Source file pred_elim.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
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
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
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
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
976
977
978
979
980
981
982
983
984
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
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
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
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
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
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
(** {1 Blocked Clause Elimination} *)
open Logtk
open Libzipperposition
let k_enabled = Flex_state.create_key ()
let k_check_at = Flex_state.create_key ()
let k_inprocessing = Flex_state.create_key ()
let k_max_resolvents = Flex_state.create_key ()
let k_check_gates = Flex_state.create_key ()
let k_only_original_gates = Flex_state.create_key ()
let k_only_non_conjecture_gates = Flex_state.create_key ()
let k_check_gates_semantically = Flex_state.create_key ()
let k_non_singular_pe = Flex_state.create_key ()
let k_measure_fun = Flex_state.create_key ()
let k_relax_val = Flex_state.create_key ()
let k_prefer_spe = Flex_state.create_key ()
let k_fp_mode = Flex_state.create_key ()
let _enabled = ref false
let _check_gates = ref true
let _inprocessing = ref false
let _check_at = ref 10
let _max_resolvents = ref (-1)
let _non_singular_pe = ref false
let _relax_val = ref 0
let _prefer_spe = ref false
let _measure_name = ref "relaxed"
let _original_gates_only = ref false
let _only_non_conj_gates = ref false
let _check_semantically = ref false
let section = Util.Section.make ~parent:Const.section "pred-elim"
module A = Libzipperposition_avatar
module OrigEnv = Env
module type S = sig
module Env : Env.S
(** {6 Registration} *)
val setup : ?in_fp_mode:bool -> unit -> unit
val begin_fixpoint : unit -> unit
val fixpoint_step : unit -> bool
val end_fixpoint : unit -> unit
end
let register_parameters env =
let module E = (val env : Env.S) in
E.flex_add k_enabled !_enabled;
E.flex_add k_check_at !_check_at;
E.flex_add k_inprocessing !_inprocessing;
E.flex_add k_max_resolvents !_max_resolvents;
E.flex_add k_check_gates !_check_gates;
E.flex_add k_only_original_gates !_original_gates_only;
E.flex_add k_only_non_conjecture_gates !_only_non_conj_gates;
E.flex_add k_check_gates_semantically !_check_semantically;
E.flex_add k_non_singular_pe !_non_singular_pe;
E.flex_add k_relax_val !_relax_val;
E.flex_add k_prefer_spe !_prefer_spe
module Make(E : Env.S) : S with module Env = E = struct
module Env = E
module C = Env.C
module CS = C.ClauseSet
module L = Literal
module T = Term
module SAT = Sat_solver.Make ()
type logic =
| NEqFO
| EqFO
| NonAppVarHo
| Unsupported
let log_to_int =
[(NEqFO, 0); (EqFO, 1); (NonAppVarHo, 2); (Unsupported, 3)]
let log_compare (l1:logic) (l2:logic) =
compare (List.assoc l1 log_to_int) (List.assoc l2 log_to_int)
exception UnsupportedLogic
type pred_elim_info =
{
sym : ID.t;
mutable pos_cls : CS.t;
mutable neg_cls : CS.t;
mutable offending_cls : CS.t;
mutable possible_gates : CS.t;
mutable is_gate : (C.t list * C.t list) option;
mutable sq_var_weight : float;
mutable num_lits : int;
mutable last_check : (float * int) option;
mutable heap_idx : int;
mutable deleted : bool;
}
let card t =
CS.cardinal t.pos_cls + CS.cardinal t.neg_cls +
(match t.is_gate with
| None -> 0
| Some (p, n) -> List.length p + List.length n)
+ CS.cardinal t.offending_cls
let pp_task out task =
let original = ID.payload_pred
~f:(function ID.Attr_cnf_def -> true
| _ -> false) task.sym in
CCFormat.fprintf out
"%a(%b) {@. +: @[%a@];@. -:@[%a@];@. ?:@[%a@]@. g:@[%a@]@. v^2:@[%g@]; |l|:@[%d@]; |%a|:@[%d@]; h_idx: @[%d@] @.}@."
ID.pp task.sym original (CS.pp C.pp) task.pos_cls (CS.pp C.pp) task.neg_cls
(CS.pp C.pp) task.offending_cls (CCOpt.pp (CCPair.pp (CCList.pp C.pp) (CCList.pp C.pp))) task.is_gate task.sq_var_weight
task.num_lits ID.pp task.sym (card task) task.heap_idx
let copy_task t =
let c = {
sym = t.sym; pos_cls = CS.empty; neg_cls = CS.empty; offending_cls = CS.empty;
possible_gates = CS.empty; is_gate = None; sq_var_weight = 0.0;
num_lits = 0; last_check = None; heap_idx = -1; deleted = false;
} in
c.pos_cls <- t.pos_cls; c.neg_cls <- t.neg_cls;
c.offending_cls <- t.offending_cls; c.possible_gates <- t.possible_gates;
c.sq_var_weight <- t.sq_var_weight; c.num_lits <- t.num_lits;
c.last_check <- t.last_check; c.heap_idx <- t.heap_idx;
c
module TaskWrapper = struct
type t = pred_elim_info
let idx task = task.heap_idx
let set_idx task idx =
task.heap_idx <- idx
let lt a b =
assert((not a.deleted) || (not b.deleted));
if not a.deleted && not b.deleted then (
let open CCOrd in
(compare (card a) (card b)
<?> (compare, (not (CCOpt.is_some a.is_gate)), (not (CCOpt.is_some b.is_gate)))
<?> (compare, a.num_lits, b.num_lits)
<?> (compare, a.sq_var_weight, b.sq_var_weight)
<?> (ID.compare, a.sym, b.sym)) < 0
)
else (a.deleted)
end
module TaskSet = struct
include MyHeap.Make(TaskWrapper)
let remove_el h el =
assert (in_heap el);
el.deleted <- true;
decrease h el;
let min_el = remove_min h in
assert(ID.equal min_el.sym el.sym);
el.deleted <- false
let update h ~old ~new_ =
assert(ID.equal old.sym new_.sym);
assert(old.heap_idx == new_.heap_idx);
assert(in_heap new_ && in_heap old);
if TaskWrapper.lt new_ old then (decrease h new_)
else if TaskWrapper.lt old new_ then (increase h new_)
else ()
end
let k_measure_fun = Flex_state.create_key ()
let _task_queue = TaskSet.create ()
let _newly_added = ref CS.empty
let _tracked = ref CS.empty
let _logic = ref NEqFO
let refine_logic new_val =
if !_logic != Unsupported then (
_logic := new_val
)
let logic_to_str = function
| EqFO -> "eq" | NEqFO -> "neq" | NonAppVarHo -> "non_appvar"
| Unsupported -> "unsupported"
let _ignored_symbols = ref ID.Set.empty
let mk_pred_elim_info sym =
{
sym; pos_cls = CS.empty; neg_cls = CS.empty;
offending_cls=CS.empty; possible_gates = CS.empty;
is_gate=None; sq_var_weight=0.0; last_check=None; heap_idx=(-1); num_lits=0; deleted=false;
}
let _pred_sym_idx = ref ID.Map.empty
let get_sym_sign lit =
match lit with
| L.Equation(lhs,rhs,_) ->
let sign = L.is_positivoid lit in
let is_poly =
not (Type.VarSet.is_empty (T.ty_vars lhs))
|| not (Type.VarSet.is_empty (T.ty_vars rhs))
in
if not is_poly && not (Type.is_fun (T.ty lhs)) then (
if Type.is_prop (T.ty lhs) then (
if not (CCOpt.is_some (T.head lhs)) then (
raise UnsupportedLogic;
);
if not (Term.is_fo_term lhs) then (
refine_logic NonAppVarHo;
);
if L.is_predicate_lit lit then (
let hd_sym = T.head_exn lhs in
Some (hd_sym, sign)
) else (
Util.debugf ~section 1 "unsupported because of @[%a@]@." (fun k -> k L.pp lit);
_logic := Unsupported;
raise UnsupportedLogic;
)) else (if T.is_fo_term lhs && T.is_fo_term rhs then refine_logic EqFO
else refine_logic NonAppVarHo; None)
) else (
_logic := Unsupported;
Util.debugf ~section 1 "unsupported because of @[%a@]@." (fun k -> k L.pp lit);
raise UnsupportedLogic)
| _ -> None
let remove_symbol entry =
_pred_sym_idx := ID.Map.remove entry.sym !_pred_sym_idx;
_ignored_symbols := ID.Set.add entry.sym !_ignored_symbols;
if TaskSet.in_heap entry then (
TaskSet.remove_el _task_queue entry
)
let calc_sq_var cl =
let n = List.length (Literals.vars (C.lits cl)) in
float_of_int (n * n)
let calc_new_stats resolvents =
List.fold_left (fun (acc_sq, acc_lit_num) cl ->
acc_sq +. calc_sq_var cl, acc_lit_num + C.length cl) (0.0, 0) resolvents
let calc_num_cls task =
CS.cardinal task.pos_cls + CS.cardinal task.neg_cls +
(match task.is_gate with
| None -> 0
| Some(ps, ns) -> List.length ps + List.length ns) +
CS.cardinal task.offending_cls
let kk_measure relax task resolvents =
let new_mu, new_lit_num = calc_new_stats resolvents in
task.num_lits >= new_lit_num && task.sq_var_weight >= new_mu
let relaxed_measure relax task resolvents =
let (new_mu, new_lit_num), new_cl_num =
calc_new_stats resolvents, List.length resolvents in
task.num_lits > new_lit_num-relax ||
calc_num_cls task > new_cl_num-relax ||
task.sq_var_weight > new_mu
let conservative_measure relax task resolvents =
let (_, new_lit_num) = calc_new_stats resolvents in
CS.cardinal (CS.filter C.is_unit_clause task.pos_cls) >= 2 ||
CS.cardinal (CS.filter C.is_unit_clause task.neg_cls) >= 2 ||
task.num_lits > new_lit_num - relax
let _measure = ref relaxed_measure
let should_schedule task =
let eligible_for_non_singular_pe task =
Env.flex_get k_non_singular_pe &&
(match task.is_gate with
| Some (pos,neg) ->
let limit =
if Env.flex_get k_max_resolvents < 0
then max_int
else Env.flex_get k_max_resolvents in
let pos_num, neg_num = List.length pos, List.length neg in
let max_resolvents =
(CS.fold (fun cl num_res ->
if num_res == limit
then limit
else (
let new_res = CCArray.fold (fun acc lit ->
match get_sym_sign lit with
| Some (sym,sign) when ID.equal task.sym sym ->
acc * (if sign then neg_num else pos_num)
| _ -> acc
) 1 (C.lits cl) in
if new_res + num_res < limit then new_res + num_res else limit
)) task.offending_cls 0)
in
if max_resolvents < limit then true
else (remove_symbol task; false)
| None -> false)
in
CS.is_empty task.offending_cls ||
eligible_for_non_singular_pe task
let possibly_ignore_sym entry =
let card s = CS.cardinal s in
let possible_resolvents =
match entry.is_gate with
| Some(pos_gates,neg_gates) ->
List.length pos_gates * card entry.neg_cls +
List.length neg_gates * card entry.pos_cls
| None ->
card entry.neg_cls * card entry.pos_cls
in
if Env.flex_get k_max_resolvents < 0 then ()
else (
if possible_resolvents > Env.flex_get k_max_resolvents
then remove_symbol entry
)
let scan_cl_lits ?(handle_gates=true) cl =
if !_logic == Unsupported then raise UnsupportedLogic;
let num_vars = List.length @@ Literals.vars (C.lits cl) in
let is_flat = function
| L.Equation(lhs,_,_) as lit ->
assert (L.is_predicate_lit lit);
let args = T.args lhs in
List.for_all T.is_var args &&
T.Set.cardinal (T.Set.of_list args) == List.length args
| _ -> assert false
in
let update_idx pos neg offending gates num_vars cl =
let update ~action sym =
_pred_sym_idx := ID.Map.update sym (fun old ->
let entry = CCOpt.get_or ~default:(mk_pred_elim_info sym) old in
let old_ = copy_task entry in
begin match action with
| `Pos ->
entry.pos_cls <- CS.add cl entry.pos_cls;
| `Neg ->
entry.neg_cls <- CS.add cl entry.neg_cls;
possibly_ignore_sym entry;
| `Offending ->
entry.offending_cls <- CS.add cl entry.offending_cls;
if TaskSet.in_heap entry && (not (should_schedule entry)) then (
TaskSet.remove_el _task_queue entry;
)
| `Gates ->
if handle_gates then(
entry.possible_gates <- CS.add cl entry.possible_gates
)
end;
if action != `Gates then (
entry.sq_var_weight <- entry.sq_var_weight +. calc_sq_var cl;
entry.num_lits <- entry.num_lits + C.length cl
);
possibly_ignore_sym entry;
if TaskSet.in_heap old_ && TaskSet.in_heap entry then (
TaskSet.update _task_queue ~old:old_ ~new_:entry
);
if ID.Set.mem entry.sym !_ignored_symbols
then None
else Some entry
) !_pred_sym_idx
in
ID.Set.iter (update ~action:`Pos) pos;
ID.Set.iter (update ~action:`Neg) neg;
ID.Set.iter (update ~action:`Offending) offending;
ID.Set.iter (update ~action:`Gates) gates;
in
try
let pos,neg,offending,gates = CCArray.foldi (fun ((pos,neg,offending,gates) as acc) idx lit ->
let symbol_is_fresh sym =
not (ID.Set.mem sym pos) && not (ID.Set.mem sym neg) &&
not (ID.Set.mem sym offending) && not (ID.Set.mem sym !_ignored_symbols)
in
(match get_sym_sign lit with
| Some (sym, sign) when symbol_is_fresh sym ->
let is_offending = ref false in
for i = idx+1 to (C.length cl)-1 do
(match get_sym_sign (C.lits cl).(i) with
| Some(sym', _) ->
is_offending := !is_offending || ID.equal sym sym'
| None -> () )
done;
if !is_offending then (
pos,neg,ID.Set.add sym offending,gates
) else (
let gates = if is_flat lit then ID.Set.add sym gates else gates in
if sign then (ID.Set.add sym pos,neg,offending,gates)
else (pos, ID.Set.add sym neg,offending,gates))
| _ -> acc)
) (ID.Set.empty, ID.Set.empty, ID.Set.empty, ID.Set.empty) (C.lits cl) in
update_idx pos neg offending gates num_vars cl
with UnsupportedLogic ->
refine_logic Unsupported;
TaskSet.clear _task_queue
let react_clause_addded cl =
if !_logic != Unsupported then(
if not (CS.mem cl !_tracked) then (
Util.debugf ~section 5 "added:@[%a@]" (fun k -> k C.pp cl);
_tracked := CS.add cl !_tracked;
scan_cl_lits ~handle_gates:false cl);
Signal.ContinueListening
) else Signal.StopListening
let react_clause_removed cl =
if !_logic != Unsupported then (
let should_retry task =
should_schedule task &&
not (ID.Set.mem task.sym !_ignored_symbols) &&
(match task.last_check with
| Some(old_sq_var_sum, old_num_lit) ->
task.sq_var_weight < old_sq_var_sum || task.num_lits < old_num_lit
| None -> true)
in
let handle_gate sign task cl =
match task.is_gate with
| Some(pos_cls, neg_cls) ->
if sign && CCList.mem ~eq:C.equal cl pos_cls
|| (not sign) && CCList.mem ~eq:C.equal cl neg_cls then (
task.pos_cls <- CS.add_list task.pos_cls pos_cls;
task.neg_cls <- CS.add_list task.neg_cls neg_cls;
if Env.flex_get k_non_singular_pe &&
TaskSet.in_heap task &&
not (CS.is_empty task.offending_cls) then (
TaskSet.remove_el _task_queue task
);
task.is_gate <- None
)
| None -> ()
in
let handled = ref ID.Set.empty in
if not (CS.mem cl !_newly_added) &&
CS.mem cl !_tracked then (
_tracked := CS.remove cl !_tracked;
Array.iteri (fun idx lit ->
match get_sym_sign lit with
| Some(sym, sign) when not (ID.Set.mem sym !handled) ->
let is_offending = ref false in
for i = idx+1 to (C.length cl) -1 do
match get_sym_sign (C.lits cl).(i) with
| Some (sym', sign) ->
is_offending := !is_offending || ID.equal sym sym'
| None -> ()
done;
_pred_sym_idx := ID.Map.update sym (function
| Some task ->
let old = copy_task task in
task.sq_var_weight <- task.sq_var_weight -. calc_sq_var cl;
task.num_lits <- task.num_lits - C.length cl;
if !is_offending then (
task.offending_cls <- CS.remove cl task.offending_cls
) else if sign then (
handle_gate sign task cl;
task.pos_cls <- CS.remove cl task.pos_cls;
) else (
handle_gate sign task cl;
task.neg_cls <- CS.remove cl task.neg_cls;
);
if not (TaskSet.in_heap task) && should_retry task then (
Util.debugf ~section 10 "retrying @[%a@]@." (fun k -> k pp_task task);
TaskSet.insert _task_queue task;
);
if TaskSet.in_heap old && TaskSet.in_heap task then (
TaskSet.update _task_queue ~new_:task ~old;
);
CCOpt.return_if (not (ID.Set.mem task.sym !_ignored_symbols)) task
| None -> None ) !_pred_sym_idx;
| _ -> ()
) (C.lits cl));
Signal.ContinueListening)
else Signal.StopListening
let replace_clauses task clauses =
Util.debugf ~section 2 "replaced clauses(%a):@. regular:@[%a@]@. gates:@[%a@]@."
(fun k -> k ID.pp task.sym (CS.pp C.pp) (CS.union task.pos_cls task.neg_cls)
(CCOpt.pp (CCPair.pp (CCList.pp C.pp) (CCList.pp C.pp))) task.is_gate);
Util.debugf ~section 2 "resolvents: @[%a@]@." (fun k -> k (CCList.pp C.pp) clauses);
_ignored_symbols := ID.Set.add task.sym !_ignored_symbols;
let remove iter =
Env.remove_active iter;
Env.remove_passive iter;
Env.remove_simpl iter;
Iter.iter (fun c -> (C.mark_redundant c);
if CS.mem c !_newly_added then (
_newly_added := CS.remove c !_newly_added;
ignore (react_clause_removed c);))
iter;
in
assert(CS.is_empty task.offending_cls || Env.flex_get k_non_singular_pe);
remove (CS.to_iter task.offending_cls);
remove (CS.to_iter task.pos_cls);
remove (CS.to_iter task.neg_cls);
(match task.is_gate with
| Some(pos_cls, neg_cls) ->
remove (CCList.to_iter pos_cls);
remove (CCList.to_iter neg_cls)
| None -> ());
_newly_added := CS.add_list !_newly_added clauses;
List.iter (fun cl -> ignore (react_clause_addded cl)) clauses;
_pred_sym_idx := ID.Map.remove task.sym !_pred_sym_idx
let is_tauto c =
Literals.is_trivial (C.lits c) || Trail.is_trivial (C.trail c)
let find_lit_by_sym sym sign cl =
CCOpt.get_exn (CCArray.find_map_i (fun idx lit ->
match get_sym_sign lit with
| Some (sym', sign') when ID.equal sym sym' && sign = sign' ->
Some (idx, CCOpt.get_exn (L.View.get_lhs lit))
| _ -> None
) (C.lits cl))
let neq_resolver ~sym ~pos_cl ~neg_cl =
let pos_sc, neg_sc = 0, 1 in
let pos_idx, pos_term = find_lit_by_sym sym true pos_cl in
let neg_idx, neg_term = find_lit_by_sym sym false neg_cl in
try
let subst = Unif.FO.unify_syn (pos_term, pos_sc) (neg_term, neg_sc) in
let renaming = Subst.Renaming.create () in
let lits =
(List.map (fun lit ->
L.apply_subst renaming subst (lit, pos_sc))
(CCArray.except_idx (C.lits pos_cl) pos_idx)) @
(List.map (fun lit ->
L.apply_subst renaming subst (lit, neg_sc))
(CCArray.except_idx (C.lits neg_cl) neg_idx))
in
let proof =
Proof.Step.simp
~tags:[Proof.Tag.T_cannot_orphan]
~rule:(Proof.Rule.mk "dp-resolution")
[C.proof_parent_subst renaming (pos_cl,pos_sc) subst;
C.proof_parent_subst renaming (neg_cl,neg_sc) subst]
in
let c =
C.create ~penalty:(max (C.penalty pos_cl) (C.penalty neg_cl))
~trail:(C.trail_l [pos_cl; neg_cl]) lits proof
in
CCOpt.return_if (not (is_tauto c)) c
with Unif.Fail -> None
let eq_resolver ~sym ~pos_cl ~neg_cl =
let handle_distinct_vars xs sc_x ys sc_y =
let is_unique xs =
List.for_all (Term.is_var) xs &&
CCList.length (CCList.sort_uniq ~cmp:T.compare xs)
== CCList.length xs
in
let mk_subst vars sc_vars terms sc_terms =
List.fold_left (fun subst (v,t) ->
Subst.FO.bind' subst (T.as_var_exn v, sc_vars) (t, sc_terms)
) Subst.empty (CCList.combine vars terms)
in
if is_unique xs then Some (mk_subst xs sc_x ys sc_y)
else if is_unique ys then Some (mk_subst ys sc_y xs sc_x)
else None
in
let pos_sc, neg_sc = 0, 1 in
let renaming = Subst.Renaming.create () in
let pos_idx, pos_term = find_lit_by_sym sym true pos_cl in
let neg_idx, neg_term = find_lit_by_sym sym false neg_cl in
let pos_args, neg_args = CCPair.map_same T.args (pos_term, neg_term) in
let proof subst renaming =
Proof.Step.simp
~tags:[Proof.Tag.T_cannot_orphan]
~rule:(Proof.Rule.mk "dp-resolution")
[C.proof_parent_subst renaming (pos_cl,pos_sc) subst;
C.proof_parent_subst renaming (neg_cl,neg_sc) subst]
in
let c =
match handle_distinct_vars pos_args pos_sc neg_args neg_sc with
| Some subst ->
let pos_lits = Literals.apply_subst renaming subst (C.lits pos_cl, pos_sc) in
let neg_lits = Literals.apply_subst renaming subst (C.lits neg_cl, neg_sc) in
let lits = (CCArray.except_idx pos_lits pos_idx) @ (CCArray.except_idx neg_lits neg_idx) in
C.create ~penalty:(max (C.penalty pos_cl) (C.penalty neg_cl))
~trail:(C.trail_l [pos_cl; neg_cl]) lits (proof subst renaming)
| None ->
let subst = Subst.empty in
let pos_cl' = C.apply_subst ~renaming (pos_cl, pos_sc) subst in
let neg_cl' = C.apply_subst ~renaming (neg_cl, neg_sc) subst in
let apply t = Subst.FO.apply renaming subst t in
let lits =
(List.map (fun (p,n) -> L.mk_neq (apply (p, pos_sc)) (apply (n, neg_sc)))
(List.combine pos_args neg_args)) @
(CCArray.except_idx (C.lits pos_cl') pos_idx) @
(CCArray.except_idx (C.lits neg_cl') neg_idx)
in
C.create ~penalty:(max (C.penalty pos_cl') (C.penalty neg_cl'))
~trail:(C.trail_l [pos_cl'; neg_cl']) lits (proof subst renaming)
in
CCOpt.return_if (not (is_tauto c)) c
let check_if_gate task =
let sym = task.sym in
let gates_l = CS.to_list task.possible_gates in
let filter_gates ?(sign=None) ~lit_num_filter gates_l =
List.filter (fun cl ->
not (is_tauto cl) &&
lit_num_filter (Array.length (C.lits cl)) &&
(match (CCArray.find_idx (fun lit ->
match get_sym_sign lit with
| Some(sym', sign') -> ID.equal sym sym' &&
((CCOpt.is_none sign) || CCOpt.get_exn sign == sign')
| None -> false) (C.lits cl)) with
| Some (i, lit) ->
let free_vars = T.VarSet.of_list (L.vars lit) in
CCOpt.is_none (CCArray.find_map_i (fun j lit' ->
if (i=j || T.VarSet.subset (T.VarSet.of_list (L.vars lit')) free_vars) then None
else Some j
) (C.lits cl))
| _ -> false))
(CCList.fast_sort (fun cl cl' -> compare (C.length cl) (C.length cl')) gates_l)
in
let find_and_or bin_clauses long_clauses =
CCList.find_map (fun long_cl ->
let sym_lits, other_lits = List.partition (fun lit ->
match get_sym_sign lit with
| Some(sym',_) -> ID.equal sym sym'
| _ -> false
) (CCArray.to_list @@ C.lits long_cl) in
assert (List.length sym_lits = 1);
let sym_name_lit = List.hd sym_lits in
let bin_gates = CCArray.of_list bin_clauses in
if List.length other_lits > CCArray.length bin_gates then None
else (
let matched = CCBV.create ~size:(CCArray.length bin_gates) false in
let is_gate = List.for_all (fun lit ->
let found = ref false in
let i = ref 0 in
while not !found && !i < CCArray.length bin_gates do
let cl = bin_gates.(!i) in
if not (CCBV.get matched !i) then (
let idx_name_opt = CCArray.find_idx (fun lit ->
match get_sym_sign lit with
| Some(sym',_) -> ID.equal sym sym'
| None -> false
) (C.lits cl) in
let idx_name, _ = CCOpt.get_exn idx_name_opt in
let name_lit = L.negate (C.lits cl).(idx_name) in
let other_lit = L.negate (C.lits cl).(1 - idx_name) in
let is_matched =
not @@ Iter.is_empty
(L.variant (lit,0) (other_lit,1)
|> Iter.filter (fun (subst,_) ->
not @@ Iter.is_empty @@
L.variant ~subst (sym_name_lit, 0) (name_lit,1)))
in
if is_matched then (
CCBV.set matched !i;
found := true
));
incr i;
done;
!found
) other_lits in
let bin_cls = CCBV.select matched bin_gates in
if is_gate then Some(long_cl, bin_cls)
else None))
long_clauses
in
let diff_vars_cnt cl =
List.length @@ Literals.vars (C.lits cl)
in
let check_and () =
let pos_gates = filter_gates ~sign:(Some true) ~lit_num_filter:(fun n -> n > 2) gates_l in
let neg_gates = filter_gates ~sign:(Some false) ~lit_num_filter:((=) 2) gates_l in
match find_and_or neg_gates pos_gates with
| Some (pos_cl, neg_cls) when (diff_vars_cnt pos_cl <= 3) ->
let to_remove = CS.of_list (pos_cl :: neg_cls) in
task.neg_cls <- CS.diff task.neg_cls to_remove;
task.pos_cls <- CS.diff task.pos_cls to_remove;
task.is_gate <- Some([pos_cl], neg_cls);
true
| _ -> false
in
let check_or () =
let pos_gates = filter_gates ~sign:(Some true) ~lit_num_filter:((=) 2) gates_l in
let neg_gates = filter_gates ~sign:(Some false) ~lit_num_filter:(fun n -> n > 2) gates_l in
match find_and_or pos_gates neg_gates with
| Some(neg_cl, pos_cls) when (diff_vars_cnt neg_cl <= 3) ->
let to_remove = CS.of_list (neg_cl :: pos_cls) in
task.neg_cls <- CS.diff task.neg_cls to_remove;
task.pos_cls <- CS.diff task.pos_cls to_remove;
task.is_gate <- Some(pos_cls, [neg_cl]);
true
| _ -> false
in
let check_ite () = false in
let check_sat () =
SAT.clear ();
let orig_sc,new_sc = 0,1 in
let rename_clause ~name_lit c =
let lits = C.lits c in
CCArray.find_map_i (fun i lit ->
match lit with
| L.Equation(lhs,_,_) when L.is_predicate_lit lit ->
begin try
let subst = Unif.FO.variant (lhs, new_sc) (name_lit, orig_sc) in
let lits = Literals.apply_subst Subst.Renaming.none subst
((CCArray.of_list (CCArray.except_idx lits i)), new_sc) in
Some (i,lits,c)
with Unif.Fail -> None end
| _ -> None) lits
in
let split_clauses used_cls =
let pos_cls, neg_cls = CCList.partition (fun cl ->
CCArray.exists (fun lit ->
match get_sym_sign lit with
| Some(id,sign) -> ID.equal id task.sym && sign
| _ -> false) (C.lits cl)
) used_cls
in
if List.exists (fun pos_cl ->
List.exists (fun neg_cl ->
CCOpt.is_some @@
neq_resolver ~sym:task.sym ~pos_cl ~neg_cl) neg_cls
) pos_cls then None
else Some (pos_cls, neg_cls)
in
let find_definition_set cls =
List.iter (fun (i,lits,c) ->
if not (is_tauto c) then (
CCList.filter_map BBox.inject_lit (CCArray.to_list lits)
|> SAT.add_clause ~proof:(C.proof_step c))
) cls;
(match SAT.check ~full:true () with
| Sat_solver.Unsat _ ->
let proof = Proof.S.step (SAT.get_proof ()) in
let parents = List.map (fun p -> Proof.S.step @@ Proof.Parent.proof p) (Proof.Step.parents proof) in
Util.debugf ~section 5 "SAT prover found unsat set: %d@." (fun k -> k (CCList.length parents));
let used_cls = CCList.filter_map (fun (_,_,cl) ->
CCOpt.return_if (CCList.mem ~eq:Proof.Step.equal (C.proof_step cl) parents) cl) cls in
Util.debugf ~section 5 "used clauses: @[%a@]@." (fun k -> k (CCList.pp C.pp) used_cls);
split_clauses used_cls
| _ -> None)
in
let is_def = function
| (Literal.Equation(lhs,_,_) as lit) when Literal.is_predicate_lit lit ->
CCOpt.is_some (Term.head lhs) && List.for_all T.is_var (T.args lhs)
| _ -> false
in
match gates_l with
| x :: xs ->
let i,name_lit = CCOpt.get_exn (CCArray.find_map_i (fun i lit ->
match lit with
| L.Equation(lhs,rhs,_) when L.is_predicate_lit lit ->
if ID.equal task.sym (T.head_exn lhs) then Some(i,lhs) else None
| _ -> None) (C.lits x))
in
let cls =
(i,CCArray.of_list @@ CCArray.except_idx (C.lits x) i,x)
:: (CCList.filter_map (rename_clause ~name_lit) xs) in
(match find_definition_set cls with
| Some (core_pos,core_neg) ->
let to_remove = CS.of_list (core_pos @ core_neg) in
if CS.cardinal to_remove != 2 ||
CS.for_all (fun c -> C.length c == 2 &&
CCArray.for_all is_def (C.lits c))
to_remove then (
Util.debugf ~section 3 "semantic pos def: @[%a@]@."
(fun k -> k (CCList.pp C.pp) core_pos);
Util.debugf ~section 3 "semantic neg def: @[%a@]@."
(fun k -> k (CCList.pp C.pp) core_neg);
task.neg_cls <- CS.diff task.neg_cls to_remove;
task.pos_cls <- CS.diff task.pos_cls to_remove;
task.is_gate <- Some(core_pos, core_neg);
true
) else false
| _ -> false)
| _ -> false
in
if Env.flex_get k_check_gates &&
((not (Env.flex_get k_only_original_gates))
|| not @@ ID.payload_pred
~f:(function
ID.Attr_cnf_def -> true
| _ -> false)
task.sym) &&
((not (Env.flex_get k_only_non_conjecture_gates))
|| not @@ Signature.sym_in_conj task.sym (Env.signature ())) then (
if Env.flex_get k_check_gates_semantically then ignore (check_sat ())
else ignore (check_and () || check_or () || check_ite ()))
let schedule_tasks () =
ID.Map.iter (fun _ task ->
check_if_gate task;
if should_schedule task then (
Util.debugf ~section 5 "inserting: @[%a@]" (fun k -> k pp_task task);
TaskSet.insert _task_queue task
)) !_pred_sym_idx
let get_resolver () =
if !_logic == NEqFO then neq_resolver else eq_resolver
let calc_resolvents ~sym ~pos ~neg =
CCList.flat_map (fun pos_cl ->
CCList.filter_map (fun neg_cl ->
get_resolver () ~sym ~pos_cl ~neg_cl
) neg
) pos
let calc_non_singular_resolvents ~sym ~pos ~neg ~offending =
let find_lit_by_sym_opt sym sign cl =
try
CCOpt.return (find_lit_by_sym sym sign cl)
with _ -> None
in
let rec aux has_pred no_pred =
(match has_pred with
| [] -> no_pred
| cl :: cls ->
let new_cls =
(match find_lit_by_sym_opt sym true cl with
| Some _ ->
CCList.filter_map (fun neg_cl ->
get_resolver () ~sym ~pos_cl:cl ~neg_cl) neg
| None ->
(match find_lit_by_sym_opt sym false cl with
| Some _ ->
CCList.filter_map (fun pos_cl ->
get_resolver () ~sym ~pos_cl ~neg_cl:cl) pos
| None -> invalid_arg ""))
in
let has_lit cl =
let (<+>) = CCOpt.(<+>) in
CCOpt.is_some (find_lit_by_sym_opt sym true cl <+>
find_lit_by_sym_opt sym false cl)
in
let has_pred', no_pred' = List.partition has_lit new_cls in
aux (has_pred' @ cls) (no_pred' @ no_pred))
in
aux (CS.to_list offending) []
let measure_decreases () =
Env.flex_get k_measure_fun
let do_pred_elim () =
let removed_cls = ref None in
let updated_removed inc =
match !removed_cls with
| None -> removed_cls := Some inc
| Some inc' -> removed_cls := Some (inc' + inc)
in
let process_task task =
assert(CS.is_empty task.offending_cls || Env.flex_get k_non_singular_pe);
let pos_cls, neg_cls =
CCPair.map_same CS.to_list (task.pos_cls, task.neg_cls)
in
let sym = task.sym in
let resolvents =
match task.is_gate with
| Some (pos_gates, neg_gates) ->
if Env.flex_get k_prefer_spe && CS.is_empty task.offending_cls then (
let results =
(calc_resolvents ~sym ~pos:pos_gates ~neg:neg_cls)
@ (calc_resolvents ~sym ~pos:pos_cls ~neg:neg_gates)
@ (calc_resolvents ~sym ~pos:pos_cls ~neg:neg_cls)
in
if measure_decreases () (Env.flex_get k_relax_val) task results
then (results)
else (
(calc_resolvents ~sym ~pos:pos_gates ~neg:neg_cls)
@ (calc_resolvents ~sym ~pos:pos_cls ~neg:neg_gates)
))
else
((calc_non_singular_resolvents ~sym ~pos:pos_gates ~neg:neg_gates
~offending:task.offending_cls)
@ (calc_resolvents ~sym ~pos:pos_gates ~neg:neg_cls)
@ (calc_resolvents ~sym ~pos:pos_cls ~neg:neg_gates))
| None ->
assert(CS.is_empty task.offending_cls);
calc_resolvents ~sym ~pos:pos_cls ~neg:neg_cls
in
if measure_decreases () (Env.flex_get k_relax_val) task resolvents then (
Util.debugf ~section 1 "task info: @[%a@]" (fun k -> k pp_task task);
updated_removed (calc_num_cls task - List.length resolvents);
replace_clauses task resolvents;
) else (
task.last_check <- Some (task.sq_var_weight, task.num_lits)
)
in
let module S = TaskSet in
while not (S.is_empty _task_queue) do
let task = S.remove_min _task_queue in
if not (ID.Set.mem task.sym !_ignored_symbols) then(
Util.debugf ~section 5 "checking: @[%a@]" (fun k -> k pp_task task);
process_task (task)
);
done;
Env.add_passive (CS.to_iter !_newly_added);
_newly_added := CS.empty;
!removed_cls
let steps = ref 0
let do_predicate_elimination () =
steps := (!steps + 1) mod (Env.flex_get k_check_at);
if !steps = 0 then (
ignore( do_pred_elim ());
)
let initialize () =
let init_clauses =
CS.to_list (Env.ProofState.ActiveSet.clauses ())
@ CS.to_list (Env.ProofState.PassiveSet.clauses ())
in
begin try
Util.debugf ~section 5 "init_cl: @[%a@]@."
(fun k -> k (CCList.pp C.pp) init_clauses);
let init_clause_num = List.length init_clauses in
CCFormat.printf "%% PE start: %d@." init_clause_num;
List.iter (fun cl ->
scan_cl_lits cl;
_tracked := CS.add cl !_tracked;
) init_clauses;
CCFormat.printf "logic: %s@." (logic_to_str !_logic);
if !_logic == Unsupported then (
raise UnsupportedLogic
);
schedule_tasks ();
Util.debugf ~section 5 "state:@[%a@]@."
(fun k -> k (Iter.pp_seq pp_task) (ID.Map.values !_pred_sym_idx));
Util.debugf ~section 1 "logic has%sequalities"
(fun k -> k (if !_logic == EqFO then " " else " no "));
Signal.on Env.ProofState.PassiveSet.on_add_clause react_clause_addded;
Signal.on Env.ProofState.PassiveSet.on_remove_clause react_clause_removed;
Signal.on Env.ProofState.ActiveSet.on_add_clause react_clause_addded;
Signal.on Env.ProofState.ActiveSet.on_remove_clause react_clause_removed;
Signal.on_every Env.on_forward_simplified (fun (c, new_state) ->
if !_logic != Unsupported then (
match new_state with
| Some c' ->
ignore(react_clause_removed c);
ignore(react_clause_addded c')
| _ -> ignore(react_clause_removed c)
));
ignore(do_pred_elim ());
Util.debugf ~section 5 "after elim: @[%a@]@."
(fun k -> k (CS.pp C.pp) (Env.ProofState.PassiveSet.clauses ()));
Util.debugf ~section 5 "state:@[%a@]@."
(fun k -> k (Iter.pp_seq pp_task) (ID.Map.values !_pred_sym_idx));
let clause_diff =
init_clause_num -
(Iter.length (Env.get_active ()) + Iter.length (Env.get_passive ())) in
CCFormat.printf "%% PE eliminated: %d@." clause_diff;
if Env.flex_get k_inprocessing then (
Env.add_clause_elimination_rule ~priority:2 "pred_elim"
do_predicate_elimination
) else if not @@ Env.flex_get k_fp_mode then raise UnsupportedLogic
with UnsupportedLogic ->
Util.debugf ~section 1 "logic is unsupported" CCFun.id;
_logic := Unsupported;
_pred_sym_idx := ID.Map.empty
end;
Signal.StopListening
let register () =
Signal.on Env.on_start initialize
let fixpoint_active = ref false
let begin_fixpoint () =
fixpoint_active := true;
let env = (module E : OrigEnv.S) in
register_parameters env;
Env.flex_add k_measure_fun (match !_measure_name with
| "kk" -> kk_measure
| "relaxed" -> relaxed_measure
| "conservative" -> conservative_measure
| _ -> invalid_arg "measure function not found");
let init_clauses =
CS.to_list (Env.ProofState.ActiveSet.clauses ())
@ CS.to_list (Env.ProofState.PassiveSet.clauses ())
in
begin try
List.iter (fun cl ->
scan_cl_lits cl;
_tracked := CS.add cl !_tracked;
) init_clauses;
schedule_tasks ();
Signal.on Env.ProofState.PassiveSet.on_add_clause (fun c ->
if !fixpoint_active then react_clause_addded c
else Signal.StopListening
);
Signal.on Env.ProofState.PassiveSet.on_remove_clause (fun c ->
if !fixpoint_active then react_clause_removed c
else Signal.StopListening
);
let ans = (do_pred_elim ()) in
CCFormat.printf "%% PE start fixpoint: @[%a@]@." (CCOpt.pp CCInt.pp) ans;
Util.debugf ~section 2 "Clause number changed for %a" (fun k -> k (CCOpt.pp CCInt.pp) ans)
with UnsupportedLogic ->
Util.debugf ~section 1 "logic is unsupported" CCFun.id;
_logic := Unsupported;
_pred_sym_idx := ID.Map.empty
end
let fixpoint_step () =
CCFormat.printf "relax val: %d@." (Env.flex_get k_relax_val);
let ans = do_pred_elim () in
Util.debugf ~section 1 "Clause number changed for %a" (fun k -> k (CCOpt.pp CCInt.pp) ans);
if CCOpt.is_some ans then (
CCFormat.printf "%% PE fixpoint: %d@." (CCOpt.get_exn ans)
);
CCOpt.is_some ans
let end_fixpoint () =
_logic := Unsupported;
_pred_sym_idx := ID.Map.empty;
fixpoint_active := false
let setup ?(in_fp_mode=false) () =
Env.flex_add k_fp_mode in_fp_mode;
Env.flex_add k_measure_fun (match !_measure_name with
| "kk" -> kk_measure
| "relaxed" -> relaxed_measure
| "conservative" -> conservative_measure
| _ -> invalid_arg "measure function not found");
if Env.flex_get k_enabled then (
if not (Env.flex_get A.k_avatar_enabled) then (register ())
else (
CCFormat.printf "AVATAR is not yet compatible with PredElim@."
)
)
end
let extension =
let action env =
let module E = (val env : Env.S) in
register_parameters env;
let module PredElim = Make(E) in
E.flex_add k_enabled !_enabled;
E.flex_add k_check_at !_check_at;
E.flex_add k_inprocessing !_inprocessing;
E.flex_add k_max_resolvents !_max_resolvents;
E.flex_add k_check_gates !_check_gates;
E.flex_add k_non_singular_pe !_non_singular_pe;
E.flex_add k_relax_val !_relax_val;
PredElim.setup ()
in
{ Extensions.default with Extensions.
name="pred_elim";
prio = 50;
env_actions=[action];
}
let () =
Options.add_opts [
"--pred-elim", Arg.Bool ((:=) _enabled), " enable predicate elimination";
"--pred-elim-relax-value", Arg.Int ((:=) _relax_val), " value of relax constant for our new measure";
"--pred-elim-measure-fun", Arg.Symbol (["kk"; "relaxed"; "conservative"], ((:=) _measure_name)),
" use either standard Korovin-Khasidashvili measure or our relaxed measure for measuring the proof state size";
"--pred-elim-check-gates", Arg.Bool ((:=) _check_gates), " enable recognition of gate clauses";
"--pred-elim-only-original-gates", Arg.Bool ((:=) _original_gates_only), " recognize only gates that are not introduced by Zipperposition";
"--pred-elim-check-gates-semantically", Arg.Bool ((:=) _check_semantically), " recognize gates semantically, as described in our SAT techniques paper";
"--pred-elin-only-non-conjecture-gates", Arg.Bool ((:=) _only_non_conj_gates), " recognize only non-conjecture symbols as possible gates";
"--pred-elim-prefer-spe", Arg.Bool ((:=) _prefer_spe), " try DPE only when SPE fails";
"--pred-elim-relax-value", Arg.Int ((:=) _relax_val), " value of relax constant for our new measure";
"--pred-elim-measure-fun", Arg.Symbol (["kk"; "relaxed"; "conservative"], ((:=) _measure_name)), " use either standard Korovin-Khasidashvili measure or our relaxed measure for measuring the proof state size";
"--pred-elim-non-singular", Arg.Bool ((:=) _non_singular_pe), " enable PE when gate is recognized and there are multiple occurrences of a symbol";
"--pred-elim-inprocessing", Arg.Bool ((:=) _inprocessing), " predicate elimination as inprocessing rule";
"--pred-elim-check-at", Arg.Int ((:=) _check_at), " when to perform predicate elimination inprocessing";
"--pred-elim-max-resolvents", Arg.Int ((:=) _max_resolvents), " after how many resolvents to stop tracking a symbol";
]