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
|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(*i $Id$ i*)
open Pp
open Util
open Names
open Term
open Declarations
open Environ
open Reduction
open Inductive
open Instantiate
open Miniml
open Mlutil
open Closure
open Summary
(*s Extraction results. *)
(* The flag [type_var] gives us information about an identifier
coming from a Lambda or a Product:
\begin{itemize}
\item [Arity] denotes identifiers of type an arity of some sort [Set],
[Prop] or [Type], that is $(x_1:X_1)\ldots(x_n:X_n)s$ with [s = Set],
[Prop] or [Type]
\item [NotArity] denotes the other cases. It may be inexact after
instanciation. For example [(X:Type)X] is [NotArity] and may give [Set]
after instanciation, which is rather [Arity]
\item [Logic] denotes identifiers of type an arity of sort [Prop],
or of type of type [Prop]
\item [Info] is the opposite. The same example [(X:Type)X] shows
that an [Info] term might in fact be [Logic] later on.
\end{itemize} *)
type info = Logic | Info
type arity = Arity | NotArity
type type_var = info * arity
let logic_arity = (Logic, Arity)
let info_arity = (Info, Arity)
let logic = (Logic, NotArity)
let default = (Info, NotArity)
(* The [signature] type is used to know how many arguments a CIC
object expects, and what these arguments will become in the ML
object. *)
(* Convention: outmost lambda/product gives the head of the list *)
type signature = type_var list
(* When dealing with CIC contexts, we maintain corresponding contexts
telling whether a variable will be kept or will disappear.
Cf. [renum_db]. *)
(* Convention: innermost ([Rel 1]) is at the head of the list *)
type extraction_context = bool list
(* The [type_extraction_result] is the result of the [extract_type] function
that extracts a CIC object into an ML type. It is either:
\begin{itemize}
\item a real ML type, followed by its signature and its list of type
variables (['a],\ldots)
\item a CIC arity, without counterpart in ML
\item a non-informative type, which will receive special treatment
\end{itemize} *)
type type_extraction_result =
| Tmltype of ml_type * signature * identifier list
| Tarity
| Tprop
(* The [term_extraction_result] is the result of the [extract_term]
function that extracts a CIC object into an ML term *)
type term_extraction_result =
| Rmlterm of ml_ast
| Rprop
(* The [extraction_result] is the result of the [extract_constr]
function that extracts any CIC object. It is either a ML type, a ML
object or something non-informative. *)
type extraction_result =
| Emltype of ml_type * signature * identifier list
| Emlterm of ml_ast
(*s Utility functions. *)
let whd_betaiotalet = clos_norm_flags (UNIFORM, red_add betaiota_red ZETA)
let is_axiom sp = (Global.lookup_constant sp).const_body = None
type lamprod = Lam | Prod
let flexible_name = id_of_string "flex"
let id_of_name = function
| Anonymous -> id_of_string "x"
| Name id -> id
(* [get_arity c] returns [Some s] if [c] is an arity of sort [s],
and [None] otherwise. *)
let rec get_arity env c =
match kind_of_term (whd_betadeltaiota env Evd.empty c) with
| IsProd (x,t,c0) -> get_arity (push_rel_assum (x,t) env) c0
| IsCast (t,_) -> get_arity env t
| IsSort s -> Some s
| _ -> None
(* idem, but goes through [Lambda] as well. Cf. [find_conclusion]. *)
let rec get_lam_arity env c =
match kind_of_term (whd_betadeltaiota env Evd.empty c) with
| IsLambda (x,t,c0) -> get_lam_arity (push_rel_assum (x,t) env) c0
| IsProd (x,t,c0) -> get_lam_arity (push_rel_assum (x,t) env) c0
| IsCast (t,_) -> get_lam_arity env t
| IsSort s -> Some s
| _ -> None
(*s Detection of non-informative parts. *)
let is_non_info_sort env s = is_Prop (whd_betadeltaiota env Evd.empty s)
let is_non_info_type env t =
let s = Typing.type_of env Evd.empty t in
(is_non_info_sort env s) || ((get_arity env t) = (Some (Prop Null)))
let is_non_info_term env c =
let t = Typing.type_of env Evd.empty c in
let s = Typing.type_of env Evd.empty t in
(is_non_info_sort env s) ||
match get_arity env t with
| Some (Prop Null) -> true
| Some (Type _) -> (get_lam_arity env c = Some (Prop Null))
| _ -> false
(* [v_of_t] transforms a type [t] into a [type_var] flag. *)
let v_of_t env t = match get_arity env t with
| Some (Prop Null) -> logic_arity
| Some _ -> info_arity
| _ -> if is_non_info_type env t then logic else default
(* Operations on binders *)
type binders = (identifier * constr) list
(* Convention: right binders give [Rel 1] at the head, like those answered by
[decompose_prod]. Left binders are the converse. *)
let rec lbinders_fold f acc env = function
| [] -> acc
| (n,t) :: l ->
f n t (v_of_t env t) (lbinders_fold f acc (push_rel (n,None,t) env) l)
let rec rbinders_fold f init env = function
| [] -> env, init
| (n,t) :: l -> let env, res = rbinders_fold f init env l in
(push_rel (n,None,t) env), (f n t (v_of_t env t) res)
let nb_notarity =
lbinders_fold (fun _ _ v acc -> if snd v = NotArity then succ acc else acc) 0
(* The next function transforms an arity into a signature. It is used
for example with the types of inductive definitions, which are known
to be already in arity form. *)
let sign_of_lbinders = lbinders_fold (fun _ _ v acc -> v::acc) []
let rec signature_of_arity env c = match kind_of_term c with
| IsProd (n, t, c') ->
let env' = push_rel (n,None,t) env in
(v_of_t env t) :: (signature_of_arity env' c')
| IsSort _ -> []
| _ -> assert false
let rec vl_of_binders env vl b = match b with
| [] -> vl
| (n,t) :: l
when ((v_of_t env t) = info_arity) ->
let id = next_ident_away (id_of_name n) vl in
let env' = push_rel (Name id, None, t) env in
vl_of_binders env' (id :: vl) l
| (n,t) :: l ->
vl_of_binders (push_rel (n, None, t) env) vl l
let rec vl_of_arity env vl c =
vl_of_binders env vl (List.rev (fst (decompose_prod c)))
(* [list_of_ml_arrows] applied to the ML type [a->b->]\dots[z->t]
returns the list [[a;b;...;z]]. It is used when making the ML types
of inductive definitions. We also suppress [Prop] parts. *)
let rec list_of_ml_arrows = function
| Tarr (Miniml.Tprop, b) -> list_of_ml_arrows b
| Tarr (a, b) -> a :: list_of_ml_arrows b
| t -> []
(* [renum_db] gives the new de Bruijn indices for variables in an ML
term. This translation is made according to an [extraction_context]. *)
let renum_db ctx n =
let rec renum = function
| (1, true :: _) -> 1
| (n, true :: s) -> succ (renum (pred n, s))
| (n, false :: s) -> renum (pred n, s)
| _ -> assert false
in
renum (n, ctx)
(*s Environment for the bodies of some mutual fixpoints. *)
let rec push_many_rels_ctx keep_prop env ctx = function
| (fi,ti) :: l ->
let v = v_of_t env ti in
let keep = (v = default) || (keep_prop && v = logic) in
push_many_rels_ctx keep_prop (push_rel (fi,None,ti) env) (keep :: ctx) l
| [] ->
(env, ctx)
let fix_environment env ctx fl tl =
let tl' = Array.mapi lift tl in
push_many_rels_ctx true env ctx (List.combine fl (Array.to_list tl'))
(* Decomposition of a function expecting n arguments at least. We eta-expanse
if needed *)
let force_n_prod n env c =
if nb_prod c < n then whd_betadeltaiota env Evd.empty c else c
let decompose_lam_eta n env c =
let dif = n - (nb_lam c) in
if dif <= 0 then
decompose_lam_n n c
else
let tyc = Typing.type_of env Evd.empty c in
let (type_binders,_) = decompose_prod_n n (force_n_prod n env tyc) in
let (binders, e) = decompose_lam c in
let binders = (list_firstn dif type_binders) @ binders in
let e = applist (lift dif e, List.rev_map mkRel (interval 1 dif)) in
(binders, e)
let rec abstract_n n a =
if n = 0 then a else MLlam (anonymous, ml_lift 1 (abstract_n (n-1) a))
let dest_fix_cofix = function
| IsFix ((_,i),(ti,fi,ci)) -> (false,i,ti,fi,ci)
| IsCoFix (i,(ti,fi,ci)) -> (true,i,ti,fi,ci)
| _ -> assert false
(*s Eta-expansion to bypass ML type inference limitations (due to possible
polymorphic references, the ML type system does not generalize all
type variables that could be generalized). *)
let eta_expanse ec = function
| Tmltype (Tarr _, _, _) ->
(match ec with
| Emlterm (MLlam _) -> ec
| Emlterm a -> Emlterm (MLlam (anonymous, MLapp (a, [MLrel 1])))
| _ -> ec)
| _ -> ec
(*s Error message when extraction ends on an axiom. *)
let axiom_message sp =
errorlabstrm "axiom_message"
[< 'sTR "You must specify an extraction for axiom"; 'sPC;
pr_sp sp; 'sPC; 'sTR "first" >]
(*s Tables to keep the extraction of inductive types and constructors. *)
type inductive_extraction_result =
| Iml of signature * identifier list
| Iprop
let inductive_extraction_table =
ref (Gmap.empty : (inductive_path, inductive_extraction_result) Gmap.t)
let add_inductive_extraction i e =
inductive_extraction_table := Gmap.add i e !inductive_extraction_table
let lookup_inductive_extraction i = Gmap.find i !inductive_extraction_table
type constructor_extraction_result =
| Cml of ml_type list * signature * int
| Cprop
let constructor_extraction_table =
ref (Gmap.empty : (constructor_path, constructor_extraction_result) Gmap.t)
let add_constructor_extraction c e =
constructor_extraction_table := Gmap.add c e !constructor_extraction_table
let lookup_constructor_extraction i = Gmap.find i !constructor_extraction_table
let constant_table =
ref (Gmap.empty : (section_path, extraction_result) Gmap.t)
(* Tables synchronization. *)
let freeze () =
!inductive_extraction_table, !constructor_extraction_table, !constant_table
let unfreeze (it,cst,ct) =
inductive_extraction_table := it;
constructor_extraction_table := cst;
constant_table := ct
let _ = declare_summary "Extraction tables"
{ freeze_function = freeze;
unfreeze_function = unfreeze;
init_function = (fun () -> ());
survive_section = true }
(*s Extraction of a type. *)
(* When calling [extract_type] we suppose that the type of [c] is an
arity. This is for example checked in [extract_constr].
Relation with [v_of_t]: it is less precise, since we do not
delta-reduce in [extract_type] in general.
\begin{itemize}
\item If [v_of_t env t = NotArity,_],
then [extract_type env t] is a [Tmltype].
\item If [extract_type env t = Tarity], then [v_of_t env t = Arity,_]
\end{itemize} *)
let rec extract_type env c =
extract_type_rec env [] c []
and extract_type_rec env vl c args =
(* We accumulate the two contexts, the generated variable list *)
let ty = Typing.type_of env Evd.empty (applist (c, args)) in
(* Since [ty] is an arity, there is two non-informative case:
[ty] is an arity of sort [Prop], or
[c] has a non-informative head symbol *)
match get_arity env ty with
| None ->
assert false (* Cf. precondition. *)
| Some (Prop Null) ->
Tprop
| Some _ -> extract_type_rec_info env vl c args
and extract_type_rec_info env vl c args =
match (kind_of_term (whd_betaiotalet env Evd.empty c)) with
| IsSort _ ->
assert (args = []); (* A sort can't be applied. *)
Tarity
| IsProd (n,t,d) ->
assert (args = []); (* A product can't be applied. *)
extract_prod_lam env vl (n,t,d) Prod
| IsLambda (n,t,d) ->
assert (args = []); (* [c] is now in head normal form. *)
extract_prod_lam env vl (n,t,d) Lam
| IsApp (d, args') ->
(* We just accumulate the arguments. *)
extract_type_rec_info env vl d (Array.to_list args' @ args)
| IsRel n ->
(match lookup_rel_value n env with
| Some t ->
extract_type_rec_info env vl (lift n t) args
| None ->
let id = id_of_name (fst (lookup_rel_type n env)) in
Tmltype (Tvar id, [], vl))
| IsConst (sp,a) when is_axiom sp ->
let id = next_ident_away (basename sp) vl in
Tmltype (Tvar id, [], id :: vl)
| IsConst (sp,a) ->
let cty = constant_type env Evd.empty (sp,a) in
if is_arity env Evd.empty cty then
(match extract_constant sp with
| Emltype (Miniml.Tarity,_,_) -> Tarity
| Emltype (Miniml.Tprop,_,_) -> Tprop
| Emltype (mlt, sc, vlc) ->
extract_type_app env vl (ConstRef sp,sc,vlc) args
| Emlterm _ -> assert false)
else begin
(* We can't keep as ML type abbreviation a CIC constant
which type is not an arity: we reduce this constant. *)
let cvalue = constant_value env (sp,a) in
extract_type_rec_info env vl (applist (cvalue, args)) []
end
| IsMutInd (spi,_) ->
(match extract_inductive spi with
|Iml (si,vli) ->
extract_type_app env vl (IndRef spi,si,vli) args
|Iprop -> assert false
(* Cf. initial tests *))
| IsMutCase _
| IsFix _ | IsCoFix _ ->
let id = next_ident_away flexible_name vl in
Tmltype (Tvar id, [], id :: vl)
(* CIC type without counterpart in ML: we generate a
new flexible type variable. *)
| IsCast (c, _) ->
extract_type_rec_info env vl c args
| _ ->
assert false
(* Auxiliary function used to factor code in lambda and product cases *)
and extract_prod_lam env vl (n,t,d) flag =
let tag = v_of_t env t in
let env' = push_rel (n, None, t) env in
match tag,flag with
| (Info, Arity), _ ->
let id' = next_ident_away (id_of_name n) vl in
let env' = push_rel (Name id', None, t) env in
(match extract_type_rec_info env' (id'::vl) d [] with
| Tmltype (mld, sign, vl') -> Tmltype (mld, tag::sign, vl')
| et -> et)
| (Logic, Arity), _ | _, Lam ->
(match extract_type_rec_info env' vl d [] with
| Tmltype (mld, sign, vl') -> Tmltype (mld, tag::sign, vl')
| et -> et)
| (Logic, NotArity), Prod ->
(match extract_type_rec_info env' vl d [] with
| Tmltype (mld, sign, vl') ->
Tmltype (Tarr (Miniml.Tprop, mld), tag::sign, vl')
| et -> et)
| (Info, NotArity), Prod ->
(match extract_type_rec_info env' vl d [] with
| Tmltype (mld, sign, vl') ->
(match extract_type_rec_info env vl' t [] with
| Tprop | Tarity ->
assert false
(* Cf. relation between [extract_type] and [v_of_t] *)
| Tmltype (mlt,_,vl'') ->
Tmltype (Tarr(mlt,mld), tag::sign, vl''))
| et -> et)
(* Auxiliary function dealing with type application.
Precondition: [r] is of type an arity. *)
and extract_type_app env vl (r,sc,vlc) args =
let nargs = List.length args in
assert (List.length sc >= nargs);
(* [r] is of type an arity, so it can't be applied to more than n args,
where n is the number of products in this arity type. *)
let (sign_args,sign_rem) = list_chop nargs sc in
let (mlargs,vl') =
List.fold_right
(fun (v,a) ((args,vl) as acc) -> match v with
| _, NotArity -> acc
| Logic, Arity -> acc (* TO JUSTIFY *)
| Info, Arity -> match extract_type_rec_info env vl a [] with
| Tarity -> (Miniml.Tarity :: args, vl)
(* we pass a dummy type [arity] as argument *)
| Tprop -> (Miniml.Tprop :: args, vl)
| Tmltype (mla,_,vl') -> (mla :: args, vl'))
(List.combine sign_args args)
([],vl)
in
let nvlargs = List.length vlc - List.length mlargs in
assert (nvlargs >= 0);
let vl'' =
List.fold_right
(fun id l -> (next_ident_away id l) :: l)
(list_firstn nvlargs vlc) vl'
in
let vlargs =
List.rev_map (fun i -> Tvar i) (list_firstn nvlargs vl'') in
Tmltype (Tapp ((Tglob r) :: mlargs @ vlargs), sign_rem, vl'')
(*s Extraction of a term.
Precondition: [c] has a type which is not an arity.
This is normaly checked in [extract_constr]. *)
and extract_term env ctx c =
let t = Typing.type_of env Evd.empty c in
extract_term_with_type env ctx c t
and extract_term_with_type env ctx c t =
let s = Typing.type_of env Evd.empty t in
(* The only non-informative case: [s] is [Prop] *)
if is_Prop (whd_betadeltaiota env Evd.empty s) then
Rprop
else
Rmlterm (extract_term_info_with_type env ctx c t)
(* Variants with a stronger precondition: [c] is informative.
We directly return a [ml_ast], not a [term_extraction_result] *)
and extract_term_info env ctx c =
let t = Typing.type_of env Evd.empty c in
extract_term_info_with_type env ctx c t
and extract_term_info_with_type env ctx c t =
match kind_of_term c with
| IsLambda (n, t, d) ->
let v = v_of_t env t in
let env' = push_rel (n,None,t) env in
let ctx' = (snd v = NotArity) :: ctx in
let d' = extract_term_info env' ctx' d in
(* If [d] was of type an arity, [c] too would be so *)
(match v with
| _,Arity -> d'
| l,NotArity ->
let id = if l = Logic then prop_name else id_of_name n in
MLlam (id, d'))
| IsRel n ->
(* TODO : magic or not *)
MLrel (renum_db ctx n)
| IsApp (f,a) ->
let tyf = Typing.type_of env Evd.empty f in
let s = signature_of_application env f tyf a in
extract_app env ctx (f,tyf,s) (Array.to_list a)
| IsConst (sp,_) ->
MLglob (ConstRef sp)
| IsMutConstruct (cp,_) ->
let (s,n) = signature_of_constructor cp in
let rec abstract rels i = function
| [] ->
let rels = List.rev_map (fun x -> MLrel (i-x)) rels in
if (is_singleton_constructor cp) then
match rels with
| [var]->var
| _ -> assert false
else
MLcons (ConstructRef cp, rels)
| (Info,NotArity) :: l ->
MLlam (id_of_name Anonymous, abstract (i :: rels) (succ i) l)
| (Logic,NotArity) :: l ->
MLlam (id_of_name Anonymous, abstract rels (succ i) l)
| (_,Arity) :: l ->
abstract rels i l
in
abstract_n n (abstract [] 1 s)
| IsMutCase ((ni,(ip,cnames,_,_,_)),p,c,br) ->
let extract_branch_aux j b =
let (binders,e) = decompose_lam_eta ni.(j) env b in
let binders = List.rev binders in
let (env',ctx') = push_many_rels_ctx false env ctx binders in
(* Some pathological cases need an [extract_constr] here
rather than an [extract_term]. See exemples in
[test_extraction.v] *)
let e' = match extract_constr env' ctx' e with
| Emltype _ -> MLarity
| Emlterm a -> a
in (binders,e')
in
let extract_branch j b =
let cp = (ip,succ j) in
let (s,_) = signature_of_constructor cp in
assert (List.length s = ni.(j));
(* number of arguments, without parameters *)
let (binders, e') = extract_branch_aux j b in
let ids =
List.fold_right
(fun (v,(n,_)) acc ->
if v = default then (id_of_name n :: acc) else acc)
(List.combine s binders) []
in
(ConstructRef cp, ids, e')
in
(* [c] has an inductive type, not an arity type *)
(match extract_term env ctx c with
| Rmlterm a ->
if (is_singleton_inductive ip) then
begin
(* informative singleton case *)
assert (Array.length br = 1);
let (_,ids,e') = extract_branch 0 br.(0) in
assert (List.length ids = 1);
MLletin (List.hd ids,a,e')
end
else
MLcase (a, Array.mapi extract_branch br)
| Rprop -> (* Logical singleton elimination *)
assert (Array.length br = 1);
snd (extract_branch_aux 0 br.(0)))
| IsFix _ | IsCoFix _ as c ->
let (cofix,i,ti,fi,ci) = dest_fix_cofix c in
let n = Array.length ti in
let (env', ctx') = fix_environment env ctx fi ti in
let extract_fix_body c t =
match extract_constr_with_type env' ctx' c (lift n t) with
| Emltype _ -> MLarity
| Emlterm a -> a
in
let ei = Array.to_list (array_map2 extract_fix_body ci ti) in
MLfix (i, List.map id_of_name fi, ei)
| IsLetIn (n, c1, t1, c2) ->
let id = id_of_name n in
let env' = push_rel (n,Some c1,t1) env in
let tag = v_of_t env t1 in
(match tag with
| (Info, NotArity) ->
let c1' = extract_term_info_with_type env ctx c1 t1 in
let c2' = extract_term_info env' (true :: ctx) c2 in
(* If [c2] was of type an arity, [c] too would be so *)
MLletin (id,c1',c2')
| _ ->
extract_term_info env' (false :: ctx) c2)
| IsCast (c, _) ->
extract_term_info_with_type env ctx c t
| IsMutInd _ | IsProd _ | IsSort _ | IsVar _ | IsMeta _ | IsEvar _ ->
assert false
and extract_app env ctx (f,tyf,sf) args =
let nargs = List.length args in
assert (List.length sf >= nargs);
(* We have reduced type of [f] if needed to ensure this property *)
let mlargs =
List.fold_right
(fun (v,a) args -> match v with
| (_,Arity) -> args
| (Logic,NotArity) -> MLprop :: args
| (Info,NotArity) ->
(* We can't trust the tag [Vdefault], we use [extract_constr] *)
match extract_constr env ctx a with
| Emltype _ -> MLarity :: args
| Emlterm mla -> mla :: args)
(List.combine (list_firstn nargs sf) args)
[]
in
(* [f : arity] implies [(f args):arity], that can't be *)
let f' = extract_term_info_with_type env ctx f tyf in
MLapp (f', mlargs)
and signature_of_application env f t a =
let nargs = Array.length a in
let t = force_n_prod nargs env t in
let nbp = nb_prod t in
let s = match extract_type env t with
| Tmltype (_,s,_) -> s
| Tarity -> assert false (* Cf. precondition *)
| Tprop -> assert false
in
if nbp >= nargs then
s
else
let f' = mkApp (f, Array.sub a 0 nbp) in
let a' = Array.sub a nbp (nargs-nbp) in
let t' = Typing.type_of env Evd.empty f' in
s @ signature_of_application env f' t' a'
(*s Extraction of a constr. *)
and extract_constr_with_type env ctx c t =
match v_of_t env t with
| (Logic, Arity) -> Emltype (Miniml.Tarity, [], [])
| (Logic, NotArity) -> Emlterm MLprop
| (Info, Arity) ->
(match extract_type env c with
| Tprop -> Emltype (Miniml.Tprop, [], [])
| Tarity -> Emltype (Miniml.Tarity, [], [])
| Tmltype (t, sign, vl) -> Emltype (t, sign, vl))
| (Info, NotArity) ->
Emlterm (extract_term_info_with_type env ctx c t)
and extract_constr env ctx c =
extract_constr_with_type env ctx c (Typing.type_of env Evd.empty c)
(*s Extraction of a constant. *)
and extract_constant sp =
try
Gmap.find sp !constant_table
with Not_found ->
let env = Global.env() in
let cb = Global.lookup_constant sp in
let typ = cb.const_type in
match cb.const_body with
| None ->
(match v_of_t env typ with
| (Info,_) -> axiom_message sp
| (Logic,Arity) -> Emltype (Miniml.Tarity,[],[])
| (Logic,NotArity) -> Emlterm MLprop)
| Some body ->
let e = extract_constr_with_type env [] body typ in
let e = eta_expanse e (extract_type env typ) in
constant_table := Gmap.add sp e !constant_table;
e
(*s Extraction of an inductive. *)
and extract_inductive ((sp,_) as i) =
extract_mib sp;
lookup_inductive_extraction i
and extract_constructor (((sp,_),_) as c) =
extract_mib sp;
lookup_constructor_extraction c
and is_singleton_inductive (sp,_) =
let mib = Global.lookup_mind sp in
(mib.mind_ntypes = 1) &&
let mis = build_mis ((sp,0),[||]) mib in
(mis_nconstr mis = 1) &&
match extract_constructor ((sp,0),1) with
| Cml ([_],_,_)-> true
| _ -> false
and is_singleton_constructor ((sp,i),_) =
is_singleton_inductive (sp,i)
and signature_of_constructor cp = match extract_constructor cp with
| Cprop -> assert false
| Cml (_,s,n) -> (s,n)
and extract_mib sp =
if not (Gmap.mem (sp,0) !inductive_extraction_table) then begin
let mib = Global.lookup_mind sp in
let genv = Global.env () in
(* first pass: we store inductive signatures together with
an initial type var list. *)
Array.iteri
(fun i ib ->
let mis = build_mis ((sp,i),[||]) mib in
if (mis_sort mis) = (Prop Null) then
add_inductive_extraction (sp,i) Iprop
else
add_inductive_extraction (sp,i)
(Iml (signature_of_arity genv ib.mind_nf_arity,
vl_of_arity genv [] ib.mind_nf_arity)))
mib.mind_packets;
(* second pass: we extract constructors arities and we accumulate
type variables. *)
let mis = build_mis ((sp,0),[||]) mib in
let nparams = mis_nparams mis in
let params = mis_params_ctxt mis in
let env = Environ.push_rels params genv in
let params = List.rev_map (fun (n,s,t)->(n,t)) params in
let nparams' = nb_notarity genv params in
let vlparams = vl_of_binders genv [] params in
let vl =
array_fold_left_i
(fun i vl packet ->
let ip = (sp,i) in
let mis = build_mis (ip,[||]) mib in
if mis_sort mis = Prop Null then begin
for j = 0 to mis_nconstr mis do
add_constructor_extraction (ip,succ j) Cprop
done;
vl
end else begin
array_fold_left_i
(fun j vl _ ->
let t = mis_constructor_type (succ j) mis in
let t = snd (decompose_prod_n nparams t) in
match extract_type_rec_info env vl t [] with
| Tarity | Tprop -> assert false
| Tmltype (mlt, s, v) ->
let l = list_of_ml_arrows mlt in
let cp = (ip,succ j) in
add_constructor_extraction cp (Cml (l,s,nparams'));
v)
vl packet.mind_nf_lc
end)
vlparams mib.mind_packets
in
(* third pass: we update the type variables list in every tables *)
for i = 0 to mib.mind_ntypes-1 do
match lookup_inductive_extraction (sp,i) with
| Iprop -> ()
| Iml (s,_) -> begin
add_inductive_extraction (sp,i) (Iml (s,vl));
let ip = (sp,i) in
let mis = build_mis (ip,[||]) mib in
for j = 1 to mis_nconstr mis do
let cp = (ip,j) in
match lookup_constructor_extraction cp with
| Cprop -> assert false
| Cml (t,s,n) ->
let vl = List.rev_map (fun i -> Tvar i) vl in
let t' = List.map (update_args sp vl) t in
add_constructor_extraction cp (Cml (t',s, n))
done
end
done
end
and extract_inductive_declaration sp =
extract_mib sp;
let ip = (sp,0) in
if (is_singleton_inductive ip) then
let t = match lookup_constructor_extraction (ip,1) with
| Cml ([t],_,_)-> t
| _ -> assert false
in
let vl = match lookup_inductive_extraction ip with
| Iml (_,vl) -> vl
| _ -> assert false
in
Dabbrev (IndRef ip,vl,t)
else
let mib = Global.lookup_mind sp in
let one_constructor ind j _ =
let cp = (ind,succ j) in
match lookup_constructor_extraction cp with
| Cprop -> assert false
| Cml (t,_,_) -> (ConstructRef cp, t)
in
let l =
array_fold_left_i
(fun i acc packet ->
let ip = (sp,i) in
match lookup_inductive_extraction ip with
| Iprop -> acc
| Iml (s,vl) ->
(List.rev vl,
IndRef ip,
Array.to_list
(Array.mapi (one_constructor ip) packet.mind_consnames))
:: acc )
[] mib.mind_packets
in
Dtype (List.rev l, not (mind_type_finite mib 0))
(*s Extraction of a global reference i.e. a constant or an inductive. *)
let false_rec_sp = path_of_string "Coq.Init.Specif.False_rec"
let false_rec_e = MLlam (prop_name, MLexn (id_of_string "False_rec"))
let extract_declaration r = match r with
| ConstRef sp when sp = false_rec_sp -> Dglob (r, false_rec_e)
| ConstRef sp ->
(match extract_constant sp with
| Emltype (mlt, s, vl) -> Dabbrev (r, List.rev vl, mlt)
| Emlterm t -> Dglob (r, t))
| IndRef (sp,_) -> extract_inductive_declaration sp
| ConstructRef ((sp,_),_) -> extract_inductive_declaration sp
| VarRef _ -> assert false
|