summaryrefslogtreecommitdiff
path: root/tactics/class_tactics.ml
blob: 1c15fa40bf95c054b02d4bb377e843d6817dc6da (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
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

open Pp
open Errors
open Util
open Names
open Term
open Termops
open Reduction
open Proof_type
open Tacticals
open Tacmach
open Tactics
open Patternops
open Clenv
open Typeclasses
open Globnames
open Evd
open Locus
open Misctypes
open Proofview.Notations
open Hints

(** Hint database named "typeclass_instances", now created directly in Auto *)

let typeclasses_debug = ref false
let typeclasses_depth = ref None

let typeclasses_modulo_eta = ref false
let set_typeclasses_modulo_eta d = (:=) typeclasses_modulo_eta d
let get_typeclasses_modulo_eta () = !typeclasses_modulo_eta

let typeclasses_dependency_order = ref false
let set_typeclasses_dependency_order d = (:=) typeclasses_dependency_order d
let get_typeclasses_dependency_order () = !typeclasses_dependency_order

open Goptions

let set_typeclasses_modulo_eta =
  declare_bool_option
    { optsync  = true;
      optdepr  = false;
      optname  = "do typeclass search modulo eta conversion";
      optkey   = ["Typeclasses";"Modulo";"Eta"];
      optread  = get_typeclasses_modulo_eta;
      optwrite = set_typeclasses_modulo_eta; }

let set_typeclasses_dependency_order =
  declare_bool_option
    { optsync  = true;
      optdepr  = false;
      optname  = "during typeclass resolution, solve instances according to their dependency order";
      optkey   = ["Typeclasses";"Dependency";"Order"];
      optread  = get_typeclasses_dependency_order;
      optwrite = set_typeclasses_dependency_order; }

(** We transform the evars that are concerned by this resolution
    (according to predicate p) into goals.
    Invariant: function p only manipulates and returns undefined evars *)

let top_sort evm undefs =
  let l' = ref [] in
  let tosee = ref undefs in
  let rec visit ev evi = 
    let evs = Evarutil.undefined_evars_of_evar_info evm evi in
      Evar.Set.iter (fun ev -> 
	if Evar.Map.mem ev !tosee then 
	  visit ev (Evar.Map.find ev !tosee)) evs;
      tosee := Evar.Map.remove ev !tosee;
      l' := ev :: !l';
  in
    while not (Evar.Map.is_empty !tosee) do
      let ev, evi = Evar.Map.min_binding !tosee in
	visit ev evi
    done;
    List.rev !l'

let evars_to_goals p evm =
  let goals = ref Evar.Map.empty in
  let map ev evi =
    let evi, goal = p evm ev evi in
    let () = if goal then goals := Evar.Map.add ev evi !goals in
    evi
  in
  let evm = Evd.raw_map_undefined map evm in
  if Evar.Map.is_empty !goals then None
  else Some (!goals, evm)

(** Typeclasses instance search tactic / eauto *)

open Auto

open Unification

let auto_core_unif_flags st freeze = {
  modulo_conv_on_closed_terms = Some st;
  use_metas_eagerly_in_conv_on_closed_terms = true;
  use_evars_eagerly_in_conv_on_closed_terms = false;
  modulo_delta = st;
  modulo_delta_types = st;
  check_applied_meta_types = false;
  use_pattern_unification = true;
  use_meta_bound_pattern_unification = true;
  frozen_evars = freeze;
  restrict_conv_on_strict_subterms = false; (* ? *)
  modulo_betaiota = true;
  modulo_eta = !typeclasses_modulo_eta;
}

let auto_unif_flags freeze st = 
  let fl = auto_core_unif_flags st freeze in
  { core_unify_flags = fl;
    merge_unify_flags = fl;
    subterm_unify_flags = fl;
    allow_K_in_toplevel_higher_order_unification = false;
    resolve_evars = false
}

let rec eq_constr_mod_evars x y =
  match kind_of_term x, kind_of_term y with
  | Evar (e1, l1), Evar (e2, l2) when not (Evar.equal e1 e2) -> true
  | _, _ -> compare_constr eq_constr_mod_evars x y

let progress_evars t =
  Proofview.Goal.nf_enter begin fun gl ->
    let concl = Proofview.Goal.concl gl in
    let check =
      Proofview.Goal.nf_enter begin fun gl' ->
        let newconcl = Proofview.Goal.concl gl' in
        if eq_constr_mod_evars concl newconcl
        then Tacticals.New.tclFAIL 0 (str"No progress made (modulo evars)")
        else Proofview.tclUNIT ()
      end
    in t <*> check
  end


let e_give_exact flags poly (c,clenv) gl =
  let c, gl =
    if poly then
      let clenv', subst = Clenv.refresh_undefined_univs clenv in
      let clenv' = connect_clenv gl clenv' in
      let c = Vars.subst_univs_level_constr subst c in
	c, {gl with sigma = clenv'.evd}
    else c, gl
  in
  let t1 = pf_type_of gl c in
    tclTHEN (Proofview.V82.of_tactic (Clenvtac.unify ~flags t1)) (exact_no_check c) gl

let unify_e_resolve poly flags (c,clenv) gls =
  let clenv' = if poly then fst (Clenv.refresh_undefined_univs clenv) else clenv in
  let clenv' = connect_clenv gls clenv' in
  let clenv' = clenv_unique_resolver ~flags clenv' gls in
  Proofview.V82.of_tactic (Clenvtac.clenv_refine true ~with_classes:false clenv') gls

let unify_resolve poly flags (c,clenv) gls =
  let clenv' = if poly then fst (Clenv.refresh_undefined_univs clenv) else clenv in
  let clenv' = connect_clenv gls clenv' in
  let clenv' = clenv_unique_resolver ~flags clenv' gls in
  Proofview.V82.of_tactic 
    (Clenvtac.clenv_refine false ~with_classes:false clenv') gls

let clenv_of_prods poly nprods (c, clenv) gls =
  if poly || Int.equal nprods 0 then Some clenv
  else
    let ty = pf_type_of gls c in
    let diff = nb_prod ty - nprods in
      if Pervasives.(>=) diff 0 then
        (* Was Some clenv... *)
	Some (mk_clenv_from_n gls (Some diff) (c,ty))
      else None

let with_prods nprods poly (c, clenv) f gls =
  match clenv_of_prods poly nprods (c, clenv) gls with
  | None -> tclFAIL 0 (str"Not enough premisses") gls
  | Some clenv' -> f (c, clenv') gls

(** Hack to properly solve dependent evars that are typeclasses *)

let rec e_trivial_fail_db db_list local_db goal =
  let tacl =
    Eauto.registered_e_assumption ::
    (tclTHEN (Proofview.V82.of_tactic Tactics.intro)
       (function g'->
	  let d = pf_last_hyp g' in
	  let hintl = make_resolve_hyp (pf_env g') (project g') d in
          (e_trivial_fail_db db_list
	      (Hint_db.add_list hintl local_db) g'))) ::
    (List.map (fun (x,_,_,_,_) -> x) 
     (e_trivial_resolve db_list local_db (project goal) (pf_concl goal)))
  in
  tclFIRST (List.map tclCOMPLETE tacl) goal

and e_my_find_search db_list local_db hdc complete sigma concl =
  let prods, concl = decompose_prod_assum concl in
  let nprods = List.length prods in
  let freeze = 
    try
      let cl = Typeclasses.class_info (fst hdc) in
	if cl.cl_strict then
	  Evd.evars_of_term concl
	else Evar.Set.empty
    with _ -> Evar.Set.empty
  in
  let hintl =
    List.map_append
      (fun db ->
	let tacs = 
	  if Hint_db.use_dn db then (* Using dnet *)
	    Hint_db.map_eauto hdc concl db
	  else Hint_db.map_existential hdc concl db
	in
	let flags = auto_unif_flags freeze (Hint_db.transparent_state db) in
	  List.map (fun x -> (flags, x)) tacs)
      (local_db::db_list)
  in
  let tac_of_hint =
    fun (flags, {pri = b; pat = p; poly = poly; code = t; name = name}) ->
      let tac =
	match t with
	  | Res_pf (term,cl) -> with_prods nprods poly (term,cl) (unify_resolve poly flags)
	  | ERes_pf (term,cl) -> with_prods nprods poly (term,cl) (unify_e_resolve poly flags)
	  | Give_exact c -> e_give_exact flags poly c
	  | Res_pf_THEN_trivial_fail (term,cl) ->
              tclTHEN (with_prods nprods poly (term,cl) (unify_e_resolve poly flags))
	        (if complete then tclIDTAC else e_trivial_fail_db db_list local_db)
	  | Unfold_nth c -> tclWEAK_PROGRESS (unfold_in_concl [AllOccurrences,c])
	  | Extern tacast ->
	    Proofview.V82.of_tactic (conclPattern concl p tacast)
      in
      let tac = if complete then tclCOMPLETE tac else tac in
	match t with
	| Extern _ -> (tac,b,true, name, lazy (pr_autotactic t))
	| _ ->
(* 	  let tac gl = with_pattern (pf_env gl) (project gl) flags p concl tac gl in *)
	    (tac,b,false, name, lazy (pr_autotactic t))
  in List.map tac_of_hint hintl

and e_trivial_resolve db_list local_db sigma concl =
  try
    e_my_find_search db_list local_db
     (decompose_app_bound concl) true sigma concl
  with Bound | Not_found -> []

let e_possible_resolve db_list local_db sigma concl =
  try
    e_my_find_search db_list local_db
      (decompose_app_bound concl) false sigma concl
  with Bound | Not_found -> []

let catchable = function
  | Refiner.FailError _ -> true
  | e -> Logic.catchable_exception e

let pr_ev evs ev = Printer.pr_constr_env (Goal.V82.env evs ev) evs (Evarutil.nf_evar evs (Goal.V82.concl evs ev))

let pr_depth l = prlist_with_sep (fun () -> str ".") int (List.rev l)

type autoinfo = { hints : hint_db; is_evar: existential_key option;
		  only_classes: bool; unique : bool;
		  auto_depth: int list; auto_last_tac: std_ppcmds Lazy.t;
		  auto_path : global_reference option list;
		  auto_cut : hints_path }
type autogoal = goal * autoinfo
type 'ans fk = unit -> 'ans
type ('a,'ans) sk = 'a -> 'ans fk -> 'ans
type 'a tac = { skft : 'ans. ('a,'ans) sk -> 'ans fk -> autogoal sigma -> 'ans }

type auto_result = autogoal list sigma

type atac = auto_result tac

(* Some utility types to avoid the need of -rectypes *)

type 'a optionk =
  | Nonek
  | Somek of 'a * 'a optionk fk

type ('a,'b) optionk2 =
  | Nonek2
  | Somek2 of 'a * 'b * ('a,'b) optionk2 fk

let make_resolve_hyp env sigma st flags only_classes pri (id, _, cty) =
  let cty = Evarutil.nf_evar sigma cty in
  let rec iscl env ty =
    let ctx, ar = decompose_prod_assum ty in
      match kind_of_term (fst (decompose_app ar)) with
      | Const (c,_) -> is_class (ConstRef c)
      | Ind (i,_) -> is_class (IndRef i)
      | _ ->
	  let env' = Environ.push_rel_context ctx env in
	  let ty' = whd_betadeltaiota env' ar in
	       if not (Term.eq_constr ty' ar) then iscl env' ty'
	       else false
  in
  let is_class = iscl env cty in
  let keep = not only_classes || is_class in
    if keep then
      let c = mkVar id in
      let name = PathHints [VarRef id] in
      let hints =
	if is_class then
	  let hints = build_subclasses ~check:false env sigma (VarRef id) None in
	    (List.map_append
	       (fun (path,pri, c) -> make_resolves env sigma ~name:(PathHints path)
		  (true,false,Flags.is_verbose()) pri false
		 (IsConstr (c,Univ.ContextSet.empty)))
	       hints)
	else []
      in
        (hints @ List.map_filter
	 (fun f -> try Some (f (c, cty, Univ.ContextSet.empty)) 
	   with Failure _ | UserError _ -> None)
	 [make_exact_entry ~name env sigma pri false; 
	  make_apply_entry ~name env sigma flags pri false])
    else []

let pf_filtered_hyps gls =
  Goal.V82.hyps gls.Evd.sigma (sig_it gls)

let make_hints g st only_classes sign =
  let paths, hintlist =
    List.fold_left
    (fun (paths, hints) hyp ->
      let consider =
	try let (_, b, t) = Global.lookup_named (pi1 hyp) in
	      (* Section variable, reindex only if the type changed *)
	      not (Term.eq_constr t (pi3 hyp))
	with Not_found -> true
     in
      if consider then 
	let path, hint =
	  PathEmpty, pf_apply make_resolve_hyp g st (true,false,false) only_classes None hyp
	in
	  (PathOr (paths, path), hint @ hints)
      else (paths, hints))
    (PathEmpty, []) sign
  in Hint_db.add_list hintlist (Hint_db.empty st true)

let make_autogoal_hints =
  let cache = ref (true, Environ.empty_named_context_val, 
		   Hint_db.empty full_transparent_state true) 
  in
    fun only_classes ?(st=full_transparent_state) g ->
      let sign = pf_filtered_hyps g in
      let (onlyc, sign', cached_hints) = !cache in
	if onlyc == only_classes && 
	  (sign == sign' || Environ.eq_named_context_val sign sign') then
	  cached_hints
	else
	  let hints = make_hints g st only_classes (Environ.named_context_of_val sign) in
	    cache := (only_classes, sign, hints); hints

let lift_tactic tac (f : goal list sigma -> autoinfo -> autogoal list sigma) : 'a tac =
  { skft = fun sk fk {it = gl,hints; sigma=s;} ->
    let res = try Some (tac {it=gl; sigma=s;})
              with e when catchable e -> None in
      match res with
      | Some gls -> sk (f gls hints) fk
      | None -> fk () }

let intro_tac : atac =
  lift_tactic (Proofview.V82.of_tactic Tactics.intro)
    (fun {it = gls; sigma = s} info ->
      let gls' =
	List.map (fun g' ->
	  let env = Goal.V82.env s g' in
	  let context = Environ.named_context_of_val (Goal.V82.hyps s g') in
	  let hint = make_resolve_hyp env s (Hint_db.transparent_state info.hints)
	    (true,false,false) info.only_classes None (List.hd context) in
	  let ldb = Hint_db.add_list hint info.hints in
	    (g', { info with is_evar = None; hints = ldb; auto_last_tac = lazy (str"intro") })) gls
      in {it = gls'; sigma = s;})

let normevars_tac : atac =
  { skft = fun sk fk {it = (gl, info); sigma = s;} ->
    let gl', sigma' = Goal.V82.nf_evar s gl in
    let info' = { info with auto_last_tac = lazy (str"normevars") } in
      sk {it = [gl', info']; sigma = sigma';} fk }

let or_tac (x : 'a tac) (y : 'a tac) : 'a tac =
  { skft = fun sk fk gls -> x.skft sk (fun () -> y.skft sk fk gls) gls }

let is_Prop env sigma concl =
  let ty = Retyping.get_type_of env sigma concl in
  match kind_of_term ty with
  | Sort (Prop Null) -> true
  | _ -> false

let is_unique env concl = 
  try 
    let (cl,u), args = dest_class_app env concl in
      cl.cl_unique
  with _ -> false

let needs_backtrack env evd oev concl =
  if Option.is_empty oev || is_Prop env evd concl then
    occur_existential concl
  else true

let hints_tac hints =
  { skft = fun sk fk {it = gl,info; sigma = s;} ->
      let env = Goal.V82.env s gl in
      let concl = Goal.V82.concl s gl in
      let tacgl = {it = gl; sigma = s;} in
      let poss = e_possible_resolve hints info.hints s concl in
      let unique = is_unique env concl in
      let rec aux i foundone = function
      | (tac, _, b, name, pp) :: tl ->
	let derivs = path_derivate info.auto_cut name in
	let res =
          try
	    if path_matches derivs [] then None else Some (tac tacgl)
	  with e when catchable e -> None
	in
	  (match res with
	  | None -> aux i foundone tl
	  | Some {it = gls; sigma = s';} ->
	    if !typeclasses_debug then
	      msg_debug (pr_depth (i :: info.auto_depth) ++ str": " ++ Lazy.force pp
			 ++ str" on" ++ spc () ++ pr_ev s gl);
	    let sgls =
	      evars_to_goals
		(fun evm ev evi ->
		  if Typeclasses.is_resolvable evi && not (Evd.is_undefined s ev) &&
		    (not info.only_classes || Typeclasses.is_class_evar evm evi)
		  then Typeclasses.mark_unresolvable evi, true
		  else evi, false) s'
	    in
	    let newgls, s' =
	      let gls' = List.map (fun g -> (None, g)) gls in
		match sgls with
		| None -> gls', s'
		| Some (evgls, s') ->
		  if not !typeclasses_dependency_order then
		    (gls' @ List.map (fun (ev,_) -> (Some ev, ev)) (Evar.Map.bindings evgls), s')
		  else 
 		    (* Reorder with dependent subgoals. *)
		    let evm = List.fold_left 
		      (fun acc g -> Evar.Map.add g (Evd.find_undefined s' g) acc) evgls gls in
		    let gls = top_sort s' evm in
		      (List.map (fun ev -> Some ev, ev) gls, s')
	    in
	    let gls' = List.map_i
	      (fun j (evar, g) ->
		let info =
		  { info with auto_depth = j :: i :: info.auto_depth; auto_last_tac = pp;
		    is_evar = evar;
		    hints =
		      if b && not (Environ.eq_named_context_val (Goal.V82.hyps s' g) 
				     (Goal.V82.hyps s' gl))
		      then make_autogoal_hints info.only_classes
			~st:(Hint_db.transparent_state info.hints) {it = g; sigma = s';}
		      else info.hints;
		    auto_cut = derivs }
		in g, info) 1 newgls in
	    let glsv = {it = gls'; sigma = s';} in
	    let fk' =
	      (fun () ->
		let do_backtrack =
		  if unique then occur_existential concl
		  else if info.unique then true
		  else if List.is_empty gls' then 
		    needs_backtrack env s' info.is_evar concl
		  else true
		in
		  if !typeclasses_debug then
		    msg_debug 
		      ((if do_backtrack then str"Backtracking after "
			else str "Not backtracking after ")
		       ++ Lazy.force pp);
		  if do_backtrack then aux (succ i) true tl
		  else fk ())
	    in
	      sk glsv fk')
      | [] ->
	if not foundone && !typeclasses_debug then
	  msg_debug (pr_depth info.auto_depth ++ str": no match for " ++
		       Printer.pr_constr_env (Goal.V82.env s gl) s concl ++
		       spc () ++ str ", " ++ int (List.length poss) ++ str" possibilities");
	fk ()
      in aux 1 false poss }

let then_list (second : atac) (sk : (auto_result, 'a) sk) : (auto_result, 'a) sk =
  let rec aux s (acc : autogoal list list) fk = function
    | (gl,info) :: gls ->
	(match info.is_evar with
	 | Some ev when Evd.is_defined s ev -> aux s acc fk gls
	 | _ ->
	     second.skft
	       (fun {it=gls';sigma=s'} fk' -> 
		 let fk'' =
		   if not info.unique && List.is_empty gls' &&
		     not (needs_backtrack (Goal.V82.env s gl) s
			    info.is_evar (Goal.V82.concl s gl))
		   then fk
		   else fk'
		 in
		   aux s' (gls'::acc) fk'' gls)
	       fk {it = (gl,info); sigma = s; })
    | [] -> Somek2 (List.rev acc, s, fk)
  in fun {it = gls; sigma = s; } fk ->
    let rec aux' = function
      | Nonek2 -> fk ()
      | Somek2 (res, s', fk') ->
	  let goals' = List.concat res in
	    sk {it = goals'; sigma = s'; } (fun () -> aux' (fk' ()))
    in aux' (aux s [] (fun () -> Nonek2) gls)

let then_tac (first : atac) (second : atac) : atac =
  { skft = fun sk fk -> first.skft (then_list second sk) fk }

let run_tac (t : 'a tac) (gl : autogoal sigma) : auto_result option =
  t.skft (fun x _ -> Some x) (fun _ -> None) gl

type run_list_res = auto_result optionk

let run_list_tac (t : 'a tac) p goals (gl : autogoal list sigma) : run_list_res =
  (then_list t (fun x fk -> Somek (x, fk)))
    gl
    (fun _ -> Nonek)

let fail_tac : atac =
  { skft = fun sk fk _ -> fk () }

let rec fix (t : 'a tac) : 'a tac =
  then_tac t { skft = fun sk fk -> (fix t).skft sk fk }

let rec fix_limit limit (t : 'a tac) : 'a tac =
  if Int.equal limit 0 then fail_tac
  else then_tac t { skft = fun sk fk -> (fix_limit (pred limit) t).skft sk fk }

let make_autogoal ?(only_classes=true) ?(unique=false) ?(st=full_transparent_state) cut ev g =
  let hints = make_autogoal_hints only_classes ~st g in
    (g.it, { hints = hints ; is_evar = ev; unique = unique;
	     only_classes = only_classes; auto_depth = []; auto_last_tac = lazy (str"none");
	     auto_path = []; auto_cut = cut })


let cut_of_hints h =
  List.fold_left (fun cut db -> PathOr (Hint_db.cut db, cut)) PathEmpty h

let make_autogoals ?(only_classes=true) ?(unique=false) 
    ?(st=full_transparent_state) hints gs evm' =
  let cut = cut_of_hints hints in
  { it = List.map_i (fun i g ->
    let (gl, auto) = make_autogoal ~only_classes ~unique 
      ~st cut (Some g) {it = g; sigma = evm'; } in
      (gl, { auto with auto_depth = [i]})) 1 gs; sigma = evm'; }

let get_result r =
  match r with
  | Nonek -> None
  | Somek (gls, fk) -> Some (gls.sigma,fk)

let run_on_evars ?(only_classes=true) ?(unique=false) ?(st=full_transparent_state) p evm hints tac =
  match evars_to_goals p evm with
  | None -> None (* This happens only because there's no evar having p *)
  | Some (goals, evm') ->
    let goals = 
      if !typeclasses_dependency_order then
	top_sort evm' goals
      else List.map (fun (ev, _) -> ev) (Evar.Map.bindings goals)
    in
    let res = run_list_tac tac p goals 
      (make_autogoals ~only_classes ~unique ~st hints goals evm') in
      match get_result res with
      | None -> raise Not_found
      | Some (evm', fk) -> 
	Some (evars_reset_evd ~with_conv_pbs:true ~with_univs:false evm' evm, fk)

let eauto_tac hints =
  then_tac normevars_tac (or_tac (hints_tac hints) intro_tac)

let eauto_tac ?limit hints =
  match limit with
  | None -> fix (eauto_tac hints)
  | Some limit -> fix_limit limit (eauto_tac hints)

let eauto ?(only_classes=true) ?st ?limit hints g =
  let gl = { it = make_autogoal ~only_classes ?st (cut_of_hints hints) None g; sigma = project g; } in
    match run_tac (eauto_tac ?limit hints) gl with
    | None -> raise Not_found
    | Some {it = goals; sigma = s; } ->
	{it = List.map fst goals; sigma = s;}

let real_eauto ?limit unique st hints p evd =
  let res =
    run_on_evars ~st ~unique p evd hints (eauto_tac ?limit hints)
  in
    match res with
    | None -> evd
    | Some (evd', fk) -> 
      if unique then
	(match get_result (fk ()) with
	| Some (evd'', fk') -> error "Typeclass resolution gives multiple solutions"
	| None -> evd')
      else evd'
    
let resolve_all_evars_once debug limit unique p evd =
  let db = searchtable_map typeclasses_db in
    real_eauto ?limit unique (Hint_db.transparent_state db) [db] p evd

(** We compute dependencies via a union-find algorithm.
    Beware of the imperative effects on the partition structure,
    it should not be shared, but only used locally. *)

module Intpart = Unionfind.Make(Evar.Set)(Evar.Map)

let deps_of_constraints cstrs evm p =
  List.iter (fun (_, _, x, y) ->
    let evx = Evarutil.undefined_evars_of_term evm x in
    let evy = Evarutil.undefined_evars_of_term evm y in
    Intpart.union_set (Evar.Set.union evx evy) p)
    cstrs

let evar_dependencies evm p =
  Evd.fold_undefined
    (fun ev evi _ ->
      let evars = Evar.Set.add ev (Evarutil.undefined_evars_of_evar_info evm evi)
      in Intpart.union_set evars p)
    evm ()

let resolve_one_typeclass env ?(sigma=Evd.empty) gl unique =
  let nc, gl, subst, _, _ = Evarutil.push_rel_context_to_named_context env gl in
  let (gl,t,sigma) =
    Goal.V82.mk_goal sigma nc gl Store.empty in
  let gls = { it = gl ; sigma = sigma; } in
  let hints = searchtable_map typeclasses_db in
  let gls' = eauto ?limit:!typeclasses_depth ~st:(Hint_db.transparent_state hints) [hints] gls in
  let evd = sig_sig gls' in
  let t' = let (ev, inst) = destEvar t in
    mkEvar (ev, Array.of_list subst)
  in
  let term = Evarutil.nf_evar evd t' in
    evd, term

let _ =
  Typeclasses.solve_instantiation_problem := 
    (fun x y z w -> resolve_one_typeclass x ~sigma:y z w)

(** [split_evars] returns groups of undefined evars according to dependencies *)

let split_evars evm =
  let p = Intpart.create () in
  evar_dependencies evm p;
  deps_of_constraints (snd (extract_all_conv_pbs evm)) evm p;
  Intpart.partition p

let is_inference_forced p evd ev =
  try
    let evi = Evd.find_undefined evd ev in
    if Typeclasses.is_resolvable evi && snd (p ev evi)
    then
      let (loc, k) = evar_source ev evd in
      match k with
	| Evar_kinds.ImplicitArg (_, _, b) -> b
	| Evar_kinds.QuestionMark _ -> false
	| _ -> true
    else true
  with Not_found -> assert false

let is_mandatory p comp evd =
  Evar.Set.exists (is_inference_forced p evd) comp

(** In case of unsatisfiable constraints, build a nice error message *)

let error_unresolvable env comp evd =
  let evd = Evarutil.nf_evar_map_undefined evd in
  let is_part ev = match comp with
  | None -> true
  | Some s -> Evar.Set.mem ev s
  in
  let fold ev evi (found, accu) =
    let ev_class = class_of_constr evi.evar_concl in
    if not (Option.is_empty ev_class) && is_part ev then
      (* focus on one instance if only one was searched for *)
      if not found then (true, Some ev)
      else (found, None)
    else (found, accu)
   in
  let (_, ev) = Evd.fold_undefined fold evd (true, None) in
    Pretype_errors.unsatisfiable_constraints
      (Evarutil.nf_env_evar evd env) evd ev comp

(** Check if an evar is concerned by the current resolution attempt,
    (and in particular is in the current component), and also update
    its evar_info.
    Invariant : this should only be applied to undefined evars,
    and return undefined evar_info *)

let select_and_update_evars p oevd in_comp evd ev evi =
  assert (evi.evar_body == Evar_empty);
  try
    let oevi = Evd.find_undefined oevd ev in
    if Typeclasses.is_resolvable oevi then
      Typeclasses.mark_unresolvable evi,
      (in_comp ev && p evd ev evi)
    else evi, false
  with Not_found ->
    Typeclasses.mark_unresolvable evi, p evd ev evi

(** Do we still have unresolved evars that should be resolved ? *)

let has_undefined p oevd evd =
  let check ev evi = snd (p oevd ev evi) in
  Evar.Map.exists check (Evd.undefined_map evd)

(** Revert the resolvability status of evars after resolution,
    potentially unprotecting some evars that were set unresolvable
    just for this call to resolution. *)

let revert_resolvability oevd evd =
  let map ev evi =
    try
      if not (Typeclasses.is_resolvable evi) then
        let evi' = Evd.find_undefined oevd ev in
        if Typeclasses.is_resolvable evi' then
          Typeclasses.mark_resolvable evi
        else evi
      else evi
    with Not_found -> evi
  in
  Evd.raw_map_undefined map evd

(** If [do_split] is [true], we try to separate the problem in
    several components and then solve them separately *)

exception Unresolved

let resolve_all_evars debug m unique env p oevd do_split fail =
  let split = if do_split then split_evars oevd else [Evar.Set.empty] in
  let in_comp comp ev = if do_split then Evar.Set.mem ev comp else true
  in
  let rec docomp evd = function
    | [] -> revert_resolvability oevd evd
    | comp :: comps ->
      let p = select_and_update_evars p oevd (in_comp comp) in
      try
	 let evd' = resolve_all_evars_once debug m unique p evd in
	 if has_undefined p oevd evd' then raise Unresolved;
	 docomp evd' comps
      with Unresolved | Not_found ->
	if fail && (not do_split || is_mandatory (p evd) comp evd)
	then (* Unable to satisfy the constraints. *)
          let comp = if do_split then Some comp else None in
	  error_unresolvable env comp evd
	else (* Best effort: do nothing on this component *)
	  docomp evd comps
  in docomp oevd split

let initial_select_evars filter =
  fun evd ev evi ->
    filter ev (snd evi.Evd.evar_source) &&
    Typeclasses.is_class_evar evd evi

let resolve_typeclass_evars debug m unique env evd filter split fail =
  let evd =
    try Evarconv.consider_remaining_unif_problems
      ~ts:(Typeclasses.classes_transparent_state ()) env evd
    with e when Errors.noncritical e -> evd
  in
    resolve_all_evars debug m unique env (initial_select_evars filter) evd split fail

let solve_inst debug depth env evd filter unique split fail =
  resolve_typeclass_evars debug depth unique env evd filter split fail

let _ =
  Typeclasses.solve_instantiations_problem :=
    solve_inst false !typeclasses_depth

let set_typeclasses_debug d = (:=) typeclasses_debug d;
  Typeclasses.solve_instantiations_problem := solve_inst d !typeclasses_depth

let get_typeclasses_debug () = !typeclasses_debug

let set_typeclasses_depth d = (:=) typeclasses_depth d;
  Typeclasses.solve_instantiations_problem := solve_inst !typeclasses_debug !typeclasses_depth

let get_typeclasses_depth () = !typeclasses_depth

open Goptions

let set_typeclasses_debug =
  declare_bool_option
    { optsync  = true;
      optdepr  = false;
      optname  = "debug output for typeclasses proof search";
      optkey   = ["Typeclasses";"Debug"];
      optread  = get_typeclasses_debug;
      optwrite = set_typeclasses_debug; }

let set_typeclasses_depth =
  declare_int_option
    { optsync  = true;
      optdepr  = false;
      optname  = "depth for typeclasses proof search";
      optkey   = ["Typeclasses";"Depth"];
      optread  = get_typeclasses_depth;
      optwrite = set_typeclasses_depth; }

let typeclasses_eauto ?(only_classes=false) ?(st=full_transparent_state) dbs gl =
  try
    let dbs = List.map_filter
      (fun db -> try Some (searchtable_map db)
        with e when Errors.noncritical e -> None)
      dbs
    in
    let st = match dbs with x :: _ -> Hint_db.transparent_state x | _ -> st in
      eauto ?limit:!typeclasses_depth ~only_classes ~st dbs gl
   with Not_found -> tclFAIL 0 (str" typeclasses eauto failed on: " ++ Printer.pr_goal gl) gl

(** Take the head of the arity of a constr.
    Used in the partial application tactic. *)

let rec head_of_constr t =
  let t = strip_outer_cast(collapse_appl t) in
    match kind_of_term t with
    | Prod (_,_,c2)  -> head_of_constr c2
    | LetIn (_,_,_,c2) -> head_of_constr c2
    | App (f,args)  -> head_of_constr f
    | _      -> t

let head_of_constr h c =
  let c = head_of_constr c in
  letin_tac None (Name h) c None Locusops.allHyps

let not_evar c = match kind_of_term c with
| Evar _ -> Tacticals.New.tclFAIL 0 (str"Evar")
| _ -> Proofview.tclUNIT ()

let is_ground c gl =
  if Evarutil.is_ground_term (project gl) c then tclIDTAC gl
  else tclFAIL 0 (str"Not ground") gl

let autoapply c i gl =
  let flags = auto_unif_flags Evar.Set.empty 
    (Hints.Hint_db.transparent_state (Hints.searchtable_map i)) in
  let cty = pf_type_of gl c in
  let ce = mk_clenv_from gl (c,cty) in
  unify_e_resolve false flags (c,ce) gl