types.ml 22 KB
Newer Older
1
2
open Recursive
open Printf
3

4

5

6
7
type label = int
type atom  = int
8

9
type const = Integer of Big_int.big_int | Atom of atom | Char of Chars.Unichar.t
10

11
12
module I = struct
  type 'a t = {
13
    ints  : Intervals.t;
14
15
16
17
    atoms : atom Atoms.t;
    times : ('a * 'a) Boolean.t;
    arrow : ('a * 'a) Boolean.t;
    record: (label * bool * 'a) Boolean.t;
18
    chars : Chars.t;
19
  }
20

21
  let empty = { 
22
23
24
    times = Boolean.empty; 
    arrow = Boolean.empty; 
    record= Boolean.empty;
25
26
    ints  = Intervals.empty;
    atoms = Atoms.empty;
27
    chars = Chars.empty;
28
  }
29

30
31
32
33
  let any =  {
    times = Boolean.full; 
    arrow = Boolean.full; 
    record= Boolean.full; 
34
    ints  = Intervals.any;
35
36
    atoms = Atoms.any;
    chars = Chars.any;
37
38
  }
	       
39
  let interval i j = { empty with ints = Intervals.atom i j }
40
41
42
  let times x y = { empty with times = Boolean.atom (x,y) }
  let arrow x y = { empty with arrow = Boolean.atom (x,y) }
  let record label opt t = { empty with record = Boolean.atom (label,opt,t) }
43
44
  let atom a = { empty with atoms = a }
  let char c = { empty with chars = c }
45
46
  let constant = function
    | Integer i -> interval i i
47
48
    | Atom a -> atom (Atoms.atom a)
    | Char c -> char (Chars.atom c)
49
50
51
52

		   
  let any_record = { empty with record = any.record }

53
  let cup x y = 
54
    if x == y then x else { 
55
56
57
58
59
      times = Boolean.cup x.times y.times;
      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;
60
      chars = Chars.cup x.chars y.chars;
61
62
63
    }
      
  let cap x y = 
64
    if x == y then x else {
65
66
67
68
69
      times = Boolean.cap x.times y.times;
      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;
70
      chars = Chars.cap x.chars y.chars;
71
72
73
    }
      
  let diff x y = 
74
    if x == y then empty else { 
75
76
77
78
79
      times = Boolean.diff x.times y.times;
      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;
80
      chars = Chars.diff x.chars y.chars;
81
82
    }

83
84
85
  let neg x = diff any x
		   
  let equal e a b =
86
    if not (Intervals.equal a.ints b.ints) then raise NotEqual;
87
    if a.atoms <> b.atoms then raise NotEqual;
88
    if a.chars <> b.chars then raise NotEqual;
89
90
91
92
93
94
95
96
97
98
99
100
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.times b.times;
    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;
      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;
101
      chars = a.chars;
102
    }
103
    
104
  let hash h a =
105
106
    (Hashtbl.hash { map h a with ints = Intervals.empty })
    + (Intervals.hash a.ints)
107
108
109
      
  let iter f a =
    ignore (map f a)
110
     
111
112
  let deep = 4
end
113

114
115
116
117
	     
module Algebra = Recursive.Make(I)
include I
include Algebra
118

119
120
121
122
123
let check d =
  Boolean.check d.times;
  Boolean.check d.arrow;
  Boolean.check d.record;
  ()
124

125
126
127
(*
let define n d = check d; define n d
*)
128

129
130
131
132
let cons d =
  let n = make () in
  define n d;
  internalize n
133

134

135
136
137
138
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 }
139
140


141
142
143
144
145
146
147
148
149
  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)
150

151
152
153
154
155
156
157
158
159
  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
160

161
162
163
164
165
166
167
  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]) 
168

169
170
  let solve v = internalize (make_node v)
end
171

172

173
let get_record r =
174
  let add = SortedMap.add (fun (o1,t1) (o2,t2) -> (o1&&o2, cap t1 t2)) in
175
  let line (p,n) =
176
177
178
179
180
181
182
183
184
185
    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
    

let counter_label = ref 0
let label_table = Hashtbl.create 63
let label_names = Hashtbl.create 63
186

187
188
189
190
191
192
193
let label s =
  try Hashtbl.find label_table s
  with Not_found ->
    incr counter_label;
    Hashtbl.add label_table s !counter_label;
    Hashtbl.add label_names !counter_label s;
    !counter_label
194

195
196
let label_name l =
  Hashtbl.find label_names l
197

198
199
200
let mk_atom = label

let atom_name = label_name
201
202
203
204
205

(* Subtyping algorithm *)

let diff_t d t = diff d (descr t)
let cap_t d t = cap d (descr t)
206
let cap_product l = 
207
208
  List.fold_left 
    (fun (d1,d2) (t1,t2) -> (cap_t d1 t1, cap_t d2 t2))
209
    (any,any)
210
    l
211

212

213
module Assumptions = Set.Make(struct type t = descr let compare = compare end)
214

215
216
let memo = ref Assumptions.empty
let cache_false = ref Assumptions.empty
217

218
exception NotEmpty
219

220
221
222
223
224
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
225
  else if not (Chars.is_empty d.chars) then false
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
  else (
    let backup = !memo in
    memo := Assumptions.add d backup;
    if 
      (empty_rec_times d.times) &&
      (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
252
  in
253
254
255
256
257
258
  let (accu1,accu2) = cap_product left in
  (empty_rec accu1) || (empty_rec accu2) ||
  (try aux accu1 accu2 right; true with NotEmpty -> false)

and empty_rec_arrow c =
  List.for_all empty_rec_arrow_aux c
259

260
261
262
and empty_rec_arrow_aux (left,right) =
  let single_right (s1,s2) =
    let rec aux accu1 accu2 = function
263
      | (t1,t2)::left ->
264
265
266
267
268
          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
269
270
    in
    let accu1 = descr s1 in
271
272
    (empty_rec accu1) ||
    (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)
273
  in
274
  List.exists single_right right
275

276
277
278
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)
279

280
let is_empty d =
281
  let old = !memo in
282
  let r = empty_rec d in
283
  if not r then memo := old; 
284
(*  cache_false := Assumptions.empty;  *)
285
  r
286

287
288
289
let non_empty d = 
  not (is_empty d)

290
let subtype d1 d2 =
291
  is_empty (diff d1 d2)
292

293
294
295
(* Sample value *)
module Sample =
struct
296

297
298
299
300
301
let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
302
  | Int of Big_int.big_int
303
  | Atom of atom
304
  | Char of Chars.Unichar.t
305
306
307
308
309
310
311
312
313
314
315
316
  | Pair of t * t
  | Record of (label * t) list
  | Fun of (node * node) list

let rec gen_atom i l =
  if SortedList.mem l i then gen_atom (succ i) l  else i

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 ->
    try Atom (Atoms.sample (gen_atom 0) d.atoms) with Not_found ->
317
    try Char (Chars.sample d.chars) with Not_found ->
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
    try sample_rec_arrow d.arrow with Not_found ->

    let memo = Assumptions.add d memo in
    try sample_rec_times memo d.times with Not_found ->
    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
    | [] -> Pair (sample_rec memo accu1, sample_rec memo accu2)
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right
342

343
344
and sample_rec_arrow c =
  find sample_rec_arrow_aux c
345

346
347
348
349
350
351
352
353
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
354
  in
355
356
357
358
359
360
361
362
363
  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
364
365
366
367
368
  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))
369

370
371
372
373
374
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
375

376
377
end

378

379
380
381
382
module Product =
struct
  type t = (descr * descr) list

383
384
385
  let other d = { d with times = empty.times }
  let is_product d = is_empty (other d)

386
387
  let need_second = function _::_::_ -> true | _ -> false

388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
  let get 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.times
405

406
407
  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty
408

409
410
411
412
413
414
  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
415

416
  let normal d =
417
418
419
420
421
422
423
    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*) 
424
	    if d1 = t1 then r := (d1,cup d2 t2) else
425
426
427
428
429
430
431
432
433
434
435
436
437
438
	      
	      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
439
    List.iter add (get d);
440
441
    List.map (!) !res

442
  let any = { empty with times = any.times }
443
  let is_empty d = d = []
444
end
445

446

447
module Record = 
448
struct
449
  type t = (label, (bool * descr)) SortedMap.t list
450
451

  let get d =
452
453
454
455
456
    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 =
457
458
459
460
461
462
463
    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
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485

  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
486
    in
487
488
    List.fold_left aux empty t

489
490
491
  let project d l =
    project_field (get_record d.record) l

492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
  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) ->
	  let aux (l,(o,t)) n = `Label (l, [t,n], if o then n else `Fail) in
	  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
	    `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)


  let normal d =
    List.fold_left merge_record `Fail (get d)
529

530

531
532
  let any = { empty with record = any.record }
  let is_empty d = d = []
533
534
end

535

536
537
538
539
540
541
542
543
544
module DescrHash = 
  Hashtbl.Make(
    struct 
      type t = descr
      let hash = hash_descr
      let equal = equal_descr
    end
  )

545
module MapDescr = Map.Make(struct type t = descr let compare = compare end)
546

547
let memo_normalize = DescrHash.create 17
548

549
550
let map_sort f l =
  SortedList.from_list (List.map f l)
551
552

let rec rec_normalize d =
553
  try DescrHash.find memo_normalize d
554
555
  with Not_found ->
    let n = make () in
556
    DescrHash.add memo_normalize d n;
557
    let times = 
558
559
560
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal d)
561
    in
562
563
564
565
    let record = 
      map_sort
	(fun f -> map_sort (fun (l,(o,d)) -> (l,o,rec_normalize d)) f, [])
	(Record.get d)
566
    in
567
    define n { d with times = times; record = record };
568
569
570
    n

let normalize n =
571
  descr (internalize (rec_normalize n))
572

573
module Print =
574
struct
575
576
577
578
579
580
581
  let print_atom ppf a = Format.fprintf ppf "`%s" (atom_name a)

  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

582
583
584
585
  let named = DescrHash.create 10
  let register_global name d = DescrHash.add named d name

  let marks = DescrHash.create 63
586
587
588
589
  let wh = ref []
  let count_name = ref 0
  let name () =
    incr count_name;
590
591
592
    "X" ^ (string_of_int !count_name)
(* TODO: 
   check that these generated names does not conflict with declared types *)
593

594
595
  let bool_iter f b =
    List.iter (fun (p,n) -> List.iter f p; List.iter f n) b
596

597
  let trivial b = b = Boolean.empty || b = Boolean.full
598

599
600
601
  let worth_abbrev d = 
    not (trivial d.times && trivial d.arrow && trivial d.record) 

602
603
604
605
606
607
608
609
610
611
612
613
614
615
  let rec mark n = mark_descr (descr n)
  and mark_descr d =
    if not (DescrHash.mem named d) then
      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;
    	bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
    	bool_iter (fun (l,o,n) -> mark n) d.record
616

617
618
619
620
621
622
623
    
  let rec print_union ppf = function
    | [] -> Format.fprintf ppf "Empty"
    | [h] -> h ppf
    | h::t -> Format.fprintf ppf "@[%t |@ %a@]" h print_union t


624
  let rec print ppf n = print_descr ppf (descr n)
625
  and print_descr ppf d = 
626
627
628
629
    try 
      let name = DescrHash.find named d in
      Format.fprintf ppf "%s" name
    with Not_found ->
630
631
632
633
634
635
      try
      	match !(DescrHash.find marks d) with
      	  | Some n -> Format.fprintf ppf "%s" n
      	  | None -> real_print_descr ppf d
      with
	  Not_found -> Format.fprintf ppf "XXX"
636
  and real_print_descr ppf d = 
637
    if d = any then Format.fprintf ppf "Any" else
638
639
640
      print_union ppf 
	(Intervals.print d.ints @
	 Chars.print d.chars @
641
642
643
644
	 Atoms.print "Atom" print_atom d.atoms @
	 Boolean.print "Pair" print_times d.times @
	 Boolean.print "Arrow" print_arrow d.arrow @
	 Boolean.print "Record" print_record d.record
645
	)
646
647
648
649
650
651
652
  and print_times ppf (t1,t2) =
    Format.fprintf ppf "@[(%a,%a)@]" print t1 print t2
  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 }@]" 
      (label_name l) (if o then "?" else "") print t
653

654
655
656
657
658
	  
  let end_print ppf =
    (match List.rev !wh with
       | [] -> ()
       | (na,d)::t ->
659
	   Format.fprintf ppf " where@ @[%s = %a" na real_print_descr d;
660
	   List.iter 
661
662
	     (fun (na,d) -> 
		Format.fprintf ppf " and@ %s = %a" na real_print_descr d)
663
664
665
666
667
668
	     t;
	   Format.fprintf ppf "@]"
    );
    Format.fprintf ppf "@]";
    count_name := 0;
    wh := [];
669
    DescrHash.clear marks
670
671
672
673
674

  let print_descr ppf d =
    mark_descr d;
    Format.fprintf ppf "@[%a" print_descr d;
    end_print ppf
675
676
677

   let print ppf n = print_descr ppf (descr n)

678
679
680
681
682
683
684
  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_sample ppf = function
685
    | Sample.Int i -> Format.fprintf ppf "%s" (Big_int.string_of_big_int i)
686
    | Sample.Atom a -> Format.fprintf ppf "`%s" (atom_name a)
687
    | Sample.Char c -> Chars.Unichar.print ppf c
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
    | Sample.Pair (x1,x2) -> 
	Format.fprintf ppf "(%a,%a)" 
        print_sample x1
        print_sample x2
    | Sample.Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
		(label_name l)
		print_sample x
	     )
	     " ; "
	  ) r
    | Sample.Fun iface ->
	Format.fprintf ppf "(fun ( %a ) x -> ...)"
	  (print_sep
	     (fun ppf (t1,t2) ->
		Format.fprintf ppf "%a -> %a; "
		print t1 print t2
	     )
	     " ; "
	  ) iface
711
712
end

713
714
module Arrow =
struct
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
  let check_simple left 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
    (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

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
  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

781
782
783
784
785
786
787
788
789
790
791
792
  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

793
  let any = { empty with arrow = any.arrow }
794
  let is_empty (_,arr) = arr = []
795
796
797
end
  

798
799
800
801
802
803
module Int = struct
  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
804

805
806
807
808
module Atom = struct
  let has_atom d a = Atoms.contains a d.atoms
end

809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
(*
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 "@]" 
*)
825

826

827
828
(* 
let pr s = Types.Print.print Format.std_formatter (Syntax.make_type (Syntax.parse s));;
829

830
831
let pr' s = Types.Print.print Format.std_formatter 
   (Types.normalize (Syntax.make_type (Syntax.parse s)));;
832

833
834
835
BUG:
pr "'a | 'b where 'a = ('a , 'a) and 'b= ('b , 'b)";;
*)
836

837

838
839
840
841
842
843
(*
  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;;
*)