summaryrefslogtreecommitdiff
path: root/plugins/funind/indfun.ml
blob: a61671f871ed57a54d8629e9e96d1b920410f2d8 (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
open Util
open Names
open Term
open Pp
open Indfun_common
open Libnames
open Rawterm
open Declarations

let is_rec_info scheme_info =
  let test_branche min acc (_,_,br) =
    acc || (
      let new_branche =
	it_mkProd_or_LetIn mkProp (fst (decompose_prod_assum br)) in
      let free_rels_in_br = Termops.free_rels new_branche in
      let max = min + scheme_info.Tactics.npredicates in
      Util.Intset.exists (fun i -> i >= min && i< max) free_rels_in_br
    )
  in
  Util.list_fold_left_i test_branche 1 false (List.rev scheme_info.Tactics.branches)


let choose_dest_or_ind scheme_info =
    if is_rec_info scheme_info
    then Tactics.new_induct false
    else Tactics.new_destruct false


let functional_induction with_clean c princl pat =
  Dumpglob.pause ();
  let res = let f,args = decompose_app c in
	      fun g ->
		let princ,bindings, princ_type =
		  match princl with
	| None -> (* No principle is given let's find the good one *)
	    begin
	      match kind_of_term f with
		| Const c' ->
		    let princ_option =
		      let finfo = (* we first try to find out a graph on f *)
			try find_Function_infos c'
			with Not_found ->
			  errorlabstrm "" (str "Cannot find induction information on "++
					     Printer.pr_lconstr (mkConst c') )
		      in
		      match Tacticals.elimination_sort_of_goal g with
			| InProp -> finfo.prop_lemma
			| InSet -> finfo.rec_lemma
			| InType -> finfo.rect_lemma
		    in
		    let princ =  (* then we get the principle *)
		      try mkConst (Option.get princ_option )
		      with Option.IsNone ->
			(*i If there is not default lemma defined then,
			  we cross our finger and try to find a lemma named f_ind
			  (or f_rec, f_rect) i*)
			let princ_name =
			  Indrec.make_elimination_ident
			    (id_of_label (con_label c'))
			    (Tacticals.elimination_sort_of_goal g)
			in
			try
			  mkConst(const_of_id princ_name )
			with Not_found -> (* This one is neither defined ! *)
			  errorlabstrm "" (str "Cannot find induction principle for "
					   ++Printer.pr_lconstr (mkConst c') )
		    in
		    (princ,Rawterm.NoBindings, Tacmach.pf_type_of g princ)
		| _ -> raise (UserError("",str "functional induction must be used with a function" ))

	    end
	| Some ((princ,binding)) ->
	    princ,binding,Tacmach.pf_type_of g princ
    in
    let princ_infos = Tactics.compute_elim_sig princ_type in
    let args_as_induction_constr =
      let c_list =
	if princ_infos.Tactics.farg_in_concl
	then [c] else []
      in
      List.map (fun c -> Tacexpr.ElimOnConstr (c,NoBindings)) (args@c_list)
    in
    let princ' = Some (princ,bindings) in
    let princ_vars =
      List.fold_right
	(fun a acc ->
	  try Idset.add (destVar a) acc
	  with _ -> acc
	)
	args
	Idset.empty
    in
    let old_idl = List.fold_right Idset.add (Tacmach.pf_ids_of_hyps g) Idset.empty in
    let old_idl = Idset.diff old_idl princ_vars in
    let subst_and_reduce g =
      if with_clean
      then
	let idl =
	  map_succeed
	    (fun id ->
	       if Idset.mem id old_idl then failwith "subst_and_reduce";
	       id
	    )
	    (Tacmach.pf_ids_of_hyps g)
	in
	let flag =
	  Rawterm.Cbv
	    {Rawterm.all_flags
	     with Rawterm.rDelta = false;
	    }
	in
	Tacticals.tclTHEN
	  (Tacticals.tclMAP (fun id -> Tacticals.tclTRY (Equality.subst_gen (do_rewrite_dependent ()) [id])) idl )
	  (Hiddentac.h_reduce flag Tacticals.allHypsAndConcl)
	  g
      else Tacticals.tclIDTAC g

    in
    Tacticals.tclTHEN
      (choose_dest_or_ind
	 princ_infos
	 args_as_induction_constr
	 princ'
	 (None,pat)
         None)
      subst_and_reduce
      g
  in
    Dumpglob.continue ();
    res




type annot =
    Struct of identifier
  | Wf of Topconstr.constr_expr * identifier option * Topconstr.constr_expr list
  | Mes of Topconstr.constr_expr * identifier option * Topconstr.constr_expr list


type newfixpoint_expr =
    identifier * annot * Topconstr.local_binder list * Topconstr.constr_expr * Topconstr.constr_expr

let rec abstract_rawconstr c = function
  | [] -> c
  | Topconstr.LocalRawDef (x,b)::bl -> Topconstr.mkLetInC(x,b,abstract_rawconstr c bl)
  | Topconstr.LocalRawAssum (idl,k,t)::bl ->
      List.fold_right (fun x b -> Topconstr.mkLambdaC([x],k,t,b)) idl
        (abstract_rawconstr c bl)

let interp_casted_constr_with_implicits sigma env impls c  =
(*   Constrintern.interp_rawconstr_with_implicits sigma env [] impls c *)
  Constrintern.intern_gen false sigma env ~impls
    ~allow_patvar:false  ~ltacvars:([],[]) c


(*
   Construct a fixpoint as a Rawterm
   and not as a constr
*)
let build_newrecursive
(lnameargsardef)  =
  let env0 = Global.env()
  and sigma = Evd.empty
  in
  let (rec_sign,rec_impls) =
    List.fold_left
      (fun (env,impls) ((_,recname),_,bl,arityc,_) ->
        let arityc = Topconstr.prod_constr_expr arityc bl in
        let arity = Constrintern.interp_type sigma env0 arityc in
	let impl = Constrintern.compute_internalization_data env0 Constrintern.Recursive arity [] in
        (Environ.push_named (recname,None,arity) env, (recname, impl) :: impls))
      (env0,[]) lnameargsardef in
  let recdef =
    (* Declare local notations *)
    let fs = States.freeze() in
    let def =
      try
	List.map
	  (fun (_,_,bl,_,def)  ->
             let def = abstract_rawconstr def bl in
             interp_casted_constr_with_implicits
	       sigma rec_sign rec_impls def
	  )
          lnameargsardef
	with e ->
	States.unfreeze fs; raise e in
    States.unfreeze fs; def
  in
  recdef,rec_impls


let compute_annot (name,annot,args,types,body) =
  let names = List.map snd (Topconstr.names_of_local_assums args) in
  match annot with
    | None ->
        if List.length names > 1 then
          user_err_loc
            (dummy_loc,"Function",
             Pp.str "the recursive argument needs to be specified");
        let new_annot = (id_of_name (List.hd names)) in
	(name,Struct new_annot,args,types,body)
    | Some r -> (name,r,args,types,body)


(* Checks whether or not the mutual bloc is recursive *)
let rec is_rec names =
  let names = List.fold_right Idset.add names Idset.empty in
  let check_id id names =  Idset.mem id names in
  let rec lookup names = function
    | RVar(_,id) -> check_id id names
    | RRef _ | REvar _ | RPatVar _ | RSort _ |  RHole _ | RDynamic _ -> false
    | RCast(_,b,_) -> lookup names b
    | RRec _ -> error "RRec not handled"
    | RIf(_,b,_,lhs,rhs) ->
	(lookup names b) || (lookup names lhs) || (lookup names rhs)
    | RLetIn(_,na,t,b) | RLambda(_,na,_,t,b) | RProd(_,na,_,t,b)  ->
	lookup names t || lookup (Nameops.name_fold Idset.remove na names) b
    | RLetTuple(_,nal,_,t,b) -> lookup names t ||
	lookup
	  (List.fold_left
	     (fun acc na -> Nameops.name_fold Idset.remove na acc)
	     names
	     nal
	  )
	  b
    | RApp(_,f,args) -> List.exists (lookup names) (f::args)
    | RCases(_,_,_,el,brl) ->
	List.exists (fun (e,_) -> lookup names e) el ||
	  List.exists (lookup_br names) brl
  and lookup_br names (_,idl,_,rt) =
    let new_names = List.fold_right Idset.remove idl names in
    lookup new_names rt
  in
  lookup names

let rec local_binders_length = function
  (* Assume that no `{ ... } contexts occur *)
  | [] -> 0
  | Topconstr.LocalRawDef _::bl -> 1 + local_binders_length bl
  | Topconstr.LocalRawAssum (idl,_,_)::bl -> List.length idl + local_binders_length bl

let prepare_body (name,annot,args,types,body) rt =
  let n = local_binders_length args in
(*   Pp.msgnl (str "nb lambda to chop : " ++ str (string_of_int n) ++ fnl () ++Printer.pr_rawconstr rt); *)
  let fun_args,rt' = chop_rlambda_n n rt in
  (fun_args,rt')


let derive_inversion fix_names =
  try
    (* we first transform the fix_names identifier into their corresponding constant *)
    let fix_names_as_constant =
      List.map (fun id -> destConst (Tacinterp.constr_of_id (Global.env ()) id)) fix_names
    in
    (*
       Then we check that the graphs have been defined
       If one of the graphs haven't been defined
       we do nothing
    *)
    List.iter (fun c -> ignore (find_Function_infos c)) fix_names_as_constant ;
    try
      Invfun.derive_correctness
	Functional_principles_types.make_scheme
	functional_induction
	fix_names_as_constant
	(*i The next call to mk_rel_id is valid since we have just construct the graph
	  Ensures by : register_built
	  i*)
	(List.map
	   (fun id -> destInd (Tacinterp.constr_of_id (Global.env ()) (mk_rel_id id)))
	   fix_names
	)
    with e ->
      msg_warning
	(str "Cannot built inversion information" ++
	   if do_observe () then Cerrors.explain_exn e else mt ())
  with _ -> ()

let warning_error names e =
  let e_explain e =
    match e with
      | ToShow e -> spc () ++ Cerrors.explain_exn e
      | _ -> if do_observe () then (spc () ++ Cerrors.explain_exn e) else mt ()
  in
  match e with
    | Building_graph e ->
	Pp.msg_warning
	  (str "Cannot define graph(s) for " ++
	     h 1 (prlist_with_sep (fun _ -> str","++spc ()) Ppconstr.pr_id names) ++
	     e_explain e)
    | Defining_principle e ->
	Pp.msg_warning
	  (str "Cannot define principle(s) for "++
	     h 1 (prlist_with_sep (fun _ -> str","++spc ()) Ppconstr.pr_id names) ++
	     e_explain e)
    | _ -> raise e

let error_error names e =
  let e_explain e =
    match e with
      | ToShow e -> spc () ++ Cerrors.explain_exn e
      | _ -> if do_observe () then (spc () ++ Cerrors.explain_exn e) else mt ()
  in
  match e with
    | Building_graph e ->
	errorlabstrm ""
	  (str "Cannot define graph(s) for " ++
	     h 1 (prlist_with_sep (fun _ -> str","++spc ()) Ppconstr.pr_id names) ++
	     e_explain e)
    | _ -> raise e

let generate_principle  on_error
    is_general do_built fix_rec_l recdefs  interactive_proof
    (continue_proof : int -> Names.constant array -> Term.constr array -> int ->
      Tacmach.tactic) : unit =
  let names = List.map (function ((_, name),_,_,_,_) -> name) fix_rec_l in
  let fun_bodies = List.map2 prepare_body fix_rec_l recdefs in
  let funs_args = List.map fst fun_bodies in
  let funs_types =  List.map (function (_,_,_,types,_) -> types) fix_rec_l in
  try
    (* We then register the Inductive graphs of the functions  *)
    Rawterm_to_relation.build_inductive names funs_args funs_types recdefs;
    if do_built
    then
      begin
	(*i The next call to mk_rel_id is valid since we have just construct the graph
	   Ensures by : do_built
	i*)
	let f_R_mut = Ident (dummy_loc,mk_rel_id (List.nth names 0)) in
	let ind_kn =
	  fst (locate_with_msg
		 (pr_reference f_R_mut++str ": Not an inductive type!")
		 locate_ind
		 f_R_mut)
	in
	let fname_kn (fname,_,_,_,_) =
	  let f_ref = Ident fname in
	  locate_with_msg
	    (pr_reference f_ref++str ": Not an inductive type!")
	    locate_constant
	    f_ref
	in
	let funs_kn = Array.of_list (List.map fname_kn fix_rec_l) in
	let _ =
	  list_map_i
	    (fun i x ->
	       let princ = destConst (Indrec.lookup_eliminator (ind_kn,i) (InProp)) in
	       let princ_type = Typeops.type_of_constant (Global.env()) princ
	       in
	       Functional_principles_types.generate_functional_principle
		 interactive_proof
		 princ_type
		 None
		 None
		 funs_kn
		 i
		 (continue_proof  0 [|funs_kn.(i)|])
	    )
	    0
	    fix_rec_l
	in
	Array.iter (add_Function is_general) funs_kn;
	()
      end
  with e ->
    on_error names e

let register_struct is_rec fixpoint_exprl =
  match fixpoint_exprl with
    | [((_,fname),_,bl,ret_type,body),_] when not is_rec ->
	let ce,imps =
	  Command.interp_definition
	    (Flags.boxed_definitions ()) bl None body (Some ret_type)
	in
	Command.declare_definition
	  fname (Decl_kinds.Global,Decl_kinds.Definition)
	  ce imps (fun _ _ -> ())
    | _ ->
        let fixpoint_exprl =
          List.map (fun ((name,annot,bl,types,body),ntn) ->
            ((name,annot,bl,types,Some body),ntn)) fixpoint_exprl in
	Command.do_fixpoint fixpoint_exprl (Flags.boxed_definitions())

let generate_correction_proof_wf f_ref tcc_lemma_ref
    is_mes functional_ref eq_ref rec_arg_num rec_arg_type nb_args relation
    (_: int) (_:Names.constant array) (_:Term.constr array) (_:int) : Tacmach.tactic =
  Functional_principles_proofs.prove_principle_for_gen
    (f_ref,functional_ref,eq_ref)
    tcc_lemma_ref is_mes  rec_arg_num rec_arg_type relation


let register_wf ?(is_mes=false) fname rec_impls wf_rel_expr wf_arg using_lemmas args ret_type body
    pre_hook
    =
  let type_of_f = Topconstr.prod_constr_expr ret_type args in
  let rec_arg_num =
    let names =
      List.map
	snd
	(Topconstr.names_of_local_assums args)
    in
    match wf_arg with
      | None ->
	  if List.length names = 1 then 1
	  else error "Recursive argument must be specified"
      | Some wf_arg ->
	  list_index (Name wf_arg) names
  in
  let unbounded_eq =
    let f_app_args =
      Topconstr.CAppExpl
	(dummy_loc,
	 (None,(Ident (dummy_loc,fname))) ,
	 (List.map
	    (function
	       | _,Anonymous -> assert false
	       | _,Name e -> (Topconstr.mkIdentC e)
	    )
	    (Topconstr.names_of_local_assums args)
	 )
	)
    in
    Topconstr.CApp (dummy_loc,(None,Topconstr.mkRefC (Qualid (dummy_loc,(qualid_of_string "Logic.eq")))),
		    [(f_app_args,None);(body,None)])
  in
  let eq = Topconstr.prod_constr_expr unbounded_eq args in
  let hook f_ref tcc_lemma_ref functional_ref eq_ref rec_arg_num rec_arg_type
      nb_args relation =
    try
      pre_hook
	(generate_correction_proof_wf f_ref tcc_lemma_ref is_mes
	   functional_ref eq_ref rec_arg_num rec_arg_type nb_args relation
	);
      derive_inversion [fname]
    with e ->
      (* No proof done *)
      ()
  in
  Recdef.recursive_definition
    is_mes fname rec_impls
    type_of_f
    wf_rel_expr
    rec_arg_num
    eq
    hook
    using_lemmas


let register_mes fname rec_impls wf_mes_expr wf_arg using_lemmas args ret_type body =
  let wf_arg_type,wf_arg =
    match wf_arg with
      | None ->
	  begin
	    match args with
	      | [Topconstr.LocalRawAssum ([(_,Name x)],k,t)] -> t,x
	      | _ -> error "Recursive argument must be specified"
	  end
      | Some wf_args ->
	  try
	    match
	      List.find
		(function
		   | Topconstr.LocalRawAssum(l,k,t) ->
		       List.exists
			 (function (_,Name id) -> id =  wf_args | _ -> false)
			 l
		   | _ -> false
		)
		args
	    with
	      | Topconstr.LocalRawAssum(_,k,t)  ->	    t,wf_args
	      | _ -> assert false
	  with Not_found -> assert false
  in
  let ltof =
    let make_dir l = make_dirpath (List.map id_of_string (List.rev l)) in
    Libnames.Qualid (dummy_loc,Libnames.qualid_of_path
      (Libnames.make_path (make_dir ["Arith";"Wf_nat"]) (id_of_string "ltof")))
  in
  let fun_from_mes =
    let applied_mes =
      Topconstr.mkAppC(wf_mes_expr,[Topconstr.mkIdentC wf_arg])    in
    Topconstr.mkLambdaC ([(dummy_loc,Name wf_arg)],Topconstr.default_binder_kind,wf_arg_type,applied_mes)
  in
  let wf_rel_from_mes =
    Topconstr.mkAppC(Topconstr.mkRefC  ltof,[wf_arg_type;fun_from_mes])
  in
  register_wf ~is_mes:true fname rec_impls wf_rel_from_mes (Some wf_arg)
    using_lemmas args ret_type body


let do_generate_principle on_error register_built interactive_proof fixpoint_exprl  =
  let recdefs,rec_impls = build_newrecursive fixpoint_exprl in
  let _is_struct =
    match fixpoint_exprl with
      | [(((_,name),Some (Wf (wf_rel,wf_x,using_lemmas)),args,types,body))] ->
	  let pre_hook =
	    generate_principle
	      on_error
	      true
	      register_built
	      fixpoint_exprl
	      recdefs
	      true
	  in
	  if register_built
	  then register_wf name rec_impls wf_rel wf_x using_lemmas args types body pre_hook;
	  false
      | [(((_,name),Some (Mes (wf_mes,wf_x,using_lemmas)),args,types,body))] ->
	  let pre_hook =
	    generate_principle
	      on_error
	      true
	      register_built
	      fixpoint_exprl
	      recdefs
	      true
	  in
	  if register_built
	  then register_mes name rec_impls wf_mes wf_x using_lemmas args types body pre_hook;
	  true
      | _ ->
	  let fix_names =
	    List.map (function ((_,name),_,_,_,_) -> name) fixpoint_exprl
	  in
	  let is_one_rec = is_rec fix_names  in
	  let old_fixpoint_exprl =
	    List.map
	      (function
		 | (name,Some (Struct id),args,types,body),_ ->
		     let annot =
		       try Some (dummy_loc, id), Topconstr.CStructRec
		       with Not_found ->
			 raise (UserError("",str "Cannot find argument " ++
					    Ppconstr.pr_id id))
		     in
		     (name,annot,args,types,body),([]:Vernacexpr.decl_notation list)
		 | (name,None,args,types,body),recdef ->
		     let names =  (Topconstr.names_of_local_assums args) in
		     if  is_one_rec recdef  && List.length names > 1 then
		       user_err_loc
			 (dummy_loc,"Function",
			  Pp.str "the recursive argument needs to be specified in Function")
		     else
		       let loc, na = List.hd names in
			 (name,(Some (loc, Nameops.out_name na), Topconstr.CStructRec),args,types,body),
		     ([]:Vernacexpr.decl_notation list)
		 | (_,Some (Wf _),_,_,_),_ | (_,Some (Mes _),_,_,_),_->
		     error
		       ("Cannot use mutual definition with well-founded recursion or measure")
	      )
	      (List.combine fixpoint_exprl recdefs)
	  in
	  (* ok all the expressions are structural *)
	  let fix_names =
	    List.map (function ((_,name),_,_,_,_) -> name) fixpoint_exprl
	  in
	  let is_rec = List.exists (is_rec fix_names) recdefs in
	  if register_built then register_struct is_rec old_fixpoint_exprl;
	  generate_principle
	    on_error
	    false
	    register_built
	    fixpoint_exprl
	    recdefs
	    interactive_proof
	    (Functional_principles_proofs.prove_princ_for_struct interactive_proof);
	  if register_built then derive_inversion fix_names;
	  true;
  in
  ()

open Topconstr
let rec add_args id new_args b =
  match b with
  | CRef r ->
      begin      match r with
	| Libnames.Ident(loc,fname) when fname = id ->
	    CAppExpl(dummy_loc,(None,r),new_args)
	| _ -> b
      end
  | CFix  _  | CCoFix _ -> anomaly "add_args : todo"
  | CArrow(loc,b1,b2) ->
      CArrow(loc,add_args id new_args  b1, add_args id new_args b2)
  | CProdN(loc,nal,b1) ->
      CProdN(loc,
	     List.map (fun (nal,k,b2) -> (nal,k,add_args id new_args b2)) nal,
	     add_args id new_args  b1)
  | CLambdaN(loc,nal,b1) ->
      CLambdaN(loc,
	       List.map (fun (nal,k,b2) -> (nal,k,add_args id new_args  b2)) nal,
	       add_args id new_args  b1)
  | CLetIn(loc,na,b1,b2) ->
      CLetIn(loc,na,add_args id new_args b1,add_args id new_args b2)
  | CAppExpl(loc,(pf,r),exprl) ->
      begin
	match r with
	| Libnames.Ident(loc,fname) when fname = id ->
	    CAppExpl(loc,(pf,r),new_args@(List.map (add_args id new_args) exprl))
	| _ -> CAppExpl(loc,(pf,r),List.map (add_args id new_args) exprl)
      end
  | CApp(loc,(pf,b),bl) ->
      CApp(loc,(pf,add_args id new_args b),
	   List.map (fun (e,o) -> add_args id new_args e,o) bl)
  | CCases(loc,sty,b_option,cel,cal) ->
      CCases(loc,sty,Option.map (add_args id new_args) b_option,
	     List.map (fun (b,(na,b_option)) ->
			 add_args id new_args b,
			 (na,Option.map (add_args id new_args) b_option)) cel,
	     List.map (fun (loc,cpl,e) -> (loc,cpl,add_args id new_args e)) cal
	    )
  | CLetTuple(loc,nal,(na,b_option),b1,b2) ->
      CLetTuple(loc,nal,(na,Option.map (add_args id new_args) b_option),
		add_args id new_args b1,
		add_args id new_args b2
	       )

  | CIf(loc,b1,(na,b_option),b2,b3) ->
      CIf(loc,add_args id new_args b1,
	  (na,Option.map (add_args id new_args) b_option),
	  add_args id new_args b2,
	  add_args id new_args b3
	 )
  | CHole _ -> b
  | CPatVar _ -> b
  | CEvar _ -> b
  | CSort _ -> b
  | CCast(loc,b1,CastConv(ck,b2))  ->
      CCast(loc,add_args id new_args b1,CastConv(ck,add_args id new_args b2))
  | CCast(loc,b1,CastCoerce) ->
      CCast(loc,add_args id new_args b1,CastCoerce)
  | CRecord (loc, w, pars) ->
      CRecord (loc,
	       (match w with Some w -> Some (add_args id new_args w) | _ -> None),
	       List.map (fun (e,o) -> e, add_args id new_args o) pars)
  | CNotation _ -> anomaly "add_args : CNotation"
  | CGeneralization _ -> anomaly "add_args : CGeneralization"
  | CPrim _ -> b
  | CDelimiters _ -> anomaly "add_args : CDelimiters"
  | CDynamic _ -> anomaly "add_args : CDynamic"
exception Stop of  Topconstr.constr_expr


(* [chop_n_arrow n t] chops the [n] first arrows in [t]
   Acts on Topconstr.constr_expr
*)
let rec chop_n_arrow n t =
  if n <= 0
  then t (* If we have already removed all the arrows then return the type *)
  else (* If not we check the form of [t] *)
    match t with
      | Topconstr.CArrow(_,_,t) ->  (* If we have an arrow, we discard it and recall [chop_n_arrow] *)
	  chop_n_arrow (n-1) t
      | Topconstr.CProdN(_,nal_ta',t') -> (* If we have a forall, to result are possible :
					     either we need to discard more than the number of arrows contained
					     in this product declaration then we just recall [chop_n_arrow] on
					     the remaining number of arrow to chop and [t'] we discard it and
					     recall [chop_n_arrow], either this product contains more arrows
					     than the number we need to chop and then we return the new type
					  *)
	  begin
	    try
	      let new_n =
		let rec aux (n:int) = function
		    [] -> n
		| (nal,k,t'')::nal_ta' ->
		    let nal_l = List.length nal in
		    if n >= nal_l
		    then
		      aux (n - nal_l) nal_ta'
		    else
		      let new_t' =
			Topconstr.CProdN(dummy_loc,
					((snd (list_chop n nal)),k,t'')::nal_ta',t')
		      in
		      raise (Stop new_t')
		in
		aux n nal_ta'
	    in
	      chop_n_arrow new_n t'
	    with Stop t -> t
	  end
      | _ -> anomaly "Not enough products"


let rec get_args b t : Topconstr.local_binder list *
    Topconstr.constr_expr * Topconstr.constr_expr =
  match b with
    | Topconstr.CLambdaN (loc, (nal_ta), b') ->
	begin
	  let n =
	    (List.fold_left (fun n (nal,_,_) ->
			       n+List.length nal) 0 nal_ta )
	  in
	  let nal_tas,b'',t'' = get_args b' (chop_n_arrow n t) in
	  (List.map (fun (nal,k,ta) ->
		       (Topconstr.LocalRawAssum (nal,k,ta))) nal_ta)@nal_tas, b'',t''
	end
    | _ -> [],b,t


let make_graph (f_ref:global_reference) =
 let c,c_body =
      match f_ref with
	| ConstRef c ->
	    begin try c,Global.lookup_constant c
	    with Not_found ->
	      raise (UserError ("",str "Cannot find " ++ Printer.pr_lconstr (mkConst c)) )
	    end
	| _ -> raise (UserError ("", str "Not a function reference") )

  in
   Dumpglob.pause ();
  (match c_body.const_body with
    | None -> error "Cannot build a graph over an axiom !"
    | Some b ->
	let env = Global.env () in
	let body = (force b) in
	let extern_body,extern_type =
	  with_full_print
	    (fun () ->
	       (Constrextern.extern_constr false env body,
		Constrextern.extern_type false env
                  (Typeops.type_of_constant_type env c_body.const_type)
	       )
	    )
	    ()
	in
	let (nal_tas,b,t)  = get_args extern_body extern_type in
	let expr_list =
	  match b with
	    | Topconstr.CFix(loc,l_id,fixexprl) ->
		let l =
		  List.map
		    (fun (id,(n,recexp),bl,t,b) ->
		       let loc, rec_id = Option.get n in
		       let new_args =
			 List.flatten
			   (List.map
			      (function
 				 | Topconstr.LocalRawDef (na,_)-> []
			      	 | Topconstr.LocalRawAssum (nal,_,_) ->
				     List.map
				       (fun (loc,n) ->
					  CRef(Libnames.Ident(loc, Nameops.out_name n)))
				       nal
			      )
			      nal_tas
			   )
		       in
		       let b' = add_args (snd id) new_args b in
		       (id, Some (Struct rec_id),nal_tas@bl,t,b')
		    )
		    fixexprl
		in
		l
	    | _ ->
		let id = id_of_label (con_label c) in
		[((dummy_loc,id),None,nal_tas,t,b)]
	in
	do_generate_principle error_error false false expr_list;
	(* We register the infos *)
	let mp,dp,_ = repr_con c in
	List.iter
	  (fun ((_,id),_,_,_,_) -> add_Function false (make_con mp dp (label_of_id id)))
	  expr_list);
  Dumpglob.continue ()


(* let make_graph _ = assert false	 *)

let do_generate_principle = do_generate_principle warning_error true