aboutsummaryrefslogtreecommitdiffhomepage
path: root/checker/closure.ml
blob: b9ae4daa866cca9703b6c22379fa0715489ca2f8 (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
(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \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 Util
open Pp
open Names
open Cic
open Term
open Esubst
open Environ

let stats = ref false
let share = ref true

(* Profiling *)
let beta = ref 0
let delta = ref 0
let zeta = ref 0
let evar = ref 0
let iota = ref 0
let prune = ref 0

let reset () =
  beta := 0; delta := 0; zeta := 0; evar := 0; iota := 0; prune := 0

let stop() =
  Feedback.msg_debug (str "[Reds: beta=" ++ int !beta ++ str" delta=" ++ int !delta ++
	 str" zeta=" ++ int !zeta ++ str" evar=" ++ int !evar ++
         str" iota=" ++ int !iota ++ str" prune=" ++ int !prune ++ str"]")

let incr_cnt red cnt =
  if red then begin
    if !stats then incr cnt;
    true
  end else
    false

let with_stats c =
  if !stats then begin
    reset();
    let r = Lazy.force c in
    stop();
    r
  end else
    Lazy.force c

module type RedFlagsSig = sig
  type reds
  type red_kind
  val fBETA : red_kind
  val fDELTA : red_kind
  val fIOTA : red_kind
  val fZETA : red_kind
  val no_red : reds
  val red_add : reds -> red_kind -> reds
  val mkflags : red_kind list -> reds
  val red_set : reds -> red_kind -> bool
end

module RedFlags = (struct

  (* [r_const=(true,cl)] means all constants but those in [cl] *)
  (* [r_const=(false,cl)] means only those in [cl] *)
  (* [r_delta=true] just mean [r_const=(true,[])] *)

  type reds = {
    r_beta : bool;
    r_delta : bool;
    r_zeta : bool;
    r_evar : bool;
    r_iota : bool }

  type red_kind = BETA | DELTA | IOTA | ZETA

  let fBETA = BETA
  let fDELTA = DELTA
  let fIOTA = IOTA
  let fZETA = ZETA
  let no_red = {
    r_beta = false;
    r_delta = false;
    r_zeta = false;
    r_evar = false;
    r_iota = false }

  let red_add red = function
    | BETA -> { red with r_beta = true }
    | DELTA -> { red with r_delta = true}
    | IOTA -> { red with r_iota = true }
    | ZETA -> { red with r_zeta = true }

  let mkflags = List.fold_left red_add no_red

  let red_set red = function
    | BETA -> incr_cnt red.r_beta beta
    | ZETA -> incr_cnt red.r_zeta zeta
    | IOTA -> incr_cnt red.r_iota iota
    | DELTA -> (* Used for Rel/Var defined in context *)
	incr_cnt red.r_delta delta

end : RedFlagsSig)

open RedFlags

let betadeltaiota = mkflags [fBETA;fDELTA;fZETA;fIOTA]
let betadeltaiotanolet = mkflags [fBETA;fDELTA;fIOTA]
let betaiotazeta = mkflags [fBETA;fIOTA;fZETA]

(* specification of the reduction function *)


(* Flags of reduction and cache of constants: 'a is a type that may be
 * mapped to constr. 'a infos implements a cache for constants and
 * abstractions, storing a representation (of type 'a) of the body of
 * this constant or abstraction.
 *  * i_tab is the cache table of the results
 *  * i_repr is the function to get the representation from the current
 *         state of the cache and the body of the constant. The result
 *         is stored in the table.
 *  * i_rels = (4,[(1,c);(3,d)]) means there are 4 free rel variables
 *    and only those with index 1 and 3 have bodies which are c and d resp.
 *
 * ref_value_cache searchs in the tab, otherwise uses i_repr to
 * compute the result and store it in the table. If the constant can't
 * be unfolded, returns None, but does not store this failure.  * This
 * doesn't take the RESET into account. You mustn't keep such a table
 * after a Reset.  * This type is not exported. Only its two
 * instantiations (cbv or lazy) are.
 *)

type table_key = Constant.t puniverses tableKey


let eq_pconstant_key (c,u) (c',u') =
  eq_constant_key c c' && Univ.Instance.equal u u'

module KeyHash =
struct
  type t = table_key
  let equal = Names.eq_table_key eq_pconstant_key

  open Hashset.Combine

  let hash = function
  | ConstKey (c,u) -> combinesmall 1 (Constant.UserOrd.hash c)
  | VarKey id -> combinesmall 2 (Id.hash id)
  | RelKey i -> combinesmall 3 (Int.hash i)
end

module KeyTable = Hashtbl.Make(KeyHash)

type 'a infos = {
  i_flags : reds;
  i_repr : 'a infos -> constr -> 'a;
  i_env : env;
  i_rels : int * (int * constr) list;
  i_tab : 'a KeyTable.t }

let ref_value_cache info ref =
  try
    Some (KeyTable.find info.i_tab ref)
  with Not_found ->
  try
    let body =
      match ref with
	| RelKey n ->
	    let (s,l) = info.i_rels in lift n (Int.List.assoc (s-n) l)
	| VarKey id -> raise Not_found
	| ConstKey cst -> constant_value info.i_env cst
    in
    let v = info.i_repr info body in
    KeyTable.add info.i_tab ref v;
    Some v
  with
    | Not_found (* List.assoc *)
    | NotEvaluableConst _ (* Const *)
      -> None

let defined_rels flags env =
(*  if red_local_const (snd flags) then*)
  fold_rel_context
      (fun decl (i,subs) ->
	 match decl with
	   | LocalAssum _ -> (i+1, subs)
	   | LocalDef (_,body,_) -> (i+1, (i,body) :: subs))
      (rel_context env) ~init:(0,[])
(*  else (0,[])*)

let mind_equiv_infos info = mind_equiv info.i_env

let create mk_cl flgs env =
  { i_flags = flgs;
    i_repr = mk_cl;
    i_env = env;
    i_rels = defined_rels flgs env;
    i_tab = KeyTable.create 17 }


(**********************************************************************)
(* Lazy reduction: the one used in kernel operations                  *)

(* type of shared terms. fconstr and frterm are mutually recursive.
 * Clone of the constr structure, but completely mutable, and
 * annotated with reduction state (reducible or not).
 *  - FLIFT is a delayed shift; allows sharing between 2 lifted copies
 *    of a given term.
 *  - FCLOS is a delayed substitution applied to a constr
 *  - FLOCKED is used to erase the content of a reference that must
 *    be updated. This is to allow the garbage collector to work
 *    before the term is computed.
 *)

(* Norm means the term is fully normalized and cannot create a redex
     when substituted
   Cstr means the term is in head normal form and that it can
     create a redex when substituted (i.e. constructor, fix, lambda)
   Whnf means we reached the head normal form and that it cannot
     create a redex when substituted
   Red is used for terms that might be reduced
*)
type red_state = Norm | Cstr | Whnf | Red

let neutr = function
  | (Whnf|Norm) -> Whnf
  | (Red|Cstr) -> Red

type fconstr = {
  mutable norm: red_state;
  mutable term: fterm }

and fterm =
  | FRel of int
  | FAtom of constr (* Metas and Sorts *)
  | FCast of fconstr * cast_kind * fconstr
  | FFlex of table_key
  | FInd of pinductive
  | FConstruct of pconstructor
  | FApp of fconstr * fconstr array
  | FProj of Projection.t * fconstr
  | FFix of fixpoint * fconstr subs
  | FCoFix of cofixpoint * fconstr subs
  | FCaseT of case_info * constr * fconstr * constr array * fconstr subs (* predicate and branches are closures *)
  | FLambda of int * (Name.t * constr) list * constr * fconstr subs
  | FProd of Name.t * fconstr * fconstr
  | FLetIn of Name.t * fconstr * fconstr * constr * fconstr subs
  | FEvar of existential_key * fconstr array (* why diff from kernel/closure? *)
  | FLIFT of int * fconstr
  | FCLOS of constr * fconstr subs
  | FLOCKED

let fterm_of v = v.term
let set_norm v = v.norm <- Norm

(* Could issue a warning if no is still Red, pointing out that we loose
   sharing. *)
let update v1 (no,t) =
  if !share then
    (v1.norm <- no;
     v1.term <- t;
     v1)
  else {norm=no;term=t}

(**********************************************************************)
(* The type of (machine) stacks (= lambda-bar-calculus' contexts)     *)

type stack_member =
  | Zapp of fconstr array
  | ZcaseT of case_info * constr * constr array * fconstr subs
  | Zproj of int * int * Projection.t
  | Zfix of fconstr * stack
  | Zshift of int
  | Zupdate of fconstr

and stack = stack_member list

let append_stack v s =
  if Array.length v = 0 then s else
  match s with
  | Zapp l :: s -> Zapp (Array.append v l) :: s
  | _ -> Zapp v :: s

(* Collapse the shifts in the stack *)
let zshift n s =
  match (n,s) with
      (0,_) -> s
    | (_,Zshift(k)::s) -> Zshift(n+k)::s
    | _ -> Zshift(n)::s

let rec stack_args_size = function
  | Zapp v :: s -> Array.length v + stack_args_size s
  | Zshift(_)::s -> stack_args_size s
  | Zupdate(_)::s -> stack_args_size s
  | _ -> 0

(* Lifting. Preserves sharing (useful only for cell with norm=Red).
   lft_fconstr always create a new cell, while lift_fconstr avoids it
   when the lift is 0. *)
let rec lft_fconstr n ft =
  match ft.term with
    | (FInd _|FConstruct _|FFlex(ConstKey _|VarKey _)) -> ft
    | FRel i -> {norm=Norm;term=FRel(i+n)}
    | FLambda(k,tys,f,e) -> {norm=Cstr; term=FLambda(k,tys,f,subs_shft(n,e))}
    | FFix(fx,e) -> {norm=Cstr; term=FFix(fx,subs_shft(n,e))}
    | FCoFix(cfx,e) -> {norm=Cstr; term=FCoFix(cfx,subs_shft(n,e))}
    | FLIFT(k,m) -> lft_fconstr (n+k) m
    | FLOCKED -> assert false
    | _ -> {norm=ft.norm; term=FLIFT(n,ft)}
let lift_fconstr k f =
  if k=0 then f else lft_fconstr k f
let lift_fconstr_vect k v =
  if k=0 then v else Array.map (fun f -> lft_fconstr k f) v

let clos_rel e i =
  match expand_rel i e with
    | Inl(n,mt) -> lift_fconstr n mt
    | Inr(k,None) -> {norm=Norm; term= FRel k}
    | Inr(k,Some p) ->
        lift_fconstr (k-p) {norm=Red;term=FFlex(RelKey p)}

(* since the head may be reducible, we might introduce lifts of 0 *)
let compact_stack head stk =
  let rec strip_rec depth = function
    | Zshift(k)::s -> strip_rec (depth+k) s
    | Zupdate(m)::s ->
        (* Be sure to create a new cell otherwise sharing would be
           lost by the update operation *)
        let h' = lft_fconstr depth head in
        let _ = update m (h'.norm,h'.term) in
        strip_rec depth s
    | stk -> zshift depth stk in
  strip_rec 0 stk

(* Put an update mark in the stack, only if needed *)
let zupdate m s =
  if !share && m.norm = Red
  then
    let s' = compact_stack m s in
    let _ = m.term <- FLOCKED in
    Zupdate(m)::s'
  else s

let mk_lambda env t =
  let (rvars,t') = decompose_lam t in
  FLambda(List.length rvars, List.rev rvars, t', env)

let destFLambda clos_fun t =
  match t.term with
      FLambda(_,[(na,ty)],b,e) -> (na,clos_fun e ty,clos_fun (subs_lift e) b)
    | FLambda(n,(na,ty)::tys,b,e) ->
        (na,clos_fun e ty,{norm=Cstr;term=FLambda(n-1,tys,b,subs_lift e)})
    | _ -> assert false

(* Optimization: do not enclose variables in a closure.
   Makes variable access much faster *)
let mk_clos e t =
  match t with
    | Rel i -> clos_rel e i
    | Var x -> { norm = Red; term = FFlex (VarKey x) }
    | Const c -> { norm = Red; term = FFlex (ConstKey c) }
    | Meta _ | Sort _ ->  { norm = Norm; term = FAtom t }
    | Ind kn -> { norm = Norm; term = FInd kn }
    | Construct kn -> { norm = Cstr; term = FConstruct kn }
    | (CoFix _|Lambda _|Fix _|Prod _|Evar _|App _|Case _|Cast _|LetIn _|Proj _) ->
        {norm = Red; term = FCLOS(t,e)}

let mk_clos_vect env v = Array.map (mk_clos env) v

(* Translate the head constructor of t from constr to fconstr. This
   function is parameterized by the function to apply on the direct
   subterms.
   Could be used insted of mk_clos. *)
let mk_clos_deep clos_fun env t =
  match t with
    | (Rel _|Ind _|Const _|Construct _|Var _|Meta _ | Sort _) ->
        mk_clos env t
    | Cast (a,k,b) ->
        { norm = Red;
          term = FCast (clos_fun env a, k, clos_fun env b)}
    | App (f,v) ->
        { norm = Red;
	  term = FApp (clos_fun env f, Array.map (clos_fun env) v) }
    | Proj (p,c) ->
	{ norm = Red;
	  term = FProj (p, clos_fun env c) }
    | Case (ci,p,c,v) ->
        { norm = Red; term = FCaseT (ci, p, clos_fun env c, v, env) }
    | Fix fx ->
        { norm = Cstr; term = FFix (fx, env) }
    | CoFix cfx ->
        { norm = Cstr; term = FCoFix(cfx,env) }
    | Lambda _ ->
        { norm = Cstr; term = mk_lambda env t }
    | Prod (n,t,c)   ->
        { norm = Whnf;
	  term = FProd (n, clos_fun env t, clos_fun (subs_lift env) c) }
    | LetIn (n,b,t,c) ->
        { norm = Red;
	  term = FLetIn (n, clos_fun env b, clos_fun env t, c, env) }
    | Evar(ev,args) ->
	{ norm = Whnf; term = FEvar(ev,Array.map (clos_fun env) args) }

(* A better mk_clos? *)
let mk_clos2 = mk_clos_deep mk_clos

(* The inverse of mk_clos_deep: move back to constr *)
let rec to_constr constr_fun lfts v =
  match v.term with
    | FRel i -> Rel (reloc_rel i lfts)
    | FFlex (RelKey p) -> Rel (reloc_rel p lfts)
    | FFlex (VarKey x) -> Var x
    | FAtom c -> exliftn lfts c
    | FCast (a,k,b) ->
        Cast (constr_fun lfts a, k, constr_fun lfts b)
    | FFlex (ConstKey op) -> Const op
    | FInd op -> Ind op
    | FConstruct op -> Construct op
    | FCaseT (ci,p,c,ve,e) ->
       let fp = mk_clos2 e p in
       let fve = mk_clos_vect e ve in
       Case (ci, constr_fun lfts fp, constr_fun lfts c, Array.map (constr_fun lfts) fve)
    | FFix ((op,(lna,tys,bds)),e) ->
        let n = Array.length bds in
        let ftys = Array.map (mk_clos e) tys in
        let fbds = Array.map (mk_clos (subs_liftn n e)) bds in
	let lfts' = el_liftn n lfts in
	Fix (op, (lna, Array.map (constr_fun lfts) ftys,
	               Array.map (constr_fun lfts') fbds))
    | FCoFix ((op,(lna,tys,bds)),e) ->
        let n = Array.length bds in
        let ftys = Array.map (mk_clos e) tys in
        let fbds = Array.map (mk_clos (subs_liftn n e)) bds in
	let lfts' = el_liftn (Array.length bds) lfts in
	CoFix (op, (lna, Array.map (constr_fun lfts) ftys,
	                 Array.map (constr_fun lfts') fbds))
    | FApp (f,ve) ->
	App (constr_fun lfts f,
	       Array.map (constr_fun lfts) ve)
    | FProj (p,c) ->
        Proj (p,constr_fun lfts c)
    | FLambda _ ->
        let (na,ty,bd) = destFLambda mk_clos2 v in
	Lambda (na, constr_fun lfts ty,
	            constr_fun (el_lift lfts) bd)
    | FProd (n,t,c)   ->
	Prod (n, constr_fun lfts t,
	         constr_fun (el_lift lfts) c)
    | FLetIn (n,b,t,f,e) ->
        let fc = mk_clos2 (subs_lift e) f in
	LetIn (n, constr_fun lfts b,
	          constr_fun lfts t,
	          constr_fun (el_lift lfts) fc)
    | FEvar (ev,args) -> Evar(ev,Array.map (constr_fun lfts) args)
    | FLIFT (k,a) -> to_constr constr_fun (el_shft k lfts) a
    | FCLOS (t,env) ->
        let fr = mk_clos2 env t in
        let unfv = update v (fr.norm,fr.term) in
        to_constr constr_fun lfts unfv
    | FLOCKED -> assert false (*mkVar(Id.of_string"_LOCK_")*)

(* This function defines the correspondance between constr and
   fconstr. When we find a closure whose substitution is the identity,
   then we directly return the constr to avoid possibly huge
   reallocation. *)
let term_of_fconstr =
  let rec term_of_fconstr_lift lfts v =
    match v.term with
      | FCLOS(t,env) when is_subs_id env && is_lift_id lfts -> t
      | FLambda(_,tys,f,e) when is_subs_id e && is_lift_id lfts ->
          compose_lam (List.rev tys) f
      | FCaseT(ci,p,c,b,env) when is_subs_id env && is_lift_id lfts ->
          Case(ci,p,term_of_fconstr_lift lfts c,b)
      | FFix(fx,e) when is_subs_id e && is_lift_id lfts -> Fix fx
      | FCoFix(cfx,e) when is_subs_id e && is_lift_id lfts -> CoFix cfx
      | _ -> to_constr term_of_fconstr_lift lfts v in
  term_of_fconstr_lift el_id



(* fstrong applies unfreeze_fun recursively on the (freeze) term and
 * yields a term.  Assumes that the unfreeze_fun never returns a
 * FCLOS term.
let rec fstrong unfreeze_fun lfts v =
  to_constr (fstrong unfreeze_fun) lfts (unfreeze_fun v)
*)

let rec zip m stk =
  match stk with
    | [] -> m
    | Zapp args :: s -> zip {norm=neutr m.norm; term=FApp(m, args)} s
    | ZcaseT(ci,p,br,e)::s ->
        let t = FCaseT(ci, p, m, br, e) in
        zip {norm=neutr m.norm; term=t} s
    | Zproj (i,j,cst) :: s -> 
        zip {norm=neutr m.norm; term=FProj (cst,m)} s
    | Zfix(fx,par)::s ->
        zip fx (par @ append_stack [|m|] s)
    | Zshift(n)::s ->
        zip (lift_fconstr n m) s
    | Zupdate(rf)::s ->
        zip (update rf (m.norm,m.term)) s

let fapp_stack (m,stk) = zip m stk

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

(* The assertions in the functions below are granted because they are
   called only when m is a constructor, a cofix
   (strip_update_shift_app), a fix (get_nth_arg) or an abstraction
   (strip_update_shift, through get_arg). *)

(* optimised for the case where there are no shifts... *)
let strip_update_shift_app head stk =
  assert (head.norm <> Red);
  let rec strip_rec rstk h depth = function
    | Zshift(k) as e :: s ->
        strip_rec (e::rstk) (lift_fconstr k h) (depth+k) s
    | (Zapp args :: s) ->
        strip_rec (Zapp args :: rstk)
          {norm=h.norm;term=FApp(h,args)} depth s
    | Zupdate(m)::s ->
        strip_rec rstk (update m (h.norm,h.term)) depth s
    | stk -> (depth,List.rev rstk, stk) in
  strip_rec [] head 0 stk


let get_nth_arg head n stk =
  assert (head.norm <> Red);
  let rec strip_rec rstk h n = function
    | Zshift(k) as e :: s ->
        strip_rec (e::rstk) (lift_fconstr k h) n s
    | Zapp args::s' ->
        let q = Array.length args in
        if n >= q
        then
          strip_rec (Zapp args::rstk)
            {norm=h.norm;term=FApp(h,args)} (n-q) s'
        else
          let bef = Array.sub args 0 n in
          let aft = Array.sub args (n+1) (q-n-1) in
          let stk' =
            List.rev (if n = 0 then rstk else (Zapp bef :: rstk)) in
          (Some (stk', args.(n)), append_stack aft s')
    | Zupdate(m)::s ->
        strip_rec rstk (update m (h.norm,h.term)) n s
    | s -> (None, List.rev rstk @ s) in
  strip_rec [] head n stk

(* Beta reduction: look for an applied argument in the stack.
   Since the encountered update marks are removed, h must be a whnf *)
let rec get_args n tys f e stk =
  match stk with
      Zupdate r :: s ->
        let _hd = update r (Cstr,FLambda(n,tys,f,e)) in
        get_args n tys f e s
    | Zshift k :: s ->
        get_args n tys f (subs_shft (k,e)) s
    | Zapp l :: s ->
        let na = Array.length l in
        if n == na then (Inl (subs_cons(l,e)),s)
        else if n < na then (* more arguments *)
          let args = Array.sub l 0 n in
          let eargs = Array.sub l n (na-n) in
          (Inl (subs_cons(args,e)), Zapp eargs :: s)
        else (* more lambdas *)
          let etys = List.skipn na tys in
          get_args (n-na) etys f (subs_cons(l,e)) s
    | _ -> (Inr {norm=Cstr;term=FLambda(n,tys,f,e)}, stk)

(* Eta expansion: add a reference to implicit surrounding lambda at end of stack *)
let rec eta_expand_stack = function
  | (Zapp _ | Zfix _ | ZcaseT _ | Zproj _
	| Zshift _ | Zupdate _ as e) :: s ->
      e :: eta_expand_stack s
  | [] ->
      [Zshift 1; Zapp [|{norm=Norm; term= FRel 1}|]]

(* Iota reduction: extract the arguments to be passed to the Case
   branches *)
let rec reloc_rargs_rec depth stk =
  match stk with
      Zapp args :: s ->
        Zapp (lift_fconstr_vect depth args) :: reloc_rargs_rec depth s
    | Zshift(k)::s -> if k=depth then s else reloc_rargs_rec (depth-k) s
    | _ -> stk

let reloc_rargs depth stk =
  if depth = 0 then stk else reloc_rargs_rec depth stk

let rec try_drop_parameters depth n argstk =
  match argstk with
      Zapp args::s ->
        let q = Array.length args in
        if n > q then try_drop_parameters depth (n-q) s
        else if Int.equal n q then reloc_rargs depth s
        else
          let aft = Array.sub args n (q-n) in
          reloc_rargs depth (append_stack aft s)
    | Zshift(k)::s -> try_drop_parameters (depth-k) n s
    | [] -> 
	if Int.equal n 0 then []
	else raise Not_found
    | _ -> assert false
	(* strip_update_shift_app only produces Zapp and Zshift items *)

let drop_parameters depth n argstk =
  try try_drop_parameters depth n argstk
  with Not_found -> assert false
    (* we know that n < stack_args_size(argstk) (if well-typed term) *) 

(** Projections and eta expansion *)

let eta_expand_ind_stack env ind m s (f, s') =
  let mib = lookup_mind (fst ind) env in
    match mib.mind_record with
    | Some (Some (_,projs,pbs)) when mib.mind_finite <> CoFinite -> 
	(* (Construct, pars1 .. parsm :: arg1...argn :: []) ~= (f, s') ->
	   arg1..argn ~= (proj1 t...projn t) where t = zip (f,s') *)
      let pars = mib.mind_nparams in
      let right = fapp_stack (f, s') in
      let (depth, args, s) = strip_update_shift_app m s in
      (** Try to drop the params, might fail on partially applied constructors. *)
      let argss = try_drop_parameters depth pars args in
	let hstack =
	  Array.map (fun p -> { norm = Red; (* right can't be a constructor though *)
			     term = FProj (Projection.make p false, right) }) projs in
	argss, [Zapp hstack]	
    | _ -> raise Not_found (* disallow eta-exp for non-primitive records *)

let rec project_nth_arg n argstk =
  match argstk with
  | Zapp args :: s -> 
      let q = Array.length args in
	if n >= q then project_nth_arg (n - q) s
	else (* n < q *) args.(n)
  | _ -> assert false
      (* After drop_parameters we have a purely applicative stack *)


(* Iota reduction: expansion of a fixpoint.
 * Given a fixpoint and a substitution, returns the corresponding
 * fixpoint body, and the substitution in which it should be
 * evaluated: its first variables are the fixpoint bodies
 *
 * FCLOS(fix Fi {F0 := T0 .. Fn-1 := Tn-1}, S)
 *    -> (S. FCLOS(F0,S) . ... . FCLOS(Fn-1,S), Ti)
 *)
(* does not deal with FLIFT *)
let contract_fix_vect fix =
  let (thisbody, make_body, env, nfix) =
    match fix with
      | FFix (((reci,i),(_,_,bds as rdcl)),env) ->
          (bds.(i),
	   (fun j -> { norm = Cstr; term = FFix (((reci,j),rdcl),env) }),
	   env, Array.length bds)
      | FCoFix ((i,(_,_,bds as rdcl)),env) ->
          (bds.(i),
	   (fun j -> { norm = Cstr; term = FCoFix ((j,rdcl),env) }),
	   env, Array.length bds)
      | _ -> assert false
  in
  (subs_cons(Array.init nfix make_body, env), thisbody)

let unfold_projection env p =
  let pb = lookup_projection p env in
  Zproj (pb.proj_npars, pb.proj_arg, p)

(*********************************************************************)
(* A machine that inspects the head of a term until it finds an
   atom or a subterm that may produce a redex (abstraction,
   constructor, cofix, letin, constant), or a neutral term (product,
   inductive) *)
let rec knh info m stk =
  match m.term with
    | FLIFT(k,a) -> knh info a (zshift k stk)
    | FCLOS(t,e) -> knht info e t (zupdate m stk)
    | FLOCKED -> assert false
    | FApp(a,b) -> knh info a (append_stack b (zupdate m stk))
    | FCaseT(ci,p,t,br,env) -> knh info t (ZcaseT(ci,p,br,env)::zupdate m stk)
    | FFix(((ri,n),(_,_,_)),_) ->
        (match get_nth_arg m ri.(n) stk with
             (Some(pars,arg),stk') -> knh info arg (Zfix(m,pars)::stk')
           | (None, stk') -> (m,stk'))
    | FCast(t,_,_) -> knh info t stk

    | FProj (p,c) ->
      if red_set info.i_flags fDELTA then
        let s = unfold_projection info.i_env p in
        knh info c (s :: zupdate m stk)
      else (m,stk)

(* cases where knh stops *)
    | (FFlex _|FLetIn _|FConstruct _|FEvar _|
       FCoFix _|FLambda _|FRel _|FAtom _|FInd _|FProd _) ->
        (m, stk)

(* The same for pure terms *)
and knht info e t stk =
  match t with
    | App(a,b) ->
        knht info e a (append_stack (mk_clos_vect e b) stk)
    | Case(ci,p,t,br) -> knht info e t (ZcaseT(ci, p, br, e)::stk)
    | Fix _ -> knh info (mk_clos2 e t) stk (* laziness *)
    | Cast(a,_,_) -> knht info  e a stk
    | Rel n -> knh info (clos_rel e n) stk
    | Proj (p,c) -> knh info (mk_clos2 e t) stk (* laziness *)
    | (Lambda _|Prod _|Construct _|CoFix _|Ind _|
       LetIn _|Const _|Var _|Evar _|Meta _|Sort _) ->
        (mk_clos2 e t, stk)


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

(* Computes a weak head normal form from the result of knh. *)
let rec knr info m stk =
  match m.term with
  | FLambda(n,tys,f,e) when red_set info.i_flags fBETA ->
      (match get_args n tys f e stk with
          Inl e', s -> knit info e' f s
        | Inr lam, s -> (lam,s))
  | FFlex(ConstKey kn) when red_set info.i_flags fDELTA ->
      (match ref_value_cache info (ConstKey kn) with
          Some v -> kni info v stk
        | None -> (set_norm m; (m,stk)))
  | FFlex(VarKey id) when red_set info.i_flags fDELTA ->
      (match ref_value_cache info (VarKey id) with
          Some v -> kni info v stk
        | None -> (set_norm m; (m,stk)))
  | FFlex(RelKey k) when red_set info.i_flags fDELTA ->
      (match ref_value_cache info (RelKey k) with
          Some v -> kni info v stk
        | None -> (set_norm m; (m,stk)))
  | FConstruct((ind,c),u) when red_set info.i_flags fIOTA ->
      (match strip_update_shift_app m stk with
       | (depth, args, ZcaseT(ci,_,br,env)::s) ->
            assert (ci.ci_npar>=0);
            let rargs = drop_parameters depth ci.ci_npar args in
            knit info env br.(c-1) (rargs@s)
       | (_, cargs, Zfix(fx,par)::s) ->
            let rarg = fapp_stack(m,cargs) in
            let stk' = par @ append_stack [|rarg|] s in
            let (fxe,fxbd) = contract_fix_vect fx.term in
            knit info fxe fxbd stk'
       | (depth, args, Zproj (n, m, cst)::s) ->
	    let rargs = drop_parameters depth n args in
	    let rarg = project_nth_arg m rargs in
	    kni info rarg s
       | (_,args,s) -> (m,args@s))
  | FCoFix _ when red_set info.i_flags fIOTA ->
      (match strip_update_shift_app m stk with
          (_, args, (((ZcaseT _|Zproj _)::_) as stk')) ->
            let (fxe,fxbd) = contract_fix_vect m.term in
            knit info fxe fxbd (args@stk')
        | (_,args,s) -> (m,args@s))
  | FLetIn (_,v,_,bd,e) when red_set info.i_flags fZETA ->
      knit info (subs_cons([|v|],e)) bd stk
  | _ -> (m,stk)

(* Computes the weak head normal form of a term *)
and kni info m stk =
  let (hm,s) = knh info m stk in
  knr info hm s
and knit info e t stk =
  let (ht,s) = knht info e t stk in
  knr info ht s

let kh info v stk = fapp_stack(kni info v stk)

(************************************************************************)
(* Initialization and then normalization *)

(* weak reduction *)
let whd_val info v =
  with_stats (lazy (term_of_fconstr (kh info v [])))

let inject = mk_clos (subs_id 0)

let whd_stack infos m stk =
  let k = kni infos m stk in
  let _ = fapp_stack k in (* to unlock Zupdates! *)
  k

(* cache of constants: the body is computed only when needed. *)
type clos_infos = fconstr infos

let infos_env x = x.i_env
let infos_flags x = x.i_flags
let oracle_of_infos x = x.i_env.env_conv_oracle

let create_clos_infos flgs env =
  create (fun _ -> inject) flgs env

let unfold_reference = ref_value_cache