summaryrefslogtreecommitdiff
path: root/pretyping/termops.ml
blob: 6371fd3a7af1117135632d03ea16342cf2cef398 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

open Pp
open Util
open Names
open Nameops
open Term
open Sign
open Environ
open Libnames
open Nametab

(* Sorts and sort family *)

let print_sort = function
  | Prop Pos -> (str "Set")
  | Prop Null -> (str "Prop")
  | Type u -> (str "Type(" ++ Univ.pr_uni u ++ str ")")

let pr_sort_family = function
  | InSet -> (str "Set")
  | InProp -> (str "Prop")
  | InType -> (str "Type")

let pr_name = function
  | Name id -> pr_id id
  | Anonymous -> str "_"

let pr_con sp = str(string_of_con sp)

let rec pr_constr c = match kind_of_term c with
  | Rel n -> str "#"++int n
  | Meta n -> str "Meta(" ++ int n ++ str ")"
  | Var id -> pr_id id
  | Sort s -> print_sort s
  | Cast (c,_, t) -> hov 1
      (str"(" ++ pr_constr c ++ cut() ++
       str":" ++ pr_constr t ++ str")")
  | Prod (Name(id),t,c) -> hov 1
      (str"forall " ++ pr_id id ++ str":" ++ pr_constr t ++ str"," ++
       spc() ++ pr_constr c)
  | Prod (Anonymous,t,c) -> hov 0
      (str"(" ++ pr_constr t ++ str " ->" ++ spc() ++
       pr_constr c ++ str")")
  | Lambda (na,t,c) -> hov 1
      (str"fun " ++ pr_name na ++ str":" ++
       pr_constr t ++ str" =>" ++ spc() ++ pr_constr c)
  | LetIn (na,b,t,c) -> hov 0
      (str"let " ++ pr_name na ++ str":=" ++ pr_constr b ++
       str":" ++ brk(1,2) ++ pr_constr t ++ cut() ++
       pr_constr c)
  | App (c,l) ->  hov 1
      (str"(" ++ pr_constr c ++ spc() ++
       prlist_with_sep spc pr_constr (Array.to_list l) ++ str")")
  | Evar (e,l) -> hov 1
      (str"Evar#" ++ int e ++ str"{" ++
       prlist_with_sep spc pr_constr (Array.to_list l) ++str"}")
  | Const c -> str"Cst(" ++ pr_con c ++ str")"
  | Ind (sp,i) -> str"Ind(" ++ pr_mind sp ++ str"," ++ int i ++ str")"
  | Construct ((sp,i),j) ->
      str"Constr(" ++ pr_mind sp ++ str"," ++ int i ++ str"," ++ int j ++ str")"
  | Case (ci,p,c,bl) -> v 0
      (hv 0 (str"<"++pr_constr p++str">"++ cut() ++ str"Case " ++
             pr_constr c ++ str"of") ++ cut() ++
       prlist_with_sep (fun _ -> brk(1,2)) pr_constr (Array.to_list bl) ++
      cut() ++ str"end")
  | Fix ((t,i),(lna,tl,bl)) ->
      let fixl = Array.mapi (fun i na -> (na,t.(i),tl.(i),bl.(i))) lna in
      hov 1
        (str"fix " ++ int i ++ spc() ++  str"{" ++
         v 0 (prlist_with_sep spc (fun (na,i,ty,bd) ->
           pr_name na ++ str"/" ++ int i ++ str":" ++ pr_constr ty ++
           cut() ++ str":=" ++ pr_constr bd) (Array.to_list fixl)) ++
         str"}")
  | CoFix(i,(lna,tl,bl)) ->
      let fixl = Array.mapi (fun i na -> (na,tl.(i),bl.(i))) lna in
      hov 1
        (str"cofix " ++ int i ++ spc() ++  str"{" ++
         v 0 (prlist_with_sep spc (fun (na,ty,bd) ->
           pr_name na ++ str":" ++ pr_constr ty ++
           cut() ++ str":=" ++ pr_constr bd) (Array.to_list fixl)) ++
         str"}")

let term_printer = ref (fun _ -> pr_constr)
let print_constr_env t = !term_printer t
let print_constr t = !term_printer (Global.env()) t
let set_print_constr f = term_printer := f

let pr_var_decl env (id,c,typ) =
  let pbody = match c with
    | None ->  (mt ())
    | Some c ->
	(* Force evaluation *)
	let pb = print_constr_env env c in
	  (str" := " ++ pb ++ cut () ) in
  let pt = print_constr_env env typ in
  let ptyp = (str" : " ++ pt) in
    (pr_id id ++ hov 0 (pbody ++ ptyp))

let pr_rel_decl env (na,c,typ) =
  let pbody = match c with
    | None -> mt ()
    | Some c ->
	(* Force evaluation *)
	let pb = print_constr_env env c in
	  (str":=" ++ spc () ++ pb ++ spc ()) in
  let ptyp = print_constr_env env typ in
    match na with
      | Anonymous -> hov 0 (str"<>" ++ spc () ++ pbody ++ str":" ++ spc () ++ ptyp)
      | Name id -> hov 0 (pr_id id ++ spc () ++ pbody ++ str":" ++ spc () ++ ptyp)

let print_named_context env =
  hv 0 (fold_named_context
	  (fun env d pps ->
	    pps ++ ws 2 ++ pr_var_decl env d)
          env ~init:(mt ()))

let print_rel_context env =
  hv 0 (fold_rel_context
	  (fun env d pps -> pps ++ ws 2 ++ pr_rel_decl env d)
          env ~init:(mt ()))

let print_env env =
  let sign_env =
    fold_named_context
      (fun env d pps ->
         let pidt =  pr_var_decl env d in
	 (pps ++ fnl () ++ pidt))
      env ~init:(mt ())
  in
  let db_env =
    fold_rel_context
      (fun env d pps ->
         let pnat = pr_rel_decl env d in (pps ++ fnl () ++ pnat))
      env ~init:(mt ())
  in
    (sign_env ++ db_env)

(*let current_module = ref empty_dirpath

let set_module m = current_module := m*)

let new_univ_level =
  let univ_gen = ref 0 in
  (fun sp ->
    incr univ_gen;
    Univ.make_universe_level (Lib.library_dp(),!univ_gen))

let new_univ () = Univ.make_universe (new_univ_level ())
let new_Type () = mkType (new_univ ())
let new_Type_sort () = Type (new_univ ())

(* This refreshes universes in types; works only for inferred types (i.e. for
   types of the form (x1:A1)...(xn:An)B with B a sort or an atom in
   head normal form) *)
let refresh_universes_gen strict t =
  let modified = ref false in
  let rec refresh t = match kind_of_term t with
    | Sort (Type u) when strict or u <> Univ.type0m_univ ->
	modified := true; new_Type ()
    | Prod (na,u,v) -> mkProd (na,u,refresh v)
    | _ -> t in
  let t' = refresh t in
  if !modified then t' else t

let refresh_universes = refresh_universes_gen false
let refresh_universes_strict = refresh_universes_gen true

let new_sort_in_family = function
  | InProp -> prop_sort
  | InSet -> set_sort
  | InType -> Type (new_univ ())



(* [Rel (n+m);...;Rel(n+1)] *)
let rel_vect n m = Array.init m (fun i -> mkRel(n+m-i))

let rel_list n m =
  let rec reln l p =
    if p>m then l else reln (mkRel(n+p)::l) (p+1)
  in
  reln [] 1

(* Same as [rel_list] but takes a context as argument and skips let-ins *)
let extended_rel_list n hyps =
  let rec reln l p = function
    | (_,None,_) :: hyps -> reln (mkRel (n+p) :: l) (p+1) hyps
    | (_,Some _,_) :: hyps -> reln l (p+1) hyps
    | [] -> l
  in
  reln [] 1 hyps

let extended_rel_vect n hyps = Array.of_list (extended_rel_list n hyps)



let push_rel_assum (x,t) env = push_rel (x,None,t) env

let push_rels_assum assums =
  push_rel_context (List.map (fun (x,t) -> (x,None,t)) assums)

let push_named_rec_types (lna,typarray,_) env =
  let ctxt =
    array_map2_i
      (fun i na t ->
	 match na with
	   | Name id -> (id, None, lift i t)
	   | Anonymous -> anomaly "Fix declarations must be named")
      lna typarray in
  Array.fold_left
    (fun e assum -> push_named assum e) env ctxt

let rec lookup_rel_id id sign =
  let rec lookrec = function
    | (n, (Anonymous,_,_)::l) -> lookrec (n+1,l)
    | (n, (Name id',b,t)::l)  -> if id' = id then (n,b,t) else lookrec (n+1,l)
    | (_, [])                 -> raise Not_found
  in
  lookrec (1,sign)

(* Constructs either [forall x:t, c] or [let x:=b:t in c] *)
let mkProd_or_LetIn (na,body,t) c =
  match body with
    | None -> mkProd (na, t, c)
    | Some b -> mkLetIn (na, b, t, c)

(* Constructs either [forall x:t, c] or [c] in which [x] is replaced by [b] *)
let mkProd_wo_LetIn (na,body,t) c =
  match body with
    | None -> mkProd (na,  t, c)
    | Some b -> subst1 b c

let it_mkProd init = List.fold_left (fun c (n,t)  -> mkProd (n, t, c)) init
let it_mkLambda init = List.fold_left (fun c (n,t)  -> mkLambda (n, t, c)) init

let it_named_context_quantifier f ~init =
  List.fold_left (fun c d -> f d c) init

let it_mkProd_or_LetIn init = it_named_context_quantifier mkProd_or_LetIn ~init
let it_mkProd_wo_LetIn init = it_named_context_quantifier mkProd_wo_LetIn ~init
let it_mkLambda_or_LetIn init = it_named_context_quantifier mkLambda_or_LetIn ~init
let it_mkNamedProd_or_LetIn init = it_named_context_quantifier mkNamedProd_or_LetIn ~init
let it_mkNamedProd_wo_LetIn init = it_named_context_quantifier mkNamedProd_wo_LetIn ~init
let it_mkNamedLambda_or_LetIn init = it_named_context_quantifier mkNamedLambda_or_LetIn ~init

(* *)

(* strips head casts and flattens head applications *)
let rec strip_head_cast c = match kind_of_term c with
  | App (f,cl) ->
      let rec collapse_rec f cl2 = match kind_of_term f with
	| App (g,cl1) -> collapse_rec g (Array.append cl1 cl2)
	| Cast (c,_,_) -> collapse_rec c cl2
	| _ -> if Array.length cl2 = 0 then f else mkApp (f,cl2)
      in
      collapse_rec f cl
  | Cast (c,_,_) -> strip_head_cast c
  | _ -> c

let rec drop_extra_implicit_args c = match kind_of_term c with
  (* Removed trailing extra implicit arguments, what improves compatibility
     for constants with recently added maximal implicit arguments *)
  | App (f,args) when isEvar (array_last args) ->
      drop_extra_implicit_args
	(mkApp (f,fst (array_chop (Array.length args - 1) args)))
  | _ -> c

(* Get the last arg of an application *)
let last_arg c = match kind_of_term c with
  | App (f,cl) -> array_last cl
  | _ -> anomaly "last_arg"

(* Get the last arg of an application *)
let decompose_app_vect c =
  match kind_of_term c with
  | App (f,cl) -> (f, cl)
  | _ -> (c,[||])

let adjust_app_list_size f1 l1 f2 l2 =
  let len1 = List.length l1 and len2 = List.length l2 in
  if len1 = len2 then (f1,l1,f2,l2)
  else if len1 < len2 then
   let extras,restl2 = list_chop (len2-len1) l2 in
    (f1, l1, applist (f2,extras), restl2)
  else
    let extras,restl1 = list_chop (len1-len2) l1 in
    (applist (f1,extras), restl1, f2, l2)

let adjust_app_array_size f1 l1 f2 l2 =
  let len1 = Array.length l1 and len2 = Array.length l2 in
  if len1 = len2 then (f1,l1,f2,l2)
  else if len1 < len2 then
    let extras,restl2 = array_chop (len2-len1) l2 in
    (f1, l1, appvect (f2,extras), restl2)
  else
    let extras,restl1 = array_chop (len1-len2) l1 in
    (appvect (f1,extras), restl1, f2, l2)

(* [map_constr_with_named_binders g f l c] maps [f l] on the immediate
   subterms of [c]; it carries an extra data [l] (typically a name
   list) which is processed by [g na] (which typically cons [na] to
   [l]) at each binder traversal (with name [na]); it is not recursive
   and the order with which subterms are processed is not specified *)

let map_constr_with_named_binders g f l c = match kind_of_term c with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> c
  | Cast (c,k,t) -> mkCast (f l c, k, f l t)
  | Prod (na,t,c) -> mkProd (na, f l t, f (g na l) c)
  | Lambda (na,t,c) -> mkLambda (na, f l t, f (g na l) c)
  | LetIn (na,b,t,c) -> mkLetIn (na, f l b, f l t, f (g na l) c)
  | App (c,al) -> mkApp (f l c, Array.map (f l) al)
  | Evar (e,al) -> mkEvar (e, Array.map (f l) al)
  | Case (ci,p,c,bl) -> mkCase (ci, f l p, f l c, Array.map (f l) bl)
  | Fix (ln,(lna,tl,bl)) ->
      let l' = Array.fold_left (fun l na -> g na l) l lna in
      mkFix (ln,(lna,Array.map (f l) tl,Array.map (f l') bl))
  | CoFix(ln,(lna,tl,bl)) ->
      let l' = Array.fold_left (fun l na -> g na l) l lna in
      mkCoFix (ln,(lna,Array.map (f l) tl,Array.map (f l') bl))

(* [map_constr_with_binders_left_to_right g f n c] maps [f n] on the
   immediate subterms of [c]; it carries an extra data [n] (typically
   a lift index) which is processed by [g] (which typically add 1 to
   [n]) at each binder traversal; the subterms are processed from left
   to right according to the usual representation of the constructions
   (this may matter if [f] does a side-effect); it is not recursive;
   in fact, the usual representation of the constructions is at the
   time being almost those of the ML representation (except for
   (co-)fixpoint) *)

let fold_rec_types g (lna,typarray,_) e =
  let ctxt = array_map2_i (fun i na t -> (na, None, lift i t)) lna typarray in
  Array.fold_left (fun e assum -> g assum e) e ctxt


let map_constr_with_binders_left_to_right g f l c = match kind_of_term c with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> c
  | Cast (c,k,t) -> let c' = f l c in mkCast (c',k,f l t)
  | Prod (na,t,c) ->
      let t' = f l t in
      mkProd (na, t', f (g (na,None,t) l) c)
  | Lambda (na,t,c) ->
      let t' = f l t in
      mkLambda (na, t', f (g (na,None,t) l) c)
  | LetIn (na,b,t,c) ->
      let b' = f l b in
      let t' = f l t in
      let c' = f (g (na,Some b,t) l) c in
      mkLetIn (na, b', t', c')
  | App (c,[||]) -> assert false
  | App (c,al) ->
      (*Special treatment to be able to recognize partially applied subterms*)
      let a = al.(Array.length al - 1) in
      let hd = f l (mkApp (c, Array.sub al 0 (Array.length al - 1))) in
      mkApp (hd, [| f l a |])
  | Evar (e,al) -> mkEvar (e, array_map_left (f l) al)
  | Case (ci,p,c,bl) ->
      (* In v8 concrete syntax, predicate is after the term to match! *)
      let c' = f l c in
      let p' = f l p in
      mkCase (ci, p', c', array_map_left (f l) bl)
  | Fix (ln,(lna,tl,bl as fx)) ->
      let l' = fold_rec_types g fx l in
      let (tl',bl') = array_map_left_pair (f l) tl (f l') bl in
      mkFix (ln,(lna,tl',bl'))
  | CoFix(ln,(lna,tl,bl as fx)) ->
      let l' = fold_rec_types g fx l in
      let (tl',bl') = array_map_left_pair (f l) tl (f l') bl in
      mkCoFix (ln,(lna,tl',bl'))

(* strong *)
let map_constr_with_full_binders g f l cstr = match kind_of_term cstr with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> cstr
  | Cast (c,k, t) ->
      let c' = f l c in
      let t' = f l t in
      if c==c' && t==t' then cstr else mkCast (c', k, t')
  | Prod (na,t,c) ->
      let t' = f l t in
      let c' = f (g (na,None,t) l) c in
      if t==t' && c==c' then cstr else mkProd (na, t', c')
  | Lambda (na,t,c) ->
      let t' = f l t in
      let c' = f (g (na,None,t) l) c in
      if t==t' && c==c' then cstr else  mkLambda (na, t', c')
  | LetIn (na,b,t,c) ->
      let b' = f l b in
      let t' = f l t in
      let c' = f (g (na,Some b,t) l) c in
      if b==b' && t==t' && c==c' then cstr else mkLetIn (na, b', t', c')
  | App (c,al) ->
      let c' = f l c in
      let al' = Array.map (f l) al in
      if c==c' && array_for_all2 (==) al al' then cstr else mkApp (c', al')
  | Evar (e,al) ->
      let al' = Array.map (f l) al in
      if array_for_all2 (==) al al' then cstr else mkEvar (e, al')
  | Case (ci,p,c,bl) ->
      let p' = f l p in
      let c' = f l c in
      let bl' = Array.map (f l) bl in
      if p==p' && c==c' && array_for_all2 (==) bl bl' then cstr else
        mkCase (ci, p', c', bl')
  | Fix (ln,(lna,tl,bl)) ->
      let tl' = Array.map (f l) tl in
      let l' =
        array_fold_left2 (fun l na t -> g (na,None,t) l) l lna tl in
      let bl' = Array.map (f l') bl in
      if array_for_all2 (==) tl tl' && array_for_all2 (==) bl bl'
      then cstr
      else mkFix (ln,(lna,tl',bl'))
  | CoFix(ln,(lna,tl,bl)) ->
      let tl' = Array.map (f l) tl in
      let l' =
        array_fold_left2 (fun l na t -> g (na,None,t) l) l lna tl in
      let bl' = Array.map (f l') bl in
      if array_for_all2 (==) tl tl' && array_for_all2 (==) bl bl'
      then cstr
      else mkCoFix (ln,(lna,tl',bl'))

(* [fold_constr_with_binders g f n acc c] folds [f n] on the immediate
   subterms of [c] starting from [acc] and proceeding from left to
   right according to the usual representation of the constructions as
   [fold_constr] but it carries an extra data [n] (typically a lift
   index) which is processed by [g] (which typically add 1 to [n]) at
   each binder traversal; it is not recursive *)

let fold_constr_with_binders g f n acc c = match kind_of_term c with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> acc
  | Cast (c,_, t) -> f n (f n acc c) t
  | Prod (_,t,c) -> f (g n) (f n acc t) c
  | Lambda (_,t,c) -> f (g n) (f n acc t) c
  | LetIn (_,b,t,c) -> f (g n) (f n (f n acc b) t) c
  | App (c,l) -> Array.fold_left (f n) (f n acc c) l
  | Evar (_,l) -> Array.fold_left (f n) acc l
  | Case (_,p,c,bl) -> Array.fold_left (f n) (f n (f n acc p) c) bl
  | Fix (_,(lna,tl,bl)) ->
      let n' = iterate g (Array.length tl) n in
      let fd = array_map2 (fun t b -> (t,b)) tl bl in
      Array.fold_left (fun acc (t,b) -> f n' (f n acc t) b) acc fd
  | CoFix (_,(lna,tl,bl)) ->
      let n' = iterate g (Array.length tl) n in
      let fd = array_map2 (fun t b -> (t,b)) tl bl in
      Array.fold_left (fun acc (t,b) -> f n' (f n acc t) b) acc fd

(* [iter_constr_with_full_binders g f acc c] iters [f acc] on the immediate
   subterms of [c]; it carries an extra data [acc] which is processed by [g] at
   each binder traversal; it is not recursive and the order with which
   subterms are processed is not specified *)

let iter_constr_with_full_binders g f l c = match kind_of_term c with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> ()
  | Cast (c,_, t) -> f l c; f l t
  | Prod (na,t,c) -> f l t; f (g (na,None,t) l) c
  | Lambda (na,t,c) -> f l t; f (g (na,None,t) l) c
  | LetIn (na,b,t,c) -> f l b; f l t; f (g (na,Some b,t) l) c
  | App (c,args) -> f l c; Array.iter (f l) args
  | Evar (_,args) -> Array.iter (f l) args
  | Case (_,p,c,bl) -> f l p; f l c; Array.iter (f l) bl
  | Fix (_,(lna,tl,bl)) ->
      let l' = array_fold_left2 (fun l na t -> g (na,None,t) l) l lna tl in
      Array.iter (f l) tl;
      Array.iter (f l') bl
  | CoFix (_,(lna,tl,bl)) ->
      let l' = array_fold_left2 (fun l na t -> g (na,None,t) l) l lna tl in
      Array.iter (f l) tl;
      Array.iter (f l') bl

(***************************)
(* occurs check functions  *)
(***************************)

exception Occur

let occur_meta c =
  let rec occrec c = match kind_of_term c with
    | Meta _ -> raise Occur
    | _ -> iter_constr occrec c
  in try occrec c; false with Occur -> true

let occur_existential c =
  let rec occrec c = match kind_of_term c with
    | Evar _ -> raise Occur
    | _ -> iter_constr occrec c
  in try occrec c; false with Occur -> true

let occur_meta_or_existential c =
  let rec occrec c = match kind_of_term c with
    | Evar _ -> raise Occur
    | Meta _ -> raise Occur
    | _ -> iter_constr occrec c
  in try occrec c; false with Occur -> true

let occur_const s c =
  let rec occur_rec c = match kind_of_term c with
    | Const sp when sp=s -> raise Occur
    | _ -> iter_constr occur_rec c
  in
  try occur_rec c; false with Occur -> true

let occur_evar n c =
  let rec occur_rec c = match kind_of_term c with
    | Evar (sp,_) when sp=n -> raise Occur
    | _ -> iter_constr occur_rec c
  in
  try occur_rec c; false with Occur -> true

let occur_in_global env id constr =
  let vars = vars_of_global env constr in
  if List.mem id vars then raise Occur

let occur_var env id c =
  let rec occur_rec c =
    match kind_of_term c with
    | Var _ | Const _ | Ind _ | Construct _ -> occur_in_global env id c
    | _ -> iter_constr occur_rec c
  in
  try occur_rec c; false with Occur -> true

let occur_var_in_decl env hyp (_,c,typ) =
  match c with
    | None -> occur_var env hyp typ
    | Some body ->
        occur_var env hyp typ ||
        occur_var env hyp body

(* returns the list of free debruijn indices in a term *)

let free_rels m =
  let rec frec depth acc c = match kind_of_term c with
    | Rel n       -> if n >= depth then Intset.add (n-depth+1) acc else acc
    | _ -> fold_constr_with_binders succ frec depth acc c
  in
  frec 1 Intset.empty m

(* collects all metavar occurences, in left-to-right order, preserving
 * repetitions and all. *)

let collect_metas c =
  let rec collrec acc c =
    match kind_of_term c with
      | Meta mv -> list_add_set mv acc
      | _       -> fold_constr collrec acc c
  in
  List.rev (collrec [] c)

(* collects all vars; warning: this is only visible vars, not dependencies in
   all section variables; for the latter, use global_vars_set *)
let collect_vars c =
  let rec aux vars c = match kind_of_term c with
  | Var id -> Idset.add id vars
  | _ -> fold_constr aux vars c in
  aux Idset.empty c

(* Tests whether [m] is a subterm of [t]:
   [m] is appropriately lifted through abstractions of [t] *)

let dependent_main noevar m t =
  let rec deprec m t =
    if eq_constr m t then
      raise Occur
    else
      match kind_of_term m, kind_of_term t with
	| App (fm,lm), App (ft,lt) when Array.length lm < Array.length lt ->
	    deprec m (mkApp (ft,Array.sub lt 0 (Array.length lm)));
	    Array.iter (deprec m)
	      (Array.sub lt
		(Array.length lm) ((Array.length lt) - (Array.length lm)))
	| _, Cast (c,_,_) when noevar & isMeta c -> ()
	| _, Evar _ when noevar -> ()
	| _ -> iter_constr_with_binders (lift 1) deprec m t
  in
  try deprec m t; false with Occur -> true

let dependent = dependent_main false
let dependent_no_evar = dependent_main true

let count_occurrences m t =
  let n = ref 0 in
  let rec countrec m t =
    if eq_constr m t then
      incr n
    else
      match kind_of_term m, kind_of_term t with
	| App (fm,lm), App (ft,lt) when Array.length lm < Array.length lt ->
	    countrec m (mkApp (ft,Array.sub lt 0 (Array.length lm)));
	    Array.iter (countrec m)
	      (Array.sub lt
		(Array.length lm) ((Array.length lt) - (Array.length lm)))
	| _, Cast (c,_,_) when isMeta c -> ()
	| _, Evar _ -> ()
	| _ -> iter_constr_with_binders (lift 1) countrec m t
  in
  countrec m t;
  !n

(* Synonymous *)
let occur_term = dependent

let pop t = lift (-1) t

(***************************)
(*  bindings functions *)
(***************************)

type meta_type_map = (metavariable * types) list

type meta_value_map = (metavariable * constr) list

let rec subst_meta bl c =
  match kind_of_term c with
    | Meta i -> (try List.assoc i bl with Not_found -> c)
    | _ -> map_constr (subst_meta bl) c

(* First utilities for avoiding telescope computation for subst_term *)

let prefix_application eq_fun (k,c) (t : constr) =
  let c' = collapse_appl c and t' = collapse_appl t in
  match kind_of_term c', kind_of_term t' with
    | App (f1,cl1), App (f2,cl2) ->
	let l1 = Array.length cl1
	and l2 = Array.length cl2 in
	if l1 <= l2
	   && eq_fun c' (mkApp (f2, Array.sub cl2 0 l1)) then
	  Some (mkApp (mkRel k, Array.sub cl2 l1 (l2 - l1)))
	else
	  None
    | _ -> None

let my_prefix_application eq_fun (k,c) (by_c : constr) (t : constr) =
  let c' = collapse_appl c and t' = collapse_appl t in
  match kind_of_term c', kind_of_term t' with
    | App (f1,cl1), App (f2,cl2) ->
	let l1 = Array.length cl1
	and l2 = Array.length cl2 in
	if l1 <= l2
	   && eq_fun c' (mkApp (f2, Array.sub cl2 0 l1)) then
	  Some (mkApp ((lift k by_c), Array.sub cl2 l1 (l2 - l1)))
	else
	  None
    | _ -> None

(* Recognizing occurrences of a given subterm in a term: [subst_term c t]
   substitutes [(Rel 1)] for all occurrences of term [c] in a term [t];
   works if [c] has rels *)

let subst_term_gen eq_fun c t =
  let rec substrec (k,c as kc) t =
    match prefix_application eq_fun kc t with
      | Some x -> x
      | None ->
    if eq_fun c t then mkRel k
    else
      map_constr_with_binders (fun (k,c) -> (k+1,lift 1 c)) substrec kc t
  in
  substrec (1,c) t

let subst_term = subst_term_gen eq_constr

(* Recognizing occurrences of a given subterm in a term :
   [replace_term c1 c2 t] substitutes [c2] for all occurrences of
   term [c1] in a term [t]; works if [c1] and [c2] have rels *)

let replace_term_gen eq_fun c by_c in_t =
  let rec substrec (k,c as kc) t =
    match my_prefix_application eq_fun kc by_c t with
      | Some x -> x
      | None ->
    (if eq_fun c t then (lift k by_c) else
      map_constr_with_binders (fun (k,c) -> (k+1,lift 1 c))
	substrec kc t)
  in
  substrec (0,c) in_t

let replace_term = replace_term_gen eq_constr

(* Substitute only at a list of locations or excluding a list of
   locations; in the occurrences list (b,l), b=true means no
   occurrence except the ones in l and b=false, means all occurrences
   except the ones in l *)

type hyp_location_flag = (* To distinguish body and type of local defs *)
  | InHyp
  | InHypTypeOnly
  | InHypValueOnly

type occurrences = bool * int list
let all_occurrences = (false,[])
let no_occurrences_in_set = (true,[])

let error_invalid_occurrence l =
  let l = list_uniquize (List.sort Pervasives.compare l) in
  errorlabstrm ""
    (str ("Invalid occurrence " ^ plural (List.length l) "number" ^": ") ++
     prlist_with_sep spc int l ++ str ".")

let pr_position (cl,pos) =
  let clpos = match cl with
    | None -> str " of the goal"
    | Some (id,InHyp) -> str " of hypothesis " ++ pr_id id
    | Some (id,InHypTypeOnly) -> str " of the type of hypothesis " ++ pr_id id
    | Some (id,InHypValueOnly) -> str " of the body of hypothesis " ++ pr_id id in
  int pos ++ clpos

let error_cannot_unify_occurrences nested (cl2,pos2,t2) (cl1,pos1,t1) (nowhere_except_in,locs) =
  let s = if nested then "Found nested occurrences of the pattern"
    else "Found incompatible occurrences of the pattern" in
  errorlabstrm ""
    (str s ++ str ":" ++
     spc () ++ str "Matched term " ++ quote (print_constr t2) ++
     strbrk " at position " ++ pr_position (cl2,pos2) ++ 
     strbrk " is not compatible with matched term " ++
     quote (print_constr t1) ++ strbrk " at position " ++ 
     pr_position (cl1,pos1) ++ str ".")

let is_selected pos (nowhere_except_in,locs) =
  nowhere_except_in && List.mem pos locs ||
  not nowhere_except_in && not (List.mem pos locs)

exception NotUnifiable

type 'a testing_function = {
  match_fun : constr -> 'a;
  merge_fun : 'a -> 'a -> 'a;
  mutable testing_state : 'a;
  mutable last_found : ((identifier * hyp_location_flag) option * int * constr) option
}

let subst_closed_term_occ_gen_modulo (nowhere_except_in,locs as plocs) test cl occ t =
  let maxocc = List.fold_right max locs 0 in
  let pos = ref occ in
  let nested = ref false in
  let add_subst t subst =
    try
      test.testing_state <- test.merge_fun subst test.testing_state;
      test.last_found <- Some (cl,!pos,t)
    with NotUnifiable ->
      let lastpos = Option.get test.last_found in
      error_cannot_unify_occurrences !nested (cl,!pos,t) lastpos plocs in
  let rec substrec k t =
    if nowhere_except_in & !pos > maxocc then t else
    try
      let subst = test.match_fun t in
      if is_selected !pos plocs then
        (add_subst t subst; incr pos;
         (* Check nested matching subterms *)
         nested := true; ignore (subst_below k t); nested := false;
         (* Do the effective substitution *)
         mkRel k)
      else
        (incr pos; subst_below k t)
    with NotUnifiable ->
      subst_below k t
  and subst_below k t =
    map_constr_with_binders_left_to_right (fun d k -> k+1) substrec k t
  in
  let t' = substrec 1 t in
  (!pos, t')

let is_nowhere (nowhere_except_in,locs) = nowhere_except_in && locs = [] 

let check_used_occurrences nbocc (nowhere_except_in,locs) =
  let rest = List.filter (fun o -> o >= nbocc) locs in
  if rest <> [] then error_invalid_occurrence rest

let proceed_with_occurrences f plocs x =
  if is_nowhere plocs then (* optimization *) x else
  begin
    assert (List.for_all (fun x -> x >= 0) (snd plocs));
    let (nbocc,x) = f 1 x in
    check_used_occurrences nbocc plocs;
    x
  end

let make_eq_test c = {
  match_fun = (fun c' -> if eq_constr c c' then () else raise NotUnifiable);
  merge_fun = (fun () () -> ());
  testing_state = ();
  last_found = None
} 

let subst_closed_term_occ_gen plocs pos c t =
  subst_closed_term_occ_gen_modulo plocs (make_eq_test c) None pos t

let subst_closed_term_occ plocs c t =
  proceed_with_occurrences (fun occ -> subst_closed_term_occ_gen plocs occ c)
    plocs t

let subst_closed_term_occ_modulo plocs test cl t =
  proceed_with_occurrences
    (subst_closed_term_occ_gen_modulo plocs test cl) plocs t

let map_named_declaration_with_hyploc f hyploc acc (id,bodyopt,typ) =
  let f = f (Some (id,hyploc)) in
  match bodyopt,hyploc with
  | None, InHypValueOnly ->
      errorlabstrm "" (pr_id id ++ str " has no value.")
  | None, _ | Some _, InHypTypeOnly ->
      let acc,typ = f acc typ in acc,(id,bodyopt,typ)
  | Some body, InHypValueOnly ->
      let acc,body = f acc body in acc,(id,Some body,typ)
  | Some body, InHyp ->
      let acc,body = f acc body in
      let acc,typ = f acc typ in
      acc,(id,Some body,typ)

let subst_closed_term_occ_decl (plocs,hyploc) c d =
  proceed_with_occurrences
    (map_named_declaration_with_hyploc
       (fun _ occ -> subst_closed_term_occ_gen plocs occ c) hyploc) plocs d

let subst_closed_term_occ_decl_modulo (plocs,hyploc) test d =
  proceed_with_occurrences
    (map_named_declaration_with_hyploc
       (subst_closed_term_occ_gen_modulo plocs test)
       hyploc)
    plocs d

let vars_of_env env =
  let s =
    Sign.fold_named_context (fun (id,_,_) s -> Idset.add id s)
      (named_context env) ~init:Idset.empty in
  Sign.fold_rel_context
    (fun (na,_,_) s -> match na with Name id -> Idset.add id s | _ -> s)
    (rel_context env) ~init:s

let add_vname vars = function
    Name id -> Idset.add id vars
  | _ -> vars

(*************************)
(*   Names environments  *)
(*************************)
type names_context = name list
let add_name n nl = n::nl
let lookup_name_of_rel p names =
  try List.nth names (p-1)
  with Invalid_argument _ | Failure _ -> raise Not_found
let rec lookup_rel_of_name id names =
  let rec lookrec n = function
    | Anonymous :: l  -> lookrec (n+1) l
    | (Name id') :: l -> if id' = id then n else lookrec (n+1) l
    | []            -> raise Not_found
  in
  lookrec 1 names
let empty_names_context = []

let ids_of_rel_context sign =
  Sign.fold_rel_context
    (fun (na,_,_) l -> match na with Name id -> id::l | Anonymous -> l)
    sign ~init:[]

let ids_of_named_context sign =
  Sign.fold_named_context (fun (id,_,_) idl -> id::idl) sign ~init:[]

let ids_of_context env =
  (ids_of_rel_context (rel_context env))
  @ (ids_of_named_context (named_context env))


let names_of_rel_context env =
  List.map (fun (na,_,_) -> na) (rel_context env)

let is_section_variable id =
  try let _ = Global.lookup_named id in true
  with Not_found -> false

let isGlobalRef c =
  match kind_of_term c with
  | Const _ | Ind _ | Construct _ | Var _ -> true
  | _ -> false

let has_polymorphic_type c =
  match (Global.lookup_constant c).Declarations.const_type with
  | Declarations.PolymorphicArity _ -> true
  | _ -> false

let base_sort_cmp pb s0 s1 =
  match (s0,s1) with
    | (Prop c1, Prop c2) -> c1 = Null or c2 = Pos  (* Prop <= Set *)
    | (Prop c1, Type u)  -> pb = Reduction.CUMUL
    | (Type u1, Type u2) -> true
    | _ -> false

(* eq_constr extended with universe erasure *)
let compare_constr_univ f cv_pb t1 t2 =
  match kind_of_term t1, kind_of_term t2 with
      Sort s1, Sort s2 -> base_sort_cmp cv_pb s1 s2
    | Prod (_,t1,c1), Prod (_,t2,c2) ->
	f Reduction.CONV t1 t2 & f cv_pb c1 c2
    | _ -> compare_constr (f Reduction.CONV) t1 t2

let rec constr_cmp cv_pb t1 t2 = compare_constr_univ constr_cmp cv_pb t1 t2

let eq_constr = constr_cmp Reduction.CONV

(* App(c,[t1,...tn]) -> ([c,t1,...,tn-1],tn)
   App(c,[||]) -> ([],c) *)
let split_app c = match kind_of_term c with
    App(c,l) ->
      let len = Array.length l in
      if len=0 then ([],c) else
	let last = Array.get l (len-1) in
	let prev = Array.sub l 0 (len-1) in
	c::(Array.to_list prev), last
  | _ -> assert false

let hdtl l = List.hd l, List.tl l

type subst = (rel_context*constr) Intmap.t

exception CannotFilter

let filtering env cv_pb c1 c2 =
  let evm = ref Intmap.empty in
  let define cv_pb e1 ev c1 =
    try let (e2,c2) = Intmap.find ev !evm in
    let shift = List.length e1 - List.length e2 in
    if constr_cmp cv_pb c1 (lift shift c2) then () else raise CannotFilter
    with Not_found ->
      evm := Intmap.add ev (e1,c1) !evm
  in
  let rec aux env cv_pb c1 c2 =
    match kind_of_term c1, kind_of_term c2 with
      | App _, App _ ->
	  let ((p1,l1),(p2,l2)) = (split_app c1),(split_app c2) in
	  aux env cv_pb l1 l2; if p1=[] & p2=[] then () else
	      aux env cv_pb (applist (hdtl p1)) (applist (hdtl p2))
      | Prod (n,t1,c1), Prod (_,t2,c2) ->
	  aux env cv_pb t1 t2;
	  aux ((n,None,t1)::env) cv_pb c1 c2
      | _, Evar (ev,_) -> define cv_pb env ev c1
      | Evar (ev,_), _ -> define cv_pb env ev c2
      | _ ->
	  if compare_constr_univ
	  (fun pb c1 c2 -> aux env pb c1 c2; true) cv_pb c1 c2 then ()
	  else raise CannotFilter
	  (* TODO: le reste des binders *)
  in
  aux env cv_pb c1 c2; !evm

let decompose_prod_letin : constr -> int * rel_context * constr =
  let rec prodec_rec i l c = match kind_of_term c with
    | Prod (n,t,c)    -> prodec_rec (succ i) ((n,None,t)::l) c
    | LetIn (n,d,t,c) -> prodec_rec (succ i) ((n,Some d,t)::l) c
    | Cast (c,_,_)    -> prodec_rec i l c
    | _               -> i,l,c in
  prodec_rec 0 []

let align_prod_letin c a : rel_context * constr =
  let (lc,_,_) = decompose_prod_letin c in
  let (la,l,a) = decompose_prod_letin a in
  if not (la >= lc) then invalid_arg "align_prod_letin";
  let (l1,l2) = Util.list_chop lc l in
  l2,it_mkProd_or_LetIn a l1

(* On reduit une serie d'eta-redex de tete ou rien du tout  *)
(* [x1:c1;...;xn:cn]@(f;a1...an;x1;...;xn) --> @(f;a1...an) *)
(* Remplace 2 versions précédentes buggées                  *)

let rec eta_reduce_head c =
  match kind_of_term c with
    | Lambda (_,c1,c') ->
	(match kind_of_term (eta_reduce_head c') with
           | App (f,cl) ->
               let lastn = (Array.length cl) - 1 in
               if lastn < 1 then anomaly "application without arguments"
               else
                 (match kind_of_term cl.(lastn) with
                    | Rel 1 ->
			let c' =
                          if lastn = 1 then f
			  else mkApp (f, Array.sub cl 0 lastn)
			in
			if noccurn 1 c'
                        then lift (-1) c'
                        else c
                    | _   -> c)
           | _ -> c)
    | _ -> c


(* alpha-eta conversion : ignore print names and casts *)
let eta_eq_constr =
  let rec aux t1 t2 =
    let t1 = eta_reduce_head (strip_head_cast t1)
    and t2 = eta_reduce_head (strip_head_cast t2) in
    t1=t2 or compare_constr aux t1 t2
  in aux


(* iterator on rel context *)
let process_rel_context f env =
  let sign = named_context_val env in
  let rels = rel_context env in
  let env0 = reset_with_named_context sign env in
  Sign.fold_rel_context f rels ~init:env0

let assums_of_rel_context sign =
  Sign.fold_rel_context
    (fun (na,c,t) l ->
      match c with
          Some _ -> l
        | None -> (na, t)::l)
    sign ~init:[]

let map_rel_context_in_env f env sign =
  let rec aux env acc = function
    | d::sign ->
	aux (push_rel d env) (map_rel_declaration (f env) d :: acc) sign
    | [] ->
	acc
  in
  aux env [] (List.rev sign)

let map_rel_context_with_binders f sign =
  let rec aux k = function
    | d::sign -> map_rel_declaration (f k) d :: aux (k-1) sign
    | [] -> []
  in
  aux (rel_context_length sign) sign

let substl_rel_context l =
  map_rel_context_with_binders (fun k -> substnl l (k-1))

let lift_rel_context n =
  map_rel_context_with_binders (liftn n)

let smash_rel_context sign =
  let rec aux acc = function
  | [] -> acc
  | (_,None,_ as d) :: l -> aux (d::acc) l
  | (_,Some b,_) :: l ->
      (* Quadratic in the number of let but there are probably a few of them *)
      aux (List.rev (substl_rel_context [b] (List.rev acc))) l
  in List.rev (aux [] sign)

let adjust_subst_to_rel_context sign l =
  let rec aux subst sign l =
    match sign, l with
    | (_,None,_)::sign', a::args' -> aux (a::subst) sign' args'
    | (_,Some c,_)::sign', args' ->
	aux (substl (List.rev subst) c :: subst) sign' args'
    | [], [] -> List.rev subst
    | _ -> anomaly "Instance and signature do not match"
  in aux [] (List.rev sign) l

let fold_named_context_both_sides f l ~init = list_fold_right_and_left f l init

let rec mem_named_context id = function
  | (id',_,_) :: _ when id=id' -> true
  | _ :: sign -> mem_named_context id sign
  | [] -> false

let clear_named_body id env =
  let rec aux _ = function
  | (id',Some c,t) when id = id' -> push_named (id,None,t)
  | d -> push_named d in
  fold_named_context aux env ~init:(reset_context env)

let global_vars env ids = Idset.elements (global_vars_set env ids)

let global_vars_set_of_decl env = function
  | (_,None,t) -> global_vars_set env t
  | (_,Some c,t) ->
      Idset.union (global_vars_set env t)
        (global_vars_set env c)

let dependency_closure env sign hyps =
  if Idset.is_empty hyps then [] else
    let (_,lh) =
      Sign.fold_named_context_reverse
        (fun (hs,hl) (x,_,_ as d) ->
          if Idset.mem x hs then
            (Idset.union (global_vars_set_of_decl env d) (Idset.remove x hs),
            x::hl)
          else (hs,hl))
        ~init:(hyps,[])
        sign in
    List.rev lh

(* Combinators on judgments *)

let on_judgment f j = { uj_val = f j.uj_val; uj_type = f j.uj_type }
let on_judgment_value f j = { j with uj_val = f j.uj_val }
let on_judgment_type f j = { j with uj_type = f j.uj_type }

(* Cut a context ctx in 2 parts (ctx1,ctx2) with ctx1 containing k
     variables; skips let-in's *)
let context_chop k ctx =
  let rec chop_aux acc = function
    | (0, l2) -> (List.rev acc, l2)
    | (n, ((_,Some _,_ as h)::t)) -> chop_aux (h::acc) (n, t)
    | (n, (h::t)) -> chop_aux (h::acc) (pred n, t)
    | (_, []) -> anomaly "context_chop"
  in chop_aux [] (k,ctx)

(* Do not skip let-in's *)
let env_rel_context_chop k env =
  let rels = rel_context env in
  let ctx1,ctx2 = list_chop k rels in
  push_rel_context ctx2 (reset_with_named_context (named_context_val env) env),
  ctx1

(*******************************************)
(* Functions to deal with impossible cases *)
(*******************************************)
let impossible_default_case = ref None

let set_impossible_default_clause c = impossible_default_case := Some c

let coq_unit_judge =
  let na1 = Name (id_of_string "A") in
  let na2 = Name (id_of_string "H") in
  fun () ->
    match !impossible_default_case with
    | Some (id,type_of_id) ->
	make_judge id type_of_id
    | None ->
	(* In case the constants id/ID are not defined *)
	make_judge (mkLambda (na1,mkProp,mkLambda(na2,mkRel 1,mkRel 1)))
                 (mkProd (na1,mkProp,mkArrow (mkRel 1) (mkRel 2)))