package rocq-runtime

  1. Overview
  2. Docs
package rocq-runtime
Legend:
Page
Library
Module
Module type
Parameter
Class
Class type
Source

Source file libBinding.ml

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
(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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 Declarations
open Names
open EConstr
open Environ
open Evd
open Context
open Util
open Namegen

module RelDecl = Rel.Declaration
open RelDecl

(* ************************************************************************** *)
(*                                 State                                      *)
(* ************************************************************************** *)

let _dbg = CDebug.create ~name:"API" ()

(* state *)
module State =
struct

  (* Monad *)
  type state =
    { env : env;
      names : Nameops.Fresh.t;
      subst : Esubst.lift;
    }

  type 'a t = state -> evar_map -> evar_map * 'a

  let return c = fun _ sigma -> (sigma, c)
  let bind x f = fun s sigma -> let (sigma, a) = x s sigma in f a s sigma
  let map f t = bind t (fun a -> return @@ f a)
  let run_state s sigma t = t s sigma
  let run env sigma t =
      let s = {
      env = env;
      names = Nameops.Fresh.of_list @@ Termops.ids_of_rel_context @@ rel_context env;
      subst = Esubst.el_id;
    }
  in t s sigma

  (* Notation for the monad *)
  let (let@) x f = x f
  let (let*) x f = bind x f

  (* Access the current state *)
  let get_env = fun s -> return s.env s
  let get_sigma = fun s sigma -> return sigma s sigma
  let get_names = fun s -> return s.names s
  let get_state = fun s -> return s s
  let get_context = fun s -> return (EConstr.of_rel_context @@ Environ.rel_context s.env) s


(** {6 Weaken Functions From the Former Context to the New Context } *)

  let weaken c = fun s -> return (Vars.exliftn s.subst c) s

  let weaken_rel decl =
    fun s sigma -> return (RelDecl.map_constr (fun t -> snd @@ weaken t s sigma) decl) s sigma

  let weaken_context cxt s sigma =
    let nb_cxt = List.length cxt in
    let wcxt = List.mapi (fun i x ->
      let n = nb_cxt - i -1 in
      let weak x = Vars.exliftn (Esubst.el_liftn n s.subst) x in
      match x with
      | LocalAssum (na, ty) -> LocalAssum (na, weak ty)
      | LocalDef (na, bd, ty) -> LocalDef (na, weak bd, weak ty)
      ) cxt
    in
    return wcxt s sigma

(** {6 Access Key } *)

  type access_key = int

  let fresh_key s =
    let (_, ctx) = get_context s Evar_empty in
    List.length ctx

  let make_key i =
    let* ctx = get_context in
    return @@ List.length ctx - i

(** {6 Push Functions } *)

  (* Add variables to the context *)
  let add_names names decl =
    match get_name decl with
    | Anonymous -> names
    | Name id -> Nameops.Fresh.add id names

  let push_old_rel decl s sigma =
  let s' = {
      env = EConstr.push_rel decl s.env ;
      names = add_names s.names decl;
      subst = Esubst.el_lift s.subst;
    } in
  return (s', fresh_key s) s' sigma

  let push_fresh_rel decl s sigma =
    let s' = {
      env = EConstr.push_rel decl s.env ;
      names = add_names s.names decl;
      subst = Esubst.el_shft 1 (Esubst.el_lift s.subst);
    } in
  return (s', fresh_key s) s' sigma


(** {6 Access Functions } *)

  let get_decl key =
    let* ctx = get_context in
    let n' = List.length ctx - key -1 in
    let decl = RelDecl.map_constr (Vars.lift n') (List.nth ctx n') in
    return decl

  let getters f =
    let get_X key =
      let* decl = get_decl key in
      let* cxt = get_context in
      return (f (List.length cxt - key -1) decl) in

    let geti_X keys pos_key = get_X (List.nth keys pos_key) in

    let getij_X keyss pos_k1 pos_k2 = get_X (List.nth (List.nth keyss pos_k1) pos_k2) in

    let get_Xs keys =
      fun s sigma ->
      return (Array.of_list @@ List.map (fun key -> snd @@ get_X key s sigma) keys) s sigma in

    (get_X, geti_X, getij_X, get_Xs)

  let get_sdecl_term =
    fun n d ->
    match RelDecl.get_value d with
    | Some tm -> Vars.lift 1 tm
    | None -> mkRel (1+n)

  let get_term, geti_term, getij_term, get_terms = getters get_sdecl_term

  let get_type, geti_type, getij_type, get_types = getters (fun _ d -> Vars.lift 1 (RelDecl.get_type d))

  let get_aname, geti_aname, getij_aname, get_anames = getters (fun _ cdecl -> RelDecl.get_annot cdecl)

  let index0_opt_i p l =
      let rec aux i l = match l with
      | [] -> None
      | h::_ when p i h -> Some (i, h)
      | _::t -> aux (1+i) t
      in aux 0 l

  let check_key_in k keys =
    let* k = make_key k in
    return @@ Option.map fst @@ index0_opt_i (fun _ key -> k = key) keys

(** {6 Access Functions } *)

  let list_mapi f l =
    let rec aux i l acc s sigma =
      match l with
      | [] -> (sigma, acc)
      | a::l -> let (sigma, t) = (f i a) s sigma in
                aux (i + 1) l (t::acc) s sigma
    in
  let* acc = aux 0 l [] in
  return @@ List.rev acc

  let list_map2i f la lb =
    let rec aux i la lb acc s sigma =
      match la, lb with
      | [], [] -> (sigma, acc)
      | a::la, b::lb -> let (sigma, t) = (f i a b) s sigma in
                aux (i + 1) la lb (t::acc) s sigma
      | _,_ -> assert false
    in
  let* acc = aux 0 la lb [] in
  return @@ List.rev acc

  let array_mapi f ar =
    fun s sigma ->
    let sigma_ref = ref sigma in
    let size_ar = Array.length ar in
    if size_ar = 0 then
      (!sigma_ref, [||])
    else begin
      let update_pos i =
        let (sigma, x) = f i ar.(i) s !sigma_ref in
        sigma_ref := sigma;
        x
      in
      let r = Array.init size_ar update_pos in
      (!sigma_ref, r)
    end

  let array_map2i f ar1 ar2 =
    fun s sigma ->
    let sigma_ref = ref sigma in
    let size_ar = Array.length ar1 in
    if size_ar = 0
    then (!sigma_ref, [||])
    else begin
      let update_pos i =
        let (sigma, x) = f i ar1.(i) ar2.(i) s !sigma_ref in
        sigma_ref := sigma;
        x
      in
      let r = Array.init size_ar update_pos in
      (!sigma_ref, r)
    end

end

open State

(* ************************************************************************** *)
(*                               Naming Schemes                               *)
(* ************************************************************************** *)

let name_hd decl =
  let* env = get_env in
  let* sigma = get_sigma in
  return @@ named_hd env sigma (RelDecl.get_type decl) (RelDecl.get_name decl)

type naming_scheme = rel_declaration -> rel_declaration t

(* Keep naming as is, including Anonymous *)
let naming_id decl = return decl

(* Chooses the next Id available from the binder's name.
  If the binder is Anonymous, a name is generated using the head the binder's type. *)
let naming_hd decl =
  let* name_or_hd = name_hd decl in
  return @@ set_name name_or_hd decl

let naming_hd_dep dep = if dep then naming_hd else naming_id

let naming_hd_fresh decl =
  let* env = get_env in
  let* sigma = get_sigma in
  let* names = get_names in
  let id = id_of_name_using_hdchar env sigma (RelDecl.get_type decl) (RelDecl.get_name decl) in
  let id = Namegen.mangle_id id in
  let id, avoid = Nameops.Fresh.fresh id names in
  return @@ set_name (Name id) decl

let naming_hd_fresh_dep dep = if dep then naming_hd_fresh else naming_id

(* ************************************************************************** *)
(*                            Fold Functions                                  *)
(* ************************************************************************** *)

(* fold functions for state *)
let fold_right_state f l tp t =
  let rec aux ids1 i l =
    match l with
    | [] -> t (List.rev ids1)
    | a :: l -> tp i a (fun id1 -> aux (f id1 ids1) (i+1) l)
  in
  aux [] 0 l

let fold_left_state f l tp t = fold_right_state f (List.rev l) tp t

let fold_right_state_3 f l tp t =
  let rec aux ids1 ids2 ids3 i l =
    match l with
    | [] -> t (List.rev ids1 , List.rev ids2 , List.rev ids3)
    | a :: l -> tp i a (fun (id1 , id2 , id3) -> aux (f id1 ids1) (f id2 ids2) (f id3 ids3) (i+1) l)
  in
  aux [] [] [] 0 l

let fold_left_state_3 f l tp cc =
  fold_right_state_3 f (List.rev l) tp cc


(* ************************************************************************** *)
(*                             Operations                                     *)
(* ************************************************************************** *)

let ind_relevance ind u =
  let* sigma = get_sigma in
  return @@ ERelevance.make @@ Inductive.relevance_of_ind_body ind (EInstance.kind sigma u)

(* Decompose and Manipulate Terms *)
let whd_decompose_prod_decls t =
  let* env = get_env in
  let* sigma = get_sigma in
  return @@ Reductionops.whd_decompose_prod_decls env sigma t

let decompose_lambda_decls t =
  let* sigma = get_sigma in
  return @@ decompose_lambda_decls sigma t

let decompose_app t =
  let* sigma = get_sigma in
  return @@ decompose_app sigma t

let eta_expand_instantiation inst ctxt =
  let* env = get_env in
  let* sigma = get_sigma in
  return @@ Reductionops.eta_expand_instantiation env sigma inst ctxt

let fresh_global ref =
  fun s sigma ->
  let (sigma, t) = fresh_global s.env sigma ref in
  return t s sigma

let fresh_inductive_instance ind =
  fun s sigma ->
  let sigma, ((_, u)) = Evd.fresh_inductive_instance s.env sigma ind in
  return u s sigma

let fresh_sort_ql ?sort_rigid ?name r =
  fun s sigma ->
  let sigma, q, u = Evd.new_sort_info ?sort_rigid ?name r sigma in
  return (q,u) s sigma

let new_univ_level_variable ?name r =
  fun s sigma ->
  let (sigma, l) = Evd.new_univ_level_variable ?name r sigma in
  return l s sigma

(* Typing and Retyping *)
let typing_checked_appvect f xs s sigma =
  let (sigma, t) = Typing.checked_appvect s.env sigma f xs in
  return t s sigma

let typing_check_actual_type jud ty : unit t =
  fun s sigma ->
  let sigma = Typing.check_actual_type s.env sigma jud ty in
  return () s sigma

let retyping_sort_of t =
  let* env = get_env in
  let* sigma = get_sigma in
  return @@ Retyping.get_sort_of env sigma t

let retyping_judgment_of tm =
  let* env = get_env in
  let* sigma = get_sigma in
  return @@ Retyping.get_judgment_of env sigma tm

(* debug *)
let print_term dbg s t =
  let* env = get_env in
  let* sigma = get_sigma in
  return @@ dbg Pp.(fun () -> str s ++ Termops.Internal.print_constr_env env sigma t)

let print_current_context dbg s =
  let* env = get_env in
  let* sigma = get_sigma in
  return @@ dbg Pp.(fun () -> str s ++ Termops.Internal.print_rel_context env sigma)


(* ************************************************************************** *)
(*                            Make Binders                                    *)
(* ************************************************************************** *)

(* Notations to specify functions *)
type freshness = Fresh | Old
type binder = Lambda | Prod

let wrap_binder b =
  match b with
  | Lambda -> mkLambda_or_LetIn
  | Prod -> mkProd_or_LetIn

let wrap_decl map f fresh naming_scheme decl cc s sigma =
  match fresh with
    | Fresh ->
        let (sigma, decl) = naming_scheme decl s sigma in
        let (sigma, (s', k)) = push_fresh_rel decl s sigma in
        let (sigma, v) = cc k s' sigma in
        return (map (f decl) v) s sigma
    | Old ->
        let (sigma, decl) = weaken_rel decl s sigma in
        let (sigma, decl) = naming_scheme decl s sigma in
        let (sigma, (s', k)) = push_old_rel decl s sigma in
        let (sigma, v) = cc k s' sigma in
        return (map (f decl) v) s sigma

let fid f x = f x
let fright f (a,b) = (a, f b)
let fleft f (a,b) = (f a, b)
let fopt = Option.map
let fropt = fun f -> Option.map (fun (a,b) -> (a, f b))

let add_decl a = wrap_decl fid (fun _ x -> x) a

let build_binder m binder = wrap_decl m (wrap_binder binder)
let make_binder m binder naming_scheme na ty = build_binder m binder Fresh naming_scheme (LocalAssum (na, ty))
let keep_binder m binder naming_scheme na ty = build_binder m binder Old naming_scheme (LocalAssum (na, ty))

(* 2. Iterate binders *)

(* seperate var and letin in key_vars / key_letins / key_both *)
let read_context_sep binder cxt =
  fold_left_state_3 List.append cxt (fun _ decl cc ->
    let@ key = binder decl in
    match decl with
    | LocalAssum _ -> cc ([key],[],[key])
    | LocalDef _   -> cc ([],[key],[key])
  )

let read_context_sep_forget binder cxt cc =
  read_context_sep binder cxt (fun (x,_,_) -> cc x)

let add_context fresh naming_scheme = read_context_sep_forget (add_decl fresh naming_scheme)
let add_context_sep fresh naming_scheme = read_context_sep (add_decl fresh naming_scheme)

let closure_context m binder fresh naming_scheme = read_context_sep_forget (build_binder m binder fresh naming_scheme)
let closure_context_sep m binder fresh naming_scheme = read_context_sep (build_binder m binder fresh naming_scheme)

let rebind m binder freshness naming_scheme ty cc =
  (* decompose type, and rebind local variable *)
  let* (locs, hd) =
    match binder with
    | Prod ->  whd_decompose_prod_decls ty
    | Lambda -> decompose_lambda_decls ty
  in
  let@ key_locs = closure_context m binder freshness naming_scheme locs in
  (* rebind the head *)
  let* sort = retyping_sort_of hd in
  let rev_hd = ESorts.relevance_of_sort sort in
  let name_hd = make_annot Anonymous rev_hd in
  let@ key_hd = build_binder m binder freshness naming_scheme @@ LocalAssum (name_hd, hd) in
  (* continuation *)
  cc (key_locs, key_hd)

(* takes a continuation after binder var and letin to add fresh binders and decide what to do with the keys *)
let read_by_decl cxt binder cc_letin cc_var =
  fold_left_state List.append cxt (fun pos_decl decl cc ->
    let@ key = binder decl in
    match decl with
    | LocalDef _   -> cc_letin pos_decl key cc
    | LocalAssum _ -> cc_var   pos_decl key cc
  )

(* ************************************************************************** *)
(*                           Functions on Inductive                           *)
(* ************************************************************************** *)

let get_args mib u (cxt, ty) =
  let nb_params_letin = List.length mib.mind_params_ctxt in
  let (_, args) = List.chop nb_params_letin (List.rev cxt) in
  let args = Vars.subst_instance_context u @@ EConstr.of_rel_context @@ List.rev args in
  let* (hd, xs) = decompose_app (Vars.subst_instance_constr u @@ EConstr.of_constr ty) in
  let indices = Array.sub xs mib.mind_nparams (Array.length xs - mib.mind_nparams) in
  return (args, indices)

let iterate_ctors mib ind u tp cc =
  let* ctors = array_mapi (fun _ -> get_args mib u) ind.mind_nf_lc in
  fold_right_state (fun a l -> a :: l) (Array.to_list ctors) tp cc

let make_ind ((kn, pos_ind), u) key_uparams key_nuparams key_indices =
  let tInd = mkIndU ((kn, pos_ind), u) in
  let* inst_ind = get_terms (key_uparams @ key_nuparams @ key_indices) in
  return @@ mkApp (tInd, inst_ind)

let make_cst ((kn, pos_ind), u) pos_ctor key_uparams key_nuparams args =
  let tCst = mkConstructU (((kn, pos_ind), 1+pos_ctor), u) in
  let* params = get_terms (key_uparams @ key_nuparams) in
  return @@ mkApp (tCst, (Array.concat [params; args]))

(* make fix *)
let make_fix ind_bodies focus fix_rarg fix_name fix_type tmc =
  (* data fix *)
  let rargs = List.mapi fix_rarg ind_bodies in
  let fix_names = List.mapi fix_name ind_bodies in
  let* fix_types = list_mapi fix_type ind_bodies in
  (* update context continuation *)
  let fix_context = List.rev @@ List.map2_i (fun i na ty -> LocalAssum (na, Vars.lift i ty)) 0 fix_names fix_types in
  let@ key_Fix = add_context Fresh naming_id fix_context in
  let* fix_bodies = list_mapi (fun pos_list ind -> tmc (key_Fix, pos_list, ind)) ind_bodies in
  (* result *)
  return @@ EConstr.mkFix ((Array.of_list rargs, focus), (Array.of_list fix_names, Array.of_list fix_types, Array.of_list fix_bodies))

let get_indices indb u =
  let indices, _ = List.chop indb.mind_nrealdecls indb.mind_arity_ctxt in
  weaken_context (Vars.subst_instance_context u (EConstr.of_rel_context indices))

(* make match *)
let make_case_or_projections naming_vars mib ind indb u key_uparams key_nuparams params indices mk_case_pred case_relevance tm_match tc =
  let* env = get_env in
  let* sigma = get_sigma in
  let case_info = Inductiveops.make_case_info env ind RegularStyle in

  let case_invert =
    if Inductiveops.Internal.should_invert_case env sigma (ERelevance.kind sigma case_relevance) case_info
    then Constr.CaseInvert {indices=indices}
    else Constr.NoInvert
  in

  let case_pred =
    (* indices *)
    let* indices = get_indices indb u in
    let@ key_fresh_indices, _ , key_both = add_context_sep Fresh naming_vars indices in
    (* new var *)
    let* inst_ind = get_terms (key_uparams @ key_nuparams @ key_fresh_indices) in
    let ty_var = mkApp (mkIndU (ind, u), inst_ind) in
    let* env = get_env in
    let name_var_match = make_annot Anonymous (Inductiveops.relevance_of_inductive env (ind, u)) in
    let@ key_var_match = add_decl Fresh naming_vars (LocalAssum (name_var_match, ty_var)) in
    (* return type *)
    let* fresh_annot = get_anames (key_both @ [key_var_match]) in
    let* return_type = mk_case_pred key_fresh_indices key_var_match in
    return @@ ((fresh_annot, return_type), case_relevance)
  in

  let branch pos_ctor ctor =
    let* args = get_args mib u ctor in
    let args = fst args in
    let@ key_args, key_letin, key_both = add_context_sep Old naming_vars args in
    let* branches_body = tc (key_args, key_letin, key_both, pos_ctor) in
    let* names_args = get_anames key_both in
    return (names_args, branches_body)
  in

  let* case_info, pred, case_invert, c, branches =
    let* case_pred = case_pred in
    let* branches = array_mapi branch indb.mind_nf_lc in
    let* env = get_env in
    let* sigma = get_sigma in
    return @@ EConstr.expand_case env sigma (case_info, u, params, case_pred, case_invert, tm_match, branches)
  in

  let* env = get_env in
  let* sigma = get_sigma in
  return @@ Inductiveops.simple_make_case_or_project env sigma case_info pred case_invert c branches