aboutsummaryrefslogtreecommitdiffhomepage
path: root/tactics/extratactics.ml4
blob: c414339ff8700819ce7511a59c8bb3541e878957 (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
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(*i camlp4deps: "grammar/grammar.cma" i*)

open Pp
open Pcoq
open Genarg
open Extraargs
open Mod_subst
open Names
open Tacexpr
open Glob_term
open Glob_ops
open Tactics
open Errors
open Util
open Evd
open Equality
open Misctypes

(**********************************************************************)
(* admit, replace, discriminate, injection, simplify_eq               *)
(* cutrewrite, dependent rewrite                                      *)

TACTIC EXTEND admit
  [ "admit" ] -> [ admit_as_an_axiom ]
END

let replace_in_clause_maybe_by (sigma1,c1) c2 in_hyp tac =
  Refiner.tclWITHHOLES false
    (replace_in_clause_maybe_by c1 c2 (glob_in_arg_hyp_to_clause in_hyp))
    sigma1
    (Option.map Tacinterp.eval_tactic tac)

let replace_multi_term dir_opt (sigma,c) in_hyp =
  Refiner.tclWITHHOLES false
    (replace_multi_term dir_opt c)
    sigma
    (glob_in_arg_hyp_to_clause in_hyp)

TACTIC EXTEND replace
   ["replace" open_constr(c1) "with" constr(c2) in_arg_hyp(in_hyp) by_arg_tac(tac) ]
-> [ replace_in_clause_maybe_by c1 c2 in_hyp tac ]
END

TACTIC EXTEND replace_term_left
  [ "replace"  "->" open_constr(c) in_arg_hyp(in_hyp) ]
  -> [ replace_multi_term (Some true) c in_hyp]
END

TACTIC EXTEND replace_term_right
  [ "replace"  "<-" open_constr(c) in_arg_hyp(in_hyp) ]
  -> [replace_multi_term (Some false) c in_hyp]
END

TACTIC EXTEND replace_term
  [ "replace" open_constr(c) in_arg_hyp(in_hyp) ]
  -> [ replace_multi_term None c in_hyp ]
END

let induction_arg_of_quantified_hyp = function
  | AnonHyp n -> ElimOnAnonHyp n
  | NamedHyp id -> ElimOnIdent (Loc.ghost,id)

(* Versions *_main must come first!! so that "1" is interpreted as a
   ElimOnAnonHyp and not as a "constr", and "id" is interpreted as a
   ElimOnIdent and not as "constr" *)

let elimOnConstrWithHoles tac with_evars c =
  Refiner.tclWITHHOLES with_evars (tac with_evars) 
    c.sigma (Some (ElimOnConstr c.it))

TACTIC EXTEND simplify_eq_main
| [ "simplify_eq" constr_with_bindings(c) ] ->
    [ elimOnConstrWithHoles dEq false c ]
END
TACTIC EXTEND simplify_eq
  [ "simplify_eq" ] -> [ dEq false None ]
| [ "simplify_eq" quantified_hypothesis(h) ] ->
    [ dEq false (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND esimplify_eq_main
| [ "esimplify_eq" constr_with_bindings(c) ] ->
    [ elimOnConstrWithHoles dEq true c ]
END
TACTIC EXTEND esimplify_eq
| [ "esimplify_eq" ] -> [ dEq true None ]
| [ "esimplify_eq" quantified_hypothesis(h) ] ->
    [ dEq true (Some (induction_arg_of_quantified_hyp h)) ]
END

TACTIC EXTEND discriminate_main
| [ "discriminate" constr_with_bindings(c) ] ->
    [ elimOnConstrWithHoles discr_tac false c ]
END
TACTIC EXTEND discriminate
| [ "discriminate" ] -> [ discr_tac false None ]
| [ "discriminate" quantified_hypothesis(h) ] ->
    [ discr_tac false (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND ediscriminate_main
| [ "ediscriminate" constr_with_bindings(c) ] ->
    [ elimOnConstrWithHoles discr_tac true c ]
END
TACTIC EXTEND ediscriminate
| [ "ediscriminate" ] -> [ discr_tac true None ]
| [ "ediscriminate" quantified_hypothesis(h) ] ->
    [ discr_tac true (Some (induction_arg_of_quantified_hyp h)) ]
END

let h_discrHyp id gl =
  h_discriminate_main {it = Term.mkVar id,NoBindings; sigma = Refiner.project gl} gl

TACTIC EXTEND injection_main
| [ "injection" constr_with_bindings(c) ] ->
    [ elimOnConstrWithHoles (injClause []) false c ]
END
TACTIC EXTEND injection
| [ "injection" ] -> [ injClause [] false None ]
| [ "injection" quantified_hypothesis(h) ] ->
    [ injClause [] false (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND einjection_main
| [ "einjection" constr_with_bindings(c) ] ->
    [ elimOnConstrWithHoles (injClause []) true c ]
END
TACTIC EXTEND einjection
| [ "einjection" ] -> [ injClause [] true None ]
| [ "einjection" quantified_hypothesis(h) ] -> [ injClause [] true (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND injection_as_main
| [ "injection" constr_with_bindings(c) "as" simple_intropattern_list(ipat)] ->
    [ elimOnConstrWithHoles (injClause ipat) false c ]
END
TACTIC EXTEND injection_as
| [ "injection" "as" simple_intropattern_list(ipat)] ->
    [ injClause ipat false None ]
| [ "injection" quantified_hypothesis(h) "as" simple_intropattern_list(ipat) ] ->
    [ injClause ipat false (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND einjection_as_main
| [ "einjection" constr_with_bindings(c) "as" simple_intropattern_list(ipat)] ->
    [ elimOnConstrWithHoles (injClause ipat) true c ]
END
TACTIC EXTEND einjection_as
| [ "einjection" "as" simple_intropattern_list(ipat)] ->
    [ injClause ipat true None ]
| [ "einjection" quantified_hypothesis(h) "as" simple_intropattern_list(ipat) ] ->
    [ injClause ipat true (Some (induction_arg_of_quantified_hyp h)) ]
END

let h_injHyp id gl =
  h_injection_main { it = Term.mkVar id,NoBindings; sigma = Refiner.project gl } gl

TACTIC EXTEND dependent_rewrite
| [ "dependent" "rewrite" orient(b) constr(c) ] -> [ rewriteInConcl b c ]
| [ "dependent" "rewrite" orient(b) constr(c) "in" hyp(id) ]
    -> [ rewriteInHyp b c id ]
END

TACTIC EXTEND cut_rewrite
| [ "cutrewrite" orient(b) constr(eqn) ] -> [ cutRewriteInConcl b eqn ]
| [ "cutrewrite" orient(b) constr(eqn) "in" hyp(id) ]
    -> [ cutRewriteInHyp b eqn id ]
END

(**********************************************************************)
(* Contradiction                                                      *)

open Contradiction

TACTIC EXTEND absurd
 [ "absurd" constr(c) ] -> [ absurd c ]
END

let onSomeWithHoles tac = function
  | None -> tac None
  | Some c -> Refiner.tclWITHHOLES false tac c.sigma (Some c.it)

TACTIC EXTEND contradiction
 [ "contradiction" constr_with_bindings_opt(c) ] ->
    [ onSomeWithHoles contradiction c ]
END

(**********************************************************************)
(* AutoRewrite                                                        *)

open Autorewrite

let pr_orient _prc _prlc _prt = function
  | true -> Pp.mt ()
  | false -> Pp.str " <-"

let pr_orient_string _prc _prlc _prt (orient, s) =
  pr_orient _prc _prlc _prt orient ++ Pp.spc () ++ Pp.str s

ARGUMENT EXTEND orient_string TYPED AS (bool * string) PRINTED BY pr_orient_string
| [ orient(r) preident(i) ] -> [ r, i ]
END

TACTIC EXTEND autorewrite
| [ "autorewrite" "with" ne_preident_list(l) in_arg_hyp(cl) ] ->
    [ auto_multi_rewrite  l (glob_in_arg_hyp_to_clause  cl) ]
| [ "autorewrite" "with" ne_preident_list(l) in_arg_hyp(cl) "using" tactic(t) ] ->
    [
      let cl =  glob_in_arg_hyp_to_clause cl in
      auto_multi_rewrite_with (Tacinterp.eval_tactic t) l cl

    ]
END

TACTIC EXTEND autorewrite_star
| [ "autorewrite" "*" "with" ne_preident_list(l) in_arg_hyp(cl) ] ->
    [ auto_multi_rewrite ~conds:AllMatches l (glob_in_arg_hyp_to_clause  cl) ]
| [ "autorewrite" "*" "with" ne_preident_list(l) in_arg_hyp(cl) "using" tactic(t) ] ->
    [ let cl =  glob_in_arg_hyp_to_clause cl in
	auto_multi_rewrite_with ~conds:AllMatches (Tacinterp.eval_tactic t) l cl ]
END

(**********************************************************************)
(* Rewrite star                                                       *)

let rewrite_star clause orient occs (sigma,c) (tac : glob_tactic_expr option) =
  let tac' = Option.map (fun t -> Tacinterp.eval_tactic t, FirstSolved) tac in
  Refiner. tclWITHHOLES false
    (general_rewrite_ebindings_clause clause orient occs ?tac:tac' true true (c,NoBindings)) sigma true

TACTIC EXTEND rewrite_star
| [ "rewrite" "*" orient(o) open_constr(c) "in" hyp(id) "at" occurrences(occ) by_arg_tac(tac) ] ->
    [ rewrite_star (Some id) o (occurrences_of occ) c tac ]
| [ "rewrite" "*" orient(o) open_constr(c) "at" occurrences(occ) "in" hyp(id) by_arg_tac(tac) ] ->
    [ rewrite_star (Some id) o (occurrences_of occ) c tac ]
| [ "rewrite" "*" orient(o) open_constr(c) "in" hyp(id) by_arg_tac(tac) ] ->
    [ rewrite_star (Some id) o Locus.AllOccurrences c tac ]
| [ "rewrite" "*" orient(o) open_constr(c) "at" occurrences(occ) by_arg_tac(tac) ] ->
    [ rewrite_star None o (occurrences_of occ) c tac ]
| [ "rewrite" "*" orient(o) open_constr(c) by_arg_tac(tac) ] ->
    [ rewrite_star None o Locus.AllOccurrences c tac ]
    END

(**********************************************************************)
(* Hint Rewrite                                                       *)

let add_rewrite_hint name ort t lcsr =
  let env = Global.env() and sigma = Evd.empty in
  let f c = Constrexpr_ops.constr_loc c, Constrintern.interp_constr sigma env c, ort, t in
  add_rew_rules name (List.map f lcsr)

VERNAC COMMAND EXTEND HintRewrite
  [ "Hint" "Rewrite" orient(o) ne_constr_list(l) ":" preident(b) ] ->
  [ add_rewrite_hint b o (Tacexpr.TacId []) l ]
| [ "Hint" "Rewrite" orient(o) ne_constr_list(l) "using" tactic(t)
    ":" preident(b) ] ->
  [ add_rewrite_hint b o t l ]
| [ "Hint" "Rewrite" orient(o) ne_constr_list(l) ] ->
  [ add_rewrite_hint "core" o (Tacexpr.TacId []) l ]
| [ "Hint" "Rewrite" orient(o) ne_constr_list(l) "using" tactic(t) ] ->
  [ add_rewrite_hint "core" o t l ]
END

(**********************************************************************)
(* Hint Resolve                                                       *)

open Term
open Coqlib

let project_hint pri l2r c =
  let env = Global.env() in
  let c = Constrintern.interp_constr Evd.empty env c in
  let t = Retyping.get_type_of env Evd.empty c in
  let t =
    Tacred.reduce_to_quantified_ref env Evd.empty (Lazy.force coq_iff_ref) t in
  let sign,ccl = decompose_prod_assum t in
  let (a,b) = match snd (decompose_app ccl) with
    | [a;b] -> (a,b)
    | _ -> assert false in
  let p =
    if l2r then build_coq_iff_left_proj () else build_coq_iff_right_proj () in
  let c = Reductionops.whd_beta Evd.empty (mkApp (c,Termops.extended_rel_vect 0 sign)) in
  let c = it_mkLambda_or_LetIn
    (mkApp (p,[|mkArrow a (lift 1 b);mkArrow b (lift 1 a);c|])) sign in
  (pri,true,Auto.PathAny,c)

let add_hints_iff l2r lc n bl =
  Auto.add_hints true bl
    (Auto.HintsResolveEntry (List.map (project_hint n l2r) lc))

VERNAC COMMAND EXTEND HintResolveIffLR
  [ "Hint" "Resolve" "->" ne_constr_list(lc) natural_opt(n)
    ":" preident_list(bl) ] ->
  [ add_hints_iff true lc n bl ]
| [ "Hint" "Resolve" "->" ne_constr_list(lc) natural_opt(n) ] ->
  [ add_hints_iff true lc n ["core"] ]
END
VERNAC COMMAND EXTEND HintResolveIffRL
  [ "Hint" "Resolve" "<-" ne_constr_list(lc) natural_opt(n)
    ":" preident_list(bl) ] ->
  [ add_hints_iff false lc n bl ]
| [ "Hint" "Resolve" "<-" ne_constr_list(lc) natural_opt(n) ] ->
  [ add_hints_iff false lc n ["core"] ]
END

(**********************************************************************)
(* Refine                                                             *)

open Refine

TACTIC EXTEND refine
  [ "refine" casted_open_constr(c) ] -> [ refine c ]
END

let refine_tac = h_refine

(**********************************************************************)
(* Inversion lemmas (Leminv)                                          *)

open Inv
open Leminv

VERNAC COMMAND EXTEND DeriveInversionClear
  [ "Derive" "Inversion_clear" ident(na) hyp(id) ]
  -> [ inversion_lemma_from_goal 1 na id Term.prop_sort false inv_clear_tac ]

| [ "Derive" "Inversion_clear" natural(n) ident(na) hyp(id) ]
  -> [ inversion_lemma_from_goal n na id Term.prop_sort false inv_clear_tac ]

| [ "Derive" "Inversion_clear" ident(na) "with" constr(c) "Sort" sort(s) ]
  -> [ add_inversion_lemma_exn na c s false inv_clear_tac ]

| [ "Derive" "Inversion_clear" ident(na) "with" constr(c) ]
  -> [ add_inversion_lemma_exn na c GProp false inv_clear_tac ]
END

open Term
open Glob_term

VERNAC COMMAND EXTEND DeriveInversion
| [ "Derive" "Inversion" ident(na) "with" constr(c) "Sort" sort(s) ]
  -> [ add_inversion_lemma_exn na c s false inv_tac ]

| [ "Derive" "Inversion" ident(na) "with" constr(c) ]
  -> [ add_inversion_lemma_exn na c GProp false inv_tac ]

| [ "Derive" "Inversion" ident(na) hyp(id) ]
  -> [ inversion_lemma_from_goal 1 na id Term.prop_sort false inv_tac ]

| [ "Derive" "Inversion" natural(n) ident(na) hyp(id) ]
  -> [ inversion_lemma_from_goal n na id Term.prop_sort false inv_tac ]
END

VERNAC COMMAND EXTEND DeriveDependentInversion
| [ "Derive" "Dependent" "Inversion" ident(na) "with" constr(c) "Sort" sort(s) ]
  -> [ add_inversion_lemma_exn na c s true dinv_tac ]
    END

VERNAC COMMAND EXTEND DeriveDependentInversionClear
| [ "Derive" "Dependent" "Inversion_clear" ident(na) "with" constr(c) "Sort" sort(s) ]
  -> [ add_inversion_lemma_exn na c s true dinv_clear_tac ]
END

(**********************************************************************)
(* Subst                                                              *)

TACTIC EXTEND subst
| [ "subst" ne_var_list(l) ] -> [ subst l ]
| [ "subst" ] -> [ fun gl -> subst_all gl ]
END

let simple_subst_tactic_flags =
  { only_leibniz = true; rewrite_dependent_proof = false }

TACTIC EXTEND simple_subst
| [ "simple" "subst" ] -> [ subst_all ~flags:simple_subst_tactic_flags ]
END

open Evar_tactics

(**********************************************************************)
(* Evar creation                                                      *)

TACTIC EXTEND evar
  [ "evar" "(" ident(id) ":" lconstr(typ) ")" ] -> [ let_evar (Name id) typ ]
| [ "evar" constr(typ) ] -> [ let_evar Anonymous typ ]
END

open Tacexpr
open Tacticals

TACTIC EXTEND instantiate
  [ "instantiate" "(" integer(i) ":=" glob(c) ")" hloc(hl) ] ->
    [instantiate i c hl  ]
| [ "instantiate" ] -> [ tclNORMEVAR ]
END


(**********************************************************************)
(** Nijmegen "step" tactic for setoid rewriting                       *)

open Tactics
open Tactics
open Libnames
open Glob_term
open Summary
open Libobject
open Lib

(* Registered lemmas are expected to be of the form
     x R y -> y == z -> x R z    (in the right table)
     x R y -> x == z -> z R y    (in the left table)
*)

let transitivity_right_table = ref []
let transitivity_left_table = ref []

(* [step] tries to apply a rewriting lemma; then apply [tac] intended to
   complete to proof of the last hypothesis (assumed to state an equality) *)

let step left x tac =
  let l =
    List.map (fun lem ->
      tclTHENLAST
      (apply_with_bindings (lem, ImplicitBindings [x]))
        tac)
      !(if left then transitivity_left_table else transitivity_right_table)
  in
  tclFIRST l

(* Main function to push lemmas in persistent environment *)

let cache_transitivity_lemma (_,(left,lem)) =
  if left then
    transitivity_left_table  := lem :: !transitivity_left_table
  else
    transitivity_right_table := lem :: !transitivity_right_table

let subst_transitivity_lemma (subst,(b,ref)) = (b,subst_mps subst ref)

let inTransitivity : bool * constr -> obj =
  declare_object {(default_object "TRANSITIVITY-STEPS") with
    cache_function = cache_transitivity_lemma;
    open_function = (fun i o -> if i=1 then cache_transitivity_lemma o);
    subst_function = subst_transitivity_lemma;
    classify_function = (fun o -> Substitute o) }

(* Synchronisation with reset *)

let freeze () = !transitivity_left_table, !transitivity_right_table

let unfreeze (l,r) =
  transitivity_left_table := l;
  transitivity_right_table := r

let init () =
  transitivity_left_table := [];
  transitivity_right_table := []

let _ =
  declare_summary "transitivity-steps"
    { freeze_function = freeze;
      unfreeze_function = unfreeze;
      init_function = init }

(* Main entry points *)

let add_transitivity_lemma left lem =
 let lem' = Constrintern.interp_constr Evd.empty (Global.env ()) lem in
  add_anonymous_leaf (inTransitivity (left,lem'))

(* Vernacular syntax *)

TACTIC EXTEND stepl
| ["stepl" constr(c) "by" tactic(tac) ] -> [ step true c (Tacinterp.eval_tactic tac) ]
| ["stepl" constr(c) ] -> [ step true c tclIDTAC ]
END

TACTIC EXTEND stepr
| ["stepr" constr(c) "by" tactic(tac) ] -> [ step false c (Tacinterp.eval_tactic tac) ]
| ["stepr" constr(c) ] -> [ step false c tclIDTAC ]
END

VERNAC COMMAND EXTEND AddStepl
| [ "Declare" "Left" "Step" constr(t) ] ->
    [ add_transitivity_lemma true t ]
END

VERNAC COMMAND EXTEND AddStepr
| [ "Declare" "Right" "Step" constr(t) ] ->
    [ add_transitivity_lemma false t ]
END

VERNAC COMMAND EXTEND ImplicitTactic
| [ "Declare" "Implicit" "Tactic" tactic(tac) ] ->
    [ Pfedit.declare_implicit_tactic (Tacinterp.interp tac) ]
END




(**********************************************************************)
(*spiwack : Vernac commands for retroknowledge                        *)

VERNAC COMMAND EXTEND RetroknowledgeRegister
 | [ "Register" constr(c) "as" retroknowledge_field(f) "by" constr(b)] ->
           [ let tc = Constrintern.interp_constr Evd.empty (Global.env ()) c in
             let tb = Constrintern.interp_constr Evd.empty (Global.env ()) b in
             Global.register f tc tb ]
END



(**********************************************************************)
(* sozeau: abs/gen for induction on instantiated dependent inductives, using "Ford" induction as
  defined by Conor McBride *)
TACTIC EXTEND generalize_eqs
| ["generalize_eqs" hyp(id) ] -> [ abstract_generalize ~generalize_vars:false id ]
END
TACTIC EXTEND dep_generalize_eqs
| ["dependent" "generalize_eqs" hyp(id) ] -> [ abstract_generalize ~generalize_vars:false ~force_dep:true id ]
END
TACTIC EXTEND generalize_eqs_vars
| ["generalize_eqs_vars" hyp(id) ] -> [ abstract_generalize ~generalize_vars:true id ]
END
TACTIC EXTEND dep_generalize_eqs_vars
| ["dependent" "generalize_eqs_vars" hyp(id) ] -> [ abstract_generalize ~force_dep:true ~generalize_vars:true id ]
END

(** Tactic to automatically simplify hypotheses of the form [Π Δ, x_i = t_i -> T] 
    where [t_i] is closed w.r.t. Δ. Such hypotheses are automatically generated
    during dependent induction. For internal use. *)

TACTIC EXTEND specialize_eqs
[ "specialize_eqs" hyp(id) ] -> [ specialize_eqs id ]
END

(**********************************************************************)
(* A tactic that considers a given occurrence of [c] in [t] and       *)
(* abstract the minimal set of all the occurrences of [c] so that the *)
(* abstraction [fun x -> t[x/c]] is well-typed                        *)
(*                                                                    *)
(* Contributed by Chung-Kil Hur (Winter 2009)                         *)
(**********************************************************************)

let subst_var_with_hole occ tid t = 
  let occref = if occ > 0 then ref occ else Termops.error_invalid_occurrence [occ] in
  let locref = ref 0 in
  let rec substrec = function
    | GVar (_,id) as x -> 
        if id = tid 
        then
	  (decr occref;
	   if !occref = 0 then x
           else
	     (incr locref;
	      GHole (Loc.make_loc (!locref,0),
		     Evar_kinds.QuestionMark(Evar_kinds.Define true))))
        else x
    | c -> map_glob_constr_left_to_right substrec c in
  let t' = substrec t
  in
  if !occref > 0 then Termops.error_invalid_occurrence [occ] else t'

let subst_hole_with_term occ tc t =
  let locref = ref 0 in
  let occref = ref occ in
  let rec substrec = function
    | GHole (_,Evar_kinds.QuestionMark(Evar_kinds.Define true)) ->
        decr occref;
        if !occref = 0 then tc
        else
	  (incr locref;
	   GHole (Loc.make_loc (!locref,0),
		  Evar_kinds.QuestionMark(Evar_kinds.Define true)))
    | c -> map_glob_constr_left_to_right substrec c
  in
  substrec t

open Tacmach

let out_arg = function
  | ArgVar _ -> anomaly "Unevaluated or_var variable"
  | ArgArg x -> x

let hResolve id c occ t gl = 
  let sigma = project gl in 
  let env = Termops.clear_named_body id (pf_env gl) in
  let env_ids = Termops.ids_of_context env in
  let env_names = Termops.names_of_rel_context env in
  let c_raw = Detyping.detype true env_ids env_names c in 
  let t_raw = Detyping.detype true env_ids env_names t in 
  let rec resolve_hole t_hole =
    try 
      Pretyping.understand sigma env t_hole
    with 
    | Loc.Exc_located (loc,Pretype_errors.PretypeError (_,_,Pretype_errors.UnsolvableImplicit _)) ->
        resolve_hole (subst_hole_with_term (fst (Loc.unloc loc)) c_raw t_hole)
  in
  let t_constr = resolve_hole (subst_var_with_hole occ id t_raw) in
  let t_constr_type = Retyping.get_type_of env sigma t_constr in
  change_in_concl None (mkLetIn (Anonymous,t_constr,t_constr_type,pf_concl gl)) gl

let hResolve_auto id c t gl =
  let rec resolve_auto n = 
    try
      hResolve id c n t gl
    with
    | UserError _ as e -> raise e
    | _ -> resolve_auto (n+1)
  in
  resolve_auto 1

TACTIC EXTEND hresolve_core
| [ "hresolve_core" "(" ident(id) ":=" constr(c) ")" "at" int_or_var(occ) "in" constr(t) ] -> [ hResolve id c (out_arg occ) t ]
| [ "hresolve_core" "(" ident(id) ":=" constr(c) ")" "in" constr(t) ] -> [ hResolve_auto id c t ]
END

(**
   hget_evar
*)

open Evar_refiner
open Sign

let hget_evar n gl =
  let sigma = project gl in
  let evl = evar_list sigma (pf_concl gl) in
  if List.length evl < n then
    error "Not enough uninstantiated existential variables.";
  if n <= 0 then error "Incorrect existential variable index.";
  let ev = List.nth evl (n-1) in
  let ev_type = existential_type sigma ev in
  change_in_concl None (mkLetIn (Anonymous,mkEvar ev,ev_type,pf_concl gl)) gl

TACTIC EXTEND hget_evar
| [ "hget_evar" int_or_var(n) ] -> [ hget_evar (out_arg n) ]
END

(**********************************************************************)

(**********************************************************************)
(* A tactic that reduces one match t with ... by doing destruct t.    *)
(* if t is not a variable, the tactic does                            *)
(* case_eq t;intros ... heq;rewrite heq in *|-. (but heq itself is    *)
(* preserved).                                                        *)
(* Contributed by Julien Forest and Pierre Courtieu (july 2010)       *)
(**********************************************************************)

exception Found of tactic

let rewrite_except h g =
  tclMAP (fun id -> if id = h then tclIDTAC else 
      tclTRY (Equality.general_rewrite_in true Locus.AllOccurrences true true id (mkVar h) false))
    (Tacmach.pf_ids_of_hyps g) g


let refl_equal = 
  let coq_base_constant s =
    Coqlib.gen_constant_in_modules "RecursiveDefinition"
      (Coqlib.init_modules @ [["Coq";"Arith";"Le"];["Coq";"Arith";"Lt"]]) s in
  function () -> (coq_base_constant "eq_refl")


(* This is simply an implementation of the case_eq tactic.  this code
  should be replaced by a call to the tactic but I don't know how to
  call it before it is defined. *)
let  mkCaseEq a  : tactic =
     (fun g ->
       let type_of_a = Tacmach.pf_type_of g a in
       tclTHENLIST
         [Hiddentac.h_generalize [mkApp(delayed_force refl_equal, [| type_of_a; a|])];
          (fun g2 ->
	    change_in_concl None
	     (Tacred.pattern_occs [Locus.OnlyOccurrences [1], a] (Tacmach.pf_env g2) Evd.empty (Tacmach.pf_concl g2))
		  g2);
	  simplest_case a] g);;


let case_eq_intros_rewrite x g =
  let n = nb_prod (Tacmach.pf_concl g) in
  (* Pp.msgnl (Printer.pr_lconstr x); *)
  tclTHENLIST [
      mkCaseEq x;
      (fun g -> 
	let n' = nb_prod (Tacmach.pf_concl g) in
	let h = fresh_id (Tacmach.pf_ids_of_hyps g) (id_of_string "heq") g in
	tclTHENLIST [ (tclDO (n'-n-1) intro);
		      Tacmach.introduction h;
		      rewrite_except h] g
      )
    ] g

let rec find_a_destructable_match t =
  match kind_of_term t with
    | Case (_,_,x,_) when closed0 x ->
	if isVar x then
	  (* TODO check there is no rel n. *)
	  raise (Found (Tacinterp.eval_tactic(<:tactic<destruct x>>)))
	else
	  (* let _ = Pp.msgnl (Printer.pr_lconstr x)  in *)
	  raise (Found (case_eq_intros_rewrite x))
    | _ -> iter_constr find_a_destructable_match t
	

let destauto t =
  try find_a_destructable_match t;
    error "No destructable match found"
  with Found tac -> tac

let destauto_in id g = 
  let ctype = Tacmach.pf_type_of g (mkVar id) in
(*  Pp.msgnl (Printer.pr_lconstr (mkVar id)); *)
(*  Pp.msgnl (Printer.pr_lconstr (ctype)); *)
  destauto ctype g

TACTIC EXTEND destauto
| [ "destauto" ] -> [ (fun g -> destauto (Tacmach.pf_concl g) g) ]
| [ "destauto" "in" hyp(id) ] -> [ destauto_in id ]
END


(* ********************************************************************* *)

TACTIC EXTEND constr_eq
| [ "constr_eq" constr(x) constr(y) ] -> [
    if eq_constr x y then tclIDTAC else tclFAIL 0 (str "Not equal") ]
END

TACTIC EXTEND is_evar
| [ "is_evar" constr(x) ] ->
    [ match kind_of_term x with
        | Evar _ -> tclIDTAC
        | _ -> tclFAIL 0 (str "Not an evar")
    ]
END

let rec has_evar x =
  match kind_of_term x with
    | Evar _ -> true
    | Rel _ | Var _ | Meta _ | Sort _ | Const _ | Ind _ | Construct _ ->
      false
    | Cast (t1, _, t2) | Prod (_, t1, t2) | Lambda (_, t1, t2) ->
      has_evar t1 || has_evar t2
    | LetIn (_, t1, t2, t3) ->
      has_evar t1 || has_evar t2 || has_evar t3
    | App (t1, ts) ->
      has_evar t1 || has_evar_array ts
    | Case (_, t1, t2, ts) ->
      has_evar t1 || has_evar t2 || has_evar_array ts
    | Fix ((_, tr)) | CoFix ((_, tr)) ->
      has_evar_prec tr
and has_evar_array x =
  array_exists has_evar x
and has_evar_prec (_, ts1, ts2) =
  array_exists has_evar ts1 || array_exists has_evar ts2

TACTIC EXTEND has_evar
| [ "has_evar" constr(x) ] ->
    [ if has_evar x then tclIDTAC else tclFAIL 0 (str "No evars") ]
END

TACTIC EXTEND is_hyp
| [ "is_var" constr(x) ] ->
  [ match kind_of_term x with
    | Var _ -> tclIDTAC
    | _ -> tclFAIL 0 (str "Not a variable or hypothesis") ]
END

TACTIC EXTEND is_fix
| [ "is_fix" constr(x) ] ->
  [ match kind_of_term x with
    | Fix _ -> Tacticals.tclIDTAC
    | _ -> Tacticals.tclFAIL 0 (Pp.str "not a fix definition") ]
END;;

(* Command to grab the evars left unresolved at the end of a proof. *)
(* spiwack: I put it in extratactics because it is somewhat tied with
   the semantics of the LCF-style tactics, hence with the classic tactic
   mode. *)
VERNAC COMMAND EXTEND GrabEvars
[ "Grab" "Existential" "Variables" ] ->
  [ let p = Proof_global.give_me_the_proof () in
    Proof.V82.grab_evars p ]
END