package goblint

  1. Overview
  2. Docs
package goblint
Legend:
Page
Library
Module
Module type
Parameter
Class
Class type
Source

Source file mapDomain.ml

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
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
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
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
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
552
553
554
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
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
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
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
737
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
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
(** Map domains. *)

module Pretty = GoblintCil.Pretty
open Pretty

module type PS =
sig
  include Printable.S
  type key
  (** The type of the map keys. *)

  type value
  (** The type of the values. *)

  val add: key -> value -> t -> t
  val remove: key -> t -> t
  val find: key -> t -> value
  val find_opt: key -> t -> value option
  val mem: key -> t -> bool
  val iter: (key -> value -> unit) -> t -> unit
  val map: (value -> value) -> t -> t
  val filter: (key -> value -> bool) -> t -> t
  val mapi: (key -> value -> value) -> t -> t
  val fold: (key -> value -> 'a -> 'a) -> t -> 'a -> 'a

  val add_list: (key * value) list -> t -> t
  val add_list_set: key list -> value -> t -> t
  val add_list_fun: key list -> (key -> value) -> t -> t

  val for_all: (key -> value -> bool) -> t -> bool
  val map2: (value -> value -> value) -> t -> t -> t
  val long_map2: (value -> value -> value) -> t -> t -> t
  val merge : (key -> value option -> value option -> value option) -> t -> t -> t (* TODO: unused, remove? *)

  val cardinal: t -> int
  val choose: t -> key * value
  val singleton: key -> value -> t
  val empty: unit -> t
  val is_empty: t -> bool
  val exists: (key -> value -> bool) -> t -> bool
  val bindings: t -> (key * value) list
end

module type S =
sig
  include PS
  include Lattice.S with type t := t

  val widen_with_fct: (value -> value -> value) -> t -> t -> t
  (* Widen using a custom widening function for value rather than the default one for value *)
  val join_with_fct: (value -> value -> value) -> t -> t -> t
  (* Join using a custom join function for value rather than the default one for value *)
  val leq_with_fct: (value -> value -> bool) -> t -> t -> bool
  (* Leq test using a custom leq function for value rather than the default one provided for value *)
end

(** Subsignature of {!S}, which is sufficient for {!Print}. *)
module type Bindings =
sig
  type t
  type key
  type value
  val fold: (key -> value -> 'a -> 'a) -> t -> 'a -> 'a
  val iter: (key -> value -> unit) -> t -> unit
end

(** Reusable output definitions for maps. *)
module Print (D: Printable.S) (R: Printable.S) (M: Bindings with type key = D.t and type value = R.t) =
struct
  let pretty () map =
    let doc = M.fold (fun k v acc ->
        acc ++ dprintf "%a ->@?@[%a@]\n" D.pretty k R.pretty v
      ) map nil
    in
    if doc = Pretty.nil then
      text "{}"
    else
      dprintf "@[{\n  @[%a@]}@]" Pretty.insert doc

  let show map = GobPretty.sprint pretty map

  let printXml f map =
    BatPrintf.fprintf f "<value>\n<map>\n";
    M.iter (fun k v ->
        BatPrintf.fprintf f "<key>\n%s</key>\n%a" (XmlUtil.escape (D.show k)) R.printXml v
      ) map;
    BatPrintf.fprintf f "</map>\n</value>\n"

  let to_yojson map =
    let l = M.fold (fun k v acc ->
        (D.show k, R.to_yojson v) :: acc
      ) map []
    in
    `Assoc l
end

module type Groupable =
sig
  include Printable.S
  type group (* use [@@deriving show { with_path = false }] *)
  val compare_group: group -> group -> int
  val show_group: group -> string
  val to_group: t -> group
end

(** Reusable output definitions for maps with key grouping. *)
module PrintGroupable (D: Groupable) (R: Printable.S) (M: Bindings with type key = D.t and type value = R.t) =
struct
  include Print (D) (R) (M)

  module Group =
  struct
    type t = D.group [@@deriving ord]
  end

  module GroupMap = Map.Make (Group)

  let pretty () mapping =
    let groups =
      M.fold (fun k v acc ->
          GroupMap.update (D.to_group k) (fun doc ->
              let doc = Option.value doc ~default:Pretty.nil in
              let doc' = doc ++ dprintf "%a ->@?  @[%a@]\n" D.pretty k R.pretty v in
              Some doc'
            ) acc
        ) mapping GroupMap.empty
    in
    let pretty_groups () = GroupMap.fold (fun group doc acc ->
        acc ++ dprintf "@[%s {\n  @[%a@]}@]\n" (D.show_group group) Pretty.insert doc
      ) groups nil in
    dprintf "@[{\n  @[%t@]}@]" pretty_groups

  let show map = GobPretty.sprint pretty map

  (* TODO: groups in XML, JSON? *)
end

module PMap (Domain: Printable.S) (Range: Lattice.S) : PS with
  type key = Domain.t and
  type value = Range.t =
struct
  module M = Map.Make (Domain)

  include Printable.Std
  include M
  type key = Domain.t
  type value = Range.t
  type t = Range.t M.t (* key -> value  mapping *)

  let name () = "map"

  (* And one less brainy definition *)
  let for_all2 = M.equal
  let equal x y = x == y || for_all2 Range.equal x y
  let compare x y = if equal x y then 0 else M.compare Range.compare x y
  let hash xs = fold (fun k v a -> a + (Domain.hash k * Range.hash v)) xs 0

  let empty () = M.empty


  let add_list keyvalues m =
    List.fold_left (fun acc (key,value) -> add key value acc) m keyvalues

  let add_list_set keys value m =
    List.fold_left (fun acc key -> add key value acc) m keys

  let add_list_fun keys f m =
    List.fold_left (fun acc key -> add key (f key) acc) m keys

  let long_map2 op =
    let f k v1 v2 =
      match v1, v2 with
      | Some v1, Some v2 -> Some (op v1 v2)
      | Some _, _ -> v1
      | _, Some _ -> v2
      | _ -> None
    in
    M.merge f

  let map2 op =
    (* Similar to the previous, except we ignore elements that only occur in one
     * of the mappings, so we start from an empty map *)
    let f k v1 v2 =
      match v1, v2 with
      | Some v1, Some v2 -> Some (op v1 v2)
      | _ -> None
    in
    M.merge f

  include Print (Domain) (Range) (
    struct
      type nonrec t = t
      type nonrec key = key
      type nonrec value = value
      let fold = fold
      let iter = iter
    end
    )

  (* uncomment to easily check pretty's grouping during a normal run, e.g. ./regtest 01 01: *)
  (* let add k v m = let _ = Logs.debug "%a" pretty m in M.add k v m *)

  let arbitrary () = QCheck.always M.empty (* S TODO: non-empty map *)

  let relift m =
    M.fold (fun k v acc ->
        M.add (Domain.relift k) (Range.relift v) acc
      ) m M.empty
end

(* TODO: why is HashCached.hash significantly slower as a functor compared to being inlined into PMap? *)
module HashCached (M: S) : S with
  type key = M.key and
  type value = M.value =
struct
  include Lattice.HashCached (M)

  type key = M.key
  type value = M.value

  let add k v = lift_f' (M.add k v)
  let remove k = lift_f' (M.remove k)
  let find k = lift_f (M.find k)
  let find_opt k = lift_f (M.find_opt k)
  let mem k = lift_f (M.mem k)
  let iter f = lift_f (M.iter f)
  let map f = lift_f' (M.map f)
  let mapi f = lift_f' (M.mapi f)
  let fold f x a = M.fold f (unlift x) a
  let filter f = lift_f' (M.filter f)
  let merge f = lift_f2' (M.merge f)
  let for_all f = lift_f (M.for_all f)

  let cardinal = lift_f M.cardinal
  let choose = lift_f M.choose
  let singleton k v = lift @@ M.singleton k v
  let empty () = lift @@ M.empty ()
  let is_empty = lift_f M.is_empty
  let exists p = lift_f (M.exists p)
  let bindings = lift_f M.bindings


  let add_list keyvalues = lift_f' (M.add_list keyvalues)

  let add_list_set keys value = lift_f' (M.add_list_set keys value)

  let add_list_fun keys f = lift_f' (M.add_list_fun keys f)

  let long_map2 op = lift_f2' (M.long_map2 op)

  let map2 op = lift_f2' (M.map2 op)

  let leq_with_fct f = lift_f2 (M.leq_with_fct f)
  let join_with_fct f = lift_f2' (M.join_with_fct f)
  let widen_with_fct f = lift_f2' (M.widen_with_fct f)

  let relift = lift_f' M.relift
end

(* TODO: this is very slow because every add/remove in a fold-loop relifts *)
(* TODO: currently hardcoded to assume_idempotent *)
module HConsed (M: S) : S with
  type key = M.key and
  type value = M.value =
struct
  include Lattice.HConsed (M) (struct let assume_idempotent = false end)

  type key = M.key
  type value = M.value

  let lift_f' f x = lift @@ lift_f f x
  let lift_f2' f x y = lift @@ lift_f2 f x y

  let add k v = lift_f' (M.add k v)
  let remove k = lift_f' (M.remove k)
  let find k = lift_f (M.find k)
  let find_opt k = lift_f (M.find_opt k)
  let mem k = lift_f (M.mem k)
  let iter f = lift_f (M.iter f)
  let map f = lift_f' (M.map f)
  let mapi f = lift_f' (M.mapi f)
  let fold f x a = M.fold f (unlift x) a
  let filter f = lift_f' (M.filter f)
  let merge f = lift_f2' (M.merge f)
  let for_all f = lift_f (M.for_all f)

  let cardinal = lift_f M.cardinal
  let choose = lift_f M.choose
  let singleton k v = lift @@ M.singleton k v
  let empty () = lift @@ M.empty ()
  let is_empty = lift_f M.is_empty
  let exists p = lift_f (M.exists p)
  let bindings = lift_f M.bindings


  let add_list keyvalues = lift_f' (M.add_list keyvalues)

  let add_list_set keys value = lift_f' (M.add_list_set keys value)

  let add_list_fun keys f = lift_f' (M.add_list_fun keys f)

  let long_map2 op = lift_f2' (M.long_map2 op)

  let map2 op = lift_f2' (M.map2 op)

  let leq_with_fct f = lift_f2 (M.leq_with_fct f)
  let join_with_fct f = lift_f2' (M.join_with_fct f)
  let widen_with_fct f = lift_f2' (M.widen_with_fct f)
end

module Timed (M: S) : S with
  type key = M.key and
  type value = M.value =
struct
  let time str f arg = Timing.wrap (M.name ()) (Timing.wrap str f) arg

  (* Printable.S *)
  type t = M.t

  let equal x y = time "equal" (M.equal x) y
  let compare x y = time "compare" (M.compare x) y
  let hash x = time "hash" M.hash x
  let tag x = time "tag" M.tag x
  (* TODO: time these also? *)
  let name = M.name
  let to_yojson = M.to_yojson
  let show = M.show
  let pretty = M.pretty
  let pretty_diff = M.pretty_diff
  let printXml = M.printXml
  let arbitrary = M.arbitrary

  (* Lattice.S *)
  let top () = time "top" M.top ()
  let is_top x = time "is_top" M.is_top x
  let bot () = time "bot" M.bot ()
  let is_bot x = time "is_bot" M.is_bot x
  let leq x y = time "leq" (M.leq x) y
  let join x y = time "join" (M.join x) y
  let meet x y = time "meet" (M.meet x) y
  let widen x y = time "widen" (M.widen x) y
  let narrow x y = time "narrow" (M.narrow x) y

  (* MapDomain.S *)
  type key = M.key
  type value = M.value

  let add k v x = time "add" (M.add k v) x
  let remove k x = time "remove" (M.remove k) x
  let find k x = time "find" (M.find k) x
  let find_opt k x = time "find_opt" (M.find_opt k) x
  let mem k x = time "mem" (M.mem k) x
  let iter f x = time "iter" (M.iter f) x
  let map f x = time "map" (M.map f) x
  let mapi f x = time "mapi" (M.mapi f) x
  let fold f x a = time "fold" (M.fold f x) a
  let filter f x = time "filter" (M.filter f) x
  let merge f x y = time "merge" (M.merge f x) y
  let for_all f x = time "for_all" (M.for_all f) x

  let cardinal x = time "cardinal" M.cardinal x
  let choose x = time "choose" M.choose x
  let singleton k v = time "singleton" (M.singleton k) v
  let empty () = time "empty" M.empty ()
  let is_empty x = time "is_empty" M.is_empty x
  let exists p x = time "exists" (M.exists p) x
  let bindings x = time "bindings" M.bindings x


  let add_list xs x = time "add_list" (M.add_list xs) x
  let add_list_set ks v x = time "add_list_set" (M.add_list_set ks v) x
  let add_list_fun ks f x = time "add_list_fun" (M.add_list_fun ks f) x

  let long_map2 f x y = time "long_map2" (M.long_map2 f x) y

  let map2 f x y = time "map2" (M.map2 f x) y

  let leq_with_fct f x y = time "leq_with_fct" (M.leq_with_fct f x) y
  let join_with_fct f x y = time "join_with_fct" (M.join_with_fct f x) y
  let widen_with_fct f x y = time "widen_with_fct" (M.widen_with_fct f x) y

  let relift x = M.relift x
end

module MapBot (Domain: Printable.S) (Range: Lattice.S) : S with
  type key = Domain.t and
  type value = Range.t =
struct
  include PMap (Domain) (Range)

  let leq_with_fct f m1 m2 =
    (* For each key-value in m1, the same key must be in m2 with a geq value: *)
    let p key value =
      try f value (find key m2) with Not_found -> false
    in
    m1 == m2 || for_all p m1

  let leq = leq_with_fct Range.leq

  let find x m = try find x m with | Not_found -> Range.bot ()
  let top () = Lattice.unsupported "partial map top"
  let bot () = empty ()
  let is_top _ = false
  let is_bot = is_empty

  let pretty_diff () ((m1:t),(m2:t)): Pretty.doc =
    let diff_key k v acc_opt =
      match find k m2 with
      | v2 when not (Range.leq v v2) ->
        let acc = BatOption.map_default (fun acc -> acc ++ line) Pretty.nil acc_opt in
        Some (acc ++ dprintf "Map: %a =@?@[%a@]" Domain.pretty k Range.pretty_diff (v, v2))
      | exception Lattice.BotValue ->
        let acc = BatOption.map_default (fun acc -> acc ++ line) Pretty.nil acc_opt in
        Some (acc ++ dprintf "Map: %a =@?@[%a not leq bot@]" Domain.pretty k Range.pretty v)
      | v2 -> acc_opt
    in
    match fold diff_key m1 None with
    | Some w -> w
    | None -> Pretty.dprintf "No binding grew."

  let meet m1 m2 = if m1 == m2 then m1 else map2 Range.meet m1 m2

  let join_with_fct f m1 m2 =
    if m1 == m2 then m1 else long_map2 f m1 m2
  let join = join_with_fct Range.join

  let widen_with_fct f =  long_map2 f
  let widen  = widen_with_fct Range.widen


  let narrow = map2 Range.narrow
end

module MapTop (Domain: Printable.S) (Range: Lattice.S) : S with
  type key = Domain.t and
  type value = Range.t =
struct
  include PMap (Domain) (Range)

  let leq_with_fct f m1 m2 = (* TODO use merge or sth faster? *)
    (* For each key-value in m2, the same key must be in m1 with a leq value: *)
    let p key value =
      try f (find key m1) value with Not_found -> false
    in
    m1 == m2 || for_all p m2

  let leq = leq_with_fct Range.leq

  let find x m = try find x m with | Not_found -> Range.top ()
  let top () = empty ()
  let bot () = Lattice.unsupported "partial map bot"
  let is_top = is_empty
  let is_bot _ = false

  (* let cleanup m = fold (fun k v m -> if Range.is_top v then remove k m else m) m m *)
  let meet m1 m2 = if m1 == m2 then m1 else long_map2 Range.meet m1 m2

  let join_with_fct f m1 m2 =
    if m1 == m2 then m1 else map2 f m1 m2

  let join = join_with_fct Range.join

  let widen_with_fct f = map2 f
  let widen = widen_with_fct Range.widen

  let narrow = long_map2 Range.narrow

  let pretty_diff () ((m1:t),(m2:t)): Pretty.doc =
    let diff_key k v acc_opt =
      match find k m1 with
      | v1 when not (Range.leq v1 v) ->
        let acc = BatOption.map_default (fun acc -> acc ++ line) Pretty.nil acc_opt in
        Some (acc ++ dprintf "Map: %a =@?@[%a@]" Domain.pretty k Range.pretty_diff (v1, v))
      | exception Lattice.TopValue ->
        let acc = BatOption.map_default (fun acc -> acc ++ line) Pretty.nil acc_opt in
        Some (acc ++ dprintf "Map: %a =@?@[top not leq %a@]" Domain.pretty k Range.pretty v)
      | v1 -> acc_opt
    in
    match fold diff_key m2 None with
    | Some w -> w
    | None -> Pretty.dprintf "No binding grew."
end

exception Fn_over_All of string

module LiftTop (Range: Lattice.S) (M: S with type value = Range.t): S with
  type key = M.key and
  type value = Range.t =
struct
  include Lattice.LiftTop (M)

  type key   = M.key
  type value = M.value

  let add k v = function
    | `Top -> `Top
    | `Lifted x -> `Lifted (M.add k v x)

  let remove k = function
    | `Top -> `Top
    | `Lifted x -> `Lifted (M.remove k x)

  let find k = function
    | `Top -> Range.top ()
    | `Lifted x -> M.find k x

  let find_opt k = function
    | `Top -> Some (Range.top ())
    | `Lifted x -> M.find_opt k x

  let mem k = function
    | `Top -> true
    | `Lifted x -> M.mem k x

  let map f = function
    | `Top -> `Top
    | `Lifted x -> `Lifted (M.map f x)

  let add_list xs = function
    | `Top -> `Top
    | `Lifted x -> `Lifted (M.add_list xs x)

  let add_list_set ks v = function
    | `Top -> `Top
    | `Lifted x -> `Lifted (M.add_list_set ks v x)

  let add_list_fun ks f = function
    | `Top -> `Top
    | `Lifted x -> `Lifted (M.add_list_fun ks f x)

  let map2 f x y =
    match x, y with
    | `Lifted x, `Lifted y -> `Lifted (M.map2 f x y)
    | _ -> raise (Fn_over_All "map2")

  let long_map2 f x y =
    match x, y with
    | `Lifted x, `Lifted y -> `Lifted (M.long_map2 f x y)
    | _ -> raise (Fn_over_All "long_map2")

  let for_all f = function
    | `Top -> raise (Fn_over_All "for_all")
    | `Lifted x -> M.for_all f x

  let iter f = function
    | `Top -> raise (Fn_over_All "iter")
    | `Lifted x -> M.iter f x

  let fold f x a =
    match x with
    | `Top -> raise (Fn_over_All "fold")
    | `Lifted x -> M.fold f x a

  let filter f x =
    match x with
    | `Top -> raise (Fn_over_All "filter")
    | `Lifted x -> `Lifted (M.filter f x)

  let merge f x y  =
    match x, y with
    | `Lifted x, `Lifted y -> `Lifted (M.merge f x y)
    | _ -> raise (Fn_over_All "merge")

  let leq_with_fct f x y =
    match (x,y) with
    | (_, `Top) -> true
    | (`Top, _) -> false
    | (`Lifted x, `Lifted y) -> M.leq_with_fct f x y

  let join_with_fct f x y =
    match (x,y) with
    | (`Top, x) -> `Top
    | (x, `Top) -> `Top
    | (`Lifted x, `Lifted y) -> `Lifted (M.join_with_fct f x y)

  let widen_with_fct f x y =
    match (x,y) with
    | (`Lifted x, `Lifted y) -> `Lifted (M.widen_with_fct f x y)
    | _ -> y

  let cardinal = function
    | `Top -> raise (Fn_over_All "cardinal")
    | `Lifted x -> M.cardinal x

  let choose = function
    | `Top -> raise (Fn_over_All "choose")
    | `Lifted x -> M.choose x

  let singleton k v = `Lifted (M.singleton k v)
  let empty () = `Lifted (M.empty ())
  let is_empty = function
    | `Top -> false
    | `Lifted x -> M.is_empty x
  let exists f = function
    | `Top -> raise (Fn_over_All "exists")
    | `Lifted x -> M.exists f x
  let bindings = function
    | `Top -> raise (Fn_over_All "bindings")
    | `Lifted x -> M.bindings x
  let mapi f = function
    | `Top -> `Top
    | `Lifted x -> `Lifted (M.mapi f x)
end

module MapBot_LiftTop (Domain: Printable.S) (Range: Lattice.S) : S with
  type key = Domain.t and
  type value = Range.t =
struct
  module M = MapBot (Domain) (Range)
  include LiftTop (Range) (M)
end


module LiftBot (Range: Lattice.S) (M: S with type value = Range.t): S with
  type key = M.key and
  type value = Range.t =
struct
  include Lattice.LiftBot (M)

  type key   = M.key
  type value = M.value

  let add k v = function
    | `Bot -> `Bot
    | `Lifted x -> `Lifted (M.add k v x)

  let remove k = function
    | `Bot -> `Bot
    | `Lifted x -> `Lifted (M.remove k x)

  let find k = function
    | `Bot -> Range.bot ()
    | `Lifted x -> M.find k x

  let find_opt k = function
    | `Bot -> Some (Range.bot ())
    | `Lifted x -> M.find_opt k x

  let mem k = function
    | `Bot -> false
    | `Lifted x -> M.mem k x

  let map f = function
    | `Bot -> `Bot
    | `Lifted x -> `Lifted (M.map f x)

  let add_list xs = function
    | `Bot -> `Bot
    | `Lifted x -> `Lifted (M.add_list xs x)

  let add_list_set ks v = function
    | `Bot -> `Bot
    | `Lifted x -> `Lifted (M.add_list_set ks v x)

  let add_list_fun ks f = function
    | `Bot -> `Bot
    | `Lifted x -> `Lifted (M.add_list_fun ks f x)

  let map2 f x y =
    match x, y with
    | `Lifted x, `Lifted y -> `Lifted (M.map2 f x y)
    | _ -> raise (Fn_over_All "map2")

  let long_map2 f x y =
    match x, y with
    | `Lifted x, `Lifted y -> `Lifted (M.long_map2 f x y)
    | _ -> raise (Fn_over_All "long_map2")

  let for_all f = function
    | `Bot -> raise (Fn_over_All "for_all")
    | `Lifted x -> M.for_all f x

  let iter f = function
    | `Bot -> raise (Fn_over_All "iter")
    | `Lifted x -> M.iter f x

  let fold f x a =
    match x with
    | `Bot -> raise (Fn_over_All "fold")
    | `Lifted x -> M.fold f x a

  let filter f x =
    match x with
    | `Bot -> raise (Fn_over_All "filter")
    | `Lifted x -> `Lifted (M.filter f x)

  let merge f x y  =
    match x, y with
    | `Lifted x, `Lifted y -> `Lifted (M.merge f x y)
    | _ -> raise (Fn_over_All "merge")

  let join_with_fct f x y =
    match (x,y) with
    | (`Bot, x) -> x
    | (x, `Bot) -> x
    | (`Lifted x, `Lifted y) -> `Lifted (M.join_with_fct f x y)

  let widen_with_fct f x y =
    match (x,y) with
    | (`Lifted x, `Lifted y) -> `Lifted(M.widen_with_fct f x y)
    | _ -> y

  let leq_with_fct f x y =
    match (x,y) with
    | (`Bot, _) -> true
    | (_, `Bot) -> false
    | (`Lifted x, `Lifted y) -> M.leq_with_fct f x y

  let cardinal = function
    | `Bot -> raise (Fn_over_All "cardinal")
    | `Lifted x -> M.cardinal x

  let choose = function
    | `Bot -> raise (Fn_over_All "choose")
    | `Lifted x -> M.choose x

  let singleton k v = `Lifted (M.singleton k v)
  let empty () = `Lifted (M.empty ())
  let is_empty = function
    | `Bot -> false
    | `Lifted x -> M.is_empty x
  let exists f = function
    | `Bot -> raise (Fn_over_All "exists")
    | `Lifted x -> M.exists f x
  let bindings = function
    | `Bot -> raise (Fn_over_All "bindings")
    | `Lifted x -> M.bindings x
  let mapi f = function
    | `Bot -> `Bot
    | `Lifted x -> `Lifted (M.mapi f x)
end

module MapTop_LiftBot (Domain: Printable.S) (Range: Lattice.S): S with
  type key = Domain.t and
  type value = Range.t =
struct
  module M = MapTop (Domain) (Range)
  include LiftBot (Range) (M)
end

(** Map abstracted by a single (joined) key. *)
module Joined (E: Lattice.S) (R: Lattice.S): S with type key = E.t and type value = R.t =
struct
  type key = E.t
  type value = R.t
  include Lattice.Prod (E) (R)

  let singleton e r = (e, r)
  let exists p (e, r) = p e r
  let for_all p (e, r) = p e r
  let mem e (e', _) = E.leq e e'
  let choose er = er
  let bindings er = [er]
  let remove e ((e', _) as er) =
    if E.leq e' e then
      (E.bot (), R.bot ())
    else
      er
  let map f (e, r) = (e, f r)
  let mapi f (e, r) = (e, f e r)
  let map2 f (e, r) (e', r') = (E.meet e e', f r r')
  let long_map2 f (e, r) (e', r') = (E.join e e', f r r')
  let merge f m1 m2 = failwith "MapDomain.Joined.merge" (* TODO: ? *)
  let fold f (e, r) a = f e r a
  let empty () = (E.bot (), R.bot ())
  let add e r (e', r') = (E.join e e', R.join r r')
  let is_empty (e, _) = E.is_bot e
  let iter f (e, r) = f e r
  let cardinal er =
    if is_empty er then
      0
    else
      1
  let find e (e', r) =
    if E.leq e e' then
      r
    else
      raise Not_found
  let find_opt e (e', r) =
    if E.leq e e' then
      Some r
    else
      None
  let filter p s = failwith "MapDomain.Joined.filter"
  let add_list ers m = List.fold_left (fun acc (e, r) ->
      add e r acc
    ) m ers
  let add_list_set es r m = List.fold_left (fun acc e ->
      add e r acc
    ) m es
  let add_list_fun es f m = List.fold_left (fun acc e ->
      add e (f e) acc
    ) m es

  let leq_with_fct _ _ _ = failwith "MapDomain.Joined.leq_with_fct"
  let join_with_fct _ _ _ = failwith "MapDomain.Joined.join_with_fct"
  let widen_with_fct _ _ _ = failwith "MapDomain.Joined.widen_with_fct"
end
OCaml

Innovation. Community. Security.

GitHub Discord Twitter Peertube RSS
About
Changelog Releases Industrial Users Academic Users Why OCaml
Ecosystem
Packages Community Events OCaml Planet Jobs
Resources
Install OCaml Get Started Platform Tools Language Manual Standard Library API Books Exercises Papers OCaml Playground Logo
Policies
Carbon Footprint Governance Privacy Code of Conduct