summaryrefslogtreecommitdiff
path: root/kernel/closure.ml
blob: 8e16a92241146bf47ca188a093b589857cd623c1 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
(************************************************************************)
(*  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: closure.ml 7639 2005-12-02 10:01:15Z gregoire $ *)

open Util
open Pp
open Term
open Names
open Declarations
open Environ
open Esubst

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() =
  msgnl (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

let all_opaque = (Idpred.empty, Cpred.empty)
let all_transparent = (Idpred.full, Cpred.full)

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 fCONST : constant -> red_kind
  val fVAR : identifier -> red_kind
  val no_red : reds
  val red_add : reds -> red_kind -> reds
  val red_sub : reds -> red_kind -> reds
  val red_add_transparent : reds -> transparent_state -> reds
  val mkflags : red_kind list -> reds
  val red_set : reds -> red_kind -> bool
  val red_get_const : reds -> bool * evaluable_global_reference list
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_const : transparent_state;
    r_zeta : bool;
    r_evar : bool;
    r_iota : bool }

  type red_kind = BETA | DELTA | IOTA | ZETA
	      | CONST of constant | VAR of identifier
  let fBETA = BETA
  let fDELTA = DELTA
  let fIOTA = IOTA
  let fZETA = ZETA
  let fCONST kn  = CONST kn
  let fVAR id  = VAR id
  let no_red = {
    r_beta = false;
    r_delta = false;
    r_const = all_opaque;
    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; r_const = all_transparent }
    | CONST kn ->
	let (l1,l2) = red.r_const in
	{ red with r_const = l1, Cpred.add kn l2 }
    | IOTA -> { red with r_iota = true }
    | ZETA -> { red with r_zeta = true }
    | VAR id ->
	let (l1,l2) = red.r_const in
	{ red with r_const = Idpred.add id l1, l2 }

  let red_sub red = function
    | BETA -> { red with r_beta = false }
    | DELTA -> { red with r_delta = false }
    | CONST kn ->
 	let (l1,l2) = red.r_const in
	{ red with r_const = l1, Cpred.remove kn l2 }
    | IOTA -> { red with r_iota = false }
    | ZETA -> { red with r_zeta = false }
    | VAR id ->
	let (l1,l2) = red.r_const in
	{ red with r_const = Idpred.remove id l1, l2 }

  let red_add_transparent red tr =
    { red with r_const = tr } 

  let mkflags = List.fold_left red_add no_red

  let red_set red = function
    | BETA -> incr_cnt red.r_beta beta
    | CONST kn -> 
	let (_,l) = red.r_const in
	let c = Cpred.mem kn l in
	incr_cnt c delta
    | VAR id -> (* En attendant d'avoir des kn pour les Var *)
	let (l,_) = red.r_const in
	let c = Idpred.mem id l in
	incr_cnt c delta
    | 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

  let red_get_const red =
    let p1,p2 = red.r_const in
    let (b1,l1) = Idpred.elements p1 in
    let (b2,l2) = Cpred.elements p2 in
    if b1=b2 then
      let l1' = List.map (fun x -> EvalVarRef x) l1 in
      let l2' = List.map (fun x -> EvalConstRef x) l2 in
      (b1, l1' @ l2')
    else error "unrepresentable pair of predicate"

end : RedFlagsSig)

open RedFlags

let betadeltaiota = mkflags [fBETA;fDELTA;fZETA;fIOTA]
let betadeltaiotanolet = mkflags [fBETA;fDELTA;fIOTA]
let betaiota = mkflags [fBETA;fIOTA]
let beta = mkflags [fBETA]
let betaiotazeta = mkflags [fBETA;fIOTA;fZETA]
let unfold_red kn = 
  let flag = match kn with
    | EvalVarRef id -> fVAR id
    | EvalConstRef kn -> fCONST kn
  in (* Remove fZETA for finer behaviour ? *)
  mkflags [fBETA;flag;fIOTA;fZETA]

(************************* Obsolète
(* [r_const=(true,cl)] means all constants but those in [cl] *)
(* [r_const=(false,cl)] means only those in [cl] *)
type reds = {
  r_beta : bool;
  r_const : bool * constant_path list * identifier list;
  r_zeta : bool;
  r_evar : bool;
  r_iota : bool }

let betadeltaiota_red = {
  r_beta = true;
  r_const = true,[],[];
  r_zeta = true;
  r_evar = true;
  r_iota = true } 

let betaiota_red = {
  r_beta = true;
  r_const = false,[],[];
  r_zeta = false;
  r_evar = false;
  r_iota = true }
		     
let beta_red = {
  r_beta = true;
  r_const = false,[],[];
  r_zeta = false;
  r_evar = false;
  r_iota = false }

let no_red = {
  r_beta = false;
  r_const = false,[],[];
  r_zeta = false;
  r_evar = false;
  r_iota = false }

let betaiotazeta_red = {
  r_beta = true;
  r_const = false,[],[];
  r_zeta = true;
  r_evar = false;
  r_iota = true }

let unfold_red kn =
  let c = match kn with
    | EvalVarRef id -> false,[],[id]
    | EvalConstRef kn -> false,[kn],[]
  in {
  r_beta = true;
  r_const = c;
  r_zeta = true;   (* false for finer behaviour ? *)
  r_evar = false;
  r_iota = true }

(* Sets of reduction kinds.
   Main rule: delta implies all consts (both global (= by
   kernel_name) and local (= by Rel or Var)), all evars, and zeta (= letin's).
   Rem: reduction of a Rel/Var bound to a term is Delta, but reduction of 
   a LetIn expression is Letin reduction *)

type red_kind =
    BETA | DELTA | ZETA | IOTA
  | CONST of constant_path list | CONSTBUT of constant_path list
  | VAR of identifier | VARBUT of identifier

let rec red_add red = function
  | BETA -> { red with r_beta = true }
  | DELTA ->
      (match red.r_const with
	| _,_::_,[] | _,[],_::_ -> error "Conflict in the reduction flags"
	| _ -> { red with r_const = true,[],[]; r_zeta = true; r_evar = true })
  | CONST cl ->
      (match red.r_const with
	| true,_,_ -> error "Conflict in the reduction flags"
	| _,l1,l2 -> { red with r_const = false, list_union cl l1, l2 })
  | CONSTBUT cl ->
      (match red.r_const with
	| false,_::_,_ | false,_,_::_ ->
			   error "Conflict in the reduction flags"
	| _,l1,l2 ->
	    { red with r_const = true, list_union cl l1, l2;
		r_zeta = true; r_evar = true })
  | IOTA -> { red with r_iota = true }
  | ZETA -> { red with r_zeta = true }
  | VAR id ->
      (match red.r_const with
	| true,_,_ -> error "Conflict in the reduction flags"
	| _,l1,l2 -> { red with r_const = false, l1, list_union [id] l2 })
  | VARBUT cl ->
      (match red.r_const with
	| false,_::_,_ | false,_,_::_ ->
			   error "Conflict in the reduction flags"
	| _,l1,l2 ->
	    { red with r_const = true, l1, list_union [cl] l2;
		r_zeta = true; r_evar = true })

let red_delta_set red =
  let b,_,_ = red.r_const in b

let red_local_const = red_delta_set

(* to know if a redex is allowed, only a subset of red_kind is used ... *)
let red_set red = function
  | BETA -> incr_cnt red.r_beta beta
  | CONST [kn] -> 
      let (b,l,_) = red.r_const in
      let c = List.mem kn l in
      incr_cnt ((b & not c) or (c & not b)) delta
  | VAR id -> (* En attendant d'avoir des kn pour les Var *)
     let (b,_,l) = red.r_const in
      let c = List.mem id l in
      incr_cnt ((b & not c) or (c & not b)) delta
  | ZETA -> incr_cnt red.r_zeta zeta
  | EVAR -> incr_cnt red.r_zeta evar
  | IOTA -> incr_cnt red.r_iota iota
  | DELTA -> red_delta_set red (*Used for Rel/Var defined in context*)
  (* Not for internal use *)
  | CONST _ | CONSTBUT _ | VAR _ | VARBUT _ -> failwith "not implemented"

(* Gives the constant list *)
let red_get_const red =
  let b,l1,l2 = red.r_const in
  let l1' = List.map (fun x -> EvalConstRef x) l1 in
  let l2' = List.map (fun x -> EvalVarRef x) l2 in
  b, l1' @ l2'
fin obsolète **************)
(* 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.
 *  * i_vars is the list of _defined_ named variables.
 *
 * 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 = id_key

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

let info_flags info = info.i_flags

let ref_value_cache info ref =
  try  
    Some (Hashtbl.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 (List.assoc (s-n) l)
	| VarKey id -> List.assoc id info.i_vars
	| ConstKey cst -> constant_value info.i_env cst
    in
    let v = info.i_repr info body in
    Hashtbl.add info.i_tab ref v;
    Some v
  with
    | Not_found (* List.assoc *)
    | NotEvaluableConst _ (* Const *)
      -> None

let defined_vars flags env =
(*  if red_local_const (snd flags) then*)
    Sign.fold_named_context 
      (fun (id,b,_) e ->
	 match b with
	   | None -> e
	   | Some body -> (id, body)::e)
       (named_context env) ~init:[]
(*  else []*)

let defined_rels flags env =
(*  if red_local_const (snd flags) then*)
  Sign.fold_rel_context 
      (fun (id,b,t) (i,subs) ->
	 match b with
	   | None -> (i+1, subs)
	   | Some body -> (i+1, (i,body) :: subs))
      (rel_context env) ~init:(0,[])
(*  else (0,[])*)


let rec mind_equiv info kn1 kn2 = 
  kn1 = kn2 ||
	match (lookup_mind kn1 info.i_env).mind_equiv with
	    Some kn1' -> mind_equiv info kn2 kn1'
	  | None -> match (lookup_mind kn2 info.i_env).mind_equiv with
		Some kn2' -> mind_equiv info kn2' kn1
	      | None -> false

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


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

type 'a stack_member =
  | Zapp of 'a list
  | Zcase of case_info * 'a * 'a array
  | Zfix of 'a * 'a stack
  | Zshift of int
  | Zupdate of 'a

and 'a stack = 'a stack_member list

let empty_stack = []
let append_stack_list = function
  | ([],s) -> s
  | (l1, Zapp l :: s) -> Zapp (l1@l) :: s
  | (l1, s) -> Zapp l1 :: s
let append_stack v s = append_stack_list (Array.to_list 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 l::s -> List.length l + stack_args_size s
  | Zshift(_)::s -> stack_args_size s
  | Zupdate(_)::s -> stack_args_size s
  | _ -> 0

(* When used as an argument stack (only Zapp can appear) *)
let rec decomp_stack = function
  | Zapp[v]::s -> Some (v, s)
  | Zapp(v::l)::s -> Some (v, (Zapp l :: s))
  | Zapp [] :: s -> decomp_stack s
  | _ -> None
let rec decomp_stackn = function
  | Zapp [] :: s -> decomp_stackn s
  | Zapp l :: s -> (Array.of_list l, s)
  | _ -> assert false
let array_of_stack s =
  let rec stackrec = function
  | [] -> []
  | Zapp args :: s -> args :: (stackrec s)
  | _ -> assert false
  in Array.of_list (List.concat (stackrec s))
let rec list_of_stack = function
  | [] -> []
  | Zapp args :: s -> args @ (list_of_stack s)
  | _ -> assert false
let rec app_stack = function
  | f, [] -> f
  | f, (Zapp [] :: s) -> app_stack (f, s)
  | f, (Zapp args :: s) -> 
      app_stack (applist (f, args), s)
  | _ -> assert false
let rec stack_assign s p c = match s with
  | Zapp args :: s ->
      let q = List.length args in 
      if p >= q then
	Zapp args :: stack_assign s (p-q) c
      else
        (match list_chop p args with
            (bef, _::aft) -> Zapp (bef@c::aft) :: s
          | _ -> assert false)
  | _ -> s
let rec stack_tail p s =
  if p = 0 then s else
    match s with
      | Zapp args :: s ->
	  let q = List.length args in
	  if p >= q then stack_tail (p-q) s
	  else Zapp (list_skipn p args) :: s
      | _ -> failwith "stack_tail"
let rec stack_nth s p = match s with
  | Zapp args :: s ->
      let q = List.length args in
      if p >= q then stack_nth s (p-q)
      else List.nth args p
  | _ -> raise Not_found


(**********************************************************************)
(* 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 inductive
  | FConstruct of constructor
  | FApp of fconstr * fconstr array
  | FFix of fixpoint * fconstr subs
  | FCoFix of cofixpoint * fconstr subs
  | FCases of case_info * fconstr * fconstr * fconstr array
  | FLambda of int * (name * constr) list * constr * fconstr subs
  | FProd of name * fconstr * fconstr
  | FLetIn of name * fconstr * fconstr * constr * fconstr subs
  | FEvar of existential_key * fconstr array
  | FLIFT of int * fconstr
  | FCLOS of constr * fconstr subs
  | FLOCKED

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

let mk_atom c = {norm=Norm;term=FAtom c}

(* 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}

(* 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 -> anomaly "lft_constr found locked term"
    | _ -> {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 lift_fconstr_list k l =
  if k=0 then l else List.map (fun f -> lft_fconstr k f) l

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=Norm;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

(* Closure optimization: *)
let rec compact_constr (lg, subs as s) c k =
  match kind_of_term c with
      Rel i ->
        if i < k then c,s else
          (try mkRel (k + lg - list_index (i-k+1) subs), (lg,subs)
          with Not_found -> mkRel (k+lg), (lg+1, (i-k+1)::subs))
    | (Sort _|Var _|Meta _|Ind _|Const _|Construct _) -> c,s
    | Evar(ev,v) ->
        let (v',s) = compact_vect s v k in
        if v==v' then c,s else mkEvar(ev,v'),s
    | Cast(a,ck,b) ->
        let (a',s) = compact_constr s a k in
        let (b',s) = compact_constr s b k in
        if a==a' && b==b' then c,s else mkCast(a', ck, b'), s
    | App(f,v) ->
        let (f',s) = compact_constr s f k in
        let (v',s) = compact_vect s v k in
        if f==f' && v==v' then c,s else mkApp(f',v'), s
    | Lambda(n,a,b) ->
        let (a',s) = compact_constr s a k in
        let (b',s) = compact_constr s b (k+1) in
        if a==a' && b==b' then c,s else mkLambda(n,a',b'), s
    | Prod(n,a,b) ->
        let (a',s) = compact_constr s a k in
        let (b',s) = compact_constr s b (k+1) in
        if a==a' && b==b' then c,s else mkProd(n,a',b'), s
    | LetIn(n,a,ty,b) ->
        let (a',s) = compact_constr s a k in
        let (ty',s) = compact_constr s ty k in
        let (b',s) = compact_constr s b (k+1) in
        if a==a' && ty==ty' && b==b' then c,s else mkLetIn(n,a',ty',b'), s
    | Fix(fi,(na,ty,bd)) ->
        let (ty',s) = compact_vect s ty k in
        let (bd',s) = compact_vect s bd (k+Array.length ty) in
        if ty==ty' && bd==bd' then c,s else mkFix(fi,(na,ty',bd')), s
    | CoFix(i,(na,ty,bd)) ->
        let (ty',s) = compact_vect s ty k in
        let (bd',s) = compact_vect s bd (k+Array.length ty) in
        if ty==ty' && bd==bd' then c,s else mkCoFix(i,(na,ty',bd')), s
    | Case(ci,p,a,br) ->
        let (p',s) = compact_constr s p k in
        let (a',s) = compact_constr s a k in
        let (br',s) = compact_vect s br k in
        if p==p' && a==a' && br==br' then c,s else mkCase(ci,p',a',br'),s
and compact_vect s v k = compact_v [] s v k (Array.length v - 1)
and compact_v acc s v k i =
  if i < 0 then
    let v' = Array.of_list acc in
    if array_for_all2 (==) v v' then v,s else v',s
  else
    let (a',s') = compact_constr s v.(i) k in
    compact_v (a'::acc) s' v k (i-1)

(* Computes the minimal environment of a closure.
   Idea: if the subs is not identity, the term will have to be
   reallocated entirely (to propagate the substitution). So,
   computing the set of free variables does not change the
   complexity. *)
let optimise_closure env c =
  if is_subs_id env then (env,c) else
    let (c',(_,s)) = compact_constr (0,[]) c 1 in
    let env' = List.fold_left
      (fun subs i -> subs_cons (clos_rel env i, subs)) (ESID 0) s in
    (env',c')

let mk_lambda env t =
  let (env,t) = optimise_closure env t in
  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 kind_of_term 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 _) ->
        {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 kind_of_term 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) }
    | Case (ci,p,c,v) ->
        { norm = Red;
	  term = FCases (ci, clos_fun env p, clos_fun env c,
			 Array.map (clos_fun env) v) }
    | 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 -> mkRel (reloc_rel i lfts)
    | FFlex (RelKey p) -> mkRel (reloc_rel p lfts)
    | FFlex (VarKey x) -> mkVar x
    | FAtom c -> exliftn lfts c
    | FCast (a,k,b) ->
        mkCast (constr_fun lfts a, k, constr_fun lfts b)
    | FFlex (ConstKey op) -> mkConst op
    | FInd op -> mkInd op
    | FConstruct op -> mkConstruct op
    | FCases (ci,p,c,ve) ->
	mkCase (ci, constr_fun lfts p,
                constr_fun lfts c,
		Array.map (constr_fun lfts) ve)
    | 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
	mkFix (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
	mkCoFix (op, (lna, Array.map (constr_fun lfts) ftys,
		           Array.map (constr_fun lfts') fbds))
    | FApp (f,ve) ->
	mkApp (constr_fun lfts f,
	       Array.map (constr_fun lfts) ve)
    | FLambda _ ->
        let (na,ty,bd) = destFLambda mk_clos2 v in
	mkLambda (na, constr_fun lfts ty,
	              constr_fun (el_lift lfts) bd)
    | FProd (n,t,c)   ->
	mkProd (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
	mkLetIn (n, constr_fun lfts b,
	            constr_fun lfts t,
	            constr_fun (el_lift lfts) fc)
    | FEvar (ev,args) -> mkEvar(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 -> (*anomaly "Closure.to_constr: found locked term"*)
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
      | FFix(fx,e) when is_subs_id e & is_lift_id lfts -> mkFix fx
      | FCoFix(cfx,e) when is_subs_id e & is_lift_id lfts -> mkCoFix cfx
      | _ -> to_constr term_of_fconstr_lift lfts v in
  term_of_fconstr_lift ELID



(* 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 ->
        let args = Array.of_list args in
        zip {norm=neutr m.norm; term=FApp(m, args)} s
    | Zcase(ci,p,br)::s ->
        let t = FCases(ci, p, m, br) in
        zip {norm=neutr m.norm; term=t} s
    | Zfix(fx,par)::s ->
        zip fx (par @ append_stack_list ([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 head stk =
  assert (head.norm <> Red);
  let rec strip_rec h depth = function
    | Zshift(k)::s -> strip_rec (lift_fconstr k h) (depth+k) s
    | Zupdate(m)::s ->
        strip_rec (update m (h.norm,h.term)) depth s
    | stk -> (depth,stk) in
  strip_rec head 0 stk

(* 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,Array.of_list 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 rec get_nth_arg head n stk =
  assert (head.norm <> Red);
  let rec strip_rec rstk h depth n = function
    | Zshift(k) as e :: s ->
        strip_rec (e::rstk) (lift_fconstr k h) (depth+k) n s
    | Zapp args::s' ->
        let q = List.length args in
        if n >= q
        then
          strip_rec (Zapp args::rstk)
            {norm=h.norm;term=FApp(h,Array.of_list args)} depth (n-q) s'
        else
          (match list_chop n args with
              (bef, v::aft) -> 
                let stk' =
                  List.rev (if n = 0 then rstk else (Zapp bef :: rstk)) in
                (Some (stk', v), append_stack_list (aft,s'))
            | _ -> assert false)
    | Zupdate(m)::s ->
        strip_rec rstk (update m (h.norm,h.term)) depth n s
    | s -> (None, List.rev rstk @ s) in
  strip_rec [] head 0 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 get_arg h stk =
  let (depth,stk') = strip_update_shift h stk in
  match  decomp_stack stk' with
      Some (v, s') -> (Some (depth,v), s')
    | None -> (None, zshift depth stk')

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 = List.length l in
        if n == na then
          let e' = List.fold_left (fun e arg -> subs_cons(arg,e)) e l in
          (Inl e',s)
        else if n < na then (* more arguments *)
          let (args,eargs) = list_chop n l in
          let e' = List.fold_left (fun e arg -> subs_cons(arg,e)) e args in
          (Inl e', Zapp eargs :: s)
        else (* more lambdas *)
          let (_,etys) = list_chop na tys in
          let e' = List.fold_left (fun e arg -> subs_cons(arg,e)) e l in
          get_args (n-na) etys f e' s
    | _ -> (Inr {norm=Cstr;term=FLambda(n,tys,f,e)}, stk)


(* 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_list 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 drop_parameters depth n stk =
  match stk with
      Zapp args::s ->
        let q = List.length args in
        if n > q then drop_parameters depth (n-q) s
        else if n = q then reloc_rargs depth s
        else
          let aft = list_skipn n args in
          reloc_rargs depth (append_stack_list (aft,s))
    | Zshift(k)::s -> drop_parameters (depth-k) n s
    | [] -> assert (n=0); []
    | _ -> assert false (* we know that n < stack_args_size(stk) *)


(* 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)
      | _ -> anomaly "Closure.contract_fix_vect: not a (co)fixpoint" 
  in
  let rec subst_bodies_from_i i env =
    if i = nfix then
      (env, thisbody)
    else
      subst_bodies_from_i (i+1) (subs_cons (make_body i, env))
  in       
  subst_bodies_from_i 0 env


(*********************************************************************)
(* 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 m stk =
  match m.term with
    | FLIFT(k,a) -> knh a (zshift k stk)
    | FCLOS(t,e) -> knht e t (zupdate m stk)
    | FLOCKED -> anomaly "Closure.knh: found lock"
    | FApp(a,b) -> knh a (append_stack b (zupdate m stk))
    | FCases(ci,p,t,br) -> knh t (Zcase(ci,p,br)::zupdate m stk)
    | FFix(((ri,n),(_,_,_)),_) ->
        (match get_nth_arg m ri.(n) stk with
             (Some(pars,arg),stk') -> knh arg (Zfix(m,pars)::stk')
           | (None, stk') -> (m,stk'))
    | FCast(t,_,_) -> knh t stk
(* cases where knh stops *)
    | (FFlex _|FLetIn _|FConstruct _|FEvar _|
       FCoFix _|FLambda _|FRel _|FAtom _|FInd _|FProd _) ->
        (m, stk)

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


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

(* Computes a 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 (fCONST kn) ->
      (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 (fVAR id) ->
      (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) when red_set info.i_flags fIOTA ->
      (match strip_update_shift_app m stk with
          (depth, args, Zcase(ci,_,br)::s) ->
            assert (ci.ci_npar>=0);
            let rargs = drop_parameters depth ci.ci_npar args in
            kni info 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'
        | (_,args,s) -> (m,args@s))
  | FCoFix _ when red_set info.i_flags fIOTA ->
      (match strip_update_shift_app m stk with
          (_, args, ((Zcase _::_) 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 m stk in
  knr info hm s
and knit info e t stk =
  let (ht,s) = knht e t stk in
  knr info ht s

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

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

let rec zip_term zfun m stk =
  match stk with
    | [] -> m
    | Zapp args :: s ->
        let args = Array.of_list args in
        zip_term zfun (mkApp(m, Array.map zfun args)) s
    | Zcase(ci,p,br)::s ->
        let t = mkCase(ci, zfun p, m, Array.map zfun br) in
        zip_term zfun t s
    | Zfix(fx,par)::s ->
        let h = mkApp(zip_term zfun (zfun fx) par,[|m|]) in
        zip_term zfun h s
    | Zshift(n)::s ->
        zip_term zfun (lift n m) s
    | Zupdate(rf)::s ->
        zip_term zfun m s

(* Computes the strong normal form of a term.
   1- Calls kni
   2- tries to rebuild the term. If a closure still has to be computed,
      calls itself recursively. *)
let rec kl info m =
  if is_val m then (incr prune; term_of_fconstr m)
  else
    let (nm,s) = kni info m [] in
    let _ = fapp_stack(nm,s) in (* to unlock Zupdates! *)
    zip_term (kl info) (norm_head info nm) s

(* no redex: go up for atoms and already normalized terms, go down
   otherwise. *) 
and norm_head info m =
  if is_val m then (incr prune; term_of_fconstr m) else
    match m.term with
      | FLambda(n,tys,f,e) ->
          let (e',rvtys) =
            List.fold_left (fun (e,ctxt) (na,ty) ->
              (subs_lift e, (na,kl info (mk_clos e ty))::ctxt))
              (e,[]) tys in
          let bd = kl info (mk_clos e' f) in
          List.fold_left (fun b (na,ty) -> mkLambda(na,ty,b)) bd rvtys
      | FLetIn(na,a,b,f,e) ->
          let c = mk_clos (subs_lift e) f in
          mkLetIn(na, kl info a, kl info b, kl info c)
      | FProd(na,dom,rng) ->
          mkProd(na, kl info dom, kl info rng)
      | FCoFix((n,(na,tys,bds)),e) ->
          let ftys = Array.map (mk_clos e) tys in
          let fbds =
            Array.map (mk_clos (subs_liftn (Array.length na) e)) bds in
          mkCoFix(n,(na, Array.map (kl info) ftys, Array.map (kl info) fbds))
      | FEvar(i,args) -> mkEvar(i, Array.map (kl info) args)
      | t -> term_of_fconstr m

(* Initialization and then normalization *)

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

(* strong reduction *)
let norm_val info v =
  with_stats (lazy (kl info v))

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

let unfold_reference = ref_value_cache