aboutsummaryrefslogtreecommitdiffhomepage
path: root/kernel/constr.ml
blob: 8e05e29ebb87566ac3a5041f64a9bc22d9e334fd (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
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* File initially created by Gérard Huet and Thierry Coquand in 1984 *)
(* Extension to inductive constructions by Christine Paulin for Coq V5.6 *)
(* Extension to mutual inductive constructions by Christine Paulin for
   Coq V5.10.2 *)
(* Extension to co-inductive constructions by Eduardo Gimenez *)
(* Optimization of substitution functions by Chet Murthy *)
(* Optimization of lifting functions by Bruno Barras, Mar 1997 *)
(* Hash-consing by Bruno Barras in Feb 1998 *)
(* Restructuration of Coq of the type-checking kernel by Jean-Christophe 
   Filliâtre, 1999 *)
(* Abstraction of the syntax of terms and iterators by Hugo Herbelin, 2000 *)
(* Cleaning and lightening of the kernel by Bruno Barras, Nov 2001 *)

(* This file defines the internal syntax of the Calculus of
   Inductive Constructions (CIC) terms together with constructors,
   destructors, iterators and basic functions *)

open Util
open Names
open Univ

type existential_key = Evar.t
type metavariable = int

(* This defines the strategy to use for verifiying a Cast *)
(* Warning: REVERTcast is not exported to vo-files; as of r14492, it has to *)
(* come after the vo-exported cast_kind so as to be compatible with coqchk *)
type cast_kind = VMcast | NATIVEcast | DEFAULTcast | REVERTcast

(* This defines Cases annotations *)
type case_style = LetStyle | IfStyle | LetPatternStyle | MatchStyle | RegularStyle
type case_printing =
  { ind_tags : bool list; (** tell whether letin or lambda in the arity of the inductive type *)
    cstr_tags : bool list array; (* whether each pattern var of each constructor is a let-in (true) or not (false) *)
    style     : case_style }

(* INVARIANT:
 * - Array.length ci_cstr_ndecls = Array.length ci_cstr_nargs
 * - forall (i : 0 .. pred (Array.length ci_cstr_ndecls)),
 *          ci_cstr_ndecls.(i) >= ci_cstr_nargs.(i)
 *)
type case_info =
  { ci_ind        : inductive;      (* inductive type to which belongs the value that is being matched *)
    ci_npar       : int;            (* number of parameters of the above inductive type *)
    ci_cstr_ndecls : int array;     (* For each constructor, the corresponding integer determines
                                       the number of values that can be bound in a match-construct.
                                       NOTE: parameters of the inductive type are therefore excluded from the count *)
    ci_cstr_nargs : int array;      (* for each constructor, the corresponding integers determines
                                       the number of values that can be applied to the constructor,
                                       in addition to the parameters of the related inductive type
                                       NOTE: "lets" are therefore excluded from the count
                                       NOTE: parameters of the inductive type are also excluded from the count *)
    ci_pp_info    : case_printing   (* not interpreted by the kernel *)
  }

(********************************************************************)
(*       Constructions as implemented                               *)
(********************************************************************)

(* [constr array] is an instance matching definitional [named_context] in
   the same order (i.e. last argument first) *)
type 'constr pexistential = existential_key * 'constr array
type ('constr, 'types) prec_declaration =
    Name.t array * 'types array * 'constr array
type ('constr, 'types) pfixpoint =
    (int array * int) * ('constr, 'types) prec_declaration
type ('constr, 'types) pcofixpoint =
    int * ('constr, 'types) prec_declaration
type 'a puniverses = 'a Univ.puniverses
type pconstant = constant puniverses
type pinductive = inductive puniverses
type pconstructor = constructor puniverses

(* [Var] is used for named variables and [Rel] for variables as
   de Bruijn indices. *)
type ('constr, 'types) kind_of_term =
  | Rel       of int
  | Var       of Id.t
  | Meta      of metavariable
  | Evar      of 'constr pexistential
  | Sort      of Sorts.t
  | Cast      of 'constr * cast_kind * 'types
  | Prod      of Name.t * 'types * 'types
  | Lambda    of Name.t * 'types * 'constr
  | LetIn     of Name.t * 'constr * 'types * 'constr
  | App       of 'constr * 'constr array
  | Const     of pconstant
  | Ind       of pinductive
  | Construct of pconstructor
  | Case      of case_info * 'constr * 'constr * 'constr array
  | Fix       of ('constr, 'types) pfixpoint
  | CoFix     of ('constr, 'types) pcofixpoint
  | Proj      of projection * 'constr
(* constr is the fixpoint of the previous type. Requires option
   -rectypes of the Caml compiler to be set *)
type t = (t,t) kind_of_term
type constr = t

type existential = existential_key * constr array
type rec_declaration = Name.t array * constr array * constr array
type fixpoint = (int array * int) * rec_declaration
type cofixpoint = int * rec_declaration

type types = constr

(*********************)
(* Term constructors *)
(*********************)

(* Constructs a DeBrujin index with number n *)
let rels =
  [|Rel  1;Rel  2;Rel  3;Rel  4;Rel  5;Rel  6;Rel  7; Rel  8;
    Rel  9;Rel 10;Rel 11;Rel 12;Rel 13;Rel 14;Rel 15; Rel 16|]

let mkRel n = if 0<n && n<=16 then rels.(n-1) else Rel n

(* Construct a type *)
let mkProp   = Sort Sorts.prop
let mkSet    = Sort Sorts.set
let mkType u = Sort (Sorts.Type u)
let mkSort   = function
  | Sorts.Prop Sorts.Null -> mkProp (* Easy sharing *)
  | Sorts.Prop Sorts.Pos -> mkSet
  | s -> Sort s

(* Constructs the term t1::t2, i.e. the term t1 casted with the type t2 *)
(* (that means t2 is declared as the type of t1) *)
let mkCast (t1,k2,t2) =
  match t1 with
  | Cast (c,k1, _) when (k1 == VMcast || k1 == NATIVEcast) && k1 == k2 -> Cast (c,k1,t2)
  | _ -> Cast (t1,k2,t2)

(* Constructs the product (x:t1)t2 *)
let mkProd (x,t1,t2) = Prod (x,t1,t2)

(* Constructs the abstraction [x:t1]t2 *)
let mkLambda (x,t1,t2) = Lambda (x,t1,t2)

(* Constructs [x=c_1:t]c_2 *)
let mkLetIn (x,c1,t,c2) = LetIn (x,c1,t,c2)

(* If lt = [t1; ...; tn], constructs the application (t1 ... tn) *)
(* We ensure applicative terms have at least one argument and the
   function is not itself an applicative term *)
let mkApp (f, a) =
  if Int.equal (Array.length a) 0 then f else
    match f with
      | App (g, cl) -> App (g, Array.append cl a)
      | _ -> App (f, a)

let map_puniverses f (x,u) = (f x, u)
let in_punivs a = (a, Univ.Instance.empty)

(* Constructs a constant *)
let mkConst c = Const (in_punivs c)
let mkConstU c = Const c

(* Constructs an applied projection *)
let mkProj (p,c) = Proj (p,c)

(* Constructs an existential variable *)
let mkEvar e = Evar e

(* Constructs the ith (co)inductive type of the block named kn *)
let mkInd m = Ind (in_punivs m)
let mkIndU m = Ind m

(* Constructs the jth constructor of the ith (co)inductive type of the
   block named kn. *)
let mkConstruct c = Construct (in_punivs c)
let mkConstructU c = Construct c
let mkConstructUi ((ind,u),i) = Construct ((ind,i),u)

(* Constructs the term <p>Case c of c1 | c2 .. | cn end *)
let mkCase (ci, p, c, ac) = Case (ci, p, c, ac)

(* If recindxs = [|i1,...in|]
      funnames = [|f1,...fn|]
      typarray = [|t1,...tn|]
      bodies   = [|b1,...bn|]
   then

      mkFix ((recindxs,i),(funnames,typarray,bodies))

   constructs the ith function of the block

    Fixpoint f1 [ctx1] : t1 := b1
    with     f2 [ctx2] : t2 := b2
    ...
    with     fn [ctxn] : tn := bn.

   where the length of the jth context is ij.
*)

let mkFix fix = Fix fix

(* If funnames = [|f1,...fn|]
      typarray = [|t1,...tn|]
      bodies   = [|b1,...bn|]
   then

      mkCoFix (i,(funnames,typsarray,bodies))

   constructs the ith function of the block

    CoFixpoint f1 : t1 := b1
    with       f2 : t2 := b2
    ...
    with       fn : tn := bn.
*)
let mkCoFix cofix= CoFix cofix

(* Constructs an existential variable named "?n" *)
let mkMeta  n =  Meta n

(* Constructs a Variable named id *)
let mkVar id = Var id


(************************************************************************)
(*    kind_of_term = constructions as seen by the user                 *)
(************************************************************************)

(* User view of [constr]. For [App], it is ensured there is at
   least one argument and the function is not itself an applicative
   term *)

let kind c = c

(****************************************************************************)
(*              Functions to recur through subterms                         *)
(****************************************************************************)

(* [fold f acc c] folds [f] on the immediate subterms of [c]
   starting from [acc] and proceeding from left to right according to
   the usual representation of the constructions; it is not recursive *)

let fold f acc c = match kind c with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> acc
  | Cast (c,_,t) -> f (f acc c) t
  | Prod (_,t,c) -> f (f acc t) c
  | Lambda (_,t,c) -> f (f acc t) c
  | LetIn (_,b,t,c) -> f (f (f acc b) t) c
  | App (c,l) -> Array.fold_left f (f acc c) l
  | Proj (p,c) -> f acc c
  | Evar (_,l) -> Array.fold_left f acc l
  | Case (_,p,c,bl) -> Array.fold_left f (f (f acc p) c) bl
  | Fix (_,(lna,tl,bl)) ->
    Array.fold_left2 (fun acc t b -> f (f acc t) b) acc tl bl
  | CoFix (_,(lna,tl,bl)) ->
    Array.fold_left2 (fun acc t b -> f (f acc t) b) acc tl bl

(* [iter f c] iters [f] on the immediate subterms of [c]; it is
   not recursive and the order with which subterms are processed is
   not specified *)

let iter f c = match kind c with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> ()
  | Cast (c,_,t) -> f c; f t
  | Prod (_,t,c) -> f t; f c
  | Lambda (_,t,c) -> f t; f c
  | LetIn (_,b,t,c) -> f b; f t; f c
  | App (c,l) -> f c; Array.iter f l
  | Proj (p,c) -> f c
  | Evar (_,l) -> Array.iter f l
  | Case (_,p,c,bl) -> f p; f c; Array.iter f bl
  | Fix (_,(_,tl,bl)) -> Array.iter f tl; Array.iter f bl
  | CoFix (_,(_,tl,bl)) -> Array.iter f tl; Array.iter f bl

(* [iter_with_binders g f n c] iters [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; it is not recursive and the order with which
   subterms are processed is not specified *)

let iter_with_binders g f n c = match kind c with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> ()
  | Cast (c,_,t) -> f n c; f n t
  | Prod (_,t,c) -> f n t; f (g n) c
  | Lambda (_,t,c) -> f n t; f (g n) c
  | LetIn (_,b,t,c) -> f n b; f n t; f (g n) c
  | App (c,l) -> f n c; CArray.Fun1.iter f n l
  | Evar (_,l) -> CArray.Fun1.iter f n l
  | Case (_,p,c,bl) -> f n p; f n c; CArray.Fun1.iter f n bl
  | Proj (p,c) -> f n c
  | Fix (_,(_,tl,bl)) ->
      CArray.Fun1.iter f n tl;
      CArray.Fun1.iter f (iterate g (Array.length tl) n) bl
  | CoFix (_,(_,tl,bl)) ->
      CArray.Fun1.iter f n tl;
      CArray.Fun1.iter f (iterate g (Array.length tl) n) bl

(* [map f c] maps [f] on the immediate subterms of [c]; it is
   not recursive and the order with which subterms are processed is
   not specified *)

let map f c = match kind c with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> c
  | Cast (b,k,t) ->
      let b' = f b in
      let t' = f t in
      if b'==b && t' == t then c
      else mkCast (b', k, t')
  | Prod (na,t,b) ->
      let b' = f b in
      let t' = f t in
      if b'==b && t' == t then c
      else mkProd (na, t', b')
  | Lambda (na,t,b) ->
      let b' = f b in
      let t' = f t in
      if b'==b && t' == t then c
      else mkLambda (na, t', b')
  | LetIn (na,b,t,k) ->
      let b' = f b in
      let t' = f t in
      let k' = f k in
      if b'==b && t' == t && k'==k then c
      else mkLetIn (na, b', t', k')
  | App (b,l) ->
      let b' = f b in
      let l' = Array.smartmap f l in
      if b'==b && l'==l then c
      else mkApp (b', l')
  | Proj (p,t) ->
      let t' = f t in
      if t' == t then c
      else mkProj (p, t')
  | Evar (e,l) ->
      let l' = Array.smartmap f l in
      if l'==l then c
      else mkEvar (e, l')
  | Case (ci,p,b,bl) ->
      let b' = f b in
      let p' = f p in
      let bl' = Array.smartmap f bl in
      if b'==b && p'==p && bl'==bl then c
      else mkCase (ci, p', b', bl')
  | Fix (ln,(lna,tl,bl)) ->
      let tl' = Array.smartmap f tl in
      let bl' = Array.smartmap f bl in
      if tl'==tl && bl'==bl then c
      else mkFix (ln,(lna,tl',bl'))
  | CoFix(ln,(lna,tl,bl)) ->
      let tl' = Array.smartmap f tl in
      let bl' = Array.smartmap f bl in
      if tl'==tl && bl'==bl then c
      else mkCoFix (ln,(lna,tl',bl'))

(* Like {!map} but with an accumulator. *)

let fold_map f accu c = match kind c with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> accu, c
  | Cast (b,k,t) ->
      let accu, b' = f accu b in
      let accu, t' = f accu t in
      if b'==b && t' == t then accu, c
      else accu, mkCast (b', k, t')
  | Prod (na,t,b) ->
      let accu, b' = f accu b in
      let accu, t' = f accu t in
      if b'==b && t' == t then accu, c
      else accu, mkProd (na, t', b')
  | Lambda (na,t,b) ->
      let accu, b' = f accu b in
      let accu, t' = f accu t in
      if b'==b && t' == t then accu, c
      else accu, mkLambda (na, t', b')
  | LetIn (na,b,t,k) ->
      let accu, b' = f accu b in
      let accu, t' = f accu t in
      let accu, k' = f accu k in
      if b'==b && t' == t && k'==k then accu, c
      else accu, mkLetIn (na, b', t', k')
  | App (b,l) ->
      let accu, b' = f accu b in
      let accu, l' = Array.smartfoldmap f accu l in
      if b'==b && l'==l then accu, c
      else accu, mkApp (b', l')
  | Proj (p,t) ->
      let accu, t' = f accu t in
      if t' == t then accu, c
      else accu, mkProj (p, t')
  | Evar (e,l) ->
      let accu, l' = Array.smartfoldmap f accu l in
      if l'==l then accu, c
      else accu, mkEvar (e, l')
  | Case (ci,p,b,bl) ->
      let accu, b' = f accu b in
      let accu, p' = f accu p in
      let accu, bl' = Array.smartfoldmap f accu bl in
      if b'==b && p'==p && bl'==bl then accu, c
      else accu, mkCase (ci, p', b', bl')
  | Fix (ln,(lna,tl,bl)) ->
      let accu, tl' = Array.smartfoldmap f accu tl in
      let accu, bl' = Array.smartfoldmap f accu bl in
      if tl'==tl && bl'==bl then accu, c
      else accu, mkFix (ln,(lna,tl',bl'))
  | CoFix(ln,(lna,tl,bl)) ->
      let accu, tl' = Array.smartfoldmap f accu tl in
      let accu, bl' = Array.smartfoldmap f accu bl in
      if tl'==tl && bl'==bl then accu, c
      else accu, mkCoFix (ln,(lna,tl',bl'))

(* [map_with_binders 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; it is not recursive and the order with which
   subterms are processed is not specified *)

let map_with_binders g f l c0 = match kind c0 with
  | (Rel _ | Meta _ | Var _   | Sort _ | Const _ | Ind _
    | Construct _) -> c0
  | Cast (c, k, t) ->
    let c' = f l c in
    let t' = f l t in
    if c' == c && t' == t then c0
    else mkCast (c', k, t')
  | Prod (na, t, c) ->
    let t' = f l t in
    let c' = f (g l) c in
    if t' == t && c' == c then c0
    else mkProd (na, t', c')
  | Lambda (na, t, c) ->
    let t' = f l t in
    let c' = f (g l) c in
    if t' == t && c' == c then c0
    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 l) c in
    if b' == b && t' == t && c' == c then c0
    else mkLetIn (na, b', t', c')
  | App (c, al) ->
    let c' = f l c in
    let al' = CArray.Fun1.smartmap f l al in
    if c' == c && al' == al then c0
    else mkApp (c', al')
  | Proj (p, t) ->
    let t' = f l t in
    if t' == t then c0
    else mkProj (p, t')
  | Evar (e, al) ->
    let al' = CArray.Fun1.smartmap f l al in
    if al' == al then c0
    else mkEvar (e, al')
  | Case (ci, p, c, bl) ->
    let p' = f l p in
    let c' = f l c in
    let bl' = CArray.Fun1.smartmap f l bl in
    if p' == p && c' == c && bl' == bl then c0
    else mkCase (ci, p', c', bl')
  | Fix (ln, (lna, tl, bl)) ->
    let tl' = CArray.Fun1.smartmap f l tl in
    let l' = iterate g (Array.length tl) l in
    let bl' = CArray.Fun1.smartmap f l' bl in
    if tl' == tl && bl' == bl then c0
    else mkFix (ln,(lna,tl',bl'))
  | CoFix(ln,(lna,tl,bl)) ->
    let tl' = CArray.Fun1.smartmap f l tl in
    let l' = iterate g (Array.length tl) l in
    let bl' = CArray.Fun1.smartmap f l' bl in
    mkCoFix (ln,(lna,tl',bl'))

(* [compare_head_gen_evar k1 k2 u s e eq leq c1 c2] compare [c1] and
   [c2] (using [k1] to expose the structure of [c1] and [k2] to expose
   the structure [c2]) using [eq] to compare the immediate subterms of
   [c1] of [c2] for conversion if needed, [leq] for cumulativity, [u]
   to compare universe instances, and [s] to compare sorts; Cast's,
   application associativity, binders name and Cases annotations are
   not taken into account. Note that as [kind1] and [kind2] are
   potentially different, we cannot use, in recursive case, the
   optimisation that physically equal arrays are equals (hence the
   calls to {!Array.equal_norefl}). *)

let compare_head_gen_leq_with kind1 kind2 eq_universes leq_sorts eq leq t1 t2 =
  match kind1 t1, kind2 t2 with
  | Rel n1, Rel n2 -> Int.equal n1 n2
  | Meta m1, Meta m2 -> Int.equal m1 m2
  | Var id1, Var id2 -> Id.equal id1 id2
  | Sort s1, Sort s2 -> leq_sorts s1 s2
  | Cast (c1,_,_), _ -> leq c1 t2
  | _, Cast (c2,_,_) -> leq t1 c2
  | Prod (_,t1,c1), Prod (_,t2,c2) -> eq t1 t2 && leq c1 c2
  | Lambda (_,t1,c1), Lambda (_,t2,c2) -> eq t1 t2 && eq c1 c2
  | LetIn (_,b1,t1,c1), LetIn (_,b2,t2,c2) -> eq b1 b2 && eq t1 t2 && leq c1 c2
  | App (Cast(c1, _, _),l1), _ -> leq (mkApp (c1,l1)) t2
  | _, App (Cast (c2, _, _),l2) -> leq t1 (mkApp (c2,l2))
  | App (c1,l1), App (c2,l2) ->
      Int.equal (Array.length l1) (Array.length l2) &&
        eq c1 c2 && Array.equal_norefl eq l1 l2
  | Proj (p1,c1), Proj (p2,c2) -> Projection.equal p1 p2 && eq c1 c2
  | Evar (e1,l1), Evar (e2,l2) -> Evar.equal e1 e2 && Array.equal eq l1 l2
  | Const (c1,u1), Const (c2,u2) -> eq_constant c1 c2 && eq_universes true u1 u2
  | Ind (c1,u1), Ind (c2,u2) -> eq_ind c1 c2 && eq_universes false u1 u2
  | Construct (c1,u1), Construct (c2,u2) -> eq_constructor c1 c2 && eq_universes false u1 u2
  | Case (_,p1,c1,bl1), Case (_,p2,c2,bl2) ->
      eq p1 p2 && eq c1 c2 && Array.equal eq bl1 bl2
  | Fix ((ln1, i1),(_,tl1,bl1)), Fix ((ln2, i2),(_,tl2,bl2)) ->
      Int.equal i1 i2 && Array.equal Int.equal ln1 ln2
      && Array.equal_norefl eq tl1 tl2 && Array.equal_norefl eq bl1 bl2
  | CoFix(ln1,(_,tl1,bl1)), CoFix(ln2,(_,tl2,bl2)) ->
      Int.equal ln1 ln2 && Array.equal_norefl eq tl1 tl2 && Array.equal_norefl eq bl1 bl2
  | _ -> false

(* [compare_head_gen_leq u s eq leq c1 c2] compare [c1] and [c2] using [eq] to compare
   the immediate subterms of [c1] of [c2] for conversion if needed, [leq] for cumulativity,
   [u] to compare universe instances and [s] to compare sorts; Cast's,
   application associativity, binders name and Cases annotations are
   not taken into account *)

let compare_head_gen_leq eq_universes leq_sorts eq leq t1 t2 =
  compare_head_gen_leq_with kind kind  eq_universes leq_sorts eq leq t1 t2

(* [compare_head_gen u s f c1 c2] compare [c1] and [c2] using [f] to
   compare the immediate subterms of [c1] of [c2] if needed, [u] to
   compare universe instances and [s] to compare sorts; Cast's,
   application associativity, binders name and Cases annotations are
   not taken into account.

   [compare_head_gen_with] is a variant taking kind-of-term functions,
   to expose subterms of [c1] and [c2], as arguments. *)

let compare_head_gen_with kind1 kind2 eq_universes eq_sorts eq t1 t2 =
  compare_head_gen_leq_with kind1 kind2 eq_universes eq_sorts eq eq t1 t2

let compare_head_gen eq_universes eq_sorts eq t1 t2 =
  compare_head_gen_leq eq_universes eq_sorts eq eq t1 t2

let compare_head = compare_head_gen (fun _ -> Univ.Instance.equal) Sorts.equal

(*******************************)
(*  alpha conversion functions *)
(*******************************)

(* alpha conversion : ignore print names and casts *)

let rec eq_constr m n =
  (m == n) || compare_head_gen (fun _ -> Instance.equal) Sorts.equal eq_constr m n

let equal m n = eq_constr m n (* to avoid tracing a recursive fun *)

let eq_constr_univs univs m n =
  if m == n then true
  else 
    let eq_universes _ = UGraph.check_eq_instances univs in
    let eq_sorts s1 s2 = s1 == s2 || UGraph.check_eq univs (Sorts.univ_of_sort s1) (Sorts.univ_of_sort s2) in
    let rec eq_constr' m n = 
      m == n ||	compare_head_gen eq_universes eq_sorts eq_constr' m n
    in compare_head_gen eq_universes eq_sorts eq_constr' m n

let leq_constr_univs univs m n =
  if m == n then true
  else 
    let eq_universes _ = UGraph.check_eq_instances univs in
    let eq_sorts s1 s2 = s1 == s2 || 
      UGraph.check_eq univs (Sorts.univ_of_sort s1) (Sorts.univ_of_sort s2) in
    let leq_sorts s1 s2 = s1 == s2 || 
      UGraph.check_leq univs (Sorts.univ_of_sort s1) (Sorts.univ_of_sort s2) in
    let rec eq_constr' m n = 
      m == n ||	compare_head_gen eq_universes eq_sorts eq_constr' m n
    in
    let rec compare_leq m n =
      compare_head_gen_leq eq_universes leq_sorts eq_constr' leq_constr' m n
    and leq_constr' m n = m == n || compare_leq m n in
    compare_leq m n

let eq_constr_univs_infer univs m n =
  if m == n then true, Constraint.empty
  else 
    let cstrs = ref Constraint.empty in
    let eq_universes strict = UGraph.check_eq_instances univs in
    let eq_sorts s1 s2 = 
      if Sorts.equal s1 s2 then true
      else
	let u1 = Sorts.univ_of_sort s1 and u2 = Sorts.univ_of_sort s2 in
	if UGraph.check_eq univs u1 u2 then true
	else
	  (cstrs := Univ.enforce_eq u1 u2 !cstrs;
	   true)
    in
    let rec eq_constr' m n = 
      m == n ||	compare_head_gen eq_universes eq_sorts eq_constr' m n
    in
    let res = compare_head_gen eq_universes eq_sorts eq_constr' m n in
    res, !cstrs

let leq_constr_univs_infer univs m n =
  if m == n then true, Constraint.empty
  else 
    let cstrs = ref Constraint.empty in
    let eq_universes strict l l' = UGraph.check_eq_instances univs l l' in
    let eq_sorts s1 s2 = 
      if Sorts.equal s1 s2 then true
      else
	let u1 = Sorts.univ_of_sort s1 and u2 = Sorts.univ_of_sort s2 in
	if UGraph.check_eq univs u1 u2 then true
	else (cstrs := Univ.enforce_eq u1 u2 !cstrs;
	      true)
    in
    let leq_sorts s1 s2 = 
      if Sorts.equal s1 s2 then true
      else 
	let u1 = Sorts.univ_of_sort s1 and u2 = Sorts.univ_of_sort s2 in
	if UGraph.check_leq univs u1 u2 then true
	else
	  (cstrs := Univ.enforce_leq u1 u2 !cstrs; 
	   true)
    in
    let rec eq_constr' m n = 
      m == n ||	compare_head_gen eq_universes eq_sorts eq_constr' m n
    in
    let rec compare_leq m n =
      compare_head_gen_leq eq_universes leq_sorts eq_constr' leq_constr' m n
    and leq_constr' m n = m == n || compare_leq m n in
    let res = compare_leq m n in
    res, !cstrs

let always_true _ _ = true

let rec eq_constr_nounivs m n =
  (m == n) || compare_head_gen (fun _ -> always_true) always_true eq_constr_nounivs m n

(** We only use this function over blocks! *)
let tag t = Obj.tag (Obj.repr t)

let constr_ord_int f t1 t2 =
  let (=?) f g i1 i2 j1 j2=
    let c = f i1 i2 in
    if Int.equal c 0 then g j1 j2 else c in
  let (==?) fg h i1 i2 j1 j2 k1 k2=
    let c=fg i1 i2 j1 j2 in
    if Int.equal c 0 then h k1 k2 else c in
  let fix_cmp (a1, i1) (a2, i2) =
    ((Array.compare Int.compare) =? Int.compare) a1 a2 i1 i2
  in
  match kind t1, kind t2 with
    | Rel n1, Rel n2 -> Int.compare n1 n2
    | Meta m1, Meta m2 -> Int.compare m1 m2
    | Var id1, Var id2 -> Id.compare id1 id2
    | Sort s1, Sort s2 -> Sorts.compare s1 s2
    | Cast (c1,_,_), _ -> f c1 t2
    | _, Cast (c2,_,_) -> f t1 c2
    | Prod (_,t1,c1), Prod (_,t2,c2)
    | Lambda (_,t1,c1), Lambda (_,t2,c2) ->
        (f =? f) t1 t2 c1 c2
    | LetIn (_,b1,t1,c1), LetIn (_,b2,t2,c2) ->
        ((f =? f) ==? f) b1 b2 t1 t2 c1 c2
    | App (Cast(c1,_,_),l1), _ -> f (mkApp (c1,l1)) t2
    | _, App (Cast(c2, _,_),l2) -> f t1 (mkApp (c2,l2))
    | App (c1,l1), App (c2,l2) -> (f =? (Array.compare f)) c1 c2 l1 l2
    | Proj (p1,c1), Proj (p2,c2) -> (Projection.compare =? f) p1 p2 c1 c2
    | Evar (e1,l1), Evar (e2,l2) ->
        (Evar.compare =? (Array.compare f)) e1 e2 l1 l2
    | Const (c1,u1), Const (c2,u2) -> con_ord c1 c2
    | Ind (ind1, u1), Ind (ind2, u2) -> ind_ord ind1 ind2
    | Construct (ct1,u1), Construct (ct2,u2) -> constructor_ord ct1 ct2
    | Case (_,p1,c1,bl1), Case (_,p2,c2,bl2) ->
        ((f =? f) ==? (Array.compare f)) p1 p2 c1 c2 bl1 bl2
    | Fix (ln1,(_,tl1,bl1)), Fix (ln2,(_,tl2,bl2)) ->
        ((fix_cmp =? (Array.compare f)) ==? (Array.compare f))
        ln1 ln2 tl1 tl2 bl1 bl2
    | CoFix(ln1,(_,tl1,bl1)), CoFix(ln2,(_,tl2,bl2)) ->
        ((Int.compare =? (Array.compare f)) ==? (Array.compare f))
        ln1 ln2 tl1 tl2 bl1 bl2
    | t1, t2 -> Int.compare (tag t1) (tag t2)

let rec compare m n=
  constr_ord_int compare m n

(*******************)
(*  hash-consing   *)
(*******************)

(* Hash-consing of [constr] does not use the module [Hashcons] because
   [Hashcons] is not efficient on deep tree-like data
   structures. Indeed, [Hashcons] is based the (very efficient)
   generic hash function [Hashtbl.hash], which computes the hash key
   through a depth bounded traversal of the data structure to be
   hashed. As a consequence, for a deep [constr] like the natural
   number 1000 (S (S (... (S O)))), the same hash is assigned to all
   the sub [constr]s greater than the maximal depth handled by
   [Hashtbl.hash]. This entails a huge number of collisions in the
   hash table and leads to cubic hash-consing in this worst-case.

   In order to compute a hash key that is independent of the data
   structure depth while being constant-time, an incremental hashing
   function must be devised. A standard implementation creates a cache
   of the hashing function by decorating each node of the hash-consed
   data structure with its hash key. In that case, the hash function
   can deduce the hash key of a toplevel data structure by a local
   computation based on the cache held on its substructures.
   Unfortunately, this simple implementation introduces a space
   overhead that is damageable for the hash-consing of small [constr]s
   (the most common case). One can think of an heterogeneous
   distribution of caches on smartly chosen nodes, but this is forbidden
   by the use of generic equality in Coq source code. (Indeed, this forces
   each [constr] to have a unique canonical representation.)

   Given that hash-consing proceeds inductively, we can nonetheless
   computes the hash key incrementally during hash-consing by changing
   a little the signature of the hash-consing function: it now returns
   both the hash-consed term and its hash key. This simple solution is
   implemented in the following code: it does not introduce a space
   overhead in [constr], that's why the efficiency is unchanged for
   small [constr]s. Besides, it does handle deep [constr]s without
   introducing an unreasonable number of collisions in the hash table.
   Some benchmarks make us think that this implementation of
   hash-consing is linear in the size of the hash-consed data
   structure for our daily use of Coq.
*)

let array_eqeq t1 t2 =
  t1 == t2 ||
  (Int.equal (Array.length t1) (Array.length t2) &&
   let rec aux i =
     (Int.equal i (Array.length t1)) || (t1.(i) == t2.(i) && aux (i + 1))
   in aux 0)

let hasheq t1 t2 =
  match t1, t2 with
    | Rel n1, Rel n2 -> n1 == n2
    | Meta m1, Meta m2 -> m1 == m2
    | Var id1, Var id2 -> id1 == id2
    | Sort s1, Sort s2 -> s1 == s2
    | Cast (c1,k1,t1), Cast (c2,k2,t2) -> c1 == c2 && k1 == k2 && t1 == t2
    | Prod (n1,t1,c1), Prod (n2,t2,c2) -> n1 == n2 && t1 == t2 && c1 == c2
    | Lambda (n1,t1,c1), Lambda (n2,t2,c2) -> n1 == n2 && t1 == t2 && c1 == c2
    | LetIn (n1,b1,t1,c1), LetIn (n2,b2,t2,c2) ->
      n1 == n2 && b1 == b2 && t1 == t2 && c1 == c2
    | App (c1,l1), App (c2,l2) -> c1 == c2 && array_eqeq l1 l2
    | Proj (p1,c1), Proj(p2,c2) -> p1 == p2 && c1 == c2
    | Evar (e1,l1), Evar (e2,l2) -> Evar.equal e1 e2 && array_eqeq l1 l2
    | Const (c1,u1), Const (c2,u2) -> c1 == c2 && u1 == u2
    | Ind ((sp1,i1),u1), Ind ((sp2,i2),u2) -> 
      sp1 == sp2 && Int.equal i1 i2 && u1 == u2
    | Construct (((sp1,i1),j1),u1), Construct (((sp2,i2),j2),u2) ->
      sp1 == sp2 && Int.equal i1 i2 && Int.equal j1 j2 && u1 == u2
    | Case (ci1,p1,c1,bl1), Case (ci2,p2,c2,bl2) ->
      ci1 == ci2 && p1 == p2 && c1 == c2 && array_eqeq bl1 bl2
    | Fix ((ln1, i1),(lna1,tl1,bl1)), Fix ((ln2, i2),(lna2,tl2,bl2)) ->
      Int.equal i1 i2
      && Array.equal Int.equal ln1 ln2
      && array_eqeq lna1 lna2
      && array_eqeq tl1 tl2
      && array_eqeq bl1 bl2
    | CoFix(ln1,(lna1,tl1,bl1)), CoFix(ln2,(lna2,tl2,bl2)) ->
      Int.equal ln1 ln2
      && array_eqeq lna1 lna2
      && array_eqeq tl1 tl2
      && array_eqeq bl1 bl2
    | _ -> false

(** Note that the following Make has the side effect of creating
    once and for all the table we'll use for hash-consing all constr *)

module HashsetTerm =
  Hashset.Make(struct type t = constr let equal = hasheq end)

module HashsetTermArray =
  Hashset.Make(struct type t = constr array let equal = array_eqeq end)

let term_table = HashsetTerm.create 19991
(* The associative table to hashcons terms. *)

let term_array_table = HashsetTermArray.create 4999
(* The associative table to hashcons term arrays. *)

open Hashset.Combine

let hash_cast_kind = function
| VMcast -> 0
| NATIVEcast -> 1
| DEFAULTcast -> 2
| REVERTcast -> 3

let sh_instance = Univ.Instance.share

(* [hashcons hash_consing_functions constr] computes an hash-consed
   representation for [constr] using [hash_consing_functions] on
   leaves. *)
let hashcons (sh_sort,sh_ci,sh_construct,sh_ind,sh_con,sh_na,sh_id) =
  let rec hash_term t =
    match t with
      | Var i ->
	(Var (sh_id i), combinesmall 1 (Id.hash i))
      | Sort s ->
	(Sort (sh_sort s), combinesmall 2 (Sorts.hash s))
      | Cast (c, k, t) ->
	let c, hc = sh_rec c in
	let t, ht = sh_rec t in
	(Cast (c, k, t), combinesmall 3 (combine3 hc (hash_cast_kind k) ht))
      | Prod (na,t,c) ->
	let t, ht = sh_rec t
	and c, hc = sh_rec c in
	(Prod (sh_na na, t, c), combinesmall 4 (combine3 (Name.hash na) ht hc))
      | Lambda (na,t,c) ->
	let t, ht = sh_rec t
	and c, hc = sh_rec c in
	(Lambda (sh_na na, t, c), combinesmall 5 (combine3 (Name.hash na) ht hc))
      | LetIn (na,b,t,c) ->
	let b, hb = sh_rec b in
	let t, ht = sh_rec t in
	let c, hc = sh_rec c in
	(LetIn (sh_na na, b, t, c), combinesmall 6 (combine4 (Name.hash na) hb ht hc))
      | App (c,l) ->
	let c, hc = sh_rec c in
	let l, hl = hash_term_array l in
	(App (c,l), combinesmall 7 (combine hl hc))
      | Evar (e,l) ->
	let l, hl = hash_term_array l in
	(Evar (e,l), combinesmall 8 (combine (Evar.hash e) hl))
      | Proj (p,c) ->
        let c, hc = sh_rec c in
	let p' = Projection.hcons p in
	  (Proj (p', c), combinesmall 17 (combine (Projection.hash p') hc))
      | Const (c,u) ->
	let c' = sh_con c in
	let u', hu = sh_instance u in
	(Const (c', u'), combinesmall 9 (combine (Constant.hash c) hu))
      | Ind ((kn,i) as ind,u) ->
	let u', hu = sh_instance u in
	(Ind (sh_ind ind, u'), 
	 combinesmall 10 (combine (ind_hash ind) hu))
      | Construct ((((kn,i),j) as c,u))->
	let u', hu = sh_instance u in
	(Construct (sh_construct c, u'),
	 combinesmall 11 (combine (constructor_hash c) hu))
      | Case (ci,p,c,bl) ->
	let p, hp = sh_rec p
	and c, hc = sh_rec c in
	let bl,hbl = hash_term_array bl in
	let hbl = combine (combine hc hp) hbl in
	(Case (sh_ci ci, p, c, bl), combinesmall 12 hbl)
      | Fix (ln,(lna,tl,bl)) ->
	let bl,hbl = hash_term_array bl in
	let tl,htl = hash_term_array tl in
        let () = Array.iteri (fun i x -> Array.unsafe_set lna i (sh_na x)) lna in
        let fold accu na = combine (Name.hash na) accu in
        let hna = Array.fold_left fold 0 lna in
        let h = combine3 hna hbl htl in
	(Fix (ln,(lna,tl,bl)), combinesmall 13 h)
      | CoFix(ln,(lna,tl,bl)) ->
	let bl,hbl = hash_term_array bl in
	let tl,htl = hash_term_array tl in
        let () = Array.iteri (fun i x -> Array.unsafe_set lna i (sh_na x)) lna in
        let fold accu na = combine (Name.hash na) accu in
        let hna = Array.fold_left fold 0 lna in
        let h = combine3 hna hbl htl in
	(CoFix (ln,(lna,tl,bl)), combinesmall 14 h)
      | Meta n ->
	(t, combinesmall 15 n)
      | Rel n ->
	(t, combinesmall 16 n)

  and sh_rec t =
    let (y, h) = hash_term t in
    (* [h] must be positive. *)
    let h = h land 0x3FFFFFFF in
    (HashsetTerm.repr h y term_table, h)

  (* Note : During hash-cons of arrays, we modify them *in place* *)

  and hash_term_array t =
    let accu = ref 0 in
    for i = 0 to Array.length t - 1 do
      let x, h = sh_rec (Array.unsafe_get t i) in
      accu := combine !accu h;
      Array.unsafe_set t i x
    done;
    (* [h] must be positive. *)
    let h = !accu land 0x3FFFFFFF in
    (HashsetTermArray.repr h t term_array_table, h)

  in
  (* Make sure our statically allocated Rels (1 to 16) are considered
     as canonical, and hence hash-consed to themselves *)
  ignore (hash_term_array rels);

  fun t -> fst (sh_rec t)

(* Exported hashing fonction on constr, used mainly in plugins.
   Appears to have slight differences from [snd (hash_term t)] above ? *)

let rec hash t =
  match kind t with
    | Var i -> combinesmall 1 (Id.hash i)
    | Sort s -> combinesmall 2 (Sorts.hash s)
    | Cast (c, k, t) ->
      let hc = hash c in
      let ht = hash t in
      combinesmall 3 (combine3 hc (hash_cast_kind k) ht)
    | Prod (_, t, c) -> combinesmall 4 (combine (hash t) (hash c))
    | Lambda (_, t, c) -> combinesmall 5 (combine (hash t) (hash c))
    | LetIn (_, b, t, c) ->
      combinesmall 6 (combine3 (hash b) (hash t) (hash c))
    | App (Cast(c, _, _),l) -> hash (mkApp (c,l))
    | App (c,l) ->
      combinesmall 7 (combine (hash_term_array l) (hash c))
    | Proj (p,c) ->
      combinesmall 17 (combine (Projection.hash p) (hash c))
    | Evar (e,l) ->
      combinesmall 8 (combine (Evar.hash e) (hash_term_array l))
    | Const (c,u) ->
      combinesmall 9 (combine (Constant.hash c) (Instance.hash u))
    | Ind (ind,u) ->
      combinesmall 10 (combine (ind_hash ind) (Instance.hash u))
    | Construct (c,u) ->
      combinesmall 11 (combine (constructor_hash c) (Instance.hash u))
    | Case (_ , p, c, bl) ->
      combinesmall 12 (combine3 (hash c) (hash p) (hash_term_array bl))
    | Fix (ln ,(_, tl, bl)) ->
      combinesmall 13 (combine (hash_term_array bl) (hash_term_array tl))
    | CoFix(ln, (_, tl, bl)) ->
       combinesmall 14 (combine (hash_term_array bl) (hash_term_array tl))
    | Meta n -> combinesmall 15 n
    | Rel n -> combinesmall 16 n

and hash_term_array t =
  Array.fold_left (fun acc t -> combine (hash t) acc) 0 t

module CaseinfoHash =
struct
  type t = case_info
  type u = inductive -> inductive
  let hashcons hind ci = { ci with ci_ind = hind ci.ci_ind }
  let pp_info_equal info1 info2 =
    List.equal (==) info1.ind_tags info2.ind_tags &&
    Array.equal (List.equal (==)) info1.cstr_tags info2.cstr_tags &&
    info1.style == info2.style
  let equal ci ci' =
    ci.ci_ind == ci'.ci_ind &&
    Int.equal ci.ci_npar ci'.ci_npar &&
    Array.equal Int.equal ci.ci_cstr_ndecls ci'.ci_cstr_ndecls && (* we use [Array.equal] on purpose *)
    Array.equal Int.equal ci.ci_cstr_nargs ci'.ci_cstr_nargs && (* we use [Array.equal] on purpose *)
    pp_info_equal ci.ci_pp_info ci'.ci_pp_info  (* we use (=) on purpose *)
  open Hashset.Combine
  let hash_bool b = if b then 0 else 1
  let hash_bool_list = List.fold_left (fun n b -> combine n (hash_bool b))
  let hash_pp_info info =
    let h1 = match info.style with
    | LetStyle -> 0
    | IfStyle -> 1
    | LetPatternStyle -> 2
    | MatchStyle -> 3
    | RegularStyle -> 4 in
    let h2 = hash_bool_list 0 info.ind_tags in
    let h3 = Array.fold_left hash_bool_list 0 info.cstr_tags in
    combine3 h1 h2 h3
  let hash ci =
    let h1 = ind_hash ci.ci_ind in
    let h2 = Int.hash ci.ci_npar in
    let h3 = Array.fold_left combine 0 ci.ci_cstr_ndecls in
    let h4 = Array.fold_left combine 0 ci.ci_cstr_nargs in
    let h5 = hash_pp_info ci.ci_pp_info in
    combine5 h1 h2 h3 h4 h5
end

module Hcaseinfo = Hashcons.Make(CaseinfoHash)

let case_info_hash = CaseinfoHash.hash

module Hsorts =
  Hashcons.Make(
    struct
      open Sorts

      type t = Sorts.t
      type u = universe -> universe
      let hashcons huniv = function
          Prop c -> Prop c
        | Type u -> Type (huniv u)
      let equal s1 s2 =
        s1 == s2 ||
	  match (s1,s2) with
            (Prop c1, Prop c2) -> c1 == c2
          | (Type u1, Type u2) -> u1 == u2
          |_ -> false
      let hash = function
	| Prop Null -> 0 | Prop Pos -> 1
	| Type u -> 2 + Universe.hash u
    end)

(* let hcons_sorts = Hashcons.simple_hcons Hsorts.generate hcons_univ *)
let hcons_caseinfo = Hashcons.simple_hcons Hcaseinfo.generate Hcaseinfo.hcons hcons_ind

let hcons =
  hashcons
    (Sorts.hcons,
     hcons_caseinfo,
     hcons_construct,
     hcons_ind,
     hcons_con,
     Name.hcons,
     Id.hcons)

(* let hcons_types = hcons_constr *)

(*******)
(* Type of abstract machine values *)
(** FIXME: nothing to do there *)
type values