atoms.any;
    chars = Chars.any;
54
  }
55

56
	       
57
  let interval i = { empty with ints = i }
58
  let times x y = { empty with times = Boolean.atom (x,y) }
59
  let xml x y = { empty with xml = Boolean.atom (x,y) }
60
  let arrow x y = { empty with arrow = Boolean.atom (x,y) }
61
62
  let record label opt t = 
    { empty with record = Boolean.atom (true,[label,(opt,t)]) }
63
64
  let record' x =
    { empty with record = Boolean.atom x }
65
66
  let atom a = { empty with atoms = a }
  let char c = { empty with chars = c }
67
  let constant = function
68
    | Integer i -> interval (Intervals.atom i)
69
70
    | Atom a -> atom (Atoms.atom a)
    | Char c -> char (Chars.atom c)
71
72

		   
73
  let cup x y = 
74
    if x = y then x else { 
75
      times = Boolean.cup x.times y.times;
76
      xml   = Boolean.cup x.xml y.xml;
77
78
79
80
      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;
81
      chars = Chars.cup x.chars y.chars;
82
83
84
    }
      
  let cap x y = 
85
    if x = y then x else {
86
      times = Boolean.cap x.times y.times;
87
      xml   = Boolean.cap x.xml y.xml;
88
89
90
91
      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;
92
      chars = Chars.cap x.chars y.chars;
93
94
95
    }
      
  let diff x y = 
96
    if x = y then empty else { 
97
      times = Boolean.diff x.times y.times;
98
      xml   = Boolean.diff x.xml y.xml;
99
100
101
102
      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;
103
      chars = Chars.diff x.chars y.chars;
104
105
    }

106
		   
107
108
109
110
111
112
113
114
115
  let rec equal_rec e r1 r2 =
    match (r1,r2) with
    | [],[] -> ()
    | (l1,(o1,x1))::r1,(l2,(o2,x2))::r2 ->
	if (l1 <> l2) || (o1 <> o2) then raise NotEqual;
	e x1 x2; equal_rec e r1 r2
    | _ -> raise NotEqual
(* check: faster to reverse the calls to e and to equal_rec ? *)

116
117
  let equal e a b =
    if a.atoms <> b.atoms then raise NotEqual;
118
    if a.chars <> b.chars then raise NotEqual;
119
    if a.ints <> b.ints then raise NotEqual;
120
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.times b.times;
121
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.xml b.xml;
122
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.arrow b.arrow;
123
124
125
126
    Boolean.equal (fun (o1,r1) (o2,r2) ->
		     if (o1 <> o2) then raise NotEqual;
		     equal_rec e r1 r2)
      a.record b.record
127
128
129
      
  let map f a =
    { times = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.times;
130
      xml   = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.xml;
131
      arrow = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.arrow;
132
133
134
      record= Boolean.map (fun (o,r) -> 
			     (o, List.map (fun (l,(o,x)) -> (l,(o,f x))) r))
		a.record;
135
136
      ints  = a.ints;
      atoms = a.atoms;
137
      chars = a.chars;
138
    }
139
    
140
  let hash h a =
141
142
    Hashtbl.hash (map h a)
(*
143
    (Hashtbl.hash { (map h a) with ints = Intervals.empty })
144
    + (Intervals.hash a.ints)
145
*)
146
147
148
      
  let iter f a =
    ignore (map f a)
149
     
150
151
  let deep = 4
end
152

153
     
154
module Algebra = Recursive_noshare.Make(I)
155
156
include I
include Algebra
157
158
159
160
161
162
163
164
165
module DescrHash = 
  Hashtbl.Make(
    struct 
      type t = descr
      let hash = hash_descr
      let equal = equal_descr
    end
  )

166
167
let print_descr = ref (fun _ _  -> assert false)

168
169
170
171
172
173
174
175
176
(*
let define n d = check d; define n d
*)

let cons d =
  let n = make () in
  define n d;
  internalize n

177
(*
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
let any_rec = cons { empty with record = Boolean.full }
let any_node = make ();;
define any_node   {
  times = Boolean.full; 
  xml   = Boolean.atom 
	    (cons { empty with atoms = Atoms.any },
	     cons (times any_rec any_node));
  arrow = Boolean.full; 
  record= Boolean.full; 
  ints  = Intervals.any;
  atoms = Atoms.any;
  chars = Chars.any;
};;
internalize any_node;;
let any = descr any_node
193
*)
194
195
196

let neg x = diff any x

197
198
let any_node = cons any

199
(*
200
201
202
203
204
205
206
207
let get_record r =
  let add = SortedMap.add (fun (o1,t1) (o2,t2) -> (o1&&o2, cap t1 t2)) in
  let line (p,n) =
    let accu = List.fold_left 
		 (fun accu (l,o,t) -> add l (o,descr t) accu) [] p in
    List.fold_left 
      (fun accu (l,o,t) -> add l (not o,neg (descr t)) accu) accu n in
  List.map line r
208
*)
209
    
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
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
   
255

256
module DescrMap = Map.Make(struct type t = descr let compare = compare end)
257

258
259
let check d =
  Boolean.check d.times;
260
  Boolean.check d.xml;
261
262
263
  Boolean.check d.arrow;
  Boolean.check d.record;
  ()
264

265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284


(* 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


let cup_product l = 
  List.fold_left 
    (fun (d1,d2) (t1,t2) -> (cup_t d1 t1, cup_t d2 t2))
    (empty,empty)
    l

285
286
287
let rec exists max f =
  (max > 0) && (f (max - 1) || exists (max - 1) f)

288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303

module Assumptions = Set.Make(struct type t = descr let compare = compare end)

let memo = ref Assumptions.empty
let cache_false = ref Assumptions.empty

exception NotEmpty

let rec empty_rec d =
  if Assumptions.mem d !cache_false then false 
  else if Assumptions.mem d !memo then true
  else if not (Intervals.is_empty d.ints) then false
  else if not (Atoms.is_empty d.atoms) then false
  else if not (Chars.is_empty d.chars) then false
  else (
    let backup = !memo in
304
    memo := Assumptions.add d backup;
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
    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;
      cache_false := Assumptions.add d !cache_false;
      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 ->
324
(* This avoids explosion with huge rhs (+/- degenerated partitioning)
325
326
327
328
329
330
331
332
333
   May be slower when List.length right is small; could optimize
   this case... *)
	if empty_rec (cap_t accu1 t1) || empty_rec (cap_t accu2 t2) then
	  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
          if not (empty_rec accu2') then aux accu1 accu2' right
334
335
336
    | [] -> raise NotEmpty
  in
  let (accu1,accu2) = cap_product left in
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
(*
  let right' = List.filter 
		 (fun (t1,t2) ->
		    not 
		    (empty_rec (cap_t accu1 t1) || empty_rec (cap_t accu2 t2)
		    )
		 ) right in
  if List.length right > 15 then (
    Format.fprintf Format.std_formatter "[%i=>%i]@." 
				    (List.length right) (List.length right');
    Format.fprintf Format.std_formatter "(%a,%a)@." 
				    !print_descr accu1
				    !print_descr accu2;
    List.iter (fun (t1,t2) ->
		 Format.fprintf Format.std_formatter "\ (%a,%a)@." 
		   !print_descr (descr t1)
		   !print_descr (descr t2);
	      ) right
  );
  let right = right' in
*)

359
360
361
362
  (empty_rec accu1) || (empty_rec accu2) ||
(* OPT? It does'nt seem so ...  The hope was to return false quickly
   for large right hand-side *)
  (
363
    (* (if (List.length right > 2) then
364
365
       let (cup1,cup2) = cup_product right in
       (empty_rec (diff accu1 cup1)) && (empty_rec (diff accu2 cup2))
366
367
     else true)
    && *)
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
    (try aux accu1 accu2 right; true with NotEmpty -> false)
  )

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
          if not (empty_rec accu1') then aux accu1 accu2 left;
          let accu2' = cap_t accu2 t2 in
          if not (empty_rec accu2') then aux accu1 accu2 left
      | [] -> 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

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
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))) &&
	       (empty_rec (cap left.(i) right.(i))))
	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)
	    

423
and empty_rec_record c =
424
(*
425
  let aux = List.exists (fun (_,(opt,t)) -> (not opt) && (empty_rec t)) in
426
427
*)
  List.for_all empty_rec_record_aux (get_record c)
428
429

let is_empty d =
430
(*  Printf.eprintf "+"; flush stderr; *)
431
432
  let old = !memo in
  let r = empty_rec d in
433
434
  if not r then memo := old
  else if not (is_recurs_descr d) then memo := Assumptions.add d !memo;
435
(*  cache_false := Assumptions.empty;  *)
436
(*  Printf.eprintf "-\n"; flush stderr; *)
437
438
439
440
441
442
443
444
445
446
447
448
449
450
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
478
479
480
481
482
483
  r

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

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
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)

513
*)
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
  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
535
536
537
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
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
  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
568
569
(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
570
571
	  memo := Memo.add d n !memo;
	  n
572

573
574
575
576
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
577

578
579
module Print = 
struct
580
581
582
583
584
  let rec print_union ppf = function
    | [] -> Format.fprintf ppf "Empty"
    | [h] -> h ppf
    | h::t -> Format.fprintf ppf "@[%t |@ %a@]" h print_union t

585
586
  let print_atom ppf a = 
    Format.fprintf ppf "`%s" (AtomPool.value a)
587

588
589
590
591
592
593
594
595
  let print_tag ppf a =
    match Atoms.is_atom a with
      | Some a -> Format.fprintf ppf "%s" (AtomPool.value a)
      | None -> 
	  Format.fprintf ppf "(%a)"
	    print_union
	       (Atoms.print "Atom" print_atom a)

596
597
598
599
600
  let print_const ppf = function
    | Integer i -> Format.fprintf ppf "%s" (Big_int.string_of_big_int i)
    | Atom a -> print_atom ppf a
    | Char c -> Chars.Unichar.print ppf c

601
602
603
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623

  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 =
624
    if not (DescrMap.mem d !named) then
625
626
627
628
629
630
631
632
633
      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;
634
    	bool_iter 
635
636
	  (fun (n1,n2) -> mark n1; mark n2
(*
637
638
639
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
640
641
642
    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
643
		  let l = get_record d1.record in
644
645
646
647
648
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
649
650
	       )
	       (Product.normal (descr n2))
651
*)
652
	  ) d.xml;
653
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
654
    	bool_iter (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) d.record
655
656
657
658
659

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
660
      let name = DescrMap.find d !named in
661
662
663
664
665
666
667
      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
668
	  Not_found -> assert false
669
670
671
672
673
674
675
  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 @
	 Atoms.print "Atom" print_atom d.atoms @
	 Boolean.print "Pair" print_times d.times @
676
	 Boolean.print "XML" print_xml d.xml @
677
678
679
680
681
	 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
682
  and print_xml ppf (t1,t2) =
683
684
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
685
686
687
688
689
690
691
692
693
    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
694
*)
695
696
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
697
698
699
700
701
  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)) ->
702
703
		 let sep = if !first then (first := false; "") else ";" in
		 Format.fprintf ppf "%s@ @[%s =%s@] %a" sep
704
705
706
707
		   (LabelPool.value l) (if o then "?" else "") print t
	      ) r;
    Format.fprintf ppf " %s}@]" o
(*
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
  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
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
750
751
752

	  
  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

753
let () = print_descr := Print.print_descr
754

755
756
757
758
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 }
759
760


761
762
763
764
765
766
767
768
769
  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)
770

771
772
773
774
775
776
777
778
779
  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
780

781
782
783
784
785
786
787
  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]) 
788

789
790
  let solve v = internalize (make_node v)
end
791

792

793

794

795
796
797
(* Sample value *)
module Sample =
struct
798

799

800
801
802
803
804
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
805
  | Int of Big_int.big_int
806
  | Atom of atom
807
  | Char of Chars.Unichar.t
808
809
  | Pair of (t * t)
  | Xml of (t * t)
810
811
  | Record of (label * t) list
  | Fun of (node * node) list
812
  | Other
813
  exception FoundSampleRecord of (label * t) list
814
815
816
817
818

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 ->
819
820
821
    try Atom (Atoms.sample (fun _ -> AtomPool.dummy_min) d.atoms) with 
	Not_found ->
(* Here: could create a fresh atom ... *)
822
    try Char (Chars.sample d.chars) with Not_found ->
823
824
825
    try sample_rec_arrow d.arrow with Not_found ->

    let memo = Assumptions.add d memo in
826
827
    try Pair (sample_rec_times memo d.times) with Not_found ->
    try Xml (sample_rec_times memo d.xml) with Not_found ->
828
829
830
831
832
833
834
835
836
837
    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 ->
838
839
(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
840
841
842
843
844
        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
845
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
846
847
848
849
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right
850

851
852
and sample_rec_arrow c =
  find sample_rec_arrow_aux c
853

854
855
856
857
858
859
860
861
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
862
  in
863
864
865
866
867
868
869
870
871
  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
872
873
874
875
876
  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))
877

878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
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

	    


914

915
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
916

917
918
919
920
921
922
923
924
  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
    | Int i -> Format.fprintf ppf "%s" (Big_int.string_of_big_int i)
925
926
927
928
929
    | Atom a ->    
	if a = LabelPool.dummy_min then
	  Format.fprintf ppf "(almost any atom)"
	else
	  Format.fprintf ppf "`%s" (AtomPool.value a)
930
931
    | Char c -> Chars.Unichar.print ppf c
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
932
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
933
934
935
936
937
    | Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
938
		(LabelPool.value l)
939
940
941
942
943
944
945
946
947
948
949
950
951
		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
952
953
    | Other ->
	Format.fprintf ppf "[cannot determine value]"
954
955
end

956
957


958
module Record = 
959
struct
960
961
962
963
964
  type atom = bool * (label, (bool * node)) SortedMap.t
  type t = atom Boolean.t

  let get d = d.record

965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
  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)

992
993
994
995
996
997
  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,[]))))

998
999
  let restrict_label_absent t l =
    Boolean.compute_bool
1000
      (fun ((o,r) as x) ->
1001
1002
	 try
	   let (lo,_) = List.assoc l r in
1003
	   if lo then atom (o,SortedMap.diff r [l])
1004
1005
1006
1007
1008
1009
1010
1011
1012
	   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
1013
      (fun ((o,r) as x) ->
1014
1015
1016
	 try
	   let (lo,lt) = List.assoc l r in
	   if (not lo) && (is_empty (cap d (descr lt))) then Boolean.empty
1017
	   else atom (o, SortedMap.diff r [l])
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
	 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
1028
	(fun ((o,r) as x) ->
1029
1030
	   try
	     let (_,lt) = List.assoc l r in
1031
	     Boolean.atom (descr lt, atom (o, SortedMap.diff r [l]))
1032
1033
1034
1035
1036
1037
1038
1039
	   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 =
1040
    Boolean.compute_bool
1041
      (fun ((o,r) as x) ->
1042
1043
1044
1045
1046
1047
1048
1049
	 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
1050
1051
1052
1053
1054
1055
1056

  let project_field t l =
    let r = label_present t l in
    List.fold_left (fun accu (d,_) -> cup accu d) empty r

  let project t l =
    let t = get t in
1057
1058
1059
    let r = label_present t l in
    if r = [] then raise Not_found else
      List.fold_left (fun accu (d,_) -> cup accu d) empty r
1060
1061
1062
1063
	   
  type normal = 
      [ `Success
      | `Fail
1064
1065
      | `NoField
      | `SomeField
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
      | `Label of label * (descr * normal) list * normal ]

  let first_label t =
    let min = ref None in
    let lab l = match !min with 
      | Some l' when l >= l' -> () 
      | _ -> min := Some l in
    let aux = function
      | _,[] -> ()
      | _,(l,_)::_ -> lab l in
    Boolean.iter aux t;
    match !min with
      | Some l -> `Label l
      | None -> 
	  let n = 
	    Boolean.compute
	      ~empty:0
	      ~full:3
	      ~cup:(lor)
	      ~cap:(land)
	      ~diff:(fun a b -> a land lnot b)
	      ~atom:(function (true,[]) -> 3 | (false,[]) -> 1 | _ -> assert false)
	      t in
	  match n with
	    | 0 -> `Fail
	    | 1 -> `NoField
	    | 2 -> `SomeField
	    | _ -> `Success


1096
1097
1098
1099
1100
  let normal' t l = 
    let present = label_present t l
    and absent = restrict_label_absent t l in
    List.map (fun (d,t) -> d,t) present, absent

1101
1102
1103
1104
1105
1106
1107
1108
1109
  let rec normal_aux t =
    match first_label t with
      | `Label l ->
	  let present = label_present t l
	  and absent = restrict_label_absent t l in
	  `Label (l, List.map (fun (d,t) -> d, normal_aux t) present,
		  normal_aux absent)
      | `Fail -> `Fail
      | `Success -> `Success
1110
1111
      | `NoField -> `NoField
      | `SomeField -> `SomeField
1112
1113
1114
1115
1116
1117
1118
1119
1120

  let normal t = normal_aux (get t)
    


  let descr x = { empty with record = x }
  let is_empty x = is_empty (descr x)
(*

1121
  type t = (label, (bool * descr)) SortedMap.t list
1122
1123

  let get d =
1124
1125
1126
1127
    let line r = List.for_all (fun (l,(o,d)) -> o || non_empty d) r in
    List.filter line (get_record d.record)

  let restrict_label_present t l =
1128
1129
1130
1131
1132
1133
1134
    let restr = function 
      | (true, d) -> if non_empty d then (false,d) else raise Exit 
      | x -> x in
    let aux accu r =  
      try SortedMap.change l restr (false,any) r :: accu
      with Exit -> accu in
    List.fold_left aux [] t
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156

  let restrict_label_absent t l =
    let restr = function (true, _) -> (true,empty) | _ -> raise Exit in
    let aux accu r =  
      try SortedMap.change l restr (true,empty) r :: accu
      with Exit -> accu in
    List.fold_left aux [] t

  let restrict_field t l d =
    let restr (_,d1) = 
      let d1 = cap d d1 in 
      if is_empty d1 then raise Exit else (false,d1) in
    let aux accu r = 
      try SortedMap.change l restr (false,d) r :: accu 
      with Exit -> accu in
    List.fold_left aux [] t

  let project_field t l =
    let aux accu x =
      match List.assoc l x with
	| (false,t) -> cup accu t
	| _ -> raise Not_found
1157
    in
1158
1159
    List.fold_left aux empty t

1160
1161
1162
  let project d l =
    project_field (get_record d.record) l

1163
1164
1165
1166
1167
1168
1169
1170
1171
  type normal = 
      [ `Success
      | `Fail
      | `Label of label * (descr * normal) list * normal ]

  let rec merge_record n r =
    match (n, r) with
      | (`Success, _) | (_, []) -> `Success
      | (`Fail, r) ->
1172
1173
	  let aux (l,(o,t)) n = 
	    `Label (l, [t,n], if o then n else `Fail) in
1174
1175
1176
1177
	  List.fold_right aux r `Success
      | (`Label (l1,present,absent), (l2,(o,t2))::r') ->
	  if (l1 < l2) then
	    let pr =  List.map (fun (t,x) -> (t, merge_record x r)) present in
1178
1179
1180
1181
	    let t = List.fold_left (fun a (t,_) -> diff a t) any present in
	    let pr = 
	      if non_empty t then (t, merge_record `Fail r) :: pr
	      else pr in
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
	    `Label (l1,pr,merge_record absent r)
	  else if (l2 < l1) then
	    let n' = merge_record n r' in
	    `Label (l2, [t2, n'], if o then n' else n)
	  else
	    let res = ref [] in
	    let aux a (t,x) = 
	      (let t = diff t t2 in 
	       if non_empty t then res := (t,x) :: !res);
	      (let t = cap t t2 in
	       if non_empty t then res := (t, merge_record x r') :: !res);
	      diff a t 
	    in
	    let t2 = List.fold_left aux t2 present in
	    let () = 
	      if non_empty t2 then 
	      res := (t2, merge_record `Fail r') :: !res in
	    let abs = if o then merge_record absent r' else absent in
	    `Label (l1, !res, abs)

1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
  module Unify = Map.Make(struct type t = normal let compare = compare end)

  let repository = ref Unify.empty

  let rec canonize = function
    | `Label (l,pr,ab) as x ->
	(try Unify.find x !repository 
	 with Not_found -> 
	   let pr = List.map (fun (t,n) -> canonize n,t) pr in
	   let pr = SortedMap.from_list cup pr in
	   let pr = List.map (fun (n,t) -> (t,n)) pr in
	   let x = `Label (l, pr, canonize ab) in
	   try Unify.find x !repository
	   with Not_found -> repository := Unify.add x x !repository; x
	)
    | x -> x
1218
1219

  let normal d =
1220
1221
1222
    let r = canonize (List.fold_left merge_record `Fail (get d)) in
    repository := Unify.empty;
    r
1223

1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
  type normal' =
      [ `Success
      | `Label of label * (descr * descr) list * descr option ] option

(* NOTE: this function relies on the fact that generic order
         makes smallest labels appear first *)

  let first_label d =
    let d = d.record in
    let min = ref None in
    let lab (l,o,t) = match !min with 
      | Some l' when l >= l' -> () 
      | _ -> if o && (descr t = any) then () else min := Some l in
    let line (p,n) =
      (match p with f::_ -> lab f | _ -> ());
      (match n with f::_ -> lab f | _ -> ()) in
    List.iter line d;
    match !min with
      | None -> if d = [] then `Empty else `Any
      | Some l -> `Label l

  let normal' (d : descr) l =
    let ab = ref empty in
    let rec extract f = function
      | (l',o,t) :: rem when l = l' -> 
	  f o (descr t); extract f rem
      | x :: rem -> x :: (extract f rem)
      | [] -> [] in
    let line (p,n) =
      let ao = ref true and ad = ref any in
      let p = 
	extract (fun o d -> ao := !ao && o; ad := cap !ad d) p
      and n = 
	extract (fun o d -> ao := !ao && not o; ad := diff !ad d) n
      in
      (* Note: p and n are still sorted *)
      let d = { empty with record = [(p,n)] } in
      if !ao then ab := cup d !ab;
      (!ad, d) in
    let pr = List.map line d.record in
    let pr = Product.normal_aux pr in
    let ab = if is_empty !ab then None else Some !ab in
    (pr, ab)
	    
1268
*)
1269

1270
  let any = { empty with record = any.record }
1271
(*
1272
  let is_empty d = d = []
1273
1274
1275
  let descr l =
    let line l = map_sort (fun (l,(o,d)) -> (l,o,cons d)) l, [] in 
    { empty with record = map_sort line l }
1276
*)
1277
1278
end

1279
1280


1281
let memo_normalize = ref DescrMap.empty
1282
1283
1284


let rec rec_normalize d =
1285
  try DescrMap.find d !memo_normalize
1286
1287
  with Not_found ->
    let n = make () in
1288
    memo_normalize := DescrMap.add d n !memo_normalize;
1289
    let times = 
1290
1291
1292
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal d)
1293
    in
1294
1295
1296
1297
1298
    let xml = 
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal ~kind:`XML d)
    in
1299
1300
    let record = d.record
(*
1301
1302
1303
      map_sort
	(fun f -> map_sort (fun (l,(o,d)) -> (l,o,rec_normalize d)) f, [])
	(Record.get d)
1304
*)
1305
    in
1306
    define n { d with times = times; xml = xml; record = record };
1307
1308
1309
    n

let normalize n =
1310
  descr (internalize (rec_normalize n))
1311

1312
1313
module Arrow =
struct
1314
1315
1316
1317
  let check_simple left s1 s2 =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff_t accu1 t1 in
1318
          if non_empty accu1' then aux accu1 accu2 left;
1319
          let accu2' = cap_t accu2 t2 in
1320
          if non_empty accu2' then aux accu1 accu2 left
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
      | [] -> raise NotEmpty
    in
    let accu1 = descr s1 in
    (is_empty accu1) ||
    (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)
      
  let check_strenghten t s =
    let left = match t.arrow with [ (p,[]) ] -> p | _ -> assert false in
    let rec aux = function
      | [] -> raise Not_found
      | (p,n) :: rem ->
	  if (List.