aboutsummaryrefslogtreecommitdiffhomepage
path: root/kernel/mod_subst.ml
blob: ed50c6d72523d7262841933a13f218361db854ad (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
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* Created by Claudio Sacerdoti from contents of term.ml, names.ml and
   new support for constant inlining in functor application, Nov 2004 *)
(* Optimizations and bug fixes by Élie Soubiran, from Feb 2008 *)

(* This file provides types and functions for managing name
   substitution in module constructions *)

open Pp
open Util
open Names
open Term

(* For Inline, the int is an inlining level, and the constr (if present)
   is the term into which we should inline. *)

type delta_hint =
  | Inline of int * constr option
  | Equiv of kernel_name

(* NB: earlier constructor Prefix_equiv of module_path
   is now stored in a separate table, see Deltamap.t below *)

module Deltamap = struct
  type t = module_path MPmap.t * delta_hint KNmap.t
  let empty = MPmap.empty, KNmap.empty
  let is_empty (mm, km) =
    MPmap.is_empty mm && KNmap.is_empty km
  let add_kn kn hint (mm,km) = (mm,KNmap.add kn hint km)
  let add_mp mp mp' (mm,km) = (MPmap.add mp mp' mm, km)
  let find_mp mp map = MPmap.find mp (fst map)
  let find_kn kn map = KNmap.find kn (snd map)
  let mem_mp mp map = MPmap.mem mp (fst map)
  let mem_kn kn map = KNmap.mem kn (snd map)
  let fold_kn f map i = KNmap.fold f (snd map) i
  let fold fmp fkn (mm,km) i =
    MPmap.fold fmp mm (KNmap.fold fkn km i)
  let join map1 map2 = fold add_mp add_kn map1 map2
end

(* Invariant: in the [delta_hint] map, an [Equiv] should only
   relate [kernel_name] with the same label (and section dirpath). *)

type delta_resolver = Deltamap.t

let empty_delta_resolver = Deltamap.empty

module MBImap = Map.Make
  (struct
    type t = MBId.t
    let compare = MBId.compare
   end)

module Umap = struct
  type 'a t = 'a MPmap.t * 'a MBImap.t
  let empty = MPmap.empty, MBImap.empty
  let is_empty (m1,m2) = MPmap.is_empty m1 && MBImap.is_empty m2
  let add_mbi mbi x (m1,m2) = (m1,MBImap.add mbi x m2)
  let add_mp mp x (m1,m2) = (MPmap.add mp x m1, m2)
  let find_mp mp map = MPmap.find mp (fst map)
  let find_mbi mbi map = MBImap.find mbi (snd map)
  let iter_mbi f map = MBImap.iter f (snd map)
  let fold fmp fmbi (m1,m2) i =
    MPmap.fold fmp m1 (MBImap.fold fmbi m2 i)
  let join map1 map2 = fold add_mp add_mbi map1 map2
end

type substitution = (module_path * delta_resolver) Umap.t

let empty_subst = Umap.empty

let is_empty_subst = Umap.is_empty

(* <debug> *)

let string_of_hint = function
  | Inline (_,Some _) -> "inline(Some _)"
  | Inline _ -> "inline()"
  | Equiv kn -> string_of_kn kn

let debug_string_of_delta resolve =
  let kn_to_string kn hint l =
    (string_of_kn kn ^ "=>" ^ string_of_hint hint) :: l
  in
  let mp_to_string mp mp' l =
    (string_of_mp mp ^ "=>" ^ string_of_mp mp') :: l
  in
  let l = Deltamap.fold mp_to_string kn_to_string resolve [] in
  String.concat ", " (List.rev l)

let list_contents sub =
  let one_pair (mp,reso) = (string_of_mp mp,debug_string_of_delta reso) in
  let mp_one_pair mp0 p l = (string_of_mp mp0, one_pair p)::l in
  let mbi_one_pair mbi p l = (MBId.debug_to_string mbi, one_pair p)::l in
  Umap.fold mp_one_pair mbi_one_pair sub []

let debug_string_of_subst sub =
  let l = List.map (fun (s1,(s2,s3)) -> s1^"|->"^s2^"["^s3^"]")
    (list_contents sub)
  in
  "{" ^ String.concat "; " l ^ "}"

let debug_pr_delta resolve =
  str (debug_string_of_delta resolve)

let debug_pr_subst sub =
  let l = list_contents sub in
  let f (s1,(s2,s3)) = hov 2 (str s1 ++ spc () ++ str "|-> " ++ str s2 ++
			      spc () ++ str "[" ++ str s3 ++ str "]")
  in
  str "{" ++ hov 2 (prlist_with_sep pr_comma f l) ++ str "}"

(* </debug> *)

(** Extending a [delta_resolver] *)

let add_inline_delta_resolver kn (lev,oc) = Deltamap.add_kn kn (Inline (lev,oc))

let add_kn_delta_resolver kn kn' =
  assert (Label.equal (label kn) (label kn'));
  Deltamap.add_kn kn (Equiv kn')

let add_mp_delta_resolver mp1 mp2 = Deltamap.add_mp mp1 mp2

(** Extending a [substitution] *)

let add_mbid mbid mp resolve s = Umap.add_mbi mbid (mp,resolve) s
let add_mp mp1 mp2 resolve s = Umap.add_mp mp1 (mp2,resolve) s

let map_mbid mbid mp resolve = add_mbid mbid mp resolve empty_subst
let map_mp mp1 mp2 resolve = add_mp mp1 mp2 resolve empty_subst

let mp_in_delta mp = Deltamap.mem_mp mp

let kn_in_delta kn resolver =
  try
    match Deltamap.find_kn kn resolver with
      | Equiv _ -> true
      | Inline _ -> false
  with Not_found -> false

let con_in_delta con resolver = kn_in_delta (Constant.user con) resolver
let mind_in_delta mind resolver = kn_in_delta (MutInd.user mind) resolver

let mp_of_delta resolve mp =
 try Deltamap.find_mp mp resolve with Not_found -> mp

let find_prefix resolve mp =
  let rec sub_mp = function
    | MPdot(mp,l) as mp_sup ->
	(try Deltamap.find_mp mp_sup resolve
	 with Not_found -> MPdot(sub_mp mp,l))
    | p -> Deltamap.find_mp p resolve
  in
  try sub_mp mp with Not_found -> mp

(** Applying a resolver to a kernel name *)

exception Change_equiv_to_inline of (int * constr)

let solve_delta_kn resolve kn =
  try
    match Deltamap.find_kn kn resolve with
      | Equiv kn1 -> kn1
      | Inline (lev, Some c) ->	raise (Change_equiv_to_inline (lev,c))
      | Inline (_, None) -> raise Not_found
  with Not_found ->
    let mp,dir,l = repr_kn kn in
    let new_mp = find_prefix resolve mp in
    if mp == new_mp then
      kn
    else
      make_kn new_mp dir l

let kn_of_delta resolve kn =
  try solve_delta_kn resolve kn
  with Change_equiv_to_inline _ -> kn

(** Try a 1st resolver, and then a 2nd in case it had no effect *)

let kn_of_deltas resolve1 resolve2 kn =
  let kn' = kn_of_delta resolve1 kn in
  if kn' == kn then kn_of_delta resolve2 kn else kn'

let constant_of_delta_kn resolve kn =
  Constant.make kn (kn_of_delta resolve kn)

let constant_of_deltas_kn resolve1 resolve2 kn =
  Constant.make kn (kn_of_deltas resolve1 resolve2 kn)

let mind_of_delta_kn resolve kn =
  MutInd.make kn (kn_of_delta resolve kn)

let mind_of_deltas_kn resolve1 resolve2 kn =
  MutInd.make kn (kn_of_deltas resolve1 resolve2 kn)

let inline_of_delta inline resolver =
  match inline with
    | None -> []
    | Some inl_lev ->
      let extract kn hint l =
	match hint with
	  | Inline (lev,_) -> if lev <= inl_lev then (lev,kn)::l else l
	  | _ -> l
      in
      Deltamap.fold_kn extract resolver []

let search_delta_inline resolve kn1 kn2 =
  let find kn = match Deltamap.find_kn kn resolve with
    | Inline (_,o) -> o
    | Equiv _ -> raise Not_found
  in
  try find kn1
  with Not_found ->
    if kn1 == kn2 then None
    else
      try find kn2
      with Not_found -> None

let subst_mp0 sub mp = (* 's like subst *)
 let rec aux mp =
  match mp with
    | MPfile sid -> Umap.find_mp mp sub
    | MPbound bid ->
	begin
	  try Umap.find_mbi bid sub
	  with Not_found -> Umap.find_mp mp sub
	end
    | MPdot (mp1,l) as mp2 ->
	begin
	  try Umap.find_mp mp2 sub
	  with Not_found ->
	    let mp1',resolve = aux mp1 in
	    MPdot (mp1',l),resolve
	end
 in
 try Some (aux mp) with Not_found -> None

let subst_mp sub mp =
 match subst_mp0 sub mp with
    None -> mp
  | Some (mp',_) -> mp'

let subst_kn_delta sub kn =
 let mp,dir,l = repr_kn kn in
  match subst_mp0 sub mp with
     Some (mp',resolve) ->
      solve_delta_kn resolve (make_kn mp' dir l)
   | None -> kn


let subst_kn sub kn =
 let mp,dir,l = repr_kn kn in
  match subst_mp0 sub mp with
     Some (mp',_) ->
      (make_kn mp' dir l)
   | None -> kn

exception No_subst

let subst_dual_mp sub mp1 mp2 =
  let o1 = subst_mp0 sub mp1 in
  let o2 = if mp1 == mp2 then o1 else subst_mp0 sub mp2 in
  match o1, o2 with
    | None, None -> raise No_subst
    | Some (mp1',resolve), None -> mp1', mp2, resolve, true
    | None, Some (mp2',resolve) -> mp1, mp2', resolve, false
    | Some (mp1',_), Some (mp2',resolve) -> mp1', mp2', resolve, false

let progress f x ~orelse =
  let y = f x in
  if y != x then y else orelse

let subst_ind sub mind =
  let mpu,dir,l = MutInd.repr3 mind in
  let mpc = KerName.modpath (MutInd.canonical mind) in
  try
    let mpu,mpc,resolve,user = subst_dual_mp sub mpu mpc in
    let knu = KerName.make mpu dir l in
    let knc = if mpu == mpc then knu else KerName.make mpc dir l in
    let knc' =
      progress (kn_of_delta resolve) (if user then knu else knc) ~orelse:knc
    in
    MutInd.make knu knc'
  with No_subst -> mind

let subst_con0 sub cst =
  let mpu,dir,l = Constant.repr3 cst in
  let mpc = KerName.modpath (Constant.canonical cst) in
  let mpu,mpc,resolve,user = subst_dual_mp sub mpu mpc in
  let knu = KerName.make mpu dir l in
  let knc = if mpu == mpc then knu else KerName.make mpc dir l in
  match search_delta_inline resolve knu knc with
    | Some t ->
      (* In case of inlining, discard the canonical part (cf #2608) *)
      Constant.make1 knu, t
    | None ->
      let knc' =
        progress (kn_of_delta resolve) (if user then knu else knc) ~orelse:knc
      in
      let cst' = Constant.make knu knc' in
      cst', mkConst cst'

let subst_con sub cst =
  try subst_con0 sub cst
  with No_subst -> cst, mkConst cst

(* Here the semantics is completely unclear.
   What does "Hint Unfold t" means when "t" is a parameter?
   Does the user mean "Unfold X.t" or does she mean "Unfold y"
   where X.t is later on instantiated with y? I choose the first
   interpretation (i.e. an evaluable reference is never expanded). *)
let subst_evaluable_reference subst = function
  | EvalVarRef id -> EvalVarRef id
  | EvalConstRef kn -> EvalConstRef (fst (subst_con subst kn))

let rec map_kn f f' c =
  let func = map_kn f f' in
    match kind_of_term c with
      | Const kn -> (try snd (f' kn) with No_subst -> c)
      | Ind (kn,i) ->
	  let kn' = f kn in
	  if kn'==kn then c else mkInd (kn',i)
      | Construct ((kn,i),j) ->
	  let kn' = f kn in
	  if kn'==kn then c else mkConstruct ((kn',i),j)
      | Case (ci,p,ct,l) ->
	  let ci_ind =
            let (kn,i) = ci.ci_ind in
	    let kn' = f kn in
	    if kn'==kn then ci.ci_ind else kn',i
	  in
	  let p' = func p in
	  let ct' = func ct in
	  let l' = Array.smartmap func l in
	    if (ci.ci_ind==ci_ind && p'==p
		&& l'==l && ct'==ct)then c
	    else
	      mkCase ({ci with ci_ind = ci_ind},
		      p',ct', l')
      | Cast (ct,k,t) ->
	  let ct' = func ct in
	  let t'= func t in
	    if (t'==t && ct'==ct) then c
	    else mkCast (ct', k, t')
      | Prod (na,t,ct) ->
	  let ct' = func ct in
	  let t'= func t in
	    if (t'==t && ct'==ct) then c
	    else mkProd (na, t', ct')
      | Lambda (na,t,ct) ->
	  let ct' = func ct in
	  let t'= func t in
	    if (t'==t && ct'==ct) then c
	    else mkLambda (na, t', ct')
      | LetIn (na,b,t,ct) ->
	  let ct' = func ct in
	  let t'= func t in
	  let b'= func b in
	    if (t'==t && ct'==ct && b==b') then c
	    else mkLetIn (na, b', t', ct')
      | App (ct,l) ->
	  let ct' = func ct in
	  let l' = Array.smartmap func l in
	    if (ct'== ct && l'==l) then c
	    else mkApp (ct',l')
      | Evar (e,l) ->
	  let l' = Array.smartmap func l in
	    if (l'==l) then c
	    else mkEvar (e,l')
      | Fix (ln,(lna,tl,bl)) ->
	  let tl' = Array.smartmap func tl in
	  let bl' = Array.smartmap func bl in
	    if (bl == bl'&& tl == tl') then c
	    else mkFix (ln,(lna,tl',bl'))
      | CoFix(ln,(lna,tl,bl)) ->
	  let tl' = Array.smartmap func tl in
	  let bl' = Array.smartmap func bl in
	    if (bl == bl'&& tl == tl') then c
	    else mkCoFix (ln,(lna,tl',bl'))
      | _ -> c

let subst_mps sub c =
  if is_empty_subst sub then c
  else map_kn (subst_ind sub) (subst_con0 sub) c

let rec replace_mp_in_mp mpfrom mpto mp =
  match mp with
    | _ when mp_eq mp mpfrom -> mpto
    | MPdot (mp1,l) ->
	let mp1' = replace_mp_in_mp mpfrom mpto mp1 in
	  if mp1 == mp1' then mp
	  else MPdot (mp1',l)
    | _ -> mp

let replace_mp_in_kn mpfrom mpto kn =
 let mp,dir,l = repr_kn kn in
  let mp'' = replace_mp_in_mp mpfrom mpto mp in
    if mp==mp'' then kn
    else make_kn mp'' dir l

let rec mp_in_mp mp mp1 =
  match mp1 with
    | _ when mp_eq mp1 mp -> true
    | MPdot (mp2,l) -> mp_in_mp mp mp2
    | _ -> false

let subset_prefixed_by mp resolver =
  let mp_prefix mkey mequ rslv =
    if mp_in_mp mp mkey then Deltamap.add_mp mkey mequ rslv else rslv
  in
  let kn_prefix kn hint rslv =
    match hint with
      | Inline _ -> rslv
      | Equiv _ ->
	if mp_in_mp mp (modpath kn) then Deltamap.add_kn kn hint rslv else rslv
  in
  Deltamap.fold mp_prefix kn_prefix resolver empty_delta_resolver

let subst_dom_delta_resolver subst resolver =
  let mp_apply_subst mkey mequ rslv =
    Deltamap.add_mp (subst_mp subst mkey) mequ rslv
  in
  let kn_apply_subst kkey hint rslv =
    Deltamap.add_kn (subst_kn subst kkey) hint rslv
  in
  Deltamap.fold mp_apply_subst kn_apply_subst resolver empty_delta_resolver

let subst_mp_delta sub mp mkey =
 match subst_mp0 sub mp with
    None -> empty_delta_resolver,mp
  | Some (mp',resolve) ->
      let mp1 = find_prefix resolve mp' in
      let resolve1 = subset_prefixed_by mp1 resolve in
      (subst_dom_delta_resolver
	 (map_mp mp1 mkey empty_delta_resolver) resolve1),mp1

let gen_subst_delta_resolver dom subst resolver =
  let mp_apply_subst mkey mequ rslv =
    let mkey' = if dom then subst_mp subst mkey else mkey in
    let rslv',mequ' = subst_mp_delta subst mequ mkey in
    Deltamap.join rslv' (Deltamap.add_mp mkey' mequ' rslv)
  in
  let kn_apply_subst kkey hint rslv =
    let kkey' = if dom then subst_kn subst kkey else kkey in
    let hint' = match hint with
      | Equiv kequ ->
	  (try Equiv (subst_kn_delta subst kequ)
	   with Change_equiv_to_inline (lev,c) -> Inline (lev,Some c))
      | Inline (lev,Some t) -> Inline (lev,Some (subst_mps subst t))
      | Inline (_,None) -> hint
    in
    Deltamap.add_kn kkey' hint' rslv
  in
  Deltamap.fold mp_apply_subst kn_apply_subst resolver empty_delta_resolver

let subst_codom_delta_resolver = gen_subst_delta_resolver false
let subst_dom_codom_delta_resolver = gen_subst_delta_resolver true

let update_delta_resolver resolver1 resolver2 =
  let mp_apply_rslv mkey mequ rslv =
    if Deltamap.mem_mp mkey resolver2 then rslv
    else Deltamap.add_mp mkey (find_prefix resolver2 mequ) rslv
  in
  let kn_apply_rslv kkey hint rslv =
    if Deltamap.mem_kn kkey resolver2 then rslv
    else
      let hint' = match hint with
	| Equiv kequ ->
	  (try Equiv (solve_delta_kn resolver2 kequ)
	   with Change_equiv_to_inline (lev,c) -> Inline (lev, Some c))
	| _ -> hint
      in
      Deltamap.add_kn kkey hint' rslv
  in
  Deltamap.fold mp_apply_rslv kn_apply_rslv resolver1 empty_delta_resolver

let add_delta_resolver resolver1 resolver2 =
  if resolver1 == resolver2 then
    resolver2
  else if Deltamap.is_empty resolver2 then
    resolver1
  else
    Deltamap.join (update_delta_resolver resolver1 resolver2) resolver2

let substition_prefixed_by k mp subst =
  let mp_prefixmp kmp (mp_to,reso) sub =
    if mp_in_mp mp kmp && not (mp_eq mp kmp) then
      let new_key = replace_mp_in_mp mp k kmp in
      Umap.add_mp new_key (mp_to,reso) sub
    else sub
  in
  let mbi_prefixmp mbi _ sub = sub
  in
  Umap.fold mp_prefixmp mbi_prefixmp subst empty_subst

let join subst1 subst2 =
  let apply_subst mpk add (mp,resolve) res =
    let mp',resolve' =
      match subst_mp0 subst2 mp with
	| None -> mp, None
	| Some (mp',resolve') ->  mp', Some resolve' in
    let resolve'' =
      match resolve' with
        | Some res ->
	    add_delta_resolver
	      (subst_dom_codom_delta_resolver subst2 resolve) res
	| None ->
	    subst_codom_delta_resolver subst2 resolve
    in
    let prefixed_subst = substition_prefixed_by mpk mp' subst2 in
    Umap.join prefixed_subst (add (mp',resolve'') res)
  in
  let mp_apply_subst mp = apply_subst mp (Umap.add_mp mp) in
  let mbi_apply_subst mbi = apply_subst (MPbound mbi) (Umap.add_mbi mbi) in
  let subst = Umap.fold mp_apply_subst mbi_apply_subst subst1 empty_subst in
  Umap.join subst2 subst

let rec occur_in_path mbi = function
  | MPbound bid' -> MBId.equal mbi bid'
  | MPdot (mp1,_) -> occur_in_path mbi mp1
  | _ -> false

let occur_mbid mbi sub =
  let check_one mbi' (mp,_) =
    if MBId.equal mbi mbi' || occur_in_path mbi mp then raise Exit
  in
  try
    Umap.iter_mbi check_one sub;
    false
  with Exit -> true

type 'a lazy_subst =
  | LSval of 'a
  | LSlazy of substitution list * 'a

type 'a substituted = 'a lazy_subst ref

let from_val a = ref (LSval a)

let force fsubst r =
  match !r with
  | LSval a -> a
  | LSlazy(s,a) ->
      let subst = List.fold_left join empty_subst (List.rev s) in
      let a' = fsubst subst a in
      r := LSval a';
      a'

let subst_substituted s r =
  match !r with
    | LSval a -> ref (LSlazy([s],a))
    | LSlazy(s',a) ->
	  ref (LSlazy(s::s',a))

(* debug *)
let repr_substituted r =
  match !r with
    | LSval a -> None, a
    | LSlazy(s,a) -> Some s, a