summaryrefslogtreecommitdiff
path: root/pretyping/indrec.ml
blob: d3123eb6a472fc42ab0fb9a89f3ad8d3bc758d2e (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
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* $Id: indrec.ml 11735 2009-01-02 17:22:31Z herbelin $ *)

open Pp
open Util
open Names
open Libnames
open Nameops
open Term
open Termops
open Declarations
open Entries
open Inductive
open Inductiveops
open Environ
open Reductionops
open Typeops
open Type_errors
open Safe_typing
open Nametab
open Sign

(* Errors related to recursors building *)
type recursion_scheme_error =
  | NotAllowedCaseAnalysis of (*isrec:*) bool * sorts * inductive
  | NotMutualInScheme of inductive * inductive

exception RecursionSchemeError of recursion_scheme_error

let make_prod_dep dep env = if dep then prod_name env else mkProd
let mkLambda_string s t c = mkLambda (Name (id_of_string s), t, c)

(*******************************************)
(* Building curryfied elimination          *)
(*******************************************)

(**********************************************************************)
(* Building case analysis schemes *)
(* Nouvelle version, plus concise mais plus coûteuse à cause de
   lift_constructor et lift_inductive_family qui ne se contentent pas de 
   lifter les paramètres globaux *)

let mis_make_case_com depopt env sigma ind (mib,mip as specif) kind =
  let lnamespar = mib.mind_params_ctxt in
  let dep = match depopt with 
    | None -> inductive_sort_family mip <> InProp
    | Some d -> d
  in
  if not (List.mem kind (elim_sorts specif)) then
    raise
      (RecursionSchemeError
	 (NotAllowedCaseAnalysis (false,new_sort_in_family kind,ind)));

  let ndepar = mip.mind_nrealargs + 1 in

  (* Pas génant car env ne sert pas à typer mais juste à renommer les Anonym *)
  (* mais pas très joli ... (mais manque get_sort_of à ce niveau) *)
  let env' = push_rel_context lnamespar env in

  let indf = make_ind_family(ind, extended_rel_list 0 lnamespar) in
  let constrs = get_constructors env indf in

  let rec add_branch env k = 
    if k = Array.length mip.mind_consnames then
      let nbprod = k+1 in

      let indf' = lift_inductive_family nbprod indf in
      let arsign,_ = get_arity env indf' in
      let depind = build_dependent_inductive env indf' in
      let deparsign = (Anonymous,None,depind)::arsign in

      let ci = make_case_info env ind RegularStyle in
      let pbody =
        appvect
          (mkRel (ndepar + nbprod),
           if dep then extended_rel_vect 0 deparsign
           else extended_rel_vect 1 arsign) in
      let p = 
	it_mkLambda_or_LetIn_name env'
	  ((if dep then mkLambda_name env' else mkLambda)
	   (Anonymous,depind,pbody))
          arsign
      in
      it_mkLambda_or_LetIn_name env'
       	(mkCase (ci, lift ndepar p,
		     mkRel 1,
		     rel_vect ndepar k))
       	deparsign
    else
      let cs = lift_constructor (k+1) constrs.(k) in
      let t = build_branch_type env dep (mkRel (k+1)) cs in
      mkLambda_string "f" t
	(add_branch (push_rel (Anonymous, None, t) env) (k+1))
  in
  let typP = make_arity env' dep indf (new_sort_in_family kind) in
  it_mkLambda_or_LetIn_name env 
    (mkLambda_string "P" typP
       (add_branch (push_rel (Anonymous,None,typP) env') 0)) lnamespar
    
(* check if the type depends recursively on one of the inductive scheme *)

(**********************************************************************)
(* Building the recursive elimination *)

(*
 * t is the type of the constructor co and recargs is the information on 
 * the recursive calls. (It is assumed to be in form given by the user).
 * build the type of the corresponding branch of the recurrence principle
 * assuming f has this type, branch_rec gives also the term 
 *   [x1]..[xk](f xi (F xi) ...) to be put in the corresponding branch of 
 * the case operation
 * FPvect gives for each inductive definition if we want an elimination 
 * on it with which predicate and which recursive function. 
 *)

let type_rec_branch is_rec dep env sigma (vargs,depPvect,decP) tyi cs recargs = 
  let make_prod = make_prod_dep dep in
  let nparams = List.length vargs in
  let process_pos env depK pk =
    let rec prec env i sign p =
      let p',largs = whd_betadeltaiota_nolet_stack env sigma p in
      match kind_of_term p' with
	| Prod (n,t,c) ->
	    let d = (n,None,t) in
	    make_prod env (n,t,prec (push_rel d env) (i+1) (d::sign) c)
	| LetIn (n,b,t,c) ->
	    let d = (n,Some b,t) in
	    mkLetIn (n,b,t,prec (push_rel d env) (i+1) (d::sign) c)
     	| Ind (_,_) ->
	    let realargs = list_skipn nparams largs in
	    let base = applist (lift i pk,realargs) in
            if depK then 
	      Reduction.beta_appvect
                base [|applist (mkRel (i+1),extended_rel_list 0 sign)|]
            else 
	      base
      	| _ -> assert false 
    in
    prec env 0 []
  in
  let rec process_constr env i c recargs nhyps li =
    if nhyps > 0 then match kind_of_term c with 
      | Prod (n,t,c_0) ->
          let (optionpos,rest) = 
	    match recargs with 
	      | [] -> None,[]
              | ra::rest ->
                  (match dest_recarg ra with 
	            | Mrec j when is_rec -> (depPvect.(j),rest)
	            | Imbr _  -> 
		        Flags.if_verbose warning "Ignoring recursive call"; 
		        (None,rest) 
                    | _ -> (None, rest))
	  in 
          (match optionpos with 
	     | None -> 
		 make_prod env
		   (n,t,
		    process_constr (push_rel (n,None,t) env) (i+1) c_0 rest
		      (nhyps-1) (i::li))
             | Some(dep',p) -> 
		 let nP = lift (i+1+decP) p in
                 let env' = push_rel (n,None,t) env in
		 let t_0 = process_pos env' dep' nP (lift 1 t) in 
		 make_prod_dep (dep or dep') env
                   (n,t,
		    mkArrow t_0
		      (process_constr
			(push_rel (Anonymous,None,t_0) env')
			 (i+2) (lift 1 c_0) rest (nhyps-1) (i::li))))
      | LetIn (n,b,t,c_0) ->
	  mkLetIn (n,b,t,
		   process_constr
		     (push_rel (n,Some b,t) env)
		     (i+1) c_0 recargs (nhyps-1) li)
      | _ -> assert false
    else
      if dep then
	let realargs = List.map (fun k -> mkRel (i-k)) (List.rev li) in
        let params = List.map (lift i) vargs in
        let co = applist (mkConstruct cs.cs_cstr,params@realargs) in
	Reduction.beta_appvect c [|co|]
      else c
  in
  let nhyps = List.length cs.cs_args in
  let nP = match depPvect.(tyi) with 
    | Some(_,p) -> lift (nhyps+decP) p
    | _ -> assert false in
  let base = appvect (nP,cs.cs_concl_realargs) in
  let c = it_mkProd_or_LetIn base cs.cs_args in
  process_constr env 0 c recargs nhyps []

let make_rec_branch_arg env sigma (nparrec,fvect,decF) f cstr recargs = 
  let process_pos env fk  =
    let rec prec env i hyps p =
      let p',largs = whd_betadeltaiota_nolet_stack env sigma p in
      match kind_of_term p' with
	| Prod (n,t,c) ->
	    let d = (n,None,t) in
	    lambda_name env (n,t,prec (push_rel d env) (i+1) (d::hyps) c)
	| LetIn (n,b,t,c) ->
	    let d = (n,Some b,t) in
	    mkLetIn (n,b,t,prec (push_rel d env) (i+1) (d::hyps) c)
     	| Ind _ -> 
            let realargs = list_skipn nparrec largs
            and arg = appvect (mkRel (i+1),extended_rel_vect 0 hyps) in 
            applist(lift i fk,realargs@[arg])
     	| _ -> assert false
    in
    prec env 0 []
  in
  (* ici, cstrprods est la liste des produits du constructeur instantié *)
  let rec process_constr env i f = function
    | (n,None,t as d)::cprest, recarg::rest -> 
        let optionpos = 
	  match dest_recarg recarg with 
            | Norec   -> None
            | Imbr _  -> None
            | Mrec i  -> fvect.(i)
	in 
        (match optionpos with 
           | None ->
	       lambda_name env
		 (n,t,process_constr (push_rel d env) (i+1)
		    (whd_beta (applist (lift 1 f, [(mkRel 1)])))
		    (cprest,rest))
           | Some(_,f_0) -> 
	       let nF = lift (i+1+decF) f_0 in
               let env' = push_rel d env in
	       let arg = process_pos env' nF (lift 1 t) in 
               lambda_name env
		 (n,t,process_constr env' (i+1)
		    (whd_beta (applist (lift 1 f, [(mkRel 1); arg])))
		    (cprest,rest)))
    | (n,Some c,t as d)::cprest, rest ->
	mkLetIn
	  (n,c,t,
	   process_constr (push_rel d env) (i+1) (lift 1 f)
	     (cprest,rest))
    | [],[] -> f
    | _,[] | [],_ -> anomaly "process_constr"

  in
  process_constr env 0 f (List.rev cstr.cs_args, recargs)


(* Cut a context ctx in 2 parts (ctx1,ctx2) with ctx1 containing k 
   variables *)
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)
    | (_, []) -> failwith "context_chop"
  in chop_aux [] (k,ctx)


(* Main function *)
let mis_make_indrec env sigma listdepkind mib =
  let nparams = mib.mind_nparams in
  let nparrec = mib. mind_nparams_rec in
  let lnonparrec,lnamesparrec = 
    context_chop (nparams-nparrec) mib.mind_params_ctxt in
  let nrec = List.length listdepkind in
  let depPvec =
    Array.create mib.mind_ntypes (None : (bool * constr) option) in 
  let _ = 
    let rec 
	assign k = function 
	  | [] -> ()
          | (indi,mibi,mipi,dep,_)::rest -> 
              (Array.set depPvec (snd indi) (Some(dep,mkRel k));
               assign (k-1) rest)
    in 
      assign nrec listdepkind in 
  let recargsvec =
    Array.map (fun mip -> mip.mind_recargs) mib.mind_packets in
  (* recarg information for non recursive parameters *)
  let rec recargparn l n = 
    if n = 0 then l else recargparn (mk_norec::l) (n-1) in
  let recargpar = recargparn [] (nparams-nparrec) in
  let make_one_rec p =
    let makefix nbconstruct =
      let rec mrec i ln ltyp ldef = function
	| (indi,mibi,mipi,dep,_)::rest ->
	    let tyi = snd indi in
	    let nctyi =
              Array.length mipi.mind_consnames in (* nb constructeurs du type*)
	      
            (* arity in the context of the fixpoint, i.e.
               P1..P_nrec f1..f_nbconstruct *)
	    let args = extended_rel_list (nrec+nbconstruct) lnamesparrec in
	    let indf = make_ind_family(indi,args) in
	      
	    let arsign,_ = get_arity env indf in
	    let depind = build_dependent_inductive env indf in
	    let deparsign = (Anonymous,None,depind)::arsign in
	      
	    let nonrecpar = rel_context_length lnonparrec in
	    let larsign = rel_context_length deparsign in
	    let ndepar = larsign - nonrecpar in
	    let dect = larsign+nrec+nbconstruct in
	      
            (* constructors in context of the Cases expr, i.e.
               P1..P_nrec f1..f_nbconstruct F_1..F_nrec a_1..a_nar x:I *)
	    let args' = extended_rel_list (dect+nrec) lnamesparrec in
	    let args'' = extended_rel_list ndepar lnonparrec in
            let indf' = make_ind_family(indi,args'@args'') in
	      
	    let branches = 
	      let constrs = get_constructors env indf' in
	      let fi = rel_vect (dect-i-nctyi) nctyi in
	      let vecfi = Array.map 
		(fun f -> appvect (f,extended_rel_vect ndepar lnonparrec))
		fi 
	      in
		array_map3
		  (make_rec_branch_arg env sigma 
		      (nparrec,depPvec,larsign))
                  vecfi constrs (dest_subterms recargsvec.(tyi)) 
	    in
	      
	    let j = (match depPvec.(tyi) with 
	      | Some (_,c) when isRel c -> destRel c 
	      | _ -> assert false) 
	    in
	      
	    (* Predicate in the context of the case *)
	      
	    let depind' = build_dependent_inductive env indf' in
	    let arsign',_ = get_arity env indf' in
	    let deparsign' = (Anonymous,None,depind')::arsign' in
	      
	    let pargs =
	      let nrpar = extended_rel_list (2*ndepar) lnonparrec 
	      and nrar = if dep then extended_rel_list 0 deparsign'
		else extended_rel_list 1 arsign'
	      in nrpar@nrar
		
	    in

	    (* body of i-th component of the mutual fixpoint *)
	    let deftyi = 
	      let ci = make_case_info env indi RegularStyle in
	      let concl = applist (mkRel (dect+j+ndepar),pargs) in 
	      let pred =
		it_mkLambda_or_LetIn_name env 
		  ((if dep then mkLambda_name env else mkLambda)
		      (Anonymous,depind',concl))
		  arsign'
	      in
		it_mkLambda_or_LetIn_name env
		  (mkCase (ci, pred, 
		          mkRel 1,
			  branches))
		  (lift_rel_context nrec deparsign)
	    in
	      
	    (* type of i-th component of the mutual fixpoint *)
	      
	    let typtyi =
	      let concl = 
		let pargs = if dep then extended_rel_vect 0 deparsign
		  else extended_rel_vect 1 arsign
		in appvect (mkRel (nbconstruct+ndepar+nonrecpar+j),pargs)
	      in it_mkProd_or_LetIn_name env
		concl
		deparsign
	    in
	      mrec (i+nctyi) (rel_context_nhyps arsign ::ln) (typtyi::ltyp) 
                (deftyi::ldef) rest
        | [] -> 
	    let fixn = Array.of_list (List.rev ln) in
            let fixtyi = Array.of_list (List.rev ltyp) in
            let fixdef = Array.of_list (List.rev ldef) in 
            let names = Array.create nrec (Name(id_of_string "F")) in
	      mkFix ((fixn,p),(names,fixtyi,fixdef))
      in 
	mrec 0 [] [] [] 
    in 
    let rec make_branch env i = function 
      | (indi,mibi,mipi,dep,_)::rest ->
          let tyi = snd indi in
	  let nconstr = Array.length mipi.mind_consnames in
	  let rec onerec env j = 
	    if j = nconstr then 
	      make_branch env (i+j) rest 
	    else 
	      let recarg = (dest_subterms recargsvec.(tyi)).(j) in
	      let recarg = recargpar@recarg in
	      let vargs = extended_rel_list (nrec+i+j) lnamesparrec in
	      let cs = get_constructor (indi,mibi,mipi,vargs) (j+1) in
	      let p_0 =
		type_rec_branch
                  true dep env sigma (vargs,depPvec,i+j) tyi cs recarg
	      in 
		mkLambda_string "f" p_0
		  (onerec (push_rel (Anonymous,None,p_0) env) (j+1))
	  in onerec env 0
      | [] -> 
	  makefix i listdepkind
    in
    let rec put_arity env i = function 
      | (indi,_,_,dep,kinds)::rest -> 
	  let indf = make_ind_family (indi,extended_rel_list i lnamesparrec) in
	  let typP = make_arity env dep indf (new_sort_in_family kinds) in
	    mkLambda_string "P" typP
	      (put_arity (push_rel (Anonymous,None,typP) env) (i+1) rest)
      | [] -> 
	  make_branch env 0 listdepkind 
    in
      
    (* Body on make_one_rec *)
    let (indi,mibi,mipi,dep,kind) = List.nth listdepkind p in
      
      if (mis_is_recursive_subset
	(List.map (fun (indi,_,_,_,_) -> snd indi) listdepkind)
	mipi.mind_recargs) 
      then 
	let env' = push_rel_context lnamesparrec env in
	  it_mkLambda_or_LetIn_name env (put_arity env' 0 listdepkind) 
	    lnamesparrec
      else 
	mis_make_case_com (Some dep) env sigma indi (mibi,mipi) kind 
  in 
    (* Body of mis_make_indrec *)
    list_tabulate make_one_rec nrec

(**********************************************************************)
(* This builds elimination predicate for Case tactic *)

let make_case_com depopt env sigma ity kind =
  let (mib,mip) = lookup_mind_specif env ity in 
    mis_make_case_com depopt env sigma ity (mib,mip) kind

let make_case_dep env   = make_case_com (Some true) env
let make_case_nodep env = make_case_com (Some false) env 
let make_case_gen env   = make_case_com None env


(**********************************************************************)
(* [instantiate_indrec_scheme s rec] replace the sort of the scheme
   [rec] by [s] *)

let change_sort_arity sort = 
  let rec drec a = match kind_of_term a with
    | Cast (c,_,_) -> drec c 
    | Prod (n,t,c) -> mkProd (n, t, drec c)
    | LetIn (n,b,t,c) -> mkLetIn (n,b, t, drec c)
    | Sort _ -> mkSort sort
    | _ -> assert false
  in 
    drec 

(* [npar] is the number of expected arguments (then excluding letin's) *)
let instantiate_indrec_scheme sort =
  let rec drec npar elim =
    match kind_of_term elim with
      | Lambda (n,t,c) -> 
	  if npar = 0 then 
	    mkLambda (n, change_sort_arity sort t, c)
	  else 
	    mkLambda (n, t, drec (npar-1) c)
      | LetIn (n,b,t,c) -> mkLetIn (n,b,t,drec npar c)
      | _ -> anomaly "instantiate_indrec_scheme: wrong elimination type"
  in
  drec

(* Change the sort in the type of an inductive definition, builds the
   corresponding eta-expanded term *)
let instantiate_type_indrec_scheme sort npars term =
  let rec drec np elim =
    match kind_of_term elim with
      | Prod (n,t,c) -> 
	  if np = 0 then 
            let t' = change_sort_arity sort t in
            mkProd (n, t', c),
            mkLambda (n, t', mkApp(term,Termops.rel_vect 0 (npars+1)))
	  else 
            let c',term' = drec (np-1) c in
	    mkProd (n, t, c'), mkLambda (n, t, term')
      | LetIn (n,b,t,c) -> let c',term' = drec np c in
           mkLetIn (n,b,t,c'), mkLetIn (n,b,t,term') 
      | _ -> anomaly "instantiate_type_indrec_scheme: wrong elimination type"
  in
  drec npars

(**********************************************************************)
(* Interface to build complex Scheme *)
(* Check inductive types only occurs once 
(otherwise we obtain a meaning less scheme) *)

let check_arities listdepkind = 
  let _ = List.fold_left
    (fun ln ((_,ni as mind),mibi,mipi,dep,kind) -> 
       let kelim = elim_sorts (mibi,mipi) in
       if not (List.exists ((=) kind) kelim) then raise
	 (RecursionSchemeError
	   (NotAllowedCaseAnalysis (true,new_sort_in_family kind,mind)))
       else if List.mem ni ln then raise
	 (RecursionSchemeError (NotMutualInScheme (mind,mind)))
       else ni::ln)
	    [] listdepkind
  in true

let build_mutual_indrec env sigma = function 
  | (mind,mib,mip,dep,s)::lrecspec ->
      let (sp,tyi) = mind in
      let listdepkind = 
    	(mind,mib,mip, dep,s)::
    	(List.map
	   (function (mind',mibi',mipi',dep',s') ->
	      let (sp',_) = mind' in
	      if sp=sp' then
                let (mibi',mipi') = lookup_mind_specif env mind' in
		(mind',mibi',mipi',dep',s')
	      else
		  raise (RecursionSchemeError (NotMutualInScheme (mind,mind'))))
	   lrecspec)
      in
      let _ = check_arities listdepkind in 
      mis_make_indrec env sigma listdepkind mib
  | _ -> anomaly "build_indrec expects a non empty list of inductive types"

let build_indrec env sigma ind =
  let (mib,mip) = lookup_mind_specif env ind in
  let kind = inductive_sort_family mip in
  let dep = kind <> InProp in
    List.hd (mis_make_indrec env sigma [(ind,mib,mip,dep,kind)] mib)

(**********************************************************************)
(* To handle old Case/Match syntax in Pretyping                       *)

(*****************************************)
(* To interpret Case and Match operators *)
(* Expects a dependent predicate *)

let type_rec_branches recursive env sigma indt p c = 
  let IndType (indf,realargs) = indt in
  let (ind,params) = dest_ind_family indf in
  let (mib,mip) = lookup_mind_specif env ind in
  let recargs = mip.mind_recargs in
  let tyi = snd ind in
  let init_depPvec i = if i = tyi then Some(true,p) else None in
  let depPvec = Array.init mib.mind_ntypes init_depPvec in
  let constructors = get_constructors env indf in
  let lft =
    array_map2
      (type_rec_branch recursive true env sigma (params,depPvec,0) tyi)
      constructors (dest_subterms recargs) in
  (lft,Reduction.beta_appvect p (Array.of_list (realargs@[c])))
(* Non recursive case. Pb: does not deal with unification
    let (p,ra,_) = type_case_branches env (ind,params@realargs) pj c in
    (p,ra)
*)

(*s Eliminations. *)

let elimination_suffix = function
  | InProp -> "_ind"
  | InSet  -> "_rec"
  | InType -> "_rect"

let make_elimination_ident id s = add_suffix id (elimination_suffix s)

(* Look up function for the default elimination constant *)

let lookup_eliminator ind_sp s =
  let kn,i = ind_sp in
  let mp,dp,l = repr_kn kn in
  let ind_id = (Global.lookup_mind kn).mind_packets.(i).mind_typename in
  let id = add_suffix ind_id (elimination_suffix s) in
  (* Try first to get an eliminator defined in the same section as the *)
  (* inductive type *)
  let ref = ConstRef (make_con mp dp (label_of_id id)) in
  try 
    let _ = sp_of_global ref in
    constr_of_global ref
  with Not_found ->
  (* Then try to get a user-defined eliminator in some other places *)
  (* using short name (e.g. for "eq_rec") *)
  try constr_of_global (Nametab.locate (make_short_qualid id))
  with Not_found ->
    errorlabstrm "default_elim"
      (strbrk "Cannot find the elimination combinator " ++
       pr_id id ++ strbrk ", the elimination of the inductive definition " ++
       pr_global_env Idset.empty (IndRef ind_sp) ++ 
       strbrk " on sort " ++ pr_sort_family s ++
       strbrk " is probably not allowed.")


(*  let env = Global.env() in
  let path = sp_of_global None (IndRef ind_sp) in
  let dir, base = repr_path path in
  let id = add_suffix base (elimination_suffix s) in
  (* Try first to get an eliminator defined in the same section as the *)
  (* inductive type *)
  try construct_absolute_reference (Names.make_path dir id)
  with Not_found ->
  (* Then try to get a user-defined eliminator in some other places *)
  (* using short name (e.g. for "eq_rec") *)
    try constr_of_global (Nametab.locate (make_short_qualid id))
    with Not_found ->
      errorlabstrm "default_elim"
	(str "Cannot find the elimination combinator " ++
           pr_id id ++ spc () ++
	   str "The elimination of the inductive definition " ++
           pr_id base ++ spc () ++ str "on sort " ++ 
           spc () ++ pr_sort_family s ++
	   str " is probably not allowed")
*)