types.ml 29.1 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
28
29
module I = struct
  type 'a t = {
    ints  : Intervals.t;
    atoms : atom Atoms.t;
    times : ('a * 'a) Boolean.t;
30
    xml   : ('a * 'a) Boolean.t;
31
32
    arrow : ('a * 'a) Boolean.t;
    record: (label * bool * 'a) Boolean.t;
33
    chars : Chars.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
61
  let arrow x y = { empty with arrow = Boolean.atom (x,y) }
  let record label opt t = { empty with record = Boolean.atom (label,opt,t) }
62
63
  let atom a = { empty with atoms = a }
  let char c = { empty with chars = c }
64
  let constant = function
65
    | Integer i -> interval (Intervals.atom i)
66
67
    | Atom a -> atom (Atoms.atom a)
    | Char c -> char (Chars.atom c)
68
69

		   
70
  let cup x y = 
71
    if x = y then x else { 
72
      times = Boolean.cup x.times y.times;
73
      xml   = Boolean.cup x.xml y.xml;
74
75
76
77
      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;
78
      chars = Chars.cup x.chars y.chars;
79
80
81
    }
      
  let cap x y = 
82
    if x = y then x else {
83
      times = Boolean.cap x.times y.times;
84
      xml   = Boolean.cap x.xml y.xml;
85
86
87
88
      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;
89
      chars = Chars.cap x.chars y.chars;
90
91
92
    }
      
  let diff x y = 
93
    if x = y then empty else { 
94
      times = Boolean.diff x.times y.times;
95
      xml   = Boolean.diff x.xml y.xml;
96
97
98
99
      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;
100
      chars = Chars.diff x.chars y.chars;
101
102
    }

103
104
105
		   
  let equal e a b =
    if a.atoms <> b.atoms then raise NotEqual;
106
    if a.chars <> b.chars then raise NotEqual;
107
    if a.ints <> b.ints then raise NotEqual;
108
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.times b.times;
109
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.xml b.xml;
110
111
112
113
114
115
116
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.arrow b.arrow;
    Boolean.equal (fun (l1,o1,x1) (l2,o2,x2) -> 
		     if (l1 <> l2) || (o1 <> o2) then raise NotEqual;
		     e x1 x2) a.record b.record
      
  let map f a =
    { times = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.times;
117
      xml   = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.xml;
118
119
120
121
      arrow = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.arrow;
      record= Boolean.map (fun (l,o,x) -> (l,o, f x)) a.record;
      ints  = a.ints;
      atoms = a.atoms;
122
      chars = a.chars;
123
124
125
    }
    
  let hash h a =
126
127
    Hashtbl.hash (map h a)
(*
128
    (Hashtbl.hash { (map h a) with ints = Intervals.empty })
129
    + (Intervals.hash a.ints)
130
*)
131
132
133
      
  let iter f a =
    ignore (map f a)
134
     
135
136
137
  let deep = 4
end

138
     
139
module Algebra = Recursive_noshare.Make(I)
140
141
include I
include Algebra
142
143
144
145
146
147
148
149
150
module DescrHash = 
  Hashtbl.Make(
    struct 
      type t = descr
      let hash = hash_descr
      let equal = equal_descr
    end
  )

151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
(*
let define n d = check d; define n d
*)

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

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

let neg x = diff any x

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
    

188
module DescrMap = Map.Make(struct type t = descr let compare = compare end)
189
190
191

let check d =
  Boolean.check d.times;
192
  Boolean.check d.xml;
193
194
195
196
  Boolean.check d.arrow;
  Boolean.check d.record;
  ()

197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
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
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
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
340
341
342
343
344
345
346


(* 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


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
    memo := Assumptions.add d backup;
    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 ->
        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
    | [] -> 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 *)
  (
    ((*if (List length right > 2) then
       let (cup1,cup2) = cup_product right in
       (empty_rec (diff accu1 cup1)) && (empty_rec (diff accu2 cup2))
     else*) true)
    && 
    (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

and empty_rec_record c =
  let aux = List.exists (fun (_,(opt,t)) -> (not opt) && (empty_rec t)) in
  List.for_all aux (get_record c)

let is_empty d =
  let old = !memo in
  let r = empty_rec d in
  if not r then memo := old; 
(*  cache_false := Assumptions.empty;  *)
  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

347
(*
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
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)

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
  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

  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
	  memo := Memo.add d n !memo;
	  n
431

432
433
434
435
  let any = { empty with times = any.times }
  and any_xml = { empty with xml = any.xml }
  let is_empty d = d = []
end
436

437
438
module Print = 
struct
439
440
441
442
443
  let rec print_union ppf = function
    | [] -> Format.fprintf ppf "Empty"
    | [h] -> h ppf
    | h::t -> Format.fprintf ppf "@[%t |@ %a@]" h print_union t

444
445
  let print_atom ppf a = 
    Format.fprintf ppf "`%s" (AtomPool.value a)
446

447
448
449
450
451
452
453
454
  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)

455
456
457
458
459
  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

460
461
462
  let named = State.ref "Types.Printf.named" DescrMap.empty
  let register_global name d = 
    named := DescrMap.add d name !named
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482

  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 =
483
    if not (DescrMap.mem d !named) then
484
485
486
487
488
489
490
491
492
      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;
493
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.xml;
494
495
496
497
498
499
500
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
    	bool_iter (fun (l,o,n) -> mark n) d.record

    
  let rec print ppf n = print_descr ppf (descr n)
  and print_descr ppf d = 
    try 
501
      let name = DescrMap.find d !named in
502
503
504
505
506
507
508
      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
509
	  Not_found -> assert false
510
511
512
513
514
515
516
  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 @
517
	 Boolean.print "XML" print_xml d.xml @
518
519
520
521
522
	 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
523
524
525
526
527
528
529
530
531
532
  and print_xml ppf (t1,t2) =
    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
533
534
535
536
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
  and print_record ppf (l,o,t) =
    Format.fprintf ppf "@[{ %s =%s %a }@]" 
537
      (LabelPool.value l) (if o then "?" else "") print t
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
  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
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583

	  
  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



584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
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

let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
633
  | Int of Big_int.big_int
634
  | Atom of atom
635
  | Char of Chars.Unichar.t
636
637
  | Pair of (t * t)
  | Xml of (t * t)
638
639
640
641
642
643
644
  | Record of (label * t) list
  | Fun of (node * node) list

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 ->
645
646
647
    try Atom (Atoms.sample (fun _ -> AtomPool.dummy_min) d.atoms) with 
	Not_found ->
(* Here: could create a fresh atom ... *)
648
    try Char (Chars.sample d.chars) with Not_found ->
649
650
651
    try sample_rec_arrow d.arrow with Not_found ->

    let memo = Assumptions.add d memo in
652
653
    try Pair (sample_rec_times memo d.times) with Not_found ->
    try Xml (sample_rec_times memo d.xml) with Not_found ->
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
    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 ->
        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
669
    | [] -> (sample_rec memo accu1, sample_rec memo accu2)
670
671
672
673
674
675
676
677
  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

678
679
680
681
682
683
684
685
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
686
  in
687
688
689
690
691
692
693
694
695
  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
696
697
698
699
700
701
702
703
704
705
706
  else Fun left


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

and sample_rec_record_aux memo fields =
  let aux acc (l,(o,t)) = if o then acc else (l, sample_rec memo t) :: acc in
  List.fold_left aux [] fields

let get x = sample_rec Assumptions.empty x
707

708
709
710
711
712
713
714
715
  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)
716
717
718
719
720
    | Atom a ->    
	if a = LabelPool.dummy_min then
	  Format.fprintf ppf "(almost any atom)"
	else
	  Format.fprintf ppf "`%s" (AtomPool.value a)
721
722
    | Char c -> Chars.Unichar.print ppf c
    | Pair (x1,x2) -> Format.fprintf ppf "(%a,%a)" print x1 print x2
723
    | Xml (x1,x2) -> Format.fprintf ppf "XML(%a,%a)" print x1 print x2
724
725
726
727
728
    | Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
729
		(LabelPool.value l)
730
731
732
733
734
735
736
737
738
739
740
741
742
		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
743
744
745
746
747
748
749
750
751
752
753
754
755
end



module Record = 
struct
  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 =
756
757
758
759
760
761
762
    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
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787

  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

788
789
790
  let project d l =
    project_field (get_record d.record) l

791
792
793
794
795
796
797
798
799
  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) ->
800
801
	  let aux (l,(o,t)) n = 
	    `Label (l, [t,n], if o then n else `Fail) in
802
803
804
805
	  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
806
807
808
809
	    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
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
	    `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)

830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
  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
846
847

  let normal d =
848
849
850
    let r = canonize (List.fold_left merge_record `Fail (get d)) in
    repository := Unify.empty;
    r
851

852
853
854
855
856
857
858
859
860
861
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
  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)
	    
896
897
898

  let any = { empty with record = any.record }
  let is_empty d = d = []
899
900
901
  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 }
902
903
904
905
end



906
let memo_normalize = ref DescrMap.empty
907
908
909


let rec rec_normalize d =
910
  try DescrMap.find d !memo_normalize
911
912
  with Not_found ->
    let n = make () in
913
    memo_normalize := DescrMap.add d n !memo_normalize;
914
915
916
917
918
    let times = 
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal d)
    in
919
920
921
922
923
    let xml = 
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal ~kind:`XML d)
    in
924
925
926
927
928
    let record = 
      map_sort
	(fun f -> map_sort (fun (l,(o,d)) -> (l,o,rec_normalize d)) f, [])
	(Record.get d)
    in
929
    define n { d with times = times; xml = xml; record = record };
930
931
932
    n

let normalize n =
933
  descr (internalize (rec_normalize n))
934

935
936
module Arrow =
struct
937
938
939
940
  let check_simple left s1 s2 =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff_t accu1 t1 in
941
          if non_empty accu1' then aux accu1 accu2 left;
942
          let accu2' = cap_t accu2 t2 in
943
          if non_empty accu2' then aux accu1 accu2 left
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
      | [] -> 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

962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
  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

985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
  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

1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
  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

1038
  let any = { empty with arrow = any.arrow }
1039
  let is_empty (_,arr) = arr = []
1040
1041
1042
end
  

1043
module Int = struct
1044
1045
  let has_int d i = Intervals.contains i d.ints

1046
1047
1048
1049
1050
  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
1051

1052
1053
1054
1055
module Atom = struct
  let has_atom d a = Atoms.contains a d.atoms
end

1056
1057
module Char = struct
  let has_char d c = Chars.contains c d.chars
1058
  let any = { empty with chars = Chars.any }
1059
1060
end

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
1090
1091
1092
1093
1094
1095
(*
let rec print_normal_record ppf = function
  | Success -> Format.fprintf ppf "Yes"
  | Fail -> Format.fprintf ppf "No"
  | FirstLabel (l,present,absent) ->
      Format.fprintf ppf "%s?@[<v>@\n" (label_name l);
      List.iter
        (fun (t,n) ->
	   Format.fprintf ppf "(%a)=>@[%a@]@\n" 
	     Print.print_descr t
	     print_normal_record n
	) present;
      if absent <> Fail then
	Format.fprintf ppf "(absent)=>@[%a@]@\n" print_normal_record absent;
      Format.fprintf ppf "@]" 
*)


(* 
let pr s = Types.Print.print Format.std_formatter (Syntax.make_type (Syntax.parse s));;

let pr' s = Types.Print.print Format.std_formatter 
   (Types.normalize (Syntax.make_type (Syntax.parse s)));;

BUG:
pr "'a | 'b where 'a = ('a , 'a) and 'b= ('b , 'b)";;
*)


(*
  let nr s =
    let t = Types.descr (Syntax.make_type (Syntax.parse s)) in
    let n = Types.normal_record' t.Types.record in
    Types.print_normal_record Format.std_formatter n;;
*)