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
|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* $Id: logic.ml 12240 2009-07-15 09:52:52Z herbelin $ *)
open Pp
open Util
open Names
open Nameops
open Evd
open Term
open Termops
open Sign
open Environ
open Reductionops
open Inductive
open Inductiveops
open Typing
open Proof_trees
open Proof_type
open Typeops
open Type_errors
open Retyping
open Evarutil
open Tacexpr
type refiner_error =
(* Errors raised by the refiner *)
| BadType of constr * constr * constr
| UnresolvedBindings of name list
| CannotApply of constr * constr
| NotWellTyped of constr
| NonLinearProof of constr
| MetaInType of constr
(* Errors raised by the tactics *)
| IntroNeedsProduct
| DoesNotOccurIn of constr * identifier
exception RefinerError of refiner_error
open Pretype_errors
let rec catchable_exception = function
| Stdpp.Exc_located(_,e) -> catchable_exception e
| LtacLocated(_,e) -> catchable_exception e
| Util.UserError _ | TypeError _
| RefinerError _ | Indrec.RecursionSchemeError _
| Nametab.GlobalizationError _ | PretypeError (_,VarNotFound _)
(* unification errors *)
| PretypeError(_,(CannotUnify _|CannotUnifyLocal _|CannotGeneralize _
|NoOccurrenceFound _|CannotUnifyBindingType _|NotClean _
|CannotFindWellTypedAbstraction _
|UnsolvableImplicit _)) -> true
| Typeclasses_errors.TypeClassError
(_, Typeclasses_errors.UnsatisfiableConstraints _) -> true
| _ -> false
let error_no_such_hypothesis id =
error ("No such hypothesis: " ^ string_of_id id ^ ".")
(* Tells if the refiner should check that the submitted rules do not
produce invalid subgoals *)
let check = ref false
let with_check = Flags.with_option check
(* [apply_to_hyp sign id f] splits [sign] into [tail::[id,_,_]::head] and
returns [tail::(f head (id,_,_) (rev tail))] *)
let apply_to_hyp sign id f =
try apply_to_hyp sign id f
with Hyp_not_found ->
if !check then error "No such assumption."
else sign
let apply_to_hyp_and_dependent_on sign id f g =
try apply_to_hyp_and_dependent_on sign id f g
with Hyp_not_found ->
if !check then error "No such assumption."
else sign
let check_typability env sigma c =
if !check then let _ = type_of env sigma c in ()
(************************************************************************)
(************************************************************************)
(* Implementation of the structural rules (moving and deleting
hypotheses around) *)
(* The Clear tactic: it scans the context for hypotheses to be removed
(instead of iterating on the list of identifier to be removed, which
forces the user to give them in order). *)
let clear_hyps sigma ids sign cl =
let evdref = ref (Evd.create_goal_evar_defs sigma) in
let (hyps,concl) = Evarutil.clear_hyps_in_evi evdref sign cl ids in
(hyps,concl,evars_of !evdref)
(* The ClearBody tactic *)
let recheck_typability (what,id) env sigma t =
try check_typability env sigma t
with _ ->
let s = match what with
| None -> "the conclusion"
| Some id -> "hypothesis "^(string_of_id id) in
error
("The correctness of "^s^" relies on the body of "^(string_of_id id))
let remove_hyp_body env sigma id =
let sign =
apply_to_hyp_and_dependent_on (named_context_val env) id
(fun (_,c,t) _ ->
match c with
| None -> error ((string_of_id id)^" is not a local definition.")
| Some c ->(id,None,t))
(fun (id',c,t as d) sign ->
(if !check then
begin
let env = reset_with_named_context sign env in
match c with
| None -> recheck_typability (Some id',id) env sigma t
| Some b ->
let b' = mkCast (b,DEFAULTcast, t) in
recheck_typability (Some id',id) env sigma b'
end;d))
in
reset_with_named_context sign env
(* Reordering of the context *)
(* faire le minimum d'echanges pour que l'ordre donne soit un *)
(* sous-ordre du resultat. Par exemple, 2 hyps non mentionnee ne sont *)
(* pas echangees. Choix: les hyps mentionnees ne peuvent qu'etre *)
(* reculees par rapport aux autres (faire le contraire!) *)
let mt_q = (Idmap.empty,[])
let push_val y = function
(_,[] as q) -> q
| (m, (x,l)::q) -> (m, (x,Idset.add y l)::q)
let push_item x v (m,l) =
(Idmap.add x v m, (x,Idset.empty)::l)
let mem_q x (m,_) = Idmap.mem x m
let rec find_q x (m,q) =
let v = Idmap.find x m in
let m' = Idmap.remove x m in
let rec find accs acc = function
[] -> raise Not_found
| [(x',l)] ->
if x=x' then ((v,Idset.union accs l),(m',List.rev acc))
else raise Not_found
| (x',l as i)::((x'',l'')::q as itl) ->
if x=x' then
((v,Idset.union accs l),
(m',List.rev acc@(x'',Idset.add x (Idset.union l l''))::q))
else find (Idset.union l accs) (i::acc) itl in
find Idset.empty [] q
let occur_vars_in_decl env hyps d =
if Idset.is_empty hyps then false else
let ohyps = global_vars_set_of_decl env d in
Idset.exists (fun h -> Idset.mem h ohyps) hyps
let reorder_context env sign ord =
let ords = List.fold_right Idset.add ord Idset.empty in
if List.length ord <> Idset.cardinal ords then
error "Order list has duplicates";
let rec step ord expected ctxt_head moved_hyps ctxt_tail =
match ord with
| [] -> List.rev ctxt_tail @ ctxt_head
| top::ord' when mem_q top moved_hyps ->
let ((d,h),mh) = find_q top moved_hyps in
if occur_vars_in_decl env h d then
errorlabstrm "reorder_context"
(str "Cannot move declaration " ++ pr_id top ++ spc() ++
str "before " ++
prlist_with_sep pr_spc pr_id
(Idset.elements (Idset.inter h
(global_vars_set_of_decl env d))));
step ord' expected ctxt_head mh (d::ctxt_tail)
| _ ->
(match ctxt_head with
| [] -> error_no_such_hypothesis (List.hd ord)
| (x,_,_ as d) :: ctxt ->
if Idset.mem x expected then
step ord (Idset.remove x expected)
ctxt (push_item x d moved_hyps) ctxt_tail
else
step ord expected
ctxt (push_val x moved_hyps) (d::ctxt_tail)) in
step ord ords sign mt_q []
let reorder_val_context env sign ord =
val_of_named_context (reorder_context env (named_context_of_val sign) ord)
let check_decl_position env sign (x,_,_ as d) =
let needed = global_vars_set_of_decl env d in
let deps = dependency_closure env (named_context_of_val sign) needed in
if List.mem x deps then
error ("Cannot create self-referring hypothesis "^string_of_id x);
x::deps
(* Auxiliary functions for primitive MOVE tactic
*
* [move_hyp with_dep toleft (left,(hfrom,typfrom),right) hto] moves
* hyp [hfrom] at location [hto] which belongs to the hyps on the
* left side [left] of the full signature if [toleft=true] or to the hyps
* on the right side [right] if [toleft=false].
* If [with_dep] then dependent hypotheses are moved accordingly. *)
let rec get_hyp_after h = function
| [] -> error_no_such_hypothesis h
| (hyp,_,_) :: right ->
if hyp = h then
match right with (id,_,_)::_ -> MoveBefore id | [] -> MoveToEnd false
else
get_hyp_after h right
let split_sign hfrom hto l =
let rec splitrec left toleft = function
| [] -> error_no_such_hypothesis hfrom
| (hyp,c,typ) as d :: right ->
if hyp = hfrom then
(left,right,d, toleft or hto = MoveToEnd true)
else
splitrec (d::left)
(toleft or hto = MoveAfter hyp or hto = MoveBefore hyp)
right
in
splitrec [] false l
let hyp_of_move_location = function
| MoveAfter id -> id
| MoveBefore id -> id
| _ -> assert false
let move_hyp with_dep toleft (left,(idfrom,_,_ as declfrom),right) hto =
let env = Global.env() in
let test_dep (hyp,c,typ as d) (hyp2,c,typ2 as d2) =
if toleft
then occur_var_in_decl env hyp2 d
else occur_var_in_decl env hyp d2
in
let rec moverec first middle = function
| [] ->
if match hto with MoveToEnd _ -> false | _ -> true then
error_no_such_hypothesis (hyp_of_move_location hto);
List.rev first @ List.rev middle
| (hyp,_,_) :: _ as right when hto = MoveBefore hyp ->
List.rev first @ List.rev middle @ right
| (hyp,_,_) as d :: right ->
let (first',middle') =
if List.exists (test_dep d) middle then
if with_dep & hto <> MoveAfter hyp then
(first, d::middle)
else
errorlabstrm "" (str "Cannot move " ++ pr_id idfrom ++
pr_move_location pr_id hto ++
str (if toleft then ": it occurs in " else ": it depends on ")
++ pr_id hyp ++ str ".")
else
(d::first, middle)
in
if hto = MoveAfter hyp then
List.rev first' @ List.rev middle' @ right
else
moverec first' middle' right
in
if toleft then
let right =
List.fold_right push_named_context_val right empty_named_context_val in
List.fold_left (fun sign d -> push_named_context_val d sign)
right (moverec [] [declfrom] left)
else
let right =
List.fold_right push_named_context_val
(moverec [] [declfrom] right) empty_named_context_val in
List.fold_left (fun sign d -> push_named_context_val d sign)
right left
let rename_hyp id1 id2 sign =
apply_to_hyp_and_dependent_on sign id1
(fun (_,b,t) _ -> (id2,b,t))
(fun d _ -> map_named_declaration (replace_vars [id1,mkVar id2]) d)
(************************************************************************)
(************************************************************************)
(* Implementation of the logical rules *)
(* Will only be used on terms given to the Refine rule which have meta
variables only in Application and Case *)
let error_unsupported_deep_meta c =
errorlabstrm "" (strbrk "Application of lemmas whose beta-iota normal " ++
strbrk "form contains metavariables deep inside the term is not " ++
strbrk "supported; try \"refine\" instead.")
let collect_meta_variables c =
let rec collrec deep acc c = match kind_of_term c with
| Meta mv -> if deep then error_unsupported_deep_meta () else mv::acc
| Cast(c,_,_) -> collrec deep acc c
| (App _| Case _) -> fold_constr (collrec deep) acc c
| _ -> fold_constr (collrec true) acc c
in
List.rev (collrec false [] c)
let check_meta_variables c =
if not (list_distinct (collect_meta_variables c)) then
raise (RefinerError (NonLinearProof c))
let check_conv_leq_goal env sigma arg ty conclty =
if !check & not (is_conv_leq env sigma ty conclty) then
raise (RefinerError (BadType (arg,ty,conclty)))
let goal_type_of env sigma c =
(if !check then type_of else Retyping.get_type_of) env sigma c
let rec mk_refgoals sigma goal goalacc conclty trm =
let env = evar_env goal in
let hyps = goal.evar_hyps in
let mk_goal hyps concl = mk_goal hyps concl goal.evar_extra in
(*
if not (occur_meta trm) then
let t'ty = (unsafe_machine env sigma trm).uj_type in
let _ = conv_leq_goal env sigma trm t'ty conclty in
(goalacc,t'ty)
else
*)
match kind_of_term trm with
| Meta _ ->
let conclty = nf_betaiota sigma conclty in
if !check && occur_meta conclty then
raise (RefinerError (MetaInType conclty));
(mk_goal hyps conclty)::goalacc, conclty
| Cast (t,_, ty) ->
check_typability env sigma ty;
check_conv_leq_goal env sigma trm ty conclty;
mk_refgoals sigma goal goalacc ty t
| App (f,l) ->
let (acc',hdty) =
match kind_of_term f with
| Ind _ | Const _
when (isInd f or has_polymorphic_type (destConst f)) ->
(* Sort-polymorphism of definition and inductive types *)
goalacc,
type_of_global_reference_knowing_conclusion env sigma f conclty
| _ ->
mk_hdgoals sigma goal goalacc f
in
let (acc'',conclty') =
mk_arggoals sigma goal acc' hdty (Array.to_list l) in
check_conv_leq_goal env sigma trm conclty' conclty;
(acc'',conclty')
| Case (_,p,c,lf) ->
let (acc',lbrty,conclty') = mk_casegoals sigma goal goalacc p c in
check_conv_leq_goal env sigma trm conclty' conclty;
let acc'' =
array_fold_left2
(fun lacc ty fi -> fst (mk_refgoals sigma goal lacc ty fi))
acc' lbrty lf
in
(acc'',conclty')
| _ ->
if occur_meta trm then
anomaly "refiner called with a meta in non app/case subterm";
let t'ty = goal_type_of env sigma trm in
check_conv_leq_goal env sigma trm t'ty conclty;
(goalacc,t'ty)
(* Same as mkREFGOALS but without knowing te type of the term. Therefore,
* Metas should be casted. *)
and mk_hdgoals sigma goal goalacc trm =
let env = evar_env goal in
let hyps = goal.evar_hyps in
let mk_goal hyps concl = mk_goal hyps concl goal.evar_extra in
match kind_of_term trm with
| Cast (c,_, ty) when isMeta c ->
check_typability env sigma ty;
(mk_goal hyps (nf_betaiota sigma ty))::goalacc,ty
| Cast (t,_, ty) ->
check_typability env sigma ty;
mk_refgoals sigma goal goalacc ty t
| App (f,l) ->
let (acc',hdty) =
if isInd f or isConst f
& not (array_exists occur_meta l) (* we could be finer *)
then
(goalacc,type_of_global_reference_knowing_parameters env sigma f l)
else mk_hdgoals sigma goal goalacc f
in
mk_arggoals sigma goal acc' hdty (Array.to_list l)
| Case (_,p,c,lf) ->
let (acc',lbrty,conclty') = mk_casegoals sigma goal goalacc p c in
let acc'' =
array_fold_left2
(fun lacc ty fi -> fst (mk_refgoals sigma goal lacc ty fi))
acc' lbrty lf
in
(acc'',conclty')
| _ ->
if !check && occur_meta trm then
anomaly "refined called with a dependent meta";
goalacc, goal_type_of env sigma trm
and mk_arggoals sigma goal goalacc funty = function
| [] -> goalacc,funty
| harg::tlargs as allargs ->
let t = whd_betadeltaiota (evar_env goal) sigma funty in
match kind_of_term t with
| Prod (_,c1,b) ->
let (acc',hargty) = mk_refgoals sigma goal goalacc c1 harg in
mk_arggoals sigma goal acc' (subst1 harg b) tlargs
| LetIn (_,c1,_,b) ->
mk_arggoals sigma goal goalacc (subst1 c1 b) allargs
| _ -> raise (RefinerError (CannotApply (t,harg)))
and mk_casegoals sigma goal goalacc p c =
let env = evar_env goal in
let (acc',ct) = mk_hdgoals sigma goal goalacc c in
let (acc'',pt) = mk_hdgoals sigma goal acc' p in
let pj = {uj_val=p; uj_type=pt} in
let indspec =
try find_mrectype env sigma (nf_evar sigma ct)
with Not_found -> anomaly "mk_casegoals" in
let (lbrty,conclty) =
type_case_branches_with_names env indspec pj c in
(acc'',lbrty,conclty)
let convert_hyp sign sigma (id,b,bt as d) =
let env = Global.env() in
let reorder = ref [] in
let sign' =
apply_to_hyp sign id
(fun _ (_,c,ct) _ ->
let env = Global.env_of_context sign in
if !check && not (is_conv env sigma bt ct) then
error ("Incorrect change of the type of "^(string_of_id id)^".");
if !check && not (Option.Misc.compare (is_conv env sigma) b c) then
error ("Incorrect change of the body of "^(string_of_id id)^".");
if !check then reorder := check_decl_position env sign d;
d) in
reorder_val_context env sign' !reorder
(* Normalizing evars in a goal. Called by tactic Local_constraints
(i.e. when the sigma of the proof tree changes). Detect if the
goal is unchanged *)
let norm_goal sigma gl =
let red_fun = Evarutil.nf_evar sigma in
let ncl = red_fun gl.evar_concl in
let ngl =
{ gl with
evar_concl = ncl;
evar_hyps = map_named_val red_fun gl.evar_hyps } in
if Evd.eq_evar_info ngl gl then None else Some ngl
(************************************************************************)
(************************************************************************)
(* Primitive tactics are handled here *)
let prim_refiner r sigma goal =
let env = evar_env goal in
let sign = goal.evar_hyps in
let cl = goal.evar_concl in
let mk_goal hyps concl = mk_goal hyps concl goal.evar_extra in
match r with
(* Logical rules *)
| Intro id ->
if !check && mem_named_context id (named_context_of_val sign) then
error "New variable is already declared";
(match kind_of_term (strip_outer_cast cl) with
| Prod (_,c1,b) ->
let sg = mk_goal (push_named_context_val (id,None,c1) sign)
(subst1 (mkVar id) b) in
([sg], sigma)
| LetIn (_,c1,t1,b) ->
let sg =
mk_goal (push_named_context_val (id,Some c1,t1) sign)
(subst1 (mkVar id) b) in
([sg], sigma)
| _ ->
raise (RefinerError IntroNeedsProduct))
| Cut (b,replace,id,t) ->
let sg1 = mk_goal sign (nf_betaiota sigma t) in
let sign,cl,sigma =
if replace then
let nexthyp = get_hyp_after id (named_context_of_val sign) in
let sign,cl,sigma = clear_hyps sigma [id] sign cl in
move_hyp true false ([],(id,None,t),named_context_of_val sign)
nexthyp,
cl,sigma
else
(if !check && mem_named_context id (named_context_of_val sign) then
error "New variable is already declared";
push_named_context_val (id,None,t) sign,cl,sigma) in
let sg2 = mk_goal sign cl in
if b then ([sg1;sg2],sigma) else ([sg2;sg1],sigma)
| FixRule (f,n,rest,j) ->
let rec check_ind env k cl =
match kind_of_term (strip_outer_cast cl) with
| Prod (na,c1,b) ->
if k = 1 then
try
fst (find_inductive env sigma c1)
with Not_found ->
error "Cannot do a fixpoint on a non inductive type."
else
check_ind (push_rel (na,None,c1) env) (k-1) b
| _ -> error "Not enough products."
in
let (sp,_) = check_ind env n cl in
let firsts,lasts = list_chop j rest in
let all = firsts@(f,n,cl)::lasts in
let rec mk_sign sign = function
| (f,n,ar)::oth ->
let (sp',_) = check_ind env n ar in
if not (sp=sp') then
error ("Fixpoints should be on the same " ^
"mutual inductive declaration.");
if !check && mem_named_context f (named_context_of_val sign) then
error
("Name "^string_of_id f^" already used in the environment");
mk_sign (push_named_context_val (f,None,ar) sign) oth
| [] ->
List.map (fun (_,_,c) -> mk_goal sign c) all
in
(mk_sign sign all, sigma)
| Cofix (f,others,j) ->
let rec check_is_coind env cl =
let b = whd_betadeltaiota env sigma cl in
match kind_of_term b with
| Prod (na,c1,b) -> check_is_coind (push_rel (na,None,c1) env) b
| _ ->
try
let _ = find_coinductive env sigma b in ()
with Not_found ->
error ("All methods must construct elements " ^
"in coinductive types.")
in
let firsts,lasts = list_chop j others in
let all = firsts@(f,cl)::lasts in
List.iter (fun (_,c) -> check_is_coind env c) all;
let rec mk_sign sign = function
| (f,ar)::oth ->
(try
(let _ = lookup_named_val f sign in
error "Name already used in the environment.")
with
| Not_found ->
mk_sign (push_named_context_val (f,None,ar) sign) oth)
| [] -> List.map (fun (_,c) -> mk_goal sign c) all
in
(mk_sign sign all, sigma)
| Refine c ->
check_meta_variables c;
let (sgl,cl') = mk_refgoals sigma goal [] cl c in
let sgl = List.rev sgl in
(sgl, sigma)
(* Conversion rules *)
| Convert_concl (cl',_) ->
check_typability env sigma cl';
if (not !check) || is_conv_leq env sigma cl' cl then
let sg = mk_goal sign cl' in
([sg], sigma)
else
error "convert-concl rule passed non-converting term"
| Convert_hyp (id,copt,ty) ->
([mk_goal (convert_hyp sign sigma (id,copt,ty)) cl], sigma)
(* And now the structural rules *)
| Thin ids ->
let (hyps,concl,nsigma) = clear_hyps sigma ids sign cl in
([mk_goal hyps concl], nsigma)
| ThinBody ids ->
let clear_aux env id =
let env' = remove_hyp_body env sigma id in
if !check then recheck_typability (None,id) env' sigma cl;
env'
in
let sign' = named_context_val (List.fold_left clear_aux env ids) in
let sg = mk_goal sign' cl in
([sg], sigma)
| Move (withdep, hfrom, hto) ->
let (left,right,declfrom,toleft) =
split_sign hfrom hto (named_context_of_val sign) in
let hyps' =
move_hyp withdep toleft (left,declfrom,right) hto in
([mk_goal hyps' cl], sigma)
| Order ord ->
let hyps' = reorder_val_context env sign ord in
([mk_goal hyps' cl], sigma)
| Rename (id1,id2) ->
if !check & id1 <> id2 &&
List.mem id2 (ids_of_named_context (named_context_of_val sign)) then
error ((string_of_id id2)^" is already used.");
let sign' = rename_hyp id1 id2 sign in
let cl' = replace_vars [id1,mkVar id2] cl in
([mk_goal sign' cl'], sigma)
| Change_evars ->
match norm_goal sigma goal with
Some ngl -> ([ngl],sigma)
| None -> ([goal], sigma)
(************************************************************************)
(************************************************************************)
(* Extracting a proof term from the proof tree *)
(* Util *)
type variable_proof_status = ProofVar | SectionVar of identifier
type proof_variable = name * variable_proof_status
let subst_proof_vars =
let rec aux p vars =
let _,subst =
List.fold_left (fun (n,l) var ->
let t = match var with
| Anonymous,_ -> l
| Name id, ProofVar -> (id,mkRel n)::l
| Name id, SectionVar id' -> (id,mkVar id')::l in
(n+1,t)) (p,[]) vars
in replace_vars (List.rev subst)
in aux 1
let rec rebind id1 id2 = function
| [] -> [Name id2,SectionVar id1]
| (na,k as x)::l ->
if na = Name id1 then (Name id2,k)::l else
let l' = rebind id1 id2 l in
if na = Name id2 then (Anonymous,k)::l' else x::l'
let add_proof_var id vl = (Name id,ProofVar)::vl
let proof_variable_index x =
let rec aux n = function
| (Name id,ProofVar)::l when x = id -> n
| _::l -> aux (n+1) l
| [] -> raise Not_found
in
aux 1
let prim_extractor subfun vl pft =
let cl = pft.goal.evar_concl in
match pft.ref with
| Some (Prim (Intro id), [spf]) ->
(match kind_of_term (strip_outer_cast cl) with
| Prod (_,ty,_) ->
let cty = subst_proof_vars vl ty in
mkLambda (Name id, cty, subfun (add_proof_var id vl) spf)
| LetIn (_,b,ty,_) ->
let cb = subst_proof_vars vl b in
let cty = subst_proof_vars vl ty in
mkLetIn (Name id, cb, cty, subfun (add_proof_var id vl) spf)
| _ -> error "Incomplete proof!")
| Some (Prim (Cut (b,_,id,t)),[spf1;spf2]) ->
let spf1, spf2 = if b then spf1, spf2 else spf2, spf1 in
mkLetIn (Name id,subfun vl spf1,subst_proof_vars vl t,
subfun (add_proof_var id vl) spf2)
| Some (Prim (FixRule (f,n,others,j)),spfl) ->
let firsts,lasts = list_chop j others in
let all = Array.of_list (firsts@(f,n,cl)::lasts) in
let lcty = Array.map (fun (_,_,ar) -> subst_proof_vars vl ar) all in
let names = Array.map (fun (f,_,_) -> Name f) all in
let vn = Array.map (fun (_,n,_) -> n-1) all in
let newvl = List.fold_left (fun vl (id,_,_) -> add_proof_var id vl)
(add_proof_var f vl) others in
let lfix = Array.map (subfun newvl) (Array.of_list spfl) in
mkFix ((vn,j),(names,lcty,lfix))
| Some (Prim (Cofix (f,others,j)),spfl) ->
let firsts,lasts = list_chop j others in
let all = Array.of_list (firsts@(f,cl)::lasts) in
let lcty = Array.map (fun (_,ar) -> subst_proof_vars vl ar) all in
let names = Array.map (fun (f,_) -> Name f) all in
let newvl = List.fold_left (fun vl (id,_)-> add_proof_var id vl)
(add_proof_var f vl) others in
let lfix = Array.map (subfun newvl) (Array.of_list spfl) in
mkCoFix (j,(names,lcty,lfix))
| Some (Prim (Refine c),spfl) ->
let mvl = collect_meta_variables c in
let metamap = List.combine mvl (List.map (subfun vl) spfl) in
let cc = subst_proof_vars vl c in
plain_instance metamap cc
(* Structural and conversion rules do not produce any proof *)
| Some (Prim (Convert_concl (t,k)),[pf]) ->
if k = DEFAULTcast then subfun vl pf
else mkCast (subfun vl pf,k,subst_proof_vars vl cl)
| Some (Prim (Convert_hyp _),[pf]) ->
subfun vl pf
| Some (Prim (Thin _),[pf]) ->
(* No need to make ids Anon in vl: subst_proof_vars take the most recent*)
subfun vl pf
| Some (Prim (ThinBody _),[pf]) ->
subfun vl pf
| Some (Prim (Move _|Order _),[pf]) ->
subfun vl pf
| Some (Prim (Rename (id1,id2)),[pf]) ->
subfun (rebind id1 id2 vl) pf
| Some (Prim Change_evars, [pf]) ->
subfun vl pf
| Some _ -> anomaly "prim_extractor"
| None-> error "prim_extractor handed incomplete proof"
|