summaryrefslogtreecommitdiff
path: root/Source/Core/BoogiePL.atg
blob: 644a5d3d357664663bdb852a67059c86e0043b9e (plain)
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
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511

/*---------------------------------------------------------------------------
// BoogiePL -
//--------------------------------------------------------------------------*/

/*using System;*/
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Text;
using Microsoft.Boogie;
using Microsoft.Basetypes;
using Bpl = Microsoft.Boogie;


COMPILER BoogiePL

/*--------------------------------------------------------------------------*/

readonly Program/*!*/ Pgm;

readonly Expr/*!*/ dummyExpr;
readonly Cmd/*!*/ dummyCmd;
readonly Block/*!*/ dummyBlock;
readonly Bpl.Type/*!*/ dummyType;
readonly List<Expr>/*!*/ dummyExprSeq;
readonly TransferCmd/*!*/ dummyTransferCmd;
readonly StructuredCmd/*!*/ dummyStructuredCmd;

///<summary>
///Returns the number of parsing errors encountered.  If 0, "program" returns as
///the parsed program.
///</summary>
public static int Parse (string/*!*/ filename, /*maybe null*/ List<string/*!*/> defines, out /*maybe null*/ Program program, bool useBaseName=false) /* throws System.IO.IOException */ {
  Contract.Requires(filename != null);
  Contract.Requires(cce.NonNullElements(defines,true));

  if (defines == null) {
    defines = new List<string/*!*/>();
  }

  if (filename == "stdin.bpl") {
    var s = ParserHelper.Fill(Console.In, defines);
    return Parse(s, filename, out program, useBaseName);
  } else {
    FileStream stream = new FileStream(filename, FileMode.Open, FileAccess.Read, FileShare.Read);
    var s = ParserHelper.Fill(stream, defines);
    var ret = Parse(s, filename, out program, useBaseName);
    stream.Close();
    return ret;
  }
}


public static int Parse (string s, string/*!*/ filename, out /*maybe null*/ Program program, bool useBaseName=false) /* throws System.IO.IOException */ {
  Contract.Requires(s != null);
  Contract.Requires(filename != null);

  byte[]/*!*/ buffer = cce.NonNull(UTF8Encoding.Default.GetBytes(s));
  MemoryStream ms = new MemoryStream(buffer,false);
  Errors errors = new Errors();
  Scanner scanner = new Scanner(ms, errors, filename, useBaseName);

  Parser parser = new Parser(scanner, errors, false);
  parser.Parse();
  if (parser.errors.count == 0)
  {
    program = parser.Pgm;
    program.ProcessDatatypeConstructors();
    return 0;
  }
  else
  {
    program = null;
    return parser.errors.count;
  }
}

public Parser(Scanner/*!*/ scanner, Errors/*!*/ errors, bool disambiguation)
 : this(scanner, errors)
{
  // initialize readonly fields
  Pgm = new Program();
  dummyExpr = new LiteralExpr(Token.NoToken, false);
  dummyCmd = new AssumeCmd(Token.NoToken, dummyExpr);
  dummyBlock = new Block(Token.NoToken, "dummyBlock", new List<Cmd>(), new ReturnCmd(Token.NoToken));
  dummyType = new BasicType(Token.NoToken, SimpleType.Bool);
  dummyExprSeq = new List<Expr> ();
  dummyTransferCmd = new ReturnCmd(Token.NoToken);
  dummyStructuredCmd = new BreakCmd(Token.NoToken, null);
}

// Class to represent the bounds of a bitvector expression t[a:b].
// Objects of this class only exist during parsing and are directly
// turned into BvExtract before they get anywhere else
private class BvBounds : Expr {
  public BigNum Lower;
  public BigNum Upper;
  public BvBounds(IToken/*!*/ tok, BigNum lower, BigNum upper)
    : base(tok) {
    Contract.Requires(tok != null);
    this.Lower = lower;
    this.Upper = upper;
  }
  public override Bpl.Type/*!*/ ShallowType { get {Contract.Ensures(Contract.Result<Bpl.Type>() != null); return Bpl.Type.Int; } }
  public override void Resolve(ResolutionContext/*!*/ rc) {
    // Contract.Requires(rc != null);
    rc.Error(this, "bitvector bounds in illegal position");
  }
  public override void Emit(TokenTextWriter/*!*/ stream,
                            int contextBindingStrength, bool fragileContext) {
    Contract.Assert(false);throw new cce.UnreachableException();
  }
  public override void ComputeFreeVariables(GSet<object>/*!*/ freeVars) { Contract.Assert(false);throw new cce.UnreachableException(); }
}

/*--------------------------------------------------------------------------*/
CHARACTERS
  letter = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz".
  digit = "0123456789".
  special = "'~#$^_.?`".
  glyph = "`~!@#$%^&*()-_=+[{]}|;:',<.>/?\\".

  cr        = '\r'.
  lf        = '\n'.
  tab       = '\t'.
  
  space = ' '.
  quote = '"'.

  newLine = cr + lf.
  regularStringChar = ANY - quote - newLine.

  nondigit = letter + special.
  nonquote = letter + digit + space + glyph.


/*------------------------------------------------------------------------*/
TOKENS
  ident =  [ '\\' ] nondigit {nondigit | digit}.
  bvlit = digit {digit} 'b' 'v' digit {digit}.
  digits = digit {digit}.

  string = quote { regularStringChar | "\\\"" } quote.

  decimal = digit {digit} 'e' [ '-' ] digit {digit} .
  float = digit {digit} '.' digit {digit} [ 'e' [ '-' ] digit {digit} ] .

COMMENTS FROM "/*" TO "*/" NESTED
COMMENTS FROM "//" TO lf

IGNORE cr + lf + tab


/*------------------------------------------------------------------------*/
PRODUCTIONS


/*------------------------------------------------------------------------*/
BoogiePL
= (. List<Variable>/*!*/ vs;
     List<Declaration>/*!*/ ds;
     Axiom/*!*/ ax;
     List<Declaration/*!*/>/*!*/ ts;
     Procedure/*!*/ pr;
     Implementation im;
     Implementation/*!*/ nnim;
  .)
  { Consts<out vs>             (. foreach(Bpl.Variable/*!*/ v in vs){
                                    Contract.Assert(v != null);
                                    Pgm.AddTopLevelDeclaration(v);
                                  }
                               .)
  | Function<out ds>           (. foreach(Bpl.Declaration/*!*/ d in ds){
                                    Contract.Assert(d != null);
                                    Pgm.AddTopLevelDeclaration(d);
                                  }
                               .)
  | Axiom<out ax>              (. Pgm.AddTopLevelDeclaration(ax); .)
  | UserDefinedTypes<out ts>   (. foreach(Declaration/*!*/ td in ts){
                                    Contract.Assert(td != null);
                                    Pgm.AddTopLevelDeclaration(td);
                                  }
                               .)
  | GlobalVars<out vs>         (. foreach(Bpl.Variable/*!*/ v in vs){
                                    Contract.Assert(v != null);
                                    Pgm.AddTopLevelDeclaration(v);
                                  }
                               .)
  | Procedure<out pr, out im>  (. Pgm.AddTopLevelDeclaration(pr);
                                   if (im != null) {
                                     Pgm.AddTopLevelDeclaration(im);
                                   }
                               .)
  | Implementation<out nnim>   (. Pgm.AddTopLevelDeclaration(nnim); .)
  }
  EOF
  .

/*------------------------------------------------------------------------*/
GlobalVars<.out List<Variable>/*!*/ ds.>
= (.
    Contract.Ensures(Contract.ValueAtReturn(out ds) != null);
    QKeyValue kv = null;
    ds = new List<Variable>();
    var dsx = ds;
  .)
  "var"
  { Attribute<ref kv> }
  IdsTypeWheres<true, "global variables", delegate(TypedIdent tyd) { dsx.Add(new GlobalVariable(tyd.tok, tyd, kv)); } > ";"
  .

LocalVars<.List<Variable>/*!*/ ds.>
= (.
    Contract.Ensures(Contract.ValueAtReturn(out ds) != null);
    QKeyValue kv = null;
  .)
  "var"
  { Attribute<ref kv> }
  IdsTypeWheres<true, "local variables", delegate(TypedIdent tyd) { ds.Add(new LocalVariable(tyd.tok, tyd, kv)); } > ";"
  .

ProcFormals<.bool incoming, bool allowWhereClauses, out List<Variable>/*!*/ ds.>
= (. Contract.Ensures(Contract.ValueAtReturn(out ds) != null);
     ds = new List<Variable>();
     var dsx = ds;
     var context = allowWhereClauses ? "procedure formals" : "the 'implementation' copies of formals";
  .)
  "("
  [ AttrsIdsTypeWheres<allowWhereClauses, allowWhereClauses, context, delegate(TypedIdent tyd, QKeyValue kv) { dsx.Add(new Formal(tyd.tok, tyd, incoming, kv)); }>
  ]
  ")"
  .

BoundVars<.IToken/*!*/ x, out List<Variable>/*!*/ ds.>
= (.
    Contract.Requires(x != null);
    Contract.Ensures(Contract.ValueAtReturn(out ds) != null);
    List<TypedIdent>/*!*/ tyds = new List<TypedIdent>();
    ds = new List<Variable>();
    var dsx = ds;
  .)
  AttrsIdsTypeWheres<true, false, "bound variables", delegate(TypedIdent tyd, QKeyValue kv) { dsx.Add(new BoundVariable(tyd.tok, tyd, kv)); } >
  .

/*------------------------------------------------------------------------*/
/* IdsType is used with const declarations */
IdsType<.out List<TypedIdent>/*!*/ tyds.>
= (. Contract.Ensures(Contract.ValueAtReturn(out tyds) != null); List<IToken>/*!*/ ids;  Bpl.Type/*!*/ ty; .)
  Idents<out ids> ":" Type<out ty>
  (. tyds = new List<TypedIdent>();
     foreach(Token/*!*/ id in ids){
       Contract.Assert(id != null);
       tyds.Add(new TypedIdent(id, id.val, ty, null));
     }
  .)
  .

/* AttrsIdsTypeWheres is used with the declarations of formals and bound variables */
AttrsIdsTypeWheres<. bool allowAttributes, bool allowWhereClauses, string context, System.Action<TypedIdent, QKeyValue> action .>
=
  AttributesIdsTypeWhere<allowAttributes, allowWhereClauses, context, action>
  { "," AttributesIdsTypeWhere<allowAttributes, allowWhereClauses, context, action> }
  .

IdsTypeWheres<. bool allowWhereClauses, string context, System.Action<TypedIdent> action .>
=
  IdsTypeWhere<allowWhereClauses, context, action>
  { "," IdsTypeWhere<allowWhereClauses, context, action> }
  .

AttributesIdsTypeWhere<. bool allowAttributes, bool allowWhereClauses, string context, System.Action<TypedIdent, QKeyValue> action .>
= (. QKeyValue kv = null; .)
  { Attribute<ref kv>    (. if (!allowAttributes) {
                              kv = null;
                              this.SemErr("attributes are not allowed on " + context);
                            }
                         .)
  }
  IdsTypeWhere<allowWhereClauses, context, delegate(TypedIdent tyd) { action(tyd, kv); }>
  .

/* context is allowed to be null if allowWhereClauses is true */
IdsTypeWhere<. bool allowWhereClauses, string context, System.Action<TypedIdent> action .>
= (. List<IToken>/*!*/ ids;  Bpl.Type/*!*/ ty;  Expr wh = null;  Expr/*!*/ nne; .)
  Idents<out ids> ":" Type<out ty>
  [ "where" Expression<out nne>  (. if (!allowWhereClauses) {
                                      this.SemErr("where clause not allowed on " + context);
                                    } else {
                                      wh = nne;
                                    }
                                 .)
  ]
  (. foreach(Token/*!*/ id in ids){
       Contract.Assert(id != null);
       action(new TypedIdent(id, id.val, ty, wh));
     }
  .)
  .

/*------------------------------------------------------------------------*/
Type<out Bpl.Type/*!*/ ty>
= (.Contract.Ensures(Contract.ValueAtReturn(out ty) != null); IToken/*!*/ tok; ty = dummyType; .)
  (
    TypeAtom<out ty>
  |
    Ident<out tok>       (. List<Bpl.Type>/*!*/ args = new List<Bpl.Type> (); .)
    [ TypeArgs<args> ]   (. ty = new UnresolvedTypeIdentifier (tok, tok.val, args); .)
  |
    MapType<out ty>
  )
  .

TypeArgs<.List<Bpl.Type>/*!*/ ts.>
= (.Contract.Requires(ts != null); IToken/*!*/ tok; Bpl.Type/*!*/ ty; .)
  (
    TypeAtom<out ty>     (. ts.Add(ty); .)
    [ TypeArgs<ts> ]
  |
    Ident<out tok>       (. List<Bpl.Type>/*!*/ args = new List<Bpl.Type> ();
                            ts.Add(new UnresolvedTypeIdentifier (tok, tok.val, args)); .)
    [ TypeArgs<ts> ]
  |
    MapType<out ty>      (. ts.Add(ty); .)
  )
  .

TypeAtom<out Bpl.Type/*!*/ ty>
= (.Contract.Ensures(Contract.ValueAtReturn(out ty) != null); ty = dummyType; .)
  ( "int"              (. ty = new BasicType(t, SimpleType.Int); .)
  | "real"             (. ty = new BasicType(t, SimpleType.Real); .)
  | "bool"             (. ty = new BasicType(t, SimpleType.Bool); .)
  /* note: bitvectors are handled in UnresolvedTypeIdentifier */
  |
  "("
  Type<out ty>
  ")"
  )
  .

MapType<out Bpl.Type/*!*/ ty>
= (.Contract.Ensures(Contract.ValueAtReturn(out ty) != null); IToken tok = null;
     IToken/*!*/ nnTok;
     List<Bpl.Type>/*!*/ arguments = new List<Bpl.Type>();
     Bpl.Type/*!*/ result;
     List<TypeVariable>/*!*/ typeParameters = new List<TypeVariable>();
   .)
  [ TypeParams<out nnTok, out typeParameters> (. tok = nnTok; .) ]
  "["                                         (.  if (tok == null) tok = t;  .)
    [ Types<arguments> ]
  "]"
  Type<out result>
  (.
    ty = new MapType(tok, typeParameters, arguments, result);
  .)
  .

TypeParams<.out IToken/*!*/ tok, out List<TypeVariable>/*!*/ typeParams.>
= (.Contract.Ensures(Contract.ValueAtReturn(out tok) != null); Contract.Ensures(Contract.ValueAtReturn(out typeParams) != null); List<IToken>/*!*/ typeParamToks; .)
  "<"    (.  tok = t;  .)
    Idents<out typeParamToks>
  ">"
  (.
    typeParams = new List<TypeVariable> ();
    foreach(Token/*!*/ id in typeParamToks){
      Contract.Assert(id != null);
      typeParams.Add(new TypeVariable(id, id.val));}
   .)
  .

Types<.List<Bpl.Type>/*!*/ ts.>
= (. Contract.Requires(ts != null); Bpl.Type/*!*/ ty; .)
  Type<out ty>                 (. ts.Add(ty); .)
  { "," Type<out ty>           (. ts.Add(ty); .)
  }
  .


/*------------------------------------------------------------------------*/
Consts<.out List<Variable>/*!*/ ds.>
= (. Contract.Ensures(Contract.ValueAtReturn(out ds) != null); IToken/*!*/ y; List<TypedIdent>/*!*/ xs;
     ds = new List<Variable>();
     bool u = false; QKeyValue kv = null;
     bool ChildrenComplete = false;
     List<ConstantParent/*!*/> Parents = null; .)
  "const"                 (. y = t; .)
  { Attribute<ref kv> }
  [ "unique"              (. u = true;  .)
  ]
  IdsType<out xs>
  [ OrderSpec<out ChildrenComplete, out Parents> ]
  (. bool makeClone = false;
     foreach(TypedIdent/*!*/ x in xs){
       Contract.Assert(x != null);

       // ensure that no sharing is introduced
       List<ConstantParent/*!*/> ParentsClone;
       if (makeClone && Parents != null) {
         ParentsClone = new List<ConstantParent/*!*/> ();
         foreach (ConstantParent/*!*/ p in Parents){
           Contract.Assert(p != null);
           ParentsClone.Add(new ConstantParent (
                            new IdentifierExpr (p.Parent.tok, p.Parent.Name),
                            p.Unique));}
       } else {
         ParentsClone = Parents;
       }
       makeClone = true;

       ds.Add(new Constant(y, x, u, ParentsClone, ChildrenComplete, kv));
     }
  .)
  ";"
  .

OrderSpec<.out bool ChildrenComplete, out List<ConstantParent/*!*/> Parents.>
= (.Contract.Ensures(cce.NonNullElements(Contract.ValueAtReturn(out Parents),true)); ChildrenComplete = false;
     Parents = null;
     bool u;
     IToken/*!*/ parent; .)
  "extends"                (. Parents = new List<ConstantParent/*!*/> ();
                              u = false; .)
  [
    [ "unique"             (. u = true; .)
    ]
    Ident<out parent>      (. Parents.Add(new ConstantParent (
                                          new IdentifierExpr(parent, parent.val), u)); .)
    {
      ","                  (. u = false; .)
      [ "unique"           (. u = true; .)
      ]
      Ident<out parent>    (. Parents.Add(new ConstantParent (
                                          new IdentifierExpr(parent, parent.val), u)); .)
    }
  ]
  [ "complete"             (. ChildrenComplete = true; .)
  ]
  .

/*------------------------------------------------------------------------*/
Function<.out List<Declaration>/*!*/ ds.>
= (. Contract.Ensures(Contract.ValueAtReturn(out ds) != null);
     ds = new List<Declaration>(); IToken/*!*/ z;
     IToken/*!*/ typeParamTok;
     var typeParams = new List<TypeVariable>();
     var arguments = new List<Variable>();
     TypedIdent/*!*/ tyd;
     TypedIdent retTyd = null;
     Bpl.Type/*!*/ retTy;
     QKeyValue argKv = null;
     QKeyValue kv = null;
     Expr definition = null;
     Expr/*!*/ tmp;
  .)
  "function" { Attribute<ref kv> } Ident<out z>
  [ TypeParams<out typeParamTok, out typeParams> ]
  "("
  [ VarOrType<out tyd, out argKv>      (. arguments.Add(new Formal(tyd.tok, tyd, true, argKv)); .)
  { "," VarOrType<out tyd, out argKv>  (. arguments.Add(new Formal(tyd.tok, tyd, true, argKv)); .)
  } ] ")"
  (. argKv = null; .)
  (
    "returns" "(" VarOrType<out retTyd, out argKv> ")"
    |
    ":" Type<out retTy>   (. retTyd = new TypedIdent(retTy.tok, TypedIdent.NoName, retTy); .)
  )
  ( "{" Expression<out tmp> (. definition = tmp; .) "}" | ";" )
  (.
    if (retTyd == null) {
      // construct a dummy type for the case of syntax error
      retTyd = new TypedIdent(t, TypedIdent.NoName, new BasicType(t, SimpleType.Int));
    }
    Function/*!*/ func = new Function(z, z.val, typeParams, arguments,
                                      new Formal(retTyd.tok, retTyd, false, argKv), null, kv);
    Contract.Assert(func != null);
    ds.Add(func);
    bool allUnnamed = true;
    foreach(Formal/*!*/ f in arguments){
      Contract.Assert(f != null);
      if (f.TypedIdent.HasName) {
        allUnnamed = false;
        break;
      }
    }
    if (!allUnnamed) {
      Bpl.Type prevType = null;
      for (int i = arguments.Count; 0 <= --i; ) {
        TypedIdent/*!*/ curr = cce.NonNull(arguments[i]).TypedIdent;
        if (curr.HasName) {
          // the argument was given as both an identifier and a type
          prevType = curr.Type;
        } else {
          // the argument was given as just one "thing", which syntactically parsed as a type
          if (prevType == null) {
            this.errors.SemErr(curr.tok, "the type of the last parameter is unspecified");
            break;
          }
          Bpl.Type ty = curr.Type;
          var uti = ty as UnresolvedTypeIdentifier;
          if (uti != null && uti.Arguments.Count == 0) {
            // the given "thing" was just an identifier, so let's use it as the name of the parameter
            curr.Name = uti.Name;
            curr.Type = prevType;
          } else {
            this.errors.SemErr(curr.tok, "expecting an identifier as parameter name");
          }
        }
      }
    }
    if (definition != null) {
      // generate either an axiom or a function body
      if (QKeyValue.FindBoolAttribute(kv, "inline")) {
        func.Body = definition;
      } else {
        ds.Add(func.CreateDefinitionAxiom(definition, kv));
      }
    }
  .)
  .

VarOrType<out TypedIdent/*!*/ tyd, out QKeyValue kv>
= (.
    Contract.Ensures(Contract.ValueAtReturn(out tyd) != null);
    string/*!*/ varName = TypedIdent.NoName;
    Bpl.Type/*!*/ ty;
    IToken/*!*/ tok;
    kv = null;
  .)
  { Attribute<ref kv> }
  Type<out ty>    (. tok = ty.tok; .)
  [ ":"           (. var uti = ty as UnresolvedTypeIdentifier;
                     if (uti != null && uti.Arguments.Count == 0) {
                       varName = uti.Name;
                     } else {
                       this.SemErr("expected identifier before ':'");
                     }
                  .)
    Type<out ty>
  ]
  (. tyd = new TypedIdent(tok, varName, ty); .)
  .

/*------------------------------------------------------------------------*/
Axiom<out Axiom/*!*/ m>
= (.Contract.Ensures(Contract.ValueAtReturn(out m) != null); Expr/*!*/ e; QKeyValue kv = null; .)
  "axiom"
   { Attribute<ref kv> }
   (. IToken/*!*/ x = t; .)
  Proposition<out e> ";"  (. m = new Axiom(x,e, null, kv); .)
  .

/*------------------------------------------------------------------------*/
UserDefinedTypes<.out List<Declaration/*!*/>/*!*/ ts.>
= (. Contract.Ensures(cce.NonNullElements(Contract.ValueAtReturn(out ts))); Declaration/*!*/ decl; QKeyValue kv = null; ts = new List<Declaration/*!*/> (); .)
  "type"
  { Attribute<ref kv> }
  UserDefinedType<out decl, kv>          (.  ts.Add(decl);  .)
  { "," UserDefinedType<out decl, kv>    (.  ts.Add(decl);  .) }
  ";"
  .

UserDefinedType<out Declaration/*!*/ decl, QKeyValue kv>
= (. Contract.Ensures(Contract.ValueAtReturn(out decl) != null); IToken/*!*/ id; List<IToken>/*!*/ paramTokens = new List<IToken> ();
     Bpl.Type/*!*/ body = dummyType; bool synonym = false; .)
  Ident<out id>
  [ WhiteSpaceIdents<out paramTokens> ]
  [
    "=" Type<out body>
    (. synonym = true; .)
  ]
  (.
     if (synonym) {
       List<TypeVariable>/*!*/ typeParams = new List<TypeVariable>();
       foreach(Token/*!*/ t in paramTokens){
         Contract.Assert(t != null);
         typeParams.Add(new TypeVariable(t, t.val));}
       decl = new TypeSynonymDecl(id, id.val, typeParams, body, kv);
     } else {
       decl = new TypeCtorDecl(id, id.val, paramTokens.Count, kv);
     }
   .)
  .


/*------------------------------------------------------------------------*/
Procedure<out Procedure/*!*/ proc, out /*maybe null*/ Implementation impl>
= (. Contract.Ensures(Contract.ValueAtReturn(out proc) != null); IToken/*!*/ x;
     List<TypeVariable>/*!*/ typeParams;
     List<Variable>/*!*/ ins, outs;
     List<Requires>/*!*/ pre = new List<Requires>();
     List<IdentifierExpr>/*!*/ mods = new List<IdentifierExpr>();
     List<Ensures>/*!*/ post = new List<Ensures>();

     List<Variable>/*!*/ locals = new List<Variable>();
     StmtList/*!*/ stmtList;
     QKeyValue kv = null;
     impl = null;
  .)

  "procedure"
  ProcSignature<true, out x, out typeParams, out ins, out outs, out kv>
  ( ";"
    { Spec<pre, mods, post> }
  | { Spec<pre, mods, post> }
    ImplBody<out locals, out stmtList>
    (.
      impl = new Implementation(x, x.val, typeParams,
                                Formal.StripWhereClauses(ins), Formal.StripWhereClauses(outs), locals, stmtList, kv == null ? null : (QKeyValue)kv.Clone(), this.errors);
    .)
  )
  (. proc = new Procedure(x, x.val, typeParams, ins, outs, pre, mods, post, kv); .)
  .


Implementation<out Implementation/*!*/ impl>
= (. Contract.Ensures(Contract.ValueAtReturn(out impl) != null); IToken/*!*/ x;
     List<TypeVariable>/*!*/ typeParams;
     List<Variable>/*!*/ ins, outs;
     List<Variable>/*!*/ locals;
     StmtList/*!*/ stmtList;
     QKeyValue kv;
  .)

  "implementation"
  ProcSignature<false, out x, out typeParams, out ins, out outs, out kv>
  ImplBody<out locals, out stmtList>
    (. impl = new Implementation(x, x.val, typeParams, ins, outs, locals, stmtList, kv, this.errors); .)
  .


ProcSignature<.bool allowWhereClausesOnFormals, out IToken/*!*/ name, out List<TypeVariable>/*!*/ typeParams,
              out List<Variable>/*!*/ ins, out List<Variable>/*!*/ outs, out QKeyValue kv.>
= (. Contract.Ensures(Contract.ValueAtReturn(out name) != null); Contract.Ensures(Contract.ValueAtReturn(out typeParams) != null); Contract.Ensures(Contract.ValueAtReturn(out ins) != null); Contract.Ensures(Contract.ValueAtReturn(out outs) != null);
     IToken/*!*/ typeParamTok; typeParams = new List<TypeVariable>();
     outs = new List<Variable>(); kv = null; .)
  { Attribute<ref kv> }
  Ident<out name>
  [ TypeParams<out typeParamTok, out typeParams> ]
  ProcFormals<true, allowWhereClausesOnFormals, out ins>
  [ "returns" ProcFormals<false, allowWhereClausesOnFormals, out outs> ]
  .


Spec<.List<Requires>/*!*/ pre, List<IdentifierExpr>/*!*/ mods, List<Ensures>/*!*/ post.>
= (.Contract.Requires(pre != null); Contract.Requires(mods != null); Contract.Requires(post != null); List<IToken>/*!*/ ms; .)
  ( "modifies"
    [ Idents<out ms>        (. foreach(IToken/*!*/ m in ms){
                                 Contract.Assert(m != null);
                                 mods.Add(new IdentifierExpr(m, m.val));
                               }
                            .)
    ] ";"
  | "free" SpecPrePost<true, pre, post>
  | SpecPrePost<false, pre, post>
  )
  .

SpecPrePost<.bool free, List<Requires>/*!*/ pre, List<Ensures>/*!*/ post.>
= (. Contract.Requires(pre != null); Contract.Requires(post != null); Expr/*!*/ e; Token tok = null; QKeyValue kv = null; .)
  ( "requires"              (. tok = t; .)
    { Attribute<ref kv> }
    Proposition<out e> ";"  (. pre.Add(new Requires(tok, free, e, null, kv)); .)
  | "ensures"               (. tok = t; .)
    { Attribute<ref kv> }
    Proposition<out e> ";"  (. post.Add(new Ensures(tok, free, e, null, kv)); .)
  )
  .

/*------------------------------------------------------------------------*/

ImplBody<.out List<Variable>/*!*/ locals, out StmtList/*!*/ stmtList.>
= (. Contract.Ensures(Contract.ValueAtReturn(out locals) != null); Contract.Ensures(Contract.ValueAtReturn(out stmtList) != null); locals = new List<Variable>(); .)
  "{"
  { LocalVars<locals> }
  StmtList<out stmtList>
  .

/* the StmtList also reads the final curly brace */
StmtList<out StmtList/*!*/ stmtList>
= (. Contract.Ensures(Contract.ValueAtReturn(out stmtList) != null); List<BigBlock/*!*/> bigblocks = new List<BigBlock/*!*/>();
     /* built-up state for the current BigBlock: */
     IToken startToken = null;  string currentLabel = null;
     List<Cmd> cs = null;  /* invariant: startToken != null ==> cs != null */
     /* temporary variables: */
     IToken label;  Cmd c;  BigBlock b;
     StructuredCmd ec = null;  StructuredCmd/*!*/ ecn;
     TransferCmd tc = null;  TransferCmd/*!*/ tcn;
  .)

  {
  ( LabelOrCmd<out c, out label>
    (. if (c != null) {
         // LabelOrCmd read a Cmd
         Contract.Assert(label == null);
         if (startToken == null) { startToken = c.tok;  cs = new List<Cmd>(); }
         Contract.Assert(cs != null);
         cs.Add(c);
       } else {
         // LabelOrCmd read a label
         Contract.Assert(label != null);
         if (startToken != null) {
           Contract.Assert(cs != null);
           // dump the built-up state into a BigBlock
           b = new BigBlock(startToken, currentLabel, cs, null, null);
           bigblocks.Add(b);
           cs = null;
         }
         startToken = label;
         currentLabel = label.val;
         cs = new List<Cmd>();
       }
    .)

  | StructuredCmd<out ecn>
    (. ec = ecn;
       if (startToken == null) { startToken = ec.tok;  cs = new List<Cmd>(); }
       Contract.Assert(cs != null);
       b = new BigBlock(startToken, currentLabel, cs, ec, null);
       bigblocks.Add(b);
       startToken = null;  currentLabel = null;  cs = null;
    .)

  | TransferCmd<out tcn>
    (. tc = tcn;
       if (startToken == null) { startToken = tc.tok;  cs = new List<Cmd>(); }
       Contract.Assert(cs != null);
       b = new BigBlock(startToken, currentLabel, cs, null, tc);
       bigblocks.Add(b);
       startToken = null;  currentLabel = null;  cs = null;
    .)

  )
  }
  "}"
  (. IToken/*!*/ endCurly = t;
     if (startToken == null && bigblocks.Count == 0) {
       startToken = t;  cs = new List<Cmd>();
     }
     if (startToken != null) {
       Contract.Assert(cs != null);
       b = new BigBlock(startToken, currentLabel, cs, null, null);
       bigblocks.Add(b);
     }

     stmtList = new StmtList(bigblocks, endCurly);
  .)
  .

TransferCmd<out TransferCmd/*!*/ tc>
= (. Contract.Ensures(Contract.ValueAtReturn(out tc) != null); tc = dummyTransferCmd;
     Token y;  List<IToken>/*!*/ xs;
     List<String> ss = new List<String>();
  .)
  ( "goto"             (. y = t; .)
    Idents<out xs>     (. foreach(IToken/*!*/ s in xs){
                            Contract.Assert(s != null);
                            ss.Add(s.val); }
                          tc = new GotoCmd(y, ss);
                       .)
  | "return"           (. tc = new ReturnCmd(t); .)
  ) ";"
  .

StructuredCmd<out StructuredCmd/*!*/ ec>
= (. Contract.Ensures(Contract.ValueAtReturn(out ec) != null); ec = dummyStructuredCmd;  Contract.Assume(cce.IsPeerConsistent(ec));
     IfCmd/*!*/ ifcmd;  WhileCmd/*!*/ wcmd;  BreakCmd/*!*/ bcmd;
  .)
  ( IfCmd<out ifcmd>    (. ec = ifcmd; .)
  | WhileCmd<out wcmd>  (. ec = wcmd; .)
  | BreakCmd<out bcmd>  (. ec = bcmd; .)
  )
  .

IfCmd<out IfCmd/*!*/ ifcmd>
= (. Contract.Ensures(Contract.ValueAtReturn(out ifcmd) != null); IToken/*!*/ x;
     Expr guard;
     StmtList/*!*/ thn;
     IfCmd/*!*/ elseIf;  IfCmd elseIfOption = null;
     StmtList/*!*/ els;  StmtList elseOption = null;
  .)
  "if"                       (. x = t; .)
  Guard<out guard>
  "{" StmtList<out thn>
  [ "else"
    ( IfCmd<out elseIf>      (. elseIfOption = elseIf; .)
    | "{"
      StmtList<out els>      (. elseOption = els; .)
    )
  ]
  (. ifcmd = new IfCmd(x, guard, thn, elseIfOption, elseOption); .)
  .

WhileCmd<out WhileCmd/*!*/ wcmd>
= (. Contract.Ensures(Contract.ValueAtReturn(out wcmd) != null); IToken/*!*/ x;  Token z;
     Expr guard;  Expr/*!*/ e;  bool isFree;
     List<PredicateCmd/*!*/> invariants = new List<PredicateCmd/*!*/>();
     StmtList/*!*/ body;
     QKeyValue kv = null;
  .)
  "while"             (. x = t; .)
  Guard<out guard>    (. Contract.Assume(guard == null || cce.Owner.None(guard)); .)
  {                   (. isFree = false; z = la/*lookahead token*/; .)
    [ "free"          (. isFree = true;  .)
    ]
    "invariant"
    { Attribute<ref kv> }
    Expression<out e> (. if (isFree) {
                           invariants.Add(new AssumeCmd(z, e, kv));
                         } else {
                           invariants.Add(new AssertCmd(z, e, kv));
                         }
						 kv = null;
                      .)
    ";"
  }
  "{"
  StmtList<out body>  (. wcmd = new WhileCmd(x, guard, invariants, body); .)
  .

Guard<out Expr e>
= (. Expr/*!*/ ee;  e = null; .)
  "("
  ( "*"                   (. e = null; .)
  | Expression<out ee>    (. e = ee; .)
  )
  ")"
  .

BreakCmd<out BreakCmd/*!*/ bcmd>
= (.Contract.Ensures(Contract.ValueAtReturn(out bcmd) != null); IToken/*!*/ x;  IToken/*!*/ y;
     string breakLabel = null;
  .)
  "break"             (. x = t; .)
  [ Ident<out y>      (. breakLabel = y.val; .)
  ] ";"               (. bcmd = new BreakCmd(x, breakLabel); .)
  .

/*------------------------------------------------------------------------*/

LabelOrCmd<out Cmd c, out IToken label>
/* ensures (c == null) != (label != null) */
= (. IToken/*!*/ x; Expr/*!*/ e;
     List<IToken>/*!*/ xs;
     List<IdentifierExpr> ids;
     c = dummyCmd;  label = null;
     Cmd/*!*/ cn;
     QKeyValue kv = null;
  .)
  ( LabelOrAssign<out c, out label>
  | "assert"              (. x = t; .)
    { Attribute<ref kv> }
    Proposition<out e>    (. c = new AssertCmd(x, e, kv); .)
    ";"
  | "assume"              (. x = t; .)
    { Attribute<ref kv> }
    Proposition<out e>    (. c = new AssumeCmd(x, e, kv); .)
    ";"
  | "havoc"               (. x = t; .)
    Idents<out xs> ";"    (. ids = new List<IdentifierExpr>();
                             foreach(IToken/*!*/ y in xs){
                               Contract.Assert(y != null);
                               ids.Add(new IdentifierExpr(y, y.val));
                             }
                             c = new HavocCmd(x,ids);
                          .)
  | CallCmd<out cn> ";"   (. c = cn; .)
  | ParCallCmd<out cn>    (. c = cn; .)
  | "yield"               (. x = t; .)
    ";"                   (. c = new YieldCmd(x); .)
  )
  .

/*------------------------------------------------------------------------*/

LabelOrAssign<out Cmd c, out IToken label>
/* ensures (c == null) != (label != null) */
= (. IToken/*!*/ id; IToken/*!*/ x, y; Expr/*!*/ e0;
     c = dummyCmd;  label = null;
     AssignLhs/*!*/ lhs;
     List<AssignLhs/*!*/>/*!*/ lhss;
     List<Expr/*!*/>/*!*/ rhss;
     List<Expr/*!*/>/*!*/ indexes;
  .)
  Ident<out id>              (. x = t; .)
  ( ":"                      (. c = null;  label = x; .)

  | (. lhss = new List<AssignLhs/*!*/>(); .)
    (. lhs = new SimpleAssignLhs(id, new IdentifierExpr(id, id.val)); .)

    { MapAssignIndex<out y, out indexes>    (. lhs = new MapAssignLhs(y, lhs, indexes); .) }
    (. lhss.Add(lhs); .)

    { ","
      Ident<out id>
      (. lhs = new SimpleAssignLhs(id, new IdentifierExpr(id, id.val)); .)
      { MapAssignIndex<out y, out indexes>    (. lhs = new MapAssignLhs(y, lhs, indexes); .) }
      (. lhss.Add(lhs); .)
    }

    ":="                     (. x = t; /* use location of := */ .)
    Expression<out e0>       (. rhss = new List<Expr/*!*/> ();
                                rhss.Add(e0); .)
    { ","
      Expression<out e0>     (. rhss.Add(e0); .)
    }
    ";"                      (. c = new AssignCmd(x, lhss, rhss); .)
  )
  .

MapAssignIndex<.out IToken/*!*/ x, out List<Expr/*!*/>/*!*/ indexes.>
= (.Contract.Ensures(Contract.ValueAtReturn(out x) != null); Contract.Ensures(cce.NonNullElements(Contract.ValueAtReturn(out indexes))); indexes = new List<Expr/*!*/> ();
     Expr/*!*/ e;
  .)
  "["                        (. x = t; .)
    [
      Expression<out e>      (. indexes.Add(e); .)
      { ","
        Expression<out e>    (. indexes.Add(e); .)
      }
    ]
  "]"
  .

/*------------------------------------------------------------------------*/
CallCmd<out Cmd c>
= (. Contract.Ensures(Contract.ValueAtReturn(out c) != null); 
     IToken x; 
     bool isAsync = false;
     bool isFree = false;
     QKeyValue kv = null;
     c = null;
  .)
  [ "async"          (. isAsync = true;  .)
  ]
  [ "free"          (. isFree = true;  .)
  ]
  "call"                          (. x = t; .)
  { Attribute<ref kv> }
  CallParams<isAsync, isFree, kv, x, out c> (. .)
  .

ParCallCmd<out Cmd d>
= (. Contract.Ensures(Contract.ValueAtReturn(out d) != null); 
     IToken x; 
     QKeyValue kv = null;
	 Cmd c = null;
     List<CallCmd> callCmds = new List<CallCmd>();
  .)
  "par"                          (. x = t; .)
  { Attribute<ref kv> }
  CallParams<false, false, kv, x, out c> (. callCmds.Add((CallCmd)c); .) 
  { "|" CallParams<false, false, kv, x, out c> (. callCmds.Add((CallCmd)c); .) 
  }
  ";" (. d = new ParCallCmd(x, callCmds, kv); .)
  .

CallParams<bool isAsync, bool isFree, QKeyValue kv, IToken x, out Cmd c>
= (. 
    List<IdentifierExpr> ids = new List<IdentifierExpr>();
    List<Expr> es = new List<Expr>();
    Expr en;
    IToken first; 
    IToken p;
	c = null;
  .)
  Ident<out first>
    ( "("
      [ Expression<out en>       (. es.Add(en); .)
        { "," Expression<out en> (. es.Add(en); .)
        }
      ]
      ")"                         (. c = new CallCmd(x, first.val, es, ids, kv); ((CallCmd) c).IsFree = isFree; ((CallCmd) c).IsAsync = isAsync; .)
    |
                                  (. ids.Add(new IdentifierExpr(first, first.val)); .)
      [ "," Ident<out p>  (. ids.Add(new IdentifierExpr(p, p.val)); .)
        { "," Ident<out p>  (. ids.Add(new IdentifierExpr(p, p.val)); .)
        }
      ] ":="
      Ident<out first> "("
      [ Expression<out en>       (. es.Add(en); .)
        { "," Expression<out en> (. es.Add(en); .)
        }
      ]
      ")"                         (. c = new CallCmd(x, first.val, es, ids, kv); ((CallCmd) c).IsFree = isFree; ((CallCmd) c).IsAsync = isAsync; .)
    )
  .

/*------------------------------------------------------------------------*/
Proposition<out Expr/*!*/ e>
=(.Contract.Ensures(Contract.ValueAtReturn(out e) != null);.)
  Expression<out e>
  .

/*------------------------------------------------------------------------*/
Idents<.out List<IToken>/*!*/ xs.>
= (.Contract.Ensures(Contract.ValueAtReturn(out xs) != null); IToken/*!*/ id; xs = new List<IToken>(); .)
  Ident<out id>                 (. xs.Add(id); .)
  { "," Ident<out id>           (. xs.Add(id); .)
  }
  .

/*------------------------------------------------------------------------*/
WhiteSpaceIdents<.out List<IToken>/*!*/ xs.>
= (. Contract.Ensures(Contract.ValueAtReturn(out xs) != null); IToken/*!*/ id; xs = new List<IToken>(); .)
  Ident<out id>                 (. xs.Add(id); .)
  { Ident<out id>               (. xs.Add(id); .)
  }
  .

/*------------------------------------------------------------------------*/
Expressions<.out List<Expr>/*!*/ es.>
= (. Contract.Ensures(Contract.ValueAtReturn(out es) != null); Expr/*!*/ e; es = new List<Expr>(); .)
  Expression<out e>             (. es.Add(e); .)
  { "," Expression<out e>       (. es.Add(e); .)
  }
  .

/*------------------------------------------------------------------------*/
Expression<.out Expr/*!*/ e0.>
= (. Contract.Ensures(Contract.ValueAtReturn(out e0) != null); IToken/*!*/ x; Expr/*!*/ e1; .)
  ImpliesExpression<false, out e0>
  { EquivOp        (. x = t; .)
    ImpliesExpression<false, out e1>
                   (. e0 = Expr.Binary(x, BinaryOperator.Opcode.Iff, e0, e1); .)
  }
  .

EquivOp = "<==>" | '\u21d4'.

/*------------------------------------------------------------------------*/
ImpliesExpression<bool noExplies, out Expr/*!*/ e0>
= (. Contract.Ensures(Contract.ValueAtReturn(out e0) != null); IToken/*!*/ x; Expr/*!*/ e1; .)
  LogicalExpression<out e0>
  [
    ImpliesOp      (. x = t; .)
    /* recurse because implication is right-associative */
    ImpliesExpression<true, out e1>
                   (. e0 = Expr.Binary(x, BinaryOperator.Opcode.Imp, e0, e1); .)
  |
    ExpliesOp      (. if (noExplies)
                        this.SemErr("illegal mixture of ==> and <==, use parentheses to disambiguate");
                      x = t; .)
    LogicalExpression<out e1>
                   (. e0 = Expr.Binary(x, BinaryOperator.Opcode.Imp, e1, e0); .)
    /* loop because explies is left-associative */
    {
      ExpliesOp    (. x = t; .)
      LogicalExpression<out e1>
                   (. e0 = Expr.Binary(x, BinaryOperator.Opcode.Imp, e1, e0); .)
    }
  ]
  .

ImpliesOp = "==>" | '\u21d2'.
ExpliesOp = "<==" | '\u21d0'.

/*------------------------------------------------------------------------*/
LogicalExpression<out Expr/*!*/ e0>
= (. Contract.Ensures(Contract.ValueAtReturn(out e0) != null); IToken/*!*/ x; Expr/*!*/ e1; .)
  RelationalExpression<out e0>
  [ AndOp          (. x = t; .)
    RelationalExpression<out e1>
    (. e0 = Expr.Binary(x, BinaryOperator.Opcode.And, e0, e1); .)
    { AndOp        (. x = t; .)
      RelationalExpression<out e1>
      (. e0 = Expr.Binary(x, BinaryOperator.Opcode.And, e0, e1); .)
    }
  | OrOp           (. x = t; .)
    RelationalExpression<out e1>
    (. e0 = Expr.Binary(x, BinaryOperator.Opcode.Or, e0, e1); .)
    { OrOp         (. x = t; .)
      RelationalExpression<out e1>
      (. e0 = Expr.Binary(x, BinaryOperator.Opcode.Or, e0, e1); .)
    }
  ]
  .

AndOp = "&&" | '\u2227'.
OrOp = "||" | '\u2228'.

/*------------------------------------------------------------------------*/
RelationalExpression<out Expr/*!*/ e0>
= (. Contract.Ensures(Contract.ValueAtReturn(out e0) != null); IToken/*!*/ x; Expr/*!*/ e1; BinaryOperator.Opcode op; .)
  BvTerm<out e0>
  [ RelOp<out x, out op>
    BvTerm<out e1>            (. e0 = Expr.Binary(x, op, e0, e1); .)
  ]
  .

RelOp<out IToken/*!*/ x, out BinaryOperator.Opcode op>
=                  (.Contract.Ensures(Contract.ValueAtReturn(out x) != null); x = Token.NoToken; op=BinaryOperator.Opcode.Add/*(dummy)*/; .)
  ( "=="           (. x = t; op=BinaryOperator.Opcode.Eq; .)
  | "<"            (. x = t; op=BinaryOperator.Opcode.Lt; .)
  | ">"            (. x = t; op=BinaryOperator.Opcode.Gt; .)
  | "<="           (. x = t; op=BinaryOperator.Opcode.Le; .)
  | ">="           (. x = t; op=BinaryOperator.Opcode.Ge; .)
  | "!="           (. x = t; op=BinaryOperator.Opcode.Neq; .)
  | "<:"           (. x = t; op=BinaryOperator.Opcode.Subtype; .)
  | '\u2260'       (. x = t; op=BinaryOperator.Opcode.Neq; .)
  | '\u2264'       (. x = t; op=BinaryOperator.Opcode.Le; .)
  | '\u2265'       (. x = t; op=BinaryOperator.Opcode.Ge; .)
  )
  .

/*------------------------------------------------------------------------*/
BvTerm<out Expr/*!*/ e0>
= (. Contract.Ensures(Contract.ValueAtReturn(out e0) != null); IToken/*!*/ x; Expr/*!*/ e1; .)
  Term<out e0>
  { "++"                  (. x = t; .)
    Term<out e1>          (. e0 = new BvConcatExpr(x, e0, e1); .)
  }
  .


/*------------------------------------------------------------------------*/
Term<out Expr/*!*/ e0>
= (.Contract.Ensures(Contract.ValueAtReturn(out e0) != null); IToken/*!*/ x; Expr/*!*/ e1; BinaryOperator.Opcode op; .)
  Factor<out e0>
  { AddOp<out x, out op>
    Factor<out e1>          (. e0 = Expr.Binary(x, op, e0, e1); .)
  }
  .

AddOp<out IToken/*!*/ x, out BinaryOperator.Opcode op>
=                  (.Contract.Ensures(Contract.ValueAtReturn(out x) != null); x = Token.NoToken; op=BinaryOperator.Opcode.Add/*(dummy)*/; .)
  ( "+"            (. x = t; op=BinaryOperator.Opcode.Add; .)
  | "-"            (. x = t; op=BinaryOperator.Opcode.Sub; .)
  )
  .

/*------------------------------------------------------------------------*/
Factor<out Expr/*!*/ e0>
= (.Contract.Ensures(Contract.ValueAtReturn(out e0) != null); IToken/*!*/ x; Expr/*!*/ e1; BinaryOperator.Opcode op; .)
  Power<out e0>
  { MulOp<out x, out op>
    Power<out e1> (. e0 = Expr.Binary(x, op, e0, e1); .)
  }
  .

MulOp<out IToken/*!*/ x, out BinaryOperator.Opcode op>
=                  (. Contract.Ensures(Contract.ValueAtReturn(out x) != null); x = Token.NoToken; op=BinaryOperator.Opcode.Add/*(dummy)*/; .)
  ( "*"            (. x = t; op=BinaryOperator.Opcode.Mul; .)
  | "div"          (. x = t; op=BinaryOperator.Opcode.Div; .)
  | "mod"          (. x = t; op=BinaryOperator.Opcode.Mod; .)
  | "/"            (. x = t; op=BinaryOperator.Opcode.RealDiv; .)
  )
  .

/*------------------------------------------------------------------------*/
Power<out Expr/*!*/ e0>
= (.Contract.Ensures(Contract.ValueAtReturn(out e0) != null); IToken/*!*/ x; Expr/*!*/ e1; .)
  UnaryExpression<out e0>
  [
    "**"           (. x = t; .)
    /* recurse because exponentation is right-associative */
    Power<out e1>  (. e0 = Expr.Binary(x, BinaryOperator.Opcode.Pow, e0, e1); .)
  ]
  .

/*------------------------------------------------------------------------*/
UnaryExpression<out Expr/*!*/ e>
= (. Contract.Ensures(Contract.ValueAtReturn(out e) != null); IToken/*!*/ x;
     e = dummyExpr;
  .)
  ( "-"                        (. x = t; .)
    UnaryExpression<out e>     (. e = Expr.Unary(x, UnaryOperator.Opcode.Neg, e); .)
  | NegOp                      (. x = t; .)
    UnaryExpression<out e>     (. e = Expr.Unary(x, UnaryOperator.Opcode.Not, e); .)
  | CoercionExpression<out e>
  )
  .

NegOp = "!" | '\u00ac'.

/*------------------------------------------------------------------------*/

/* This production creates ambiguities, because types can start with "<"
   (polymorphic map types), but can also be followed by "<" (inequalities).
   Coco deals with these ambiguities in a reasonable way by preferring to read
   further types (type arguments) over relational symbols. E.g., "5 : C < 0"
   will cause a parse error because "<" is treated as the beginning of a
   map type. */

CoercionExpression<out Expr/*!*/ e>
= (. Contract.Ensures(Contract.ValueAtReturn(out e) != null); IToken/*!*/ x;
     Bpl.Type/*!*/ coercedTo;
     BigNum bn;
    .)
  ArrayExpression<out e>
  { ":"                     (. x = t; .)
    (
      Type<out coercedTo>   (. e = Expr.CoerceType(x, e, coercedTo); .)
    |
      Nat<out bn>           /* This means that we really look at a bitvector
                               expression t[a:b] */
                            (. if (!(e is LiteralExpr) || !((LiteralExpr)e).isBigNum) {
                                 this.SemErr("arguments of extract need to be integer literals");
                                 e = new BvBounds(x, bn, BigNum.ZERO);
                               } else {
                                 e = new BvBounds(x, bn, ((LiteralExpr)e).asBigNum);
                               }
                             .)
    )
  }
  .

/*------------------------------------------------------------------------*/
ArrayExpression<out Expr/*!*/ e>
= (. Contract.Ensures(Contract.ValueAtReturn(out e) != null); IToken/*!*/ x;
     Expr/*!*/ index0 = dummyExpr; Expr/*!*/ e1;
     bool store; bool bvExtract;
     List<Expr>/*!*/ allArgs = dummyExprSeq;
  .)
  AtomExpression<out e>
  { "["        (. x = t; allArgs = new List<Expr> ();
                  allArgs.Add(e);
                  store = false; bvExtract = false; .)
      [
        Expression<out index0>
               (. if (index0 is BvBounds)
                    bvExtract = true;
                  else
                    allArgs.Add(index0);
               .)
        { "," Expression<out e1>
               (. if (bvExtract || e1 is BvBounds)
                    this.SemErr("bitvectors only have one dimension");
                  allArgs.Add(e1);
               .)
        }
        [ ":=" Expression<out e1>
               (. if (bvExtract || e1 is BvBounds)
                    this.SemErr("assignment to bitvectors is not possible");
                  allArgs.Add(e1); store = true;
               .)
        ]
      | ":=" Expression<out e1>       (. allArgs.Add(e1); store = true; .)
      ]
    "]"
    (. if (store)
         e = new NAryExpr(x, new MapStore(x, allArgs.Count - 2), allArgs);
       else if (bvExtract)
         e = new BvExtractExpr(x, e,
                               ((BvBounds)index0).Upper.ToIntSafe,
                               ((BvBounds)index0).Lower.ToIntSafe);
       else
         e = new NAryExpr(x, new MapSelect(x, allArgs.Count - 1), allArgs);
    .)
  }
  .


/*------------------------------------------------------------------------*/
AtomExpression<out Expr/*!*/ e>
= (. Contract.Ensures(Contract.ValueAtReturn(out e) != null); IToken/*!*/ x; int n; BigNum bn; BigDec bd;
     List<Expr>/*!*/ es;  List<Variable>/*!*/ ds;  Trigger trig;
     List<TypeVariable>/*!*/ typeParams;
     IdentifierExpr/*!*/ id;
     QKeyValue kv;
     e = dummyExpr;
     List<Variable>/*!*/ locals;
     List<Block/*!*/>/*!*/ blocks;
  .)
  ( "false"           (. e = new LiteralExpr(t, false); .)
  | "true"            (. e = new LiteralExpr(t, true); .)
  | Nat<out bn>            (. e = new LiteralExpr(t, bn); .)
  | Dec<out bd>            (. e = new LiteralExpr(t, bd); .)
  | BvLit<out bn, out n> (. e = new LiteralExpr(t, bn, n); .)

  | Ident<out x>            (. id = new IdentifierExpr(x, x.val);  e = id; .)
    [ "("
      ( Expressions<out es> (. e = new NAryExpr(x, new FunctionCall(id), es); .)
      | /* empty */         (. e = new NAryExpr(x, new FunctionCall(id), new List<Expr>()); .)
      )
      ")"
    ]

  | "old"                   (. x = t; .)
    "("
    Expression<out e>
    ")"                     (. e = new OldExpr(x, e); .)

  | "int"                   (. x = t; .)
    "("
    Expression<out e>
    ")"                     (. e = new NAryExpr(x, new ArithmeticCoercion(x, ArithmeticCoercion.CoercionType.ToInt), new List<Expr>{ e }); .)

  | "real"                  (. x = t; .)
    "("
    Expression<out e>
    ")"                     (. e = new NAryExpr(x, new ArithmeticCoercion(x, ArithmeticCoercion.CoercionType.ToReal), new List<Expr>{ e }); .)

  | "(" ( Expression<out e>                 (. if (e is BvBounds)
                                                 this.SemErr("parentheses around bitvector bounds " +
                                                        "are not allowed"); .)
        | Forall                            (. x = t; .)
          QuantifierBody<x, out typeParams, out ds, out kv, out trig, out e>
                                            (. if (typeParams.Count + ds.Count > 0)
                                                 e = new ForallExpr(x, typeParams, ds, kv, trig, e); .)
        | Exists                            (. x = t; .)
          QuantifierBody<x, out typeParams, out ds, out kv, out trig, out e>
                                            (. if (typeParams.Count + ds.Count > 0)
                                                 e = new ExistsExpr(x, typeParams, ds, kv, trig, e); .)
        | Lambda                            (. x = t; .)
          QuantifierBody<x, out typeParams, out ds, out kv, out trig, out e>
                                            (. if (trig != null)
                                                 SemErr("triggers not allowed in lambda expressions");
                                               if (typeParams.Count + ds.Count > 0)
                                                 e = new LambdaExpr(x, typeParams, ds, kv, e); .)
        )
    ")"
  | IfThenElseExpression<out e>
  | CodeExpression<out locals, out blocks> (. e = new CodeExpr(locals, blocks); .)
  )
  .

CodeExpression<.out List<Variable>/*!*/ locals, out List<Block/*!*/>/*!*/ blocks.>
= (. Contract.Ensures(Contract.ValueAtReturn(out locals) != null); Contract.Ensures(cce.NonNullElements(Contract.ValueAtReturn(out blocks))); locals = new List<Variable>(); Block/*!*/ b;
     blocks = new List<Block/*!*/>();
  .)
  "|{"
  { LocalVars<locals> }
  SpecBlock<out b>          (. blocks.Add(b); .)
  { SpecBlock<out b>        (. blocks.Add(b); .)
  }
  "}|"
  .

SpecBlock<out Block/*!*/ b>
= (. Contract.Ensures(Contract.ValueAtReturn(out b) != null); IToken/*!*/ x; IToken/*!*/ y;
     Cmd c;  IToken label;
     List<Cmd> cs = new List<Cmd>();
     List<IToken>/*!*/ xs;
     List<String> ss = new List<String>();
     b = dummyBlock;
     Expr/*!*/ e;
  .)
  Ident<out x> ":"
  { LabelOrCmd<out c, out label>
                       (. if (c != null) {
                            Contract.Assert(label == null);
                            cs.Add(c);
                          } else {
                            Contract.Assert(label != null);
                            SemErr("SpecBlock's can only have one label");
                          }
                       .)
  }
  ( "goto"             (. y = t; .)
    Idents<out xs>     (. foreach(IToken/*!*/ s in xs){
                            Contract.Assert(s != null);
                            ss.Add(s.val); }
                          b = new Block(x,x.val,cs,new GotoCmd(y,ss));
                       .)
  | "return" Expression<out e>
                       (. b = new Block(x,x.val,cs,new ReturnExprCmd(t,e)); .)
  )
  ";"
  .

Attribute<ref QKeyValue kv>
= (. Trigger trig = null; .)
  AttributeOrTrigger<ref kv, ref trig> (.  if (trig != null) this.SemErr("only attributes, not triggers, allowed here"); .)
.

AttributeOrTrigger<ref QKeyValue kv, ref Trigger trig>
= (. IToken/*!*/ tok;  Expr/*!*/ e;  List<Expr>/*!*/ es;
     string key;
     List<object/*!*/> parameters;  object/*!*/ param;
  .)
  "{"                                         (. tok = t; .)
     (
       ":" ident                              (. key = t.val;  parameters = new List<object/*!*/>(); .)
       [ AttributeParameter<out param>        (. parameters.Add(param); .)
         { "," AttributeParameter<out param>  (. parameters.Add(param); .)
         }
       ]
       (. if (key == "nopats") {
            if (parameters.Count == 1 && parameters[0] is Expr) {
              e = (Expr)parameters[0];
              if(trig==null){
                trig = new Trigger(tok, false, new List<Expr> { e }, null);
              } else {
                trig.AddLast(new Trigger(tok, false, new List<Expr> { e }, null));
              }
            } else {
              this.SemErr("the 'nopats' quantifier attribute expects a string-literal parameter");
            }
          } else {
            if (kv==null) {
              kv = new QKeyValue(tok, key, parameters, null);
            } else {
              kv.AddLast(new QKeyValue(tok, key, parameters, null));
            }
          }
       .)
     |
       Expression<out e>       (. es = new List<Expr> { e }; .)
       { "," Expression<out e> (. es.Add(e); .)
       }                       (. if (trig==null) {
                                    trig = new Trigger(tok, true, es, null);
                                  } else {
                                    trig.AddLast(new Trigger(tok, true, es, null));
                                  }
                               .)
     )
  "}"
  .

AttributeParameter<out object/*!*/ o>
= (. Contract.Ensures(Contract.ValueAtReturn(out o) != null);
     o = "error";
     Expr/*!*/ e;
  .)
  ( string                (. o = t.val.Substring(1, t.val.Length-2); .)
  | Expression<out e>     (. o = e; .)
  )
  .

IfThenElseExpression<out Expr/*!*/ e>
= (. Contract.Ensures(Contract.ValueAtReturn(out e) != null);
     IToken/*!*/ tok;
     Expr/*!*/ e0, e1, e2;
     e = dummyExpr; .)
  "if" (. tok = t; .) Expression<out e0> "then" Expression<out e1> "else" Expression<out e2>
  (. e = new NAryExpr(tok, new IfThenElse(tok), new List<Expr>{ e0, e1, e2 }); .)
  .


QuantifierBody<.IToken/*!*/ q, out List<TypeVariable>/*!*/ typeParams, out List<Variable>/*!*/ ds,
               out QKeyValue kv, out Trigger trig, out Expr/*!*/ body.>
= (. Contract.Requires(q != null); Contract.Ensures(Contract.ValueAtReturn(out typeParams) != null); Contract.Ensures(Contract.ValueAtReturn(out ds) != null); Contract.Ensures(Contract.ValueAtReturn(out body) != null);
     trig = null; typeParams = new List<TypeVariable> ();
     IToken/*!*/ tok;
     kv = null;
     ds = new List<Variable> ();
  .)
  (
     TypeParams<out tok, out typeParams>
     [ BoundVars<q, out ds> ]
  |
     BoundVars<q, out ds>
  )
  QSep
  { AttributeOrTrigger<ref kv, ref trig> }
  Expression<out body>
  .

Forall = "forall" | '\u2200'.
Exists = "exists" | '\u2203'.
Lambda = "lambda" | '\u03bb'.
QSep = "::" | '\u2022'.

/*------------------------------------------------------------------------*/
Ident<out IToken/*!*/ x>
=(.Contract.Ensures(Contract.ValueAtReturn(out x) != null);.)
  ident            (.  x = t;
                       if (x.val.StartsWith("\\"))
                         x.val = x.val.Substring(1);
                    .)
  .

/*------------------------------------------------------------------------*/
Nat<out BigNum n>
=
  digits
  (. try {
       n = BigNum.FromString(t.val);
     } catch (FormatException) {
       this.SemErr("incorrectly formatted number");
       n = BigNum.ZERO;
     }
  .)
  .

/*------------------------------------------------------------------------*/
Dec<out BigDec n>
= (. string s = ""; .)
  (
    decimal   (. s = t.val; .)
  |
    float     (. s = t.val; .)
  )
  (. try {
       n = BigDec.FromString(s);
     } catch (FormatException) {
       this.SemErr("incorrectly formatted number");
       n = BigDec.ZERO;
     }
  .)
  .

/*------------------------------------------------------------------------*/
BvLit<out BigNum n, out int m>
=
  bvlit
  (.
     int pos = t.val.IndexOf("bv");
     string a = t.val.Substring(0, pos);
     string b = t.val.Substring(pos + 2);
     try {
       n = BigNum.FromString(a);
       m = Convert.ToInt32(b);
     } catch (FormatException) {
       this.SemErr("incorrectly formatted bitvector");
       n = BigNum.ZERO;
       m = 0;
     }
  .)
  .
END BoogiePL.