package coq

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

Source file clenv.ml

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

open Pp
open CErrors
open Util
open Names
open Nameops
open Termops
open Constr
open Context
open Namegen
open Environ
open Evd
open EConstr
open Vars
open Reduction
open Reductionops
open Tacred
open Pretype_errors
open Evarutil
open Unification
open Tactypes
open Logic

(******************************************************************)
(* Clausal environments *)

type clausenv = {
  env      : env;
  evd      : evar_map;
  templval : constr freelisted;
  templtyp : constr freelisted;
  cache : Reductionops.meta_instance_subst;
}

let mk_clausenv env evd templval templtyp = {
  env; evd; templval; templtyp; cache = create_meta_instance_subst evd;
}

let update_clenv_evd clenv evd =
  mk_clausenv clenv.env evd clenv.templval clenv.templtyp

let cl_env ce = ce.env
let cl_sigma ce =  ce.evd

let clenv_term clenv c = meta_instance clenv.env clenv.cache c
let clenv_meta_type clenv mv =
  let ty =
    try Evd.meta_ftype clenv.evd mv
    with Not_found -> anomaly (str "unknown meta ?" ++ str (Nameops.string_of_meta mv) ++ str ".") in
  meta_instance clenv.env clenv.cache ty
let clenv_value clenv = meta_instance clenv.env clenv.cache clenv.templval
let clenv_type clenv = meta_instance clenv.env clenv.cache clenv.templtyp

let clenv_hnf_constr ce t = hnf_constr (cl_env ce) (cl_sigma ce) t

let clenv_get_type_of ce c = Retyping.get_type_of (cl_env ce) (cl_sigma ce) c

exception NotExtensibleClause

let clenv_push_prod cl =
  let typ = whd_all (cl_env cl) (cl_sigma cl) (clenv_type cl) in
  let rec clrec typ = match EConstr.kind cl.evd typ with
    | Cast (t,_,_) -> clrec t
    | Prod (na,t,u) ->
        let mv = new_meta () in
        let dep = not (noccurn (cl_sigma cl) 1 u) in
        let na' = if dep then na.binder_name else Anonymous in
        let e' = meta_declare mv t ~name:na' cl.evd in
        let concl = if dep then subst1 (mkMeta mv) u else u in
        let def = applist (cl.templval.rebus,[mkMeta mv]) in
        { templval = mk_freelisted def;
          templtyp = mk_freelisted concl;
          evd = e';
          env = cl.env;
          cache = create_meta_instance_subst e' }
    | _ -> raise NotExtensibleClause
  in clrec typ

(* Instantiate the first [bound] products of [t] with metas (all products if
   [bound] is [None]; unfold local defs *)

(** [clenv_environments sigma n t] returns [sigma',lmeta,ccl] where
   [lmetas] is a list of metas to be applied to a proof of [t] so that
   it produces the unification pattern [ccl]; [sigma'] is [sigma]
   extended with [lmetas]; if [n] is defined, it limits the size of
   the list even if [ccl] is still a product; otherwise, it stops when
   [ccl] is not a product; example: if [t] is [forall x y, x=y -> y=x]
   and [n] is [None], then [lmetas] is [Meta n1;Meta n2;Meta n3] and
   [ccl] is [Meta n1=Meta n2]; if [n] is [Some 1], [lmetas] is [Meta n1]
   and [ccl] is [forall y, Meta n1=y -> y=Meta n1] *)

let clenv_environments evd bound t =
  let open EConstr in
  let open Vars in
  let rec clrec (e,metas) n t =
    match n, EConstr.kind evd t with
      | (Some 0, _) -> (e, List.rev metas, t)
      | (n, Cast (t,_,_)) -> clrec (e,metas) n t
      | (n, Prod (na,t1,t2)) ->
          let mv = new_meta () in
          let dep = not (noccurn evd 1 t2) in
          let na' = if dep then na.binder_name else Anonymous in
          let e' = meta_declare mv t1 ~name:na' e in
          clrec (e', (mkMeta mv)::metas) (Option.map ((+) (-1)) n)
            (if dep then (subst1 (mkMeta mv) t2) else t2)
      | (n, LetIn (na,b,_,t)) -> clrec (e,metas) n (subst1 b t)
      | (n, _) -> (e, List.rev metas, t)
  in
  clrec (evd,[]) bound t

let mk_clenv_from_env env sigma n (c,cty) =
  let evd = clear_metas sigma in
  let (evd,args,concl) = clenv_environments evd n cty in
  { templval = mk_freelisted (applist (c,args));
    templtyp = mk_freelisted concl;
    evd = evd;
    env = env;
    cache = create_meta_instance_subst evd }

let mk_clenv_from_n gls n (c,cty) =
  let env = Proofview.Goal.env gls in
  let sigma = Tacmach.New.project gls in
  mk_clenv_from_env env sigma n (c, cty)

let mk_clenv_from gls = mk_clenv_from_n gls None

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

(* [mentions clenv mv0 mv1] is true if mv1 is defined and mentions
 * mv0, or if one of the free vars on mv1's freelist mentions
 * mv0 *)

let mentions clenv mv0 =
  let rec menrec mv1 =
    Int.equal mv0 mv1 ||
    let mlist =
      try match meta_opt_fvalue clenv.evd mv1 with
      | Some (b,_) -> b.freemetas
      | None -> Metaset.empty
      with Not_found -> Metaset.empty in
    Metaset.exists menrec mlist
  in menrec

let error_incompatible_inst clenv mv  =
  let na = meta_name clenv.evd mv in
  match na with
      Name id ->
        user_err ~hdr:"clenv_assign"
          (str "An incompatible instantiation has already been found for " ++
           Id.print id)
    | _ ->
        anomaly ~label:"clenv_assign" (Pp.str "non dependent metavar already assigned.")

(* TODO: replace by clenv_unify (mkMeta mv) rhs ? *)
let clenv_assign mv rhs clenv =
  let rhs_fls = mk_freelisted rhs in
  if Metaset.exists (mentions clenv mv) rhs_fls.freemetas then
    user_err Pp.(str "clenv_assign: circularity in unification");
  try
    if meta_defined clenv.evd mv then
      if not (EConstr.eq_constr clenv.evd (fst (meta_fvalue clenv.evd mv)).rebus rhs) then
        error_incompatible_inst clenv mv
      else
        clenv
    else
      let st = (Conv,TypeNotProcessed) in
      update_clenv_evd clenv (meta_assign mv (rhs_fls.rebus,st) clenv.evd)
  with Not_found ->
    user_err Pp.(str "clenv_assign: undefined meta")



(* [clenv_dependent hyps_only clenv]
 * returns a list of the metavars which appear in the template of clenv,
 * and which are dependent, This is computed by taking the metavars of the
 * template in right-to-left order, and collecting the metavars which appear
 * in their types, and adding in all the metavars appearing in the
 * type of clenv.
 * If [hyps_only] then metavariables occurring in the concl are _excluded_
 * If [iter] is also set then all metavariables *recursively* occurring
 * in the concl are _excluded_

   Details of the strategies used for computing the set of unresolved
   dependent metavariables

   We typically have a clause of the form

   lem(?T:Type,?T,?U:Type,?V:Type,?x:?T,?y:?U,?z:?V,?H:hyp(?x,?z)) :concl(?y,?z)

   Then, we compute:
   A  = the set of all unresolved metas
   C  = the set of metas occurring in concl (here ?y, ?z)
   C* = the recursive closure of C wrt types (here ?y, ?z, ?U, ?V)
   D  = the set of metas occurring in a type of meta (here ?x, ?T, ?z, ?U, ?V)
   NL = the set of duplicated metas even if non dependent (here ?T)
       (we make the assumption that duplicated metas have internal dependencies)

   Then, for the "apply"-style tactic (hyps_only), missing metas are
     A inter ((D minus C) union NL)

   for the optimized "apply"-style tactic (taking in care, f_equal style
   lemma, from 2/8/10, Coq > 8.3), missing metas are
     A inter (( D minus C* ) union NL)

   for the "elim"-style tactic, missing metas are
     A inter (D union C union NL)

   In any case, we respect the order given in A.
*)

let clenv_metas_in_type_of_meta clenv mv =
  (mk_freelisted (meta_instance clenv.env clenv.cache (meta_ftype clenv.evd mv))).freemetas

let dependent_in_type_of_metas clenv mvs =
  List.fold_right
    (fun mv -> Metaset.union (clenv_metas_in_type_of_meta clenv mv))
    mvs Metaset.empty

let dependent_closure clenv mvs =
  let rec aux mvs acc =
    Metaset.fold
      (fun mv deps ->
        let metas_of_meta_type = clenv_metas_in_type_of_meta clenv mv in
        aux metas_of_meta_type (Metaset.union deps metas_of_meta_type))
      mvs acc in
  aux mvs mvs

let clenv_dependent_gen hyps_only ?(iter=true) clenv =
  let all_undefined = undefined_metas clenv.evd in
  let deps_in_concl = (mk_freelisted (clenv_type clenv)).freemetas in
  let deps_in_hyps = dependent_in_type_of_metas clenv all_undefined in
  let deps_in_concl =
    if hyps_only && iter then dependent_closure clenv deps_in_concl
    else deps_in_concl in
  List.filter
    (fun mv ->
      if hyps_only then
        Metaset.mem mv deps_in_hyps && not (Metaset.mem mv deps_in_concl)
      else
        Metaset.mem mv deps_in_hyps || Metaset.mem mv deps_in_concl)
    all_undefined

let clenv_missing ce = clenv_dependent_gen true ce
let clenv_dependent ce = clenv_dependent_gen false ce

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

(* Instantiate metas that create beta/iota redexes *)

let meta_reducible_instance env evd b =
  let fm = b.freemetas in
  let fold mv accu =
    let fvalue = try meta_opt_fvalue evd mv with Not_found -> None in
    match fvalue with
    | None -> accu
    | Some (g, (_, s)) -> Metamap.add mv (g.rebus, s) accu
  in
  let metas = Metaset.fold fold fm Metamap.empty in
  let rec irec u =
    let u = whd_betaiota env Evd.empty u (* FIXME *) in
    match EConstr.kind evd u with
    | Case (ci,u,pms,p,iv,c,bl) when EConstr.isMeta evd (strip_outer_cast evd c) ->
        let m = destMeta evd (strip_outer_cast evd c) in
        (match
          try
            let g, s = Metamap.find m metas in
            let is_coerce = match s with CoerceToType -> true | _ -> false in
            if isConstruct evd g || not is_coerce then Some g else None
          with Not_found -> None
          with
            | Some g -> irec (mkCase (ci,u,pms,p,iv,g,bl))
            | None ->
              let on_ctx (na, c) = (na, irec c) in
              mkCase (ci,u,Array.map irec pms,on_ctx p,iv,c,Array.map on_ctx bl))
    | App (f,l) when EConstr.isMeta evd (strip_outer_cast evd f) ->
        let m = destMeta evd (strip_outer_cast evd f) in
        (match
          try
            let g, s = Metamap.find m metas in
            let is_coerce = match s with CoerceToType -> true | _ -> false in
            if isLambda evd g || not is_coerce then Some g else None
          with Not_found -> None
         with
           | Some g -> irec (mkApp (g,l))
           | None -> mkApp (f,Array.map irec l))
    | Meta m ->
        (try let g, s = Metamap.find m metas in
          let is_coerce = match s with CoerceToType -> true | _ -> false in
          if not is_coerce then irec g else u
         with Not_found -> u)
    | Proj (p,c) when isMeta evd c || isCast evd c && isMeta evd (pi1 (destCast evd c)) (* What if two nested casts? *) ->
      let m = try destMeta evd c with DestKO -> destMeta evd (pi1 (destCast evd c)) (* idem *) in
          (match
          try
            let g, s = Metamap.find m metas in
            let is_coerce = match s with CoerceToType -> true | _ -> false in
            if isConstruct evd g || not is_coerce then Some g else None
          with Not_found -> None
          with
            | Some g -> irec (mkProj (p,g))
            | None -> mkProj (p,c))
    | _ -> EConstr.map evd irec u
  in
  if Metaset.is_empty fm then (* nf_betaiota? *) b.rebus
  else irec b.rebus

let clenv_unify ?(flags=default_unify_flags ()) cv_pb t1 t2 clenv =
  update_clenv_evd clenv (w_unify ~flags clenv.env clenv.evd cv_pb t1 t2)

let clenv_unify_meta_types ?(flags=default_unify_flags ()) clenv =
  update_clenv_evd clenv (w_unify_meta_types ~flags:flags clenv.env clenv.evd)

let clenv_unique_resolver_gen ?(flags=default_unify_flags ()) clenv concl =
  if isMeta clenv.evd (fst (decompose_app_vect clenv.evd (whd_nored clenv.env clenv.evd clenv.templtyp.rebus))) then
    clenv_unify CUMUL ~flags (clenv_type clenv) concl
      (clenv_unify_meta_types ~flags clenv)
  else
    clenv_unify CUMUL ~flags
      (meta_reducible_instance clenv.env clenv.evd clenv.templtyp) concl clenv

let clenv_unique_resolver ?flags clenv gl =
  let concl = Proofview.Goal.concl gl in
  clenv_unique_resolver_gen ?flags clenv concl

let adjust_meta_source evd mv = function
  | loc,Evar_kinds.VarInstance id ->
    let rec match_name c l =
      match EConstr.kind evd c, l with
      | Lambda ({binder_name=Name id},_,c), a::l when EConstr.eq_constr evd a (mkMeta mv) -> Some id
      | Lambda (_,_,c), a::l -> match_name c l
      | _ -> None in
    (* This is very ad hoc code so that an evar inherits the name of the binder
       in situations like "ex_intro (fun x => P) ?ev p" *)
    let f = function (mv',(Cltyp (_,t) | Clval (_,_,t))) ->
      if Metaset.mem mv t.freemetas then
        let f,l = decompose_app evd t.rebus in
        match EConstr.kind evd f with
        | Meta mv'' ->
          (match meta_opt_fvalue evd mv'' with
          | Some (c,_) -> match_name c.rebus l
          | None -> None)
        | _ -> None
      else None in
    let id = try List.find_map f (Evd.meta_list evd) with Not_found -> id in
    loc,Evar_kinds.VarInstance id
  | src -> src

(* [clenv_pose_metas_as_evars clenv dep_mvs]
 * For each dependent evar in the clause-env which does not have a value,
 * pose a value for it by constructing a fresh evar.  We do this in
 * left-to-right order, so that every evar's type is always closed w.r.t.
 * metas.

 * Node added 14/4/08 [HH]: before this date, evars were collected in
   clenv_dependent by collect_metas in the fold_constr order which is
   (almost) the left-to-right order of dependencies in term. However,
   due to K-redexes, collect_metas was sometimes missing some metas.
   The call to collect_metas has been replaced by a call to
   undefined_metas, but then the order was the one of definition of
   the metas (numbers in increasing order) which is _not_ the
   dependency order when a clenv_fchain occurs (because clenv_fchain
   plugs a term with a list of consecutive metas in place of a - a priori -
   arbitrary metavariable belonging to another sequence of consecutive metas:
   e.g., clenv_fchain may plug (H ?1 ?2) at the position ?6 of
   (nat_ind ?3 ?4 ?5 ?6), leading to a dependency order 3<4<5<1<2).
   To ensure the dependency order, we check that the type of each meta
   to pose is already meta-free, otherwise we postpone the transformation,
   hoping that no cycle may happen.

   Another approach could have been to use decimal numbers for metas so that
   in the example above, (H ?1 ?2) would have been renumbered (H ?6.1 ?6.2)
   then making the numeric order match the dependency order.
*)

let clenv_pose_metas_as_evars clenv dep_mvs =
  let rec fold clenv = function
  | [] -> clenv
  | mv::mvs ->
      let ty = clenv_meta_type clenv mv in
      (* Postpone the evar-ization if dependent on another meta *)
      (* This assumes no cycle in the dependencies - is it correct ? *)
      if occur_meta clenv.evd ty then fold clenv (mvs@[mv])
      else
        let src = evar_source_of_meta mv clenv.evd in
        let src = adjust_meta_source clenv.evd mv src in
        let evd = clenv.evd in
        let (evd, evar) = new_evar (cl_env clenv) evd ~src ty in
        let clenv = clenv_assign mv evar {clenv with evd=evd} in
        fold clenv mvs in
  fold clenv dep_mvs

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

(* [clenv_fchain mv clenv clenv']
 *
 * Resolves the value of "mv" (which must be undefined) in clenv to be
 * the template of clenv' be the value "c", applied to "n" fresh
 * metavars, whose types are chosen by destructing "clf", which should
 * be a clausale forme generated from the type of "c".  The process of
 * resolution can cause unification of already-existing metavars, and
 * of the fresh ones which get created.  This operation is a composite
 * of operations which pose new metavars, perform unification on
 * terms, and make bindings.

   Otherwise said, from

     [clenv] = [env;sigma;metas |- c:T]
     [clenv'] = [env';sigma';metas' |- d:U]
     [mv] = [mi] of type [Ti] in [metas]

   then, if the unification of [Ti] and [U] produces map [rho], the
   chaining is [env';sigma';rho'(metas),rho(metas') |- c:rho'(T)] for
   [rho'] being [rho;mi:=d].

   In particular, it assumes that [env'] and [sigma'] extend [env] and [sigma].
*)

let fchain_flags () =
  { (default_unify_flags ()) with
    allow_K_in_toplevel_higher_order_unification = true }

let clenv_fchain ?with_univs ?(flags=fchain_flags ()) mv clenv nextclenv =
  (* Add the metavars of [nextclenv] to [clenv], with their name-environment *)
  let evd = meta_merge ?with_univs nextclenv.evd clenv.evd in
  let clenv' =
    { templval = clenv.templval;
      templtyp = clenv.templtyp;
      evd;
      env = nextclenv.env;
      cache = create_meta_instance_subst evd } in
  (* unify the type of the template of [nextclenv] with the type of [mv] *)
  let clenv'' =
    clenv_unify ~flags CUMUL
      (clenv_term clenv' nextclenv.templtyp)
      (clenv_meta_type clenv' mv)
      clenv' in
  (* assign the metavar *)
  let clenv''' =
    clenv_assign mv (clenv_term clenv' nextclenv.templval) clenv''
  in
  clenv'''

(***************************************************************)
(* Bindings *)

(* [clenv_independent clenv]
 * returns a list of metavariables which appear in the term cval,
 * and which are not dependent.  That is, they do not appear in
 * the types of other metavars which are in cval, nor in the type
 * of cval, ctyp. *)

let clenv_independent clenv =
  let mvs = collect_metas clenv.evd (clenv_value clenv) in
  let ctyp_mvs = (mk_freelisted (clenv_type clenv)).freemetas in
  let deps = Metaset.union (dependent_in_type_of_metas clenv mvs) ctyp_mvs in
  List.filter (fun mv -> not (Metaset.mem mv deps)) mvs

let qhyp_eq h1 h2 = match h1, h2 with
| NamedHyp n1, NamedHyp n2 -> Id.equal n1 n2
| AnonHyp i1, AnonHyp i2 -> Int.equal i1 i2
| _ -> false

let check_bindings bl =
  match List.duplicates qhyp_eq (List.map (fun {CAst.v=x} -> fst x) bl) with
    | NamedHyp s :: _ ->
        user_err
          (str "The variable " ++ Id.print s ++
           str " occurs more than once in binding list.");
    | AnonHyp n :: _ ->
        user_err
          (str "The position " ++ int n ++
           str " occurs more than once in binding list.")
    | [] -> ()

let explain_no_such_bound_variable evd id =
  let fold l (n, clb) =
    let na = match clb with
    | Cltyp (na, _) -> na
    | Clval (na, _, _) -> na
    in
    if na != Anonymous then Name.get_id na :: l else l
  in
  let mvl = List.fold_left fold [] (Evd.meta_list evd) in
  user_err ~hdr:"Evd.meta_with_name"
    (str"No such bound variable " ++ Id.print id ++
     (if mvl == [] then str " (no bound variables at all in the expression)."
      else
        (str" (possible name" ++
         str (if List.length mvl == 1 then " is: " else "s are: ") ++
         pr_enum Id.print mvl ++ str").")))

let meta_with_name evd id =
  let na = Name id in
  let fold (l1, l2 as l) (n, clb) =
    let (na',def) = match clb with
    | Cltyp (na, _) -> (na, false)
    | Clval (na, _, _) -> (na, true)
    in
    if Name.equal na na' then if def then (n::l1,l2) else (n::l1,n::l2)
    else l
  in
  let (mvl, mvnodef) = List.fold_left fold ([], []) (Evd.meta_list evd) in
  match mvnodef, mvl with
    | _,[]  ->
      explain_no_such_bound_variable evd id
    | ([n],_|_,[n]) ->
        n
    | _  ->
        user_err ~hdr:"Evd.meta_with_name"
          (str "Binder name \"" ++ Id.print id ++
           strbrk "\" occurs more than once in clause.")

let meta_of_binder clause loc mvs = function
  | NamedHyp s -> meta_with_name clause.evd s
  | AnonHyp n ->
      try List.nth mvs (n-1)
      with (Failure _|Invalid_argument _) ->
        user_err  (str "No such binder.")

let error_already_defined b =
  match b with
    | NamedHyp id ->
        user_err
          (str "Binder name \"" ++ Id.print id ++
           str"\" already defined with incompatible value.")
    | AnonHyp n ->
        anomaly
          (str "Position " ++ int n ++ str" already defined.")

let clenv_unify_binding_type clenv c t u =
  if isMeta clenv.evd (fst (decompose_app_vect clenv.evd (whd_nored clenv.env clenv.evd u))) then
    (* Not enough information to know if some subtyping is needed *)
    CoerceToType, clenv, c
  else
    (* Enough information so as to try a coercion now *)
    try
      let evd,c = w_coerce_to_type (cl_env clenv) clenv.evd c t u in
      TypeProcessed, { clenv with evd = evd }, c
    with
      | PretypeError (_,_,ActualTypeNotCoercible (_,_,
          (NotClean _ | ConversionFailed _))) as e ->
          raise e
      | e when precatchable_exception e ->
          TypeNotProcessed, clenv, c

let clenv_assign_binding clenv k c =
  let k_typ = clenv_hnf_constr clenv (clenv_meta_type clenv k) in
  let c_typ = nf_betaiota clenv.env clenv.evd (clenv_get_type_of clenv c) in
  let status,clenv',c = clenv_unify_binding_type clenv c c_typ k_typ in
  update_clenv_evd clenv' (meta_assign k (c,(Conv,status)) clenv'.evd)

let clenv_match_args bl clenv =
  if List.is_empty bl then
    clenv
  else
    let mvs = clenv_independent clenv in
    check_bindings bl;
    List.fold_left
      (fun clenv {CAst.loc;v=(b,c)} ->
        let k = meta_of_binder clenv loc mvs b in
        if meta_defined clenv.evd k then
          if EConstr.eq_constr clenv.evd (fst (meta_fvalue clenv.evd k)).rebus c then clenv
          else error_already_defined b
        else
          clenv_assign_binding clenv k c)
      clenv bl

exception NoSuchBinding

let clenv_constrain_last_binding c clenv =
  let all_mvs = collect_metas clenv.evd clenv.templval.rebus in
  let k = try List.last all_mvs with Failure _ -> raise NoSuchBinding in
  clenv_assign_binding clenv k c

let error_not_right_number_missing_arguments n =
  user_err
    (strbrk "Not the right number of missing arguments (expected " ++
      int n ++ str ").")

let clenv_constrain_dep_args hyps_only bl clenv =
  if List.is_empty bl then
    clenv
  else
    let occlist = clenv_dependent_gen hyps_only clenv in
    if Int.equal (List.length occlist) (List.length bl) then
      List.fold_left2 clenv_assign_binding clenv occlist bl
    else
      if hyps_only then
        (* Tolerance for compatibility <= 8.3 *)
        let occlist' = clenv_dependent_gen hyps_only ~iter:false clenv in
        if Int.equal (List.length occlist') (List.length bl) then
          List.fold_left2 clenv_assign_binding clenv occlist' bl
        else
          error_not_right_number_missing_arguments (List.length occlist)
      else
        error_not_right_number_missing_arguments (List.length occlist)


(* This function put casts around metavariables whose type could not be
 * inferred by the refiner, that is head of applications, predicates and
 * subject of Cases.
 * Does check that the casted type is closed. Anyway, the refiner would
 * fail in this case... *)

let clenv_cast_meta clenv =
  let rec crec u =
    match EConstr.kind clenv.evd u with
      | App _ | Case _ -> crec_hd u
      | Cast (c,_,_) when isMeta clenv.evd c -> u
      | Proj (p, c) -> mkProj (p, crec_hd c)
      | _  -> EConstr.map clenv.evd crec u

  and crec_hd u =
    match EConstr.kind clenv.evd (strip_outer_cast clenv.evd u) with
      | Meta mv ->
          (try
            let b = Typing.meta_type clenv.env clenv.evd mv in
            assert (not (occur_meta clenv.evd b));
            if occur_meta clenv.evd b then u
            else mkCast (mkMeta mv, DEFAULTcast, b)
          with Not_found -> u)
      | App(f,args) -> mkApp (crec_hd f, Array.map crec args)
      | Case(ci,u,pms,p,iv,c,br) ->
          (* FIXME: we only change c because [p] is always a lambda and [br] is
             most of the time??? *)
          mkCase (ci, u, pms, p, iv, crec_hd c, br)
      | Proj (p, c) -> mkProj (p, crec_hd c)
      | _ -> u
  in
  crec

let clenv_pose_dependent_evars ?(with_evars=false) clenv =
  let dep_mvs = clenv_dependent clenv in
  let env, sigma = clenv.env, clenv.evd in
  if not (List.is_empty dep_mvs) && not with_evars then
    raise
      (RefinerError (env, sigma, UnresolvedBindings (List.map (meta_name clenv.evd) dep_mvs)));
  clenv_pose_metas_as_evars clenv dep_mvs

let clenv_refine ?(with_evars=false) ?(with_classes=true) clenv =
  Proofview.Goal.enter begin fun gl ->
  let clenv = clenv_pose_dependent_evars ~with_evars clenv in
  let evd' =
    if with_classes then
      let evd' =
        Typeclasses.resolve_typeclasses ~filter:Typeclasses.all_evars
          ~fail:(not with_evars) clenv.env clenv.evd
      in
      (* After an apply, all the subgoals including those dependent shelved ones are in
         the hands of the user and resolution won't be called implicitely on them. *)
      Typeclasses.make_unresolvables (fun x -> true) evd'
    else clenv.evd
  in
  let clenv = update_clenv_evd clenv evd' in
  Proofview.tclTHEN
    (Proofview.Unsafe.tclEVARS (Evd.clear_metas evd'))
    (refiner ~check:false EConstr.Unsafe.(to_constr (clenv_cast_meta clenv (clenv_value clenv))))
  end

open Unification

let dft = default_unify_flags

let res_pf ?with_evars ?(with_classes=true) ?(flags=dft ()) clenv =
  Proofview.Goal.enter begin fun gl ->
    let clenv = clenv_unique_resolver ~flags clenv gl in
    clenv_refine ?with_evars ~with_classes clenv
  end

(* [unifyTerms] et [unify] ne semble pas gérer les Meta, en
   particulier ne semblent pas vérifier que des instances différentes
   d'une même Meta sont compatibles. D'ailleurs le "fst" jette les metas
   provenant de w_Unify. (Utilisé seulement dans prolog.ml) *)

let fail_quick_core_unif_flags = {
  modulo_conv_on_closed_terms = Some TransparentState.full;
  use_metas_eagerly_in_conv_on_closed_terms = false;
  use_evars_eagerly_in_conv_on_closed_terms = false;
  modulo_delta = TransparentState.empty;
  modulo_delta_types = TransparentState.full;
  check_applied_meta_types = false;
  use_pattern_unification = false;
  use_meta_bound_pattern_unification = true; (* ? *)
  allowed_evars = Evarsolve.AllowedEvars.all;
  restrict_conv_on_strict_subterms = false; (* ? *)
  modulo_betaiota = false;
  modulo_eta = true;
}

let fail_quick_unif_flags = {
  core_unify_flags = fail_quick_core_unif_flags;
  merge_unify_flags = fail_quick_core_unif_flags;
  subterm_unify_flags = fail_quick_core_unif_flags;
  allow_K_in_toplevel_higher_order_unification = false;
  resolve_evars = false
}

(* let unifyTerms m n = walking (fun wc -> fst (w_Unify CONV m n [] wc)) *)
let unify ?(flags=fail_quick_unif_flags) m =
  Proofview.Goal.enter begin fun gl ->
    let env = Tacmach.New.pf_env gl in
    let n = Tacmach.New.pf_concl gl in
    let evd = clear_metas (Tacmach.New.project gl) in
    try
      let evd' = w_unify env evd CONV ~flags m n in
        Proofview.Unsafe.tclEVARSADVANCE evd'
    with e when CErrors.noncritical e ->
      let info = Exninfo.reify () in
      Proofview.tclZERO ~info e
  end

(****************************************************************)
(* Clausal environment for an application *)

let make_clenv_binding_gen hyps_only n env sigma (c,t) = function
  | ImplicitBindings largs ->
      let clause = mk_clenv_from_env env sigma n (c,t) in
      clenv_constrain_dep_args hyps_only largs clause
  | ExplicitBindings lbind ->
      let t = rename_bound_vars_as_displayed sigma Id.Set.empty [] t in
      let clause = mk_clenv_from_env env sigma n
        (c, t)
      in clenv_match_args lbind clause
  | NoBindings ->
      mk_clenv_from_env env sigma n (c,t)

let make_clenv_binding_apply env sigma n = make_clenv_binding_gen true n env sigma
let make_clenv_binding env sigma = make_clenv_binding_gen false None env sigma

(****************************************************************)
(* Pretty-print *)

let pr_clenv clenv =
  h
    (str"TEMPL: " ++ Termops.Internal.print_constr_env clenv.env clenv.evd clenv.templval.rebus ++
     str" : " ++ Termops.Internal.print_constr_env clenv.env clenv.evd clenv.templtyp.rebus ++ fnl () ++
     pr_evar_map (Some 2) clenv.env clenv.evd)

(****************************************************************)
(** Evar version of mk_clenv *)

type hole = {
  hole_evar : EConstr.constr;
  hole_type : EConstr.types;
  hole_deps  : bool;
  hole_name : Name.t;
}

type clause = {
  cl_holes : hole list;
  cl_concl : EConstr.types;
}

let make_evar_clause env sigma ?len t =
  let open EConstr in
  let open Vars in
  let bound = match len with
  | None -> -1
  | Some n -> assert (0 <= n); n
  in
  (* FIXME: do the renaming online *)
  let t = rename_bound_vars_as_displayed sigma Id.Set.empty [] t in
  let rec clrec (sigma, holes) inst n t =
    if n = 0 then (sigma, holes, t)
    else match EConstr.kind sigma t with
    | Cast (t, _, _) -> clrec (sigma, holes) inst n t
    | Prod (na, t1, t2) ->
      (* Share the evar instances as we are living in the same context *)
      let inst, ctx, args, subst = match inst with
      | None ->
        (* Dummy type *)
        let ctx, _, args, subst = push_rel_context_to_named_context env sigma mkProp in
        Some (ctx, args, subst), ctx, args, subst
      | Some (ctx, args, subst) -> inst, ctx, args, subst
      in
      let (sigma, ev) = new_pure_evar ~typeclass_candidate:false ctx sigma (csubst_subst subst t1) in
      let ev = mkEvar (ev, args) in
      let dep = not (noccurn sigma 1 t2) in
      let hole = {
        hole_evar = ev;
        hole_type = t1;
        hole_deps = dep;
        (* We fix it later *)
        hole_name = na.binder_name;
      } in
      let t2 = if dep then subst1 ev t2 else t2 in
      clrec (sigma, hole :: holes) inst (pred n) t2
    | LetIn (na, b, _, t) -> clrec (sigma, holes) inst n (subst1 b t)
    | _ -> (sigma, holes, t)
  in
  let (sigma, holes, t) = clrec (sigma, []) None bound t in
  let holes = List.rev holes in
  let clause = { cl_concl = t; cl_holes = holes } in
  (sigma, clause)

let explain_no_such_bound_variable holes id =
  let fold h accu = match h.hole_name with
  | Anonymous -> accu
  | Name id -> id :: accu
  in
  let mvl = List.fold_right fold holes [] in
  let expl = match mvl with
  | [] -> str " (no bound variables at all in the expression)."
  | [id] -> str "(possible name is: " ++ Id.print id ++ str ")."
  | _ -> str "(possible names are: " ++ pr_enum Id.print mvl ++ str ")."
  in
  user_err  (str "No such bound variable " ++ Id.print id ++ expl)

let evar_with_name holes id =
  let map h = match h.hole_name with
  | Anonymous -> None
  | Name id' -> if Id.equal id id' then Some h else None
  in
  let hole = List.map_filter map holes in
  match hole with
  | [] -> explain_no_such_bound_variable holes id
  | [h] -> h.hole_evar
  | _ ->
    user_err
      (str "Binder name \"" ++ Id.print id ++
        str "\" occurs more than once in clause.")

let evar_of_binder holes = function
| NamedHyp s -> evar_with_name holes s
| AnonHyp n ->
  try
    let nondeps = List.filter (fun hole -> not hole.hole_deps) holes in
    let h = List.nth nondeps (pred n) in
    h.hole_evar
  with e when CErrors.noncritical e ->
    user_err  (str "No such binder.")

let define_with_type sigma env ev c =
  let open EConstr in
  let t = Retyping.get_type_of env sigma ev in
  let ty = Retyping.get_type_of env sigma c in
  let j = Environ.make_judge c ty in
  let (sigma, j, _trace) = Coercion.inh_conv_coerce_to ~program_mode:false true env sigma j t in
  let (ev, _) = destEvar sigma ev in
  let sigma = Evd.define ev j.Environ.uj_val sigma in
  sigma

let solve_evar_clause env sigma hyp_only clause = function
| NoBindings -> sigma
| ImplicitBindings largs ->
  let open EConstr in
  let fold holes h =
    if h.hole_deps then
      (* Some subsequent term uses the hole *)
      let (ev, _) = destEvar sigma h.hole_evar in
      let is_dep hole = occur_evar sigma ev hole.hole_type in
      let in_hyp = List.exists is_dep holes in
      let in_ccl = occur_evar sigma ev clause.cl_concl in
      let dep = if hyp_only then in_hyp && not in_ccl else in_hyp || in_ccl in
      let h = { h with hole_deps = dep } in
      h :: holes
    else
      (* The hole does not occur anywhere *)
      h :: holes
  in
  let holes = List.fold_left fold [] (List.rev clause.cl_holes) in
  let map h = if h.hole_deps then Some h.hole_evar else None in
  let evs = List.map_filter map holes in
  let len = List.length evs in
  if Int.equal len (List.length largs) then
    let fold sigma ev arg = define_with_type sigma env ev arg in
    let sigma = List.fold_left2 fold sigma evs largs in
    sigma
  else
    error_not_right_number_missing_arguments len
| ExplicitBindings lbind ->
  let () = check_bindings lbind in
  let fold sigma {CAst.v=(binder, c)} =
    let ev = evar_of_binder clause.cl_holes binder in
    define_with_type sigma env ev c
  in
  let sigma = List.fold_left fold sigma lbind in
  sigma
OCaml

Innovation. Community. Security.

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