types.ml 38.4 KB
Newer Older
1
2
3
4
open Recursive
open Printf


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
37
  let empty = { 
    times = Boolean.empty; 
38
    xml   = Boolean.empty; 
39
40
41
42
    arrow = Boolean.empty; 
    record= Boolean.empty;
    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
152
  let deep = 4
end

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
264
  Boolean.check d.arrow;
  Boolean.check d.record;
  ()

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

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

296
297
let trivially_empty d = d = empty

298
299
300
301
302
303
304
305
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
306
    memo := Assumptions.add d backup;
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
    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 ->
326
(* This avoids explosion with huge rhs (+/- degenerated partitioning)
327
328
   May be slower when List.length right is small; could optimize
   this case... *)
329
330
331
332
(*	if empty_rec (cap_t accu1 t1) || empty_rec (cap_t accu2 t2) then*)
(* THIS IS NOT SOUND !!! *)
	if trivially_empty (cap_t accu1 t1) || 
	   trivially_empty (cap_t accu2 t2) then
333
334
335
336
337
	  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
338
	  if not (empty_rec accu2') then aux accu1 accu2' right
339
340
341
342
343
344
345
    | [] -> raise NotEmpty
  in
  let (accu1,accu2) = cap_product left in
  (empty_rec accu1) || (empty_rec accu2) ||
(* OPT? It does'nt seem so ...  The hope was to return false quickly
   for large right hand-side *)
  (
346
    (* (if (List.length right > 2) then
347
348
       let (cup1,cup2) = cup_product right in
       (empty_rec (diff accu1 cup1)) && (empty_rec (diff accu2 cup2))
349
350
     else true)
    && *)
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
    (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

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
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)
	    

406
and empty_rec_record c =
407
(*
408
  let aux = List.exists (fun (_,(opt,t)) -> (not opt) && (empty_rec t)) in
409
410
*)
  List.for_all empty_rec_record_aux (get_record c)
411
412

let is_empty d =
413
(*  Printf.eprintf "+"; flush stderr; *)
414
415
  let old = !memo in
  let r = empty_rec d in
416
417
  if not r then memo := old
  else if not (is_recurs_descr d) then memo := Assumptions.add d !memo;
418
(*  cache_false := Assumptions.empty;  *)
419
(*  Printf.eprintf "-\n"; flush stderr; *)
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
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
  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

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
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)

496
*)
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
  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
518
519
520
(* Maybe, can improve this function with:
     (t,s) \ (t1,s1) = (t&t',s\s') | (t\t',s),
   don't call normal_aux *)
521

522

523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
  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
552
553
(* Could optimize this call to normal_aux because one already
   know that each line is normalized ... *)
554
555
	  memo := Memo.add d n !memo;
	  n
556

557
558
559
560
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
561

562
563
module Print = 
struct
564
565
566
567
568
  let rec print_union ppf = function
    | [] -> Format.fprintf ppf "Empty"
    | [h] -> h ppf
    | h::t -> Format.fprintf ppf "@[%t |@ %a@]" h print_union t

569
570
  let print_atom ppf a = 
    Format.fprintf ppf "`%s" (AtomPool.value a)
571

572
573
574
575
576
577
578
579
  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)

580
581
582
583
584
  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

585
586
587
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607

  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 =
608
    if not (DescrMap.mem d !named) then
609
610
611
612
613
614
615
616
617
      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;
618
    	bool_iter 
619
620
	  (fun (n1,n2) -> mark n1; mark n2
(*
621
622
623
	     List.iter
	       (fun (d1,d2) ->
		  mark_descr d2;
624
625
626
    		  bool_iter 
		    (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) 
		    d1.record
627
		  let l = get_record d1.record in
628
629
630
631
632
		  List.iter (fun labs,(_,(_,p)),ns ->
			       Array.iter mark_descr p;
			       List.iter (fun (_,(_,n)) -> 
					    Array.iter mark_descr n) ns
			    ) l
633
634
	       )
	       (Product.normal (descr n2))
635
*)
636
	  ) d.xml;
637
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
638
    	bool_iter (fun (o,l) -> List.iter (fun (l,(o,n)) -> mark n) l) d.record
639
640
641
642
643

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
644
      let name = DescrMap.find d !named in
645
646
647
648
649
650
651
      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
652
	  Not_found -> assert false
653
654
655
656
657
658
659
  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 @
660
	 Boolean.print "XML" print_xml d.xml @
661
662
663
664
665
	 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
666
  and print_xml ppf (t1,t2) =
667
668
    Format.fprintf ppf "@[XML(%a,%a)@]" print t1 print t2
(*
669
670
671
672
673
674
675
676
677
    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
678
*)
679
680
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
681
682
683
684
685
  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)) ->
686
687
		 let sep = if !first then (first := false; "") else ";" in
		 Format.fprintf ppf "%s@ @[%s =%s@] %a" sep
688
689
690
691
		   (LabelPool.value l) (if o then "?" else "") print t
	      ) r;
    Format.fprintf ppf " %s}@]" o
(*
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
  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
709
*)
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736

	  
  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

737
let () = print_descr := Print.print_descr
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
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
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 }


  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)

  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

  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]) 

  let solve v = internalize (make_node v)
end




(* Sample value *)
module Sample =
struct

783

784
785
786
787
788
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
789
  | Int of Big_int.big_int
790
  | Atom of atom
791
  | Char of Chars.Unichar.t
792
793
  | Pair of (t * t)
  | Xml of (t * t)
794
795
  | Record of (label * t) list
  | Fun of (node * node) list
796
  | Other
797
  exception FoundSampleRecord of (label * t) list
798
799
800
801
802

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 ->
803
804
805
    try Atom (Atoms.sample (fun _ -> AtomPool.dummy_min) d.atoms) with 
	Not_found ->
(* Here: could create a fresh atom ... *)
806
    try Char (Chars.sample d.chars) with Not_found ->
807
808
809
    try sample_rec_arrow d.arrow with Not_found ->

    let memo = Assumptions.add d memo in
810
811
    try Pair (sample_rec_times memo d.times) with Not_found ->
    try Xml (sample_rec_times memo d.xml) with Not_found ->
812
813
814
815
816
817
818
819
820
821
    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 ->
822
823
(*TODO: check: is this correct ?  non_empty could return true
  but because of coinduction, the call to aux may raise Not_found, no ? *)
824
825
826
827
828
        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
829
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
830
831
832
833
834
835
836
837
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right

and sample_rec_arrow c =
  find sample_rec_arrow_aux c

838
839
840
841
842
843
844
845
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
846
  in
847
848
849
850
851
852
853
854
855
  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
856
857
858
859
860
861
  else Fun left


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

862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
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

	    


898

899
let get x = try sample_rec Assumptions.empty x with Not_found -> Other
900

901
902
903
904
905
906
907
908
  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)
909
910
911
912
913
    | Atom a ->    
	if a = LabelPool.dummy_min then
	  Format.fprintf ppf "(almost any atom)"
	else
	  Format.fprintf ppf "`%s" (AtomPool.value a)
914
915
    | Char c -> Chars.Unichar.print ppf c
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
916
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
917
918
919
920
921
    | Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
922
		(LabelPool.value l)
923
924
925
926
927
928
929
930
931
932
933
934
935
		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
936
937
    | Other ->
	Format.fprintf ppf "[cannot determine value]"
938
939
940
941
942
943
end



module Record = 
struct
944
945
946
947
948
  type atom = bool * (label, (bool * node)) SortedMap.t
  type t = atom Boolean.t

  let get d = d.record

949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
  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)

976
977
978
979
980
981
  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,[]))))

982
983
  let restrict_label_absent t l =
    Boolean.compute_bool
984
      (fun ((o,r) as x) ->
985
986
	 try
	   let (lo,_) = List.assoc l r in
987
	   if lo then atom (o,SortedMap.diff r [l])
988
989
990
991
992
993
994
995
996
	   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
997
      (fun ((o,r) as x) ->
998
999
1000
	 try
	   let (lo,lt) = List.assoc l r in
	   if (not lo) && (is_empty (cap d (descr lt))) then Boolean.empty
1001
	   else atom (o, SortedMap.diff r [l])
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
	 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
1012
	(fun ((o,r) as x) ->
1013
1014
	   try
	     let (_,lt) = List.assoc l r in
1015
	     Boolean.atom (descr lt, atom (o, SortedMap.diff r [l]))
1016
1017
1018
1019
1020
1021
1022
1023
	   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 =
1024
    Boolean.compute_bool
1025
      (fun ((o,r) as x) ->
1026
1027
1028
1029
1030
1031
1032
1033
	 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
1034
1035
1036
1037
1038
1039
1040

  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
1041
1042
1043
    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
1044
1045
1046
1047
	   
  type normal = 
      [ `Success
      | `Fail
1048
1049
      | `NoField
      | `SomeField
1050
1051
1052
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
      | `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


1080
1081
1082
1083
1084
  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

1085
1086
1087
1088
1089
1090
1091
1092
1093
  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
1094
1095
      | `NoField -> `NoField
      | `SomeField -> `SomeField
1096
1097
1098
1099
1100
1101
1102
1103
1104

  let normal t = normal_aux (get t)
    


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

1105
1106
1107
1108
1109
1110
1111
  type t = (label, (bool * descr)) SortedMap.t list

  let get d =
    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 =
1112
1113
1114
1115
1116
1117
1118
    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
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143

  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
    in
    List.fold_left aux empty t

1144
1145
1146
  let project d l =
    project_field (get_record d.record) l

1147
1148
1149
1150
1151
1152
1153
1154
1155
  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) ->
1156
1157
	  let aux (l,(o,t)) n = 
	    `Label (l, [t,n], if o then n else `Fail) in
1158
1159
1160
1161
	  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
1162
1163
1164
1165
	    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
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
	    `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)

1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
  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
1202
1203

  let normal d =
1204
1205
1206
    let r = canonize (List.fold_left merge_record `Fail (get d)) in
    repository := Unify.empty;
    r
1207

1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
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
  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)
	    
1252
*)
1253
1254

  let any = { empty with record = any.record }
1255
(*
1256
  let is_empty d = d = []
1257
1258
1259
  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 }
1260
*)
1261
1262
1263
1264
end



1265
let memo_normalize = ref DescrMap.empty
1266
1267
1268


let rec rec_normalize d =
1269
  try DescrMap.find d !memo_normalize
1270
1271
  with Not_found ->
    let n = make () in
1272
    memo_normalize := DescrMap.add d n !memo_normalize;
1273
1274
1275
1276
1277
    let times = 
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal d)
    in
1278
1279
1280
1281
1282
    let xml = 
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal ~kind:`XML d)
    in
1283
1284
    let record = d.record
(*
1285
1286
1287
      map_sort
	(fun f -> map_sort (fun (l,(o,d)) -> (l,o,rec_normalize d)) f, [])
	(Record.get d)
1288
*)
1289
    in
1290
    define n { d with times = times; xml = xml; record = record };
1291
1292
1293
    n

let normalize n =
1294
  descr (internalize (rec_normalize n))
1295

1296
1297
module Arrow =
struct
1298
1299
1300
1301
  let check_simple left s1 s2 =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff_t accu1 t1 in
1302
          if non_empty accu1' then aux accu1 accu2 left;
1303
          let accu2' = cap_t accu2 t2 in
1304
          if non_empty accu2' then aux accu1 accu2 left
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
      | [] -> 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.for_all (fun (a,b) -> check_simple left a b) p) &&
	    (List.for_all (fun (a,b) -> not (check_simple left a b)) n) then
	      { empty with arrow = [ (SortedList.cup left p, n) ] }
	  else aux rem
    in
    aux s.arrow

1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
  let check_simple_iface left s1 s2 =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff accu1 t1 in
          if non_empty accu1' then aux accu1 accu2 left;
          let accu2' = cap accu2 t2 in
          if non_empty accu2' then aux accu1 accu2 left
      | [] -> 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_iface iface s =
    let rec aux = function
      | [] -> false
      | (p,n) :: rem ->
	  ((List.for_all (fun (a,b) -> check_simple_iface iface a b) p) &&
	   (List.for_all (fun (a,b) -> not (check_simple_iface iface a b)) n))
	  || (aux rem)
    in
    aux s.arrow

1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
  type t = descr * (descr * descr) list list

  let get t =
    List.fold_left
      (fun ((dom,arr) as accu) (left,right) ->
	 if Sample.check_empty_arrow_line left right 
	 then accu
	 else (
	   let left =
	     List.map 
	       (fun (t,s) -> (descr t, descr s)) left in
	   let d = List.fold_left (fun d (t,_) -> cup d t) empty left in
	   (cap dom d, left :: arr)
	 )
      )
      (any, [])
      t.arrow

  let domain (dom,_) = dom

  let apply_simple t result left = 
    let rec aux result accu1 accu2 = function
      | (t1,s1)::left ->
          let result = 
	    let accu1 = diff accu1 t1 in
            if non_empty accu1 then aux result accu1 accu2 left
            else result in
          let result =
	    let accu2 = cap accu2 s1 in
            aux result accu1 accu2 left in
	  result
      | [] -> 
          if subtype accu2 result 
	  then result
	  else cup result accu2
    in
    aux result t any left
      
  let apply (_,arr) t =
    List.fold_left (apply_simple t) empty arr

1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
  let need_arg (dom, arr) =
    List.exists (function [_] -> false | _ -> true) arr

  let apply_noarg (_,arr) =
    List.fold_left 
      (fun accu -> 
	 function 
	   | [(t,s)] -> cup accu s
	   | _ -> assert false
      )
      empty arr

1399
  let any = { empty with arrow = any.arrow }
1400
  let is_empty (_,arr) = arr = []
1401
1402
1403
end
  

1404
module Int = struct
1405
1406
  let has_int d i = Intervals.contains i d.ints

1407
1408
1409
1410
1411
  let get d = d.ints
  let put i = { empty with ints = i }
  let is_int d = is_empty { d with ints = Intervals.empty }
  let any = { empty with ints = Intervals.any }
end
1412

1413
1414
1415
1416
module Atom = struct
  let has_atom d a = Atoms.contains a d.atoms
end

1417
1418
module Char = struct
  let has_char d c = Chars.contains c d.chars
1419
  let any = { empty with chars = Chars.any }
1420
1421
end

1422
let print_stat ppf =
1423
(*  Format.fprintf ppf "nb_rec = %i@." !nb_rec;
1424
  Format.fprintf ppf "nb_norec = %i@." !nb_norec;
1425
*)
1426
1427
  ()

1428
1429
1430
1431