package rocq-runtime

  1. Overview
  2. Docs
package rocq-runtime
Legend:
Page
Library
Module
Module type
Parameter
Class
Class type
Source

Source file inductiveops.ml

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

open CErrors
open Util
open Names
open Term
open EConstr
open Vars
open Context
open Declarations
open Declareops
open Environ
open Reductionops
open Context.Rel.Declaration

(* The following three functions are similar to the ones defined in
   Inductive, but they expect an env *)

let type_of_inductive env (ind,u) =
 let u = EConstr.Unsafe.to_instance u in
 let (mib,_ as specif) = Inductive.lookup_mind_specif env ind in
 Typeops.check_hyps_inclusion env (GlobRef.IndRef ind) mib.mind_hyps;
 let t = Inductive.type_of_inductive (specif,u) in
 EConstr.of_constr @@ Arguments_renaming.rename_type t (IndRef ind)

let e_type_of_inductive env sigma (ind,u) =
 let (mib,_ as specif) = Inductive.lookup_mind_specif env ind in
 Reductionops.check_hyps_inclusion env sigma (GlobRef.IndRef ind) mib.mind_hyps;
 let t = Inductive.type_of_inductive (specif, EConstr.Unsafe.to_instance u) in
 EConstr.of_constr (Arguments_renaming.rename_type t (IndRef ind))

(* Return type as quoted by the user *)
let type_of_constructor env (cstr,u) =
 let u = EConstr.Unsafe.to_instance u in
 let (mib,_ as specif) =
   Inductive.lookup_mind_specif env (inductive_of_constructor cstr) in
 Typeops.check_hyps_inclusion env (GlobRef.ConstructRef cstr) mib.mind_hyps;
 let t = Inductive.type_of_constructor (cstr,u) specif in
 EConstr.of_constr @@ Arguments_renaming.rename_type t (ConstructRef cstr)

let e_type_of_constructor env sigma (cstr,u) =
 let (mib,_ as specif) =
   Inductive.lookup_mind_specif env (inductive_of_constructor cstr) in
 Reductionops.check_hyps_inclusion env sigma (GlobRef.ConstructRef cstr) mib.mind_hyps;
 let t = Inductive.type_of_constructor (cstr,EConstr.Unsafe.to_instance u) specif in
 EConstr.of_constr (Arguments_renaming.rename_type t (ConstructRef cstr))

(* Return constructor types in user form *)
let type_of_constructors env (ind,u as indu) =
  let indu = on_snd EConstr.Unsafe.to_instance indu in
  let specif = Inductive.lookup_mind_specif env ind in
  Array.map EConstr.of_constr (Inductive.type_of_constructors indu specif)

(* Return constructor types in normal form *)
let arities_of_constructors env (ind,u as indu) =
  let indu = on_snd EConstr.Unsafe.to_instance indu in
  let specif = Inductive.lookup_mind_specif env ind in
  Array.map EConstr.of_constr (Inductive.arities_of_constructors indu specif)

(* [inductive_family] = [inductive_instance] applied to global parameters *)
type inductive_family = inductive puniverses * constr list

let make_ind_family (mis, params) = (mis,params)
let dest_ind_family (mis,params) : inductive_family = (mis,params)

let map_ind_family f (mis,params) = (mis, List.map f params)

let liftn_inductive_family n d = map_ind_family (liftn n d)
let lift_inductive_family n = liftn_inductive_family n 1

let substnl_ind_family l n = map_ind_family (substnl l n)

let relevance_of_inductive env ind =
  let ind = on_snd EConstr.Unsafe.to_instance ind in
  ERelevance.make @@ Inductive.relevance_of_inductive env ind

let relevance_of_inductive_family env (ind,_ : inductive_family) =
  relevance_of_inductive env ind

type inductive_type = IndType of inductive_family * EConstr.constr list

let ind_of_ind_type = function IndType (((ind,_),_),_) -> ind

let make_ind_type (indf, realargs) = IndType (indf,realargs)
let dest_ind_type (IndType (indf,realargs)) = (indf,realargs)

let map_inductive_type f (IndType (indf, realargs)) =
  IndType (map_ind_family f indf, List.map f realargs)

let liftn_inductive_type n d = map_inductive_type (EConstr.Vars.liftn n d)
let lift_inductive_type n = liftn_inductive_type n 1

let substnl_ind_type l n = map_inductive_type (EConstr.Vars.substnl l n)

let relevance_of_inductive_type env (IndType (indf, _)) =
  relevance_of_inductive_family env indf

let mkAppliedInd (IndType ((ind,params), realargs)) =
  applist (mkIndU ind, params @ realargs)

let dest_recarg p = match Rtree.Kind.kind p with
| Rtree.Kind.Node (ra, _) -> ra
| Rtree.Kind.Var _ -> assert false

let dest_subterms p = match Rtree.Kind.kind p with
| Rtree.Kind.Node (ra, cstrs) ->
  let () = assert (match ra with Norec -> false | _ -> true) in
  cstrs
| Rtree.Kind.Var _ -> assert false

(* Does not consider imbricated or mutually recursive types *)
let mis_is_recursive_subset listind rarg =
  let one_is_rec rvec =
    Array.exists
      (fun ra ->
        match dest_recarg ra with
          | Mrec (RecArgInd ind) -> List.exists (Names.Ind.CanOrd.equal ind) listind
          | Mrec (RecArgPrim _) | Norec -> false) rvec
  in
  Array.exists one_is_rec (dest_subterms rarg)

let mis_is_recursive ((ind,_),mib,mip) =
  mis_is_recursive_subset (List.init mib.mind_ntypes (fun i -> (ind,i)))
    (Rtree.Kind.make mip.mind_recargs)

let mis_nf_constructor_type ((_,j),u) (mib,mip) =
  let nconstr = Array.length mip.mind_consnames in
  if j > nconstr then user_err Pp.(str "Not enough constructors in the type.");
  let (ctx, cty) = mip.mind_nf_lc.(j - 1) in
  subst_instance_constr u (EConstr.it_mkProd_or_LetIn (EConstr.of_constr cty) (EConstr.of_rel_context ctx))

(* Number of constructors *)

let nconstructors env ind =
  let (_,mip) = Inductive.lookup_mind_specif env ind in
  Array.length mip.mind_consnames

(* Arity of constructors excluding parameters, excluding local defs *)

let constructors_nrealargs env ind =
  let (_,mip) = Inductive.lookup_mind_specif env ind in
  mip.mind_consnrealargs

(* Arity of constructors excluding parameters, including local defs *)

let constructors_nrealdecls env ind =
  let (_,mip) = Inductive.lookup_mind_specif env ind in
  mip.mind_consnrealdecls

(* Arity of constructors including parameters, excluding local defs *)

let constructor_nallargs env (ind,j) =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  mip.mind_consnrealargs.(j-1) + mib.mind_nparams

(* Arity of constructors including params, including local defs *)

let constructor_nalldecls env (ind,j) = (* TOCHANGE en decls *)
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  mip.mind_consnrealdecls.(j-1) + Context.Rel.length (mib.mind_params_ctxt)

(* Arity of constructors excluding params, excluding local defs *)

let constructor_nrealargs env (ind,j) =
  let (_,mip) = Inductive.lookup_mind_specif env ind in
  mip.mind_consnrealargs.(j-1)

(* Arity of constructors excluding params, including local defs *)

let constructor_nrealdecls env (ind,j) = (* TOCHANGE en decls *)
  let (_,mip) = Inductive.lookup_mind_specif env ind in
  mip.mind_consnrealdecls.(j-1)

(* Length of arity, excluding params, excluding local defs *)

let inductive_nrealargs env ind =
  let (_,mip) = Inductive.lookup_mind_specif env ind in
  mip.mind_nrealargs

(* Length of arity, excluding params, including local defs *)

let inductive_nrealdecls env ind =
  let (_,mip) = Inductive.lookup_mind_specif env ind in
  mip.mind_nrealdecls

(* Full length of arity (w/o local defs) *)

let inductive_nallargs env ind =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  mib.mind_nparams + mip.mind_nrealargs

(* Length of arity (w/o local defs) *)

let inductive_nparams env ind =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  mib.mind_nparams

(* Length of arity (with local defs) *)

let inductive_nparamdecls env ind =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  Context.Rel.length mib.mind_params_ctxt

(* Full length of arity (with local defs) *)

let inductive_nalldecls env ind =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  Context.Rel.length (mib.mind_params_ctxt) + mip.mind_nrealdecls

(* Others *)

let inductive_paramdecls env (ind,u) =
  let u = EConstr.Unsafe.to_instance u in
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  EConstr.of_rel_context @@ Inductive.inductive_paramdecls (mib,u)

let inductive_alldecls env (ind,u) =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  Vars.subst_instance_context u (EConstr.of_rel_context mip.mind_arity_ctxt)

let inductive_alltags env ind =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  Context.Rel.to_tags mip.mind_arity_ctxt

let constructor_alltags env (ind,j) =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  Context.Rel.to_tags (fst mip.mind_nf_lc.(j-1))

let constructor_has_local_defs env (indsp,j) =
  let (mib,mip) = Inductive.lookup_mind_specif env indsp in
  let l1 = mip.mind_consnrealdecls.(j-1) + Context.Rel.length (mib.mind_params_ctxt) in
  let l2 = recarg_length mip.mind_recargs j + mib.mind_nparams in
  not (Int.equal l1 l2)

let inductive_has_local_defs env ind =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  let l1 = Context.Rel.length (mib.mind_params_ctxt) + mip.mind_nrealdecls in
  let l2 = mib.mind_nparams + mip.mind_nrealargs in
  not (Int.equal l1 l2)

(* XXX use above_prop from the ustate *)
let quality_leq q q' =
  let open Sorts.Quality in
  match q, q' with
  | QVar q, QVar q' -> Sorts.QVar.equal q q'
  | QConstant q, QConstant q' ->
    begin match q, q' with
    | QSProp, _
    | _, QType
    | QProp, QProp
      -> true
    | (QProp|QType), _ -> false
    end
  | QVar _, QConstant QType -> true
  | (QVar _|QConstant _), _ -> false

type squash = SquashToSet | SquashToQuality of Sorts.Quality.t

let is_squashed sigma ((_,mip),u) =
  let s = match mip.mind_arity with
    | RegularArity a -> a.mind_sort
    | TemplateArity a -> a.template_level
  in
  match mip.mind_squashed with
  | None -> None
  | Some squash ->
    let u = EConstr.Unsafe.to_instance u in
    let indq = EConstr.ESorts.quality sigma
        (EConstr.ESorts.make @@ UVars.subst_instance_sort u s)
    in
    match squash with
    | AlwaysSquashed -> begin match s with
        | Sorts.Set -> Some SquashToSet
        | _ -> Some (SquashToQuality indq)
      end
    | SometimesSquashed squash ->
      (* impredicative set squashes are always AlwaysSquashed,
         so here if inds=Set it is a sort poly squash (see "foo6" in test sort_poly.v) *)
      if Sorts.Quality.Set.for_all (fun q ->
          let q = UVars.subst_instance_quality u q in
          let q = UState.nf_quality (Evd.ustate sigma) q in
          quality_leq q indq) squash
      then None
      else Some (SquashToQuality indq)

let squash_elim_sort env sigma squash rtnsort = match squash with
| SquashToSet ->
  (* Squashed inductive in Set, only happens with impredicative Set *)
  begin match ESorts.kind sigma rtnsort with
  | Set | SProp | Prop -> sigma
  | QSort _ | Type _ ->
    Evd.set_eq_sort env sigma rtnsort ESorts.set
  end
| SquashToQuality (QConstant QProp) ->
  (* Squashed inductive in Prop, return sort must be Prop or SProp *)
  begin match ESorts.kind sigma rtnsort with
  | SProp | Prop -> sigma
  | QSort _ | Type _ | Set ->
    Evd.set_eq_sort env sigma rtnsort ESorts.prop
  end
| SquashToQuality (QConstant QSProp) ->
  (* Squashed inductive in SProp, return sort must be SProp. *)
  begin match ESorts.kind sigma rtnsort with
  | SProp -> sigma
  | Type _ | Set | Prop | QSort _ ->
    Evd.set_eq_sort env sigma rtnsort ESorts.sprop
  end
| SquashToQuality (QConstant QType) ->
  (* Sort poly squash to type *)
  Evd.set_leq_sort env sigma ESorts.set rtnsort
| SquashToQuality (QVar q) ->
  Evd.set_leq_sort env sigma (ESorts.make (Sorts.qsort q Univ.Universe.type0)) rtnsort

let is_allowed_elimination sigma ((mib,_),_ as specifu) s =
  let open Sorts in
  match mib.mind_record with
  | PrimRecord _ -> true
  | NotRecord | FakeRecord ->
    match is_squashed sigma specifu with
    | None -> true
    | Some SquashToSet ->
      begin match EConstr.ESorts.kind sigma s with
      | SProp|Prop|Set -> true
      | QSort _ | Type _ ->
        (* XXX in [Type u] case, should we check [u == set] in the ugraph? *)
        false
      end
    | Some (SquashToQuality indq) -> quality_leq (EConstr.ESorts.quality sigma s) indq

let make_allowed_elimination env sigma ((mib,_),_ as specifu) s =
  let open Sorts in
  match mib.mind_record with
  | PrimRecord _ -> Some sigma
  | NotRecord | FakeRecord ->
    match is_squashed sigma specifu with
    | None -> Some sigma
    | Some SquashToSet ->
      begin match EConstr.ESorts.kind sigma s with
      | SProp|Prop|Set -> Some sigma
      | QSort _ | Type _ ->
        try Some (Evd.set_leq_sort env sigma s ESorts.set)
        with UGraph.UniverseInconsistency _ -> None
      end
    | Some (SquashToQuality indq) ->
      let sq = EConstr.ESorts.quality sigma s in
      if quality_leq sq indq then Some sigma
      else
        let mk q = ESorts.make @@ Sorts.make q Univ.Universe.type0 in
        try Some (Evd.set_leq_sort env sigma (mk sq) (mk indq))
        with UGraph.UniverseInconsistency _ -> None

(* XXX questionable for sort poly inductives *)
let elim_sort (_,mip) =
  if Option.is_empty mip.mind_squashed then Sorts.InType
  else match mip.mind_arity with
    | TemplateArity x -> Sorts.family x.template_level
    | RegularArity s -> Sorts.family s.mind_sort

let top_allowed_sort env (kn,i as ind) =
  let specif = Inductive.lookup_mind_specif env ind in
  elim_sort specif

let sorts_below top =
  List.filter (fun s ->
      Sorts.family_equal s top
      || match s, top with
      | InQSort, _ -> assert false
      | _, InQSort -> false
      | InSProp, _ -> true
      | InProp, InSet -> true
      | _, InType -> true
      | (InProp|InSet|InType), _ -> false)
    Sorts.[InSProp;InProp;InSet;InType]

let sorts_for_schemes specif =
  sorts_below (elim_sort specif)

let has_dependent_elim (mib,mip) =
  match mib.mind_record with
  | PrimRecord _ -> mib.mind_finite == BiFinite || mip.mind_relevance == Irrelevant
  | NotRecord | FakeRecord -> true

(* Annotation for cases *)
let make_case_info env ind style =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  let print_info = { Constr.style } in
  { Constr.ci_ind     = ind;
    ci_npar    = mib.mind_nparams;
    ci_cstr_ndecls = mip.mind_consnrealdecls;
    ci_cstr_nargs = mip.mind_consnrealargs;
    ci_pp_info = print_info }

(*s Useful functions *)

type constructor_summary = {
  cs_cstr : constructor puniverses;
  cs_params : constr list;
  cs_nargs : int;
  cs_args : EConstr.rel_context;
  cs_concl_realargs : constr array
}

let lift_constructor n cs = {
  cs_cstr = cs.cs_cstr;
  cs_params = List.map (lift n) cs.cs_params;
  cs_nargs = cs.cs_nargs;
  cs_args = Vars.lift_rel_context n cs.cs_args;
  cs_concl_realargs = Array.map (liftn n (cs.cs_nargs+1)) cs.cs_concl_realargs
}

(* Accept either all parameters or only recursively uniform ones *)
let instantiate_params t params sign =
  let nnonrecpar = Context.Rel.nhyps sign - List.length params in
  (* Adjust the signature if recursively non-uniform parameters are not here *)
  let _,sign = Context.Rel.chop_nhyps nnonrecpar sign in
  let _,t = Term.decompose_prod_n_decls (Context.Rel.length sign) t in
  let subst = subst_of_rel_context_instance_list sign params in
  substl subst (EConstr.of_constr t)

let instantiate_constructor_params (_,u as cstru) (mib,_ as mind_specif) params =
  let typi = mis_nf_constructor_type cstru mind_specif in
  let ctx = Vars.subst_instance_context u (EConstr.of_rel_context mib.mind_params_ctxt) in
  instantiate_params (EConstr.Unsafe.to_constr typi) params ctx

let get_constructor ((ind,u),mib,mip,params) j =
  assert (j <= Array.length mip.mind_consnames);
  let typi = instantiate_constructor_params ((ind,j),u) (mib,mip) params in
  let typi = EConstr.Unsafe.to_constr typi in
  let (args,ccl) = Term.decompose_prod_decls typi in
  let (_,allargs) = Constr.decompose_app_list ccl in
  let vargs = List.skipn (List.length params) allargs in
  { cs_cstr = (ith_constructor_of_inductive ind j,u);
    cs_params = params;
    cs_nargs = Context.Rel.length args;
    cs_args = EConstr.of_rel_context args;
    cs_concl_realargs = Array.map_of_list EConstr.of_constr vargs }

let get_constructors env (ind,params) =
  let (mib,mip) = Inductive.lookup_mind_specif env (fst ind) in
  Array.init (Array.length mip.mind_consnames)
    (fun j -> get_constructor (ind,mib,mip,params) (j+1))

let get_projections = Environ.get_projections

let make_case_invert env sigma (IndType (((ind,u),params),indices)) ~case_relevance:r ci =
  let r = ERelevance.kind sigma r in
  if Typeops.should_invert_case env r ci
  then Constr.CaseInvert {indices=Array.of_list indices}
  else Constr.NoInvert

let make_project env sigma ind pred c branches ps =
  assert(Array.length branches == 1);
  let na, ty, t = destLambda sigma pred in
  let mib, mip as specif = Inductive.lookup_mind_specif env ind in
  let () =
    if (* dependent *) not (Vars.noccurn sigma 1 t) &&
         not (has_dependent_elim specif) then
      user_err
        Pp.(str"Dependent case analysis not allowed" ++
              str" on inductive type " ++ Termops.pr_global_env env (IndRef ind) ++ str ".")
  in
  let branch = branches.(0) in
  let ctx, br = decompose_lambda_n_decls sigma mip.mind_consnrealdecls.(0) branch in
  let _, u = destInd sigma (fst (decompose_app sigma ty)) in
  let u = Unsafe.to_instance u in
  let mkProj i c =
    let p, r = ps.(i) in
    let r = UVars.subst_instance_relevance u r in
    mkProj (Projection.make p true, ERelevance.make r, c)
  in
  let proj = match EConstr.destRel sigma br with
    | exception Constr.DestKO -> None
    | i ->
      begin match List.skipn (i-1) ctx with
      | exception Failure _ -> None
      | ctx -> match ctx with
        | [] -> None
        | LocalDef _ :: _ ->
          (* XXX Maybe we should produce the applied constant for this letin pseudoprojection?
             We would have to get the params etc*)
          None
        | LocalAssum _ :: ctx ->
          (* This match is just a projection *)
          Some (mkProj (Context.Rel.nhyps ctx) c)
      end
  in
  match proj with
  | Some proj -> proj
  | None ->
  let n, len, ctx =
    List.fold_right
      (fun decl (i, j, ctx) ->
         match decl with
         | LocalAssum (na, ty) ->
           let t = mkProj i (mkRel j) in
           (i + 1, j + 1, LocalDef (na, t, Vars.liftn 1 j ty) :: ctx)
         | LocalDef (na, b, ty) ->
           (i, j + 1, LocalDef (na, Vars.liftn 1 j b, Vars.liftn 1 j ty) :: ctx))
      ctx (0, 1, [])
  in
  mkLetIn (na, c, ty, it_mkLambda_or_LetIn (Vars.liftn 1 (mip.mind_consnrealdecls.(0) + 1) br) ctx)

let simple_make_case_or_project env sigma ci pred invert c branches =
  let ind = ci.Constr.ci_ind in
  let projs = get_projections env ind in
  match projs with
  | None -> mkCase (EConstr.contract_case env sigma (ci, pred, invert, c, branches))
  | Some ps -> make_project env sigma ind (fst pred) c branches ps

let make_case_or_project env sigma indt ci pred c branches =
  let IndType (((ind,_),_),_) = indt in
  let projs = get_projections env ind in
  match projs with
  | None ->
     let invert = make_case_invert env sigma indt ~case_relevance:(snd pred) ci in
     mkCase (EConstr.contract_case env sigma (ci, pred, invert, c, branches))
  | Some ps -> make_project env sigma ind (fst pred) c branches ps

(* substitution in a signature *)

let substnl_rel_context subst n sign =
  let rec aux n = function
  | d::sign -> substnl_decl subst n d :: aux (n+1) sign
  | [] -> []
  in List.rev (aux n (List.rev sign))

let substl_rel_context subst = substnl_rel_context subst 0

let get_arity env ((ind,u),params) =
  let (mib,mip) = Inductive.lookup_mind_specif env ind in
  let parsign =
    (* Dynamically detect if called with an instance of recursively
       uniform parameter only or also of recursively non-uniform
       parameters *)
    let u = EConstr.Unsafe.to_instance u in
    let nparams = List.length params in
    if Int.equal nparams mib.mind_nparams then
      Inductive.inductive_paramdecls (mib,u)
    else begin
      assert (Int.equal nparams mib.mind_nparams_rec);
      snd (Inductive.inductive_nonrec_rec_paramdecls (mib,u))
    end in
  let parsign = EConstr.of_rel_context parsign in
  let arproperlength = List.length mip.mind_arity_ctxt - List.length parsign in
  let arsign,_ = List.chop arproperlength mip.mind_arity_ctxt in
  let arsign = EConstr.of_rel_context arsign in
  let subst = subst_of_rel_context_instance_list parsign params in
  let arsign = Vars.subst_instance_context u arsign in
  substl_rel_context subst arsign

(* Functions to build standard types related to inductive *)
let build_dependent_constructor cs =
  applist
    (mkConstructU cs.cs_cstr,
     (List.map (lift cs.cs_nargs) cs.cs_params)
      @(Context.Rel.instance_list mkRel 0 cs.cs_args))

let build_dependent_inductive env ((ind, params) as indf) =
  let arsign = get_arity env indf in
  let nrealargs = List.length arsign in
  applist
    (mkIndU ind,
     (List.map (lift nrealargs) params)@(Context.Rel.instance_list mkRel 0 arsign))

(* builds the arity of an elimination predicate in sort [s] *)

let make_arity_signature env sigma dep (ind, _ as indf) =
  let arsign = get_arity env indf in
  let r = relevance_of_inductive env ind in
  let anon = make_annot Anonymous r in
  if dep then
    (* We need names everywhere *)
    Namegen.name_context env sigma
      ((LocalAssum (anon, build_dependent_inductive env indf)) :: arsign)
      (* Costly: would be better to name once for all at definition time *)
  else
    (* No need to enforce names *)
    arsign

let make_arity env sigma dep indf s =
  it_mkProd_or_LetIn (mkSort s) (make_arity_signature env sigma dep indf)

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

(** From a rel context describing the constructor arguments,
    build an expansion function.
    The term built is expecting to be substituted first by
    a substitution of the form [params, x : ind params] *)
let compute_projections env (kn, i as ind) =
  let mib = Environ.lookup_mind kn env in
  let u = UVars.make_abstract_instance (Declareops.inductive_polymorphic_context mib) in
  let u = EInstance.make u in
  let x = match mib.mind_record with
  | NotRecord | FakeRecord ->
    anomaly Pp.(str "Trying to build primitive projections for a non-primitive record")
  | PrimRecord info ->
    let id, _, _, _ = info.(i) in
    make_annot (Name id) (ERelevance.make mib.mind_packets.(i).mind_relevance)
  in
  let pkt = mib.mind_packets.(i) in
  let { mind_nparams = nparamargs; mind_params_ctxt = params } = mib in
  let params = EConstr.of_rel_context params in
  let ctx, _ = pkt.mind_nf_lc.(0) in
  let ctx, paramslet = List.chop pkt.mind_consnrealdecls.(0) ctx in
  let ctx = EConstr.of_rel_context ctx in
  (* We build a substitution smashing the lets in the record parameters so
     that typechecking projections requires just a substitution and not
     matching with a parameter context. *)
  let indty =
    (* [ty] = [Ind inst] is typed in context [params] *)
    let inst = Context.Rel.instance mkRel 0 paramslet in
    let indu = mkIndU (ind, u) in
    let ty = mkApp (indu, inst) in
    (* [Ind inst] is typed in context [params-wo-let] *)
    ty
  in
  let projections decl (proj_arg, j, pbs, subst) =
    match decl with
    | LocalDef (na,c,t) ->
        (* From [params, field1,..,fieldj |- c(params,field1,..,fieldj)]
           to [params, x:I, field1,..,fieldj |- c(params,field1,..,fieldj)] *)
        let c = liftn 1 j c in
        (* From [params, x:I, field1,..,fieldj |- c(params,field1,..,fieldj)]
           to [params, x:I |- c(params,proj1 x,..,projj x)] *)
        let c1 = substl subst c in
        (* From [params, x:I |- subst:field1,..,fieldj]
           to [params, x:I |- subst:field1,..,fieldj+1] where [subst]
           is represented with instance of field1 last *)
        let subst = c1 :: subst in
        (proj_arg, j+1, pbs, subst)
    | LocalAssum (na,t) ->
      match na.binder_name with
      | Name id ->
        let lab = Label.of_id id in
        let proj_relevant = na.binder_relevance in
        let kn = Projection.Repr.make ind ~proj_npars:mib.mind_nparams ~proj_arg lab in
        (* from [params, field1,..,fieldj |- t(params,field1,..,fieldj)]
           to [params, x:I, field1,..,fieldj |- t(params,field1,..,fieldj] *)
        let t = liftn 1 j t in
        (* from [params, x:I, field1,..,fieldj |- t(params,field1,..,fieldj)]
           to [params-wo-let, x:I |- t(params,proj1 x,..,projj x)] *)
        (* from [params, x:I, field1,..,fieldj |- t(field1,..,fieldj)]
           to [params, x:I |- t(proj1 x,..,projj x)] *)
        let ty = substl subst t in
        let term = mkProj (Projection.make kn true, proj_relevant, mkRel 1) in
        let fterm = mkProj (Projection.make kn false, proj_relevant, mkRel 1) in
        let etab = it_mkLambda_or_LetIn (mkLambda (x, indty, term)) params in
        let etat = it_mkProd_or_LetIn (mkProd (x, indty, ty)) params in
        let body = (etab, etat) in
        (proj_arg + 1, j + 1, body :: pbs, fterm :: subst)
      | Anonymous ->
        anomaly Pp.(str "Trying to build primitive projections for a non-primitive record")
  in
  let (_, _, pbs, subst) =
    List.fold_right projections ctx (0, 1, [], [])
  in
  Array.rev_of_list pbs

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

let extract_mrectype sigma t =
  let open EConstr in
  let (t, l) = decompose_app_list sigma t in
  match EConstr.kind sigma t with
    | Ind ind -> (ind, l)
    | _ -> raise Not_found

let find_mrectype_vect env sigma c =
  let (t, l) = EConstr.decompose_app sigma (whd_all env sigma c) in
  match EConstr.kind sigma t with
    | Ind ind -> (ind, l)
    | _ -> raise Not_found

let find_mrectype env sigma c =
  let (ind, v) = find_mrectype_vect env sigma c in (ind, Array.to_list v)

let find_rectype env sigma c =
  let open EConstr in
  let (t, l) = decompose_app_list sigma (whd_all env sigma c) in
  match EConstr.kind sigma t with
    | Ind (ind,u) ->
        let (mib,mip) = Inductive.lookup_mind_specif env ind in
        if mib.mind_nparams > List.length l then raise Not_found;
        let (par,rargs) = List.chop mib.mind_nparams l in
        let indu = (ind, u) in
        IndType ((indu, par), rargs)
    | _ -> raise Not_found

let find_inductive env sigma c =
  let open EConstr in
  let (t, l) = decompose_app_list sigma (whd_all env sigma c) in
  match EConstr.kind sigma t with
    | Ind ind
        when (fst (Inductive.lookup_mind_specif env (fst ind))).mind_finite <> CoFinite ->
        (ind, l)
    | _ -> raise Not_found

let find_coinductive env sigma c =
  let open EConstr in
  let (t, l) = decompose_app_list sigma (whd_all env sigma c) in
  match EConstr.kind sigma t with
    | Ind ind
        when (fst (Inductive.lookup_mind_specif env (fst ind))).mind_finite == CoFinite ->
        (ind, l)
    | _ -> raise Not_found


(* Type of Case predicates *)
let arity_of_case_predicate env (ind,params) dep k =
  let arsign = get_arity env (ind,params) in
  let r = relevance_of_inductive env ind in
  let mind = build_dependent_inductive env (ind,params) in
  let concl = if dep then mkArrow mind r (mkSort k) else mkSort k in
  it_mkProd_or_LetIn concl arsign

(***********************************************)
(* Inferring the sort of parameters of a polymorphic inductive type
   knowing the sort of the conclusion *)

let univ_level_mem l s = match s with
| Prop | Set | SProp -> false
| Type u -> Univ.univ_level_mem l u
| QSort (_, u) -> assert false (* template cannot contain sort variables *)

(* Compute the inductive argument types: replace the sorts
   that appear in the type of the inductive by the sort of the
   conclusion, and the other ones by fresh universes. *)
let rec instantiate_universes env evdref scl is = function
  | (LocalDef _ as d)::sign, exp ->
    EConstr.of_rel_decl d :: instantiate_universes env evdref scl is (sign, exp)
  | d::sign, false::exp ->
    EConstr.of_rel_decl d :: instantiate_universes env evdref scl is (sign, exp)
  | (LocalAssum (na,ty))::sign, true::exp ->
      let ctx,s = Reduction.dest_arity env ty in
      let l = match s with Type u -> Option.get @@ Univ.Universe.level u | _ -> assert false in
      let u = Univ.Universe.make l in
      let s =
        (* Does the sort of parameter [u] appear in (or equal)
           the sort of inductive [is] ? *)
        if univ_level_mem l is then
          scl (* constrained sort: replace by scl *)
        else
          (* unconstrained sort: replace by fresh universe *)
          let evm, s = Evd.new_sort_variable Evd.univ_flexible !evdref in
          let evm = Evd.set_leq_sort env evm s (EConstr.ESorts.make (Sorts.sort_of_univ u)) in
            evdref := evm; s
      in
      let ctx = EConstr.of_rel_context ctx in
      let na = EConstr.of_binder_annot na in
      (LocalAssum (na, mkArity (ctx, s))) :: instantiate_universes env evdref scl is (sign, exp)
  | sign, [] -> EConstr.of_rel_context sign (* Uniform parameters are exhausted *)
  | [], _ -> assert false

let type_of_inductive_knowing_conclusion env sigma ((mib,mip),u) conclty =
  match mip.mind_arity with
  | RegularArity s -> sigma, subst_instance_constr u (EConstr.of_constr s.mind_user_arity)
  | TemplateArity ar ->
    let templ = match mib.mind_template with
    | None -> assert false
    | Some t -> t
    in
    let _,scl = splay_arity env sigma conclty in
    let ctx = List.rev mip.mind_arity_ctxt in
    let evdref = ref sigma in
    let ctx =
      instantiate_universes
        env evdref scl ar.template_level (ctx,templ.template_param_arguments) in
    !evdref, mkArity (List.rev ctx, scl)

let type_of_projection_constant env (p,u) =
  let _, pty = lookup_projection p env in
  EConstr.Vars.subst_instance_constr u (EConstr.of_constr pty)

let type_of_projection_knowing_arg env sigma p c ty =
  let open EConstr.Vars in
  let IndType(pars,realargs) =
    try find_rectype env sigma ty
    with Not_found ->
      raise (Invalid_argument "type_of_projection_knowing_arg_type: not an inductive type")
  in
  let (_,u), pars = dest_ind_family pars in
  substl (c :: List.rev pars) (type_of_projection_constant env (p,u))

(***********************************************)
(* Guard condition *)

(* A function which checks that a term well typed verifies both
   syntactic conditions *)

let control_only_guard env sigma c =
  let evars = Evd.evar_handler sigma in
  let c = Evarutil.nf_evar sigma c in
  let check_fix_cofix e c =
    (* [c] has already been normalized upfront *)
    let c = EConstr.Unsafe.to_constr c in
    match Constr.kind c with
    | CoFix (_,(_,_,_) as cofix) ->
      Inductive.check_cofix ~evars e cofix
    | Fix fix ->
      Inductive.check_fix ~evars e fix
    | _ -> ()
  in
  let rec iter env c =
    check_fix_cofix env c;
    EConstr.iter_with_full_binders env sigma EConstr.push_rel iter env c
  in
  try iter env c
  with Type_errors.TypeError (env, e) ->
    raise (Pretype_errors.PretypeError
             (env, sigma,
              TypingError (Pretype_errors.of_type_error e)))
OCaml

Innovation. Community. Security.

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