package coq-core

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

Source file eauto.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
(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq 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 Pp
open CErrors
open Util
open Names
open Constr
open Termops
open EConstr
open Tactics
open Auto
open Genredexpr
open Locus
open Locusops
open Hints
open Proofview.Notations

module NamedDecl = Context.Named.Declaration

let eauto_unif_flags = auto_flags_of_state TransparentState.full

let e_give_exact ?(flags=eauto_unif_flags) c =
  Proofview.Goal.enter begin fun gl ->
  let sigma, t1 = Tacmach.pf_type_of gl c in
  let t2 = Tacmach.pf_concl gl in
  if occur_existential sigma t1 || occur_existential sigma t2 then
    Tacticals.tclTHENLIST
      [Proofview.Unsafe.tclEVARS sigma;
       Clenv.unify ~flags t1;
       exact_no_check c]
  else exact_check c
  end

let e_assumption =
  Proofview.Goal.enter begin fun gl ->
    let hyps = Proofview.Goal.hyps gl in
    let sigma = Proofview.Goal.sigma gl in
    let concl = Tacmach.pf_concl gl in
    if List.is_empty hyps then
      Tacticals.tclZEROMSG (str "No applicable tactic.")
    else
      let not_ground = occur_existential sigma concl in
      let map decl =
        let id = NamedDecl.get_id decl in
        let t = NamedDecl.get_type decl in
        if not_ground || occur_existential sigma t then
          Clenv.unify ~flags:eauto_unif_flags t <*> exact_no_check (mkVar id)
        else
          exact_check (mkVar id)
      in
      Tacticals.tclFIRST (List.map map hyps)
  end

(************************************************************************)
(*   PROLOG tactic                                                      *)
(************************************************************************)

open Auto

(***************************************************************************)
(* A tactic similar to Auto, but using EApply, Assumption and e_give_exact *)
(***************************************************************************)

let unify_e_resolve flags h =
  Hints.hint_res_pf ~with_evars:true ~with_classes:true ~flags h

type cost = {
  cost_priority : int;
  cost_subgoals : int;
}

let hintmap_of env sigma secvars concl =
  (* Warning: for computation sharing, we need to return a closure *)
  let hdc = try Some (decompose_app_bound sigma concl) with Bound -> None in
  match hdc with
  | None -> fun db -> Hint_db.map_none ~secvars db
  | Some hdc ->
     if occur_existential sigma concl then
       (fun db ->
          match Hint_db.map_eauto env sigma ~secvars hdc concl db with
          | ModeMatch (_, l) -> l
          | ModeMismatch -> [])
     else (fun db -> Hint_db.map_auto env sigma ~secvars hdc concl db)
   (* FIXME: should be (Hint_db.map_eauto hdc concl db) *)

let e_exact flags h =
  Proofview.Goal.enter begin fun gl ->
    let env = Proofview.Goal.env gl in
    let sigma = Proofview.Goal.sigma gl in
    let sigma, c = Hints.fresh_hint env sigma h in
    Proofview.Unsafe.tclEVARS sigma <*> e_give_exact c
  end

let rec e_trivial_fail_db db_list local_db =
  let next = Proofview.Goal.enter begin fun gl ->
    let d = NamedDecl.get_id @@ Tacmach.pf_last_hyp gl in
    let local_db = push_resolve_hyp (Tacmach.pf_env gl) (Tacmach.project gl) d local_db in
    e_trivial_fail_db db_list local_db
  end in
  Proofview.Goal.enter begin fun gl ->
  let secvars = compute_secvars gl in
  let tacl =
    e_assumption ::
    (Tacticals.tclTHEN Tactics.intro next) ::
    (e_trivial_resolve (Tacmach.pf_env gl) (Tacmach.project gl) db_list local_db secvars (Tacmach.pf_concl gl))
  in
  Tacticals.tclSOLVE tacl
  end

and e_my_find_search env sigma db_list local_db secvars concl =
  let hint_of_db = hintmap_of env sigma secvars concl in
  let hintl =
      List.map_append (fun db ->
        let flags = auto_flags_of_state (Hint_db.transparent_state db) in
          List.map (fun x -> flags, x) (hint_of_db db)) (local_db::db_list)
  in
  let tac_of_hint =
    fun (st, h) ->
      let priority = match FullHint.repr h with
      | Unfold_nth _ -> 1
      | _ -> FullHint.priority h
      in
      let tac = function
      | Res_pf h -> unify_resolve st h
      | ERes_pf h -> unify_e_resolve st h
      | Give_exact h -> e_exact st h
      | Res_pf_THEN_trivial_fail h ->
        Tacticals.tclTHEN (unify_e_resolve st h)
          (e_trivial_fail_db db_list local_db)
      | Unfold_nth c -> reduce (Unfold [AllOccurrences,c]) onConcl
      | Extern (pat, tacast) -> conclPattern concl pat tacast
      in
      (* We cannot determine statically the cost of subgoals of an Extern hint,
         so approximate it by the hint's priority. *)
      let subgoals = match FullHint.subgoals h with
      | Some subgoals -> subgoals
      | None -> priority
      in
      let b = { cost_priority = priority; cost_subgoals = subgoals } in
      let tac = FullHint.run h tac in
      (tac, b, lazy (FullHint.print env sigma h))
  in
  List.map tac_of_hint hintl

and e_trivial_resolve env sigma db_list local_db secvars gl =
  let filter (tac, pr, _) = if Int.equal pr.cost_priority 0 then Some tac else None in
  try List.map_filter filter (e_my_find_search env sigma db_list local_db secvars gl)
  with Not_found -> []

let e_possible_resolve env sigma db_list local_db secvars gl =
  try e_my_find_search env sigma db_list local_db secvars gl
  with Not_found -> []

type delayed_db = Environ.env -> Evd.evar_map -> hint_db

type search_state = {
  depth : int; (*r depth of search before failing *)
  tacres : (Proofview_monad.goal_with_state * delayed_db) list;
  last_tactic : Pp.t Lazy.t;
  prev : prev_search_state;
}

and prev_search_state = (* for info eauto *)
  | Unknown
  | Init
  | State of search_state

(*s Tactics handling a list of goals. *)

(* first_goal : goal list sigma -> goal sigma *)

module Search = struct

  let is_solved p = Int.equal p.cost_subgoals 0

  let solve_order p1 p2 = match is_solved p1, is_solved p2 with
  | true, true | false, false -> 0
  | false, true -> 1
  | true, false -> -1 (* solved comes first *)

  (* Ordering of states is lexicographic:
     1. tactics known to solve the goal
     2. priority
     3. number of generated goals. *)
  let compare (_, p1, _) (_, p2, _) =
    let d = solve_order p1 p2 in
    let d' = Int.compare p1.cost_priority p2.cost_priority in
    if not (Int.equal d 0) then d
    else if not (Int.equal d' 0) then d'
    else Int.compare p1.cost_subgoals p2.cost_subgoals

  let branching db dblist local_lemmas =
    Proofview.Goal.enter_one begin fun gl ->
    let env = Proofview.Goal.env gl in
    let sigma = Proofview.Goal.sigma gl in
    let concl = Proofview.Goal.concl gl in
    let hyps = EConstr.named_context env in
    let db = db env sigma in
    let secvars = secvars_of_hyps hyps in
    let assumption_tacs =
      let mkdb env sigma = assert false in (* no goal can be generated *)
      let map_assum id = (false, mkdb, e_give_exact (mkVar id), lazy (str "exact" ++ spc () ++ Id.print id)) in
      List.map map_assum (ids_of_named_context hyps)
    in
    let intro_tac =
      let mkdb env sigma =
        push_resolve_hyp env sigma (NamedDecl.get_id (List.hd (EConstr.named_context env))) db
      in
      (false, mkdb, Tactics.intro, lazy (str "intro"))
    in
    let rec_tacs =
      let mkdb env sigma =
        let hyps' = EConstr.named_context env in
          if hyps' == hyps then db
          else make_local_hint_db env sigma ~ts:TransparentState.full true local_lemmas
      in
      let tacs = e_possible_resolve env sigma dblist db secvars concl in
      let tacs = List.sort compare tacs in
      let tacs = List.map (fun (tac, _, pp) -> (true, mkdb, tac, pp)) tacs in
      Proofview.tclUNIT tacs
    in
    rec_tacs >>= fun rec_tacs ->
    Proofview.tclUNIT (assumption_tacs @ intro_tac :: rec_tacs)
    end

  let msg_with_position (p : int list) s = match p with
  | [] -> ()
  | _ :: _ ->
    let pp = hov 0 (str " depth=" ++ int s.depth ++ spc () ++ (Lazy.force s.last_tactic)) in
    let rec pp_rec = function
      | [] -> mt ()
      | [i] -> int i
      | i :: l -> pp_rec l ++ str "." ++ int i
    in
    Feedback.msg_debug (h (pp_rec p) ++ pp)

  let push i p = match p with [] -> [] | _ :: _ -> i :: p

  exception SearchFailure

  let is_failure (e, _) = match e with SearchFailure -> true | _ -> false

  let search ?(debug=false) dblist local_lemmas s =
    let rec explore p s =
      let () = msg_with_position p s in
      if Int.equal s.depth 0 then Proofview.tclZERO SearchFailure
      else match s.tacres with
      | [] -> Proofview.tclUNIT s
      | (gl, db) :: rest ->
        Proofview.tclEVARMAP >>= fun sigma ->
        match Proofview.Unsafe.undefined sigma [gl] with
        | [] -> explore p { s with tacres = rest }
        | gl :: _ ->
          Proofview.Unsafe.tclSETGOALS [gl] <*>
          let ps = if s.prev == Unknown then Unknown else State s in
          branching db dblist local_lemmas >>= fun tacs ->
          let map (isrec, mkdb, tac, pp) =
            Proofview.tclONCE tac >>= fun () ->
            Proofview.Unsafe.tclGETGOALS >>= fun lgls ->
            Proofview.tclEVARMAP >>= fun sigma ->
            let map gl = gl, mkdb in
            let depth =
              if isrec then if List.is_empty lgls then s.depth else pred s.depth
              else s.depth
            in
            let lgls = List.map map lgls in
            Proofview.tclUNIT { depth; tacres = lgls @ rest; last_tactic = pp; prev = ps; }
          in
          let tacs = List.map map tacs in
          explore_many 1 p tacs

    and explore_many i p = function
    | [] -> Proofview.tclZERO SearchFailure
    | tac :: l ->
      Proofview.tclORELSE (tac >>= fun s -> explore (push i p) s)
        (fun e -> explore_many (if is_failure e then succ i else i) p l)
        (* discriminate between search failures and [tac] raising an error *)
    in
    let pos = if debug then [1] else [] in
    explore pos s

end

(** Utilities for debug eauto / info eauto *)

let global_debug_eauto = ref false
let global_info_eauto = ref false

let () =
  Goptions.(declare_bool_option
    { optstage = Summary.Stage.Interp;
      optdepr  = None;
      optkey   = ["Debug";"Eauto"];
      optread  = (fun () -> !global_debug_eauto);
      optwrite = (:=) global_debug_eauto })

let () =
  Goptions.(declare_bool_option
    { optstage = Summary.Stage.Interp;
      optdepr  = None;
      optkey   = ["Info";"Eauto"];
      optread  = (fun () -> !global_info_eauto);
      optwrite = (:=) global_info_eauto })

let mk_eauto_dbg d =
  if d == Debug || !global_debug_eauto then Debug
  else if d == Info || !global_info_eauto then Info
  else Off

let pr_info_nop = function
  | Info -> Feedback.msg_notice (str "idtac.")
  | _ -> ()

let pr_dbg_header = function
  | Off -> ()
  | Debug -> Feedback.msg_notice (str "(* debug eauto: *)")
  | Info  -> Feedback.msg_notice (str "(* info eauto: *)")

let pr_info dbg s =
  if dbg != Info then ()
  else
    let rec loop s =
      match s.prev with
        | Unknown | Init -> s.depth
        | State sp ->
          let mindepth = loop sp in
          let indent = String.make (mindepth - sp.depth) ' ' in
          Feedback.msg_notice (str indent ++ Lazy.force s.last_tactic ++ str ".");
          mindepth
    in
    ignore (loop s)

(** Eauto main code *)

let make_initial_state evk dbg n localdb =
  { depth = n;
    tacres = [evk, localdb];
    last_tactic = lazy (mt());
    prev = if dbg == Info then Init else Unknown;
  }

let e_search_auto ?(debug = Off) ?depth lems db_list =
  Proofview.Goal.enter begin fun gl ->
  let p = Option.default !default_search_depth depth in
  let local_db env sigma = make_local_hint_db env sigma ~ts:TransparentState.full true lems in
  let d = mk_eauto_dbg debug in
  let debug = match d with Debug -> true | Info | Off -> false in
  let tac s = Search.search ~debug db_list lems s in
  let () = pr_dbg_header d in
  Proofview.tclORELSE
    begin
      let evk = Proofview.goal_with_state (Proofview.Goal.goal gl) (Proofview.Goal.state gl) in
      tac (make_initial_state evk d p local_db) >>= fun s ->
      let () = pr_info d s in
      let () = assert (List.is_empty s.tacres) in
      Proofview.Unsafe.tclSETGOALS []
    end
    begin function
    | (Search.SearchFailure, _) ->
      let () = pr_info_nop d in
      Proofview.tclUNIT ()
    | (e, info) -> Proofview.tclZERO ~info e
    end
  end

let eauto_with_bases ?debug ?depth lems db_list =
  Hints.wrap_hint_warning (e_search_auto ?debug ?depth lems db_list)

let gen_eauto ?debug ?depth lems dbs =
  Proofview.wrap_exceptions @@ fun () ->
  let dbs = match dbs with None -> current_pure_db () | Some dbs -> make_db_list dbs in
  eauto_with_bases ?debug ?depth lems dbs

let autounfolds ids csts gl cls =
  let open Tacred in
  let hyps = Tacmach.pf_ids_of_hyps gl in
  let env = Tacmach.pf_env gl in
  let ids = List.filter (fun id -> List.mem id hyps && Tacred.is_evaluable env (EvalVarRef id)) ids in
  let csts = List.filter (fun cst -> Tacred.is_evaluable env (EvalConstRef cst)) csts in
  let flags =
    List.fold_left (fun flags cst -> CClosure.RedFlags.(red_add flags (fCONST cst)))
      (List.fold_left (fun flags id -> CClosure.RedFlags.(red_add flags (fVAR id)))
         (CClosure.RedFlags.red_add_transparent CClosure.all TransparentState.empty) ids) csts
  in reduct_option ~check:false (Reductionops.clos_norm_flags flags, DEFAULTcast) cls

let cons a l = a :: l

exception UnknownDatabase of string

let autounfold db cls =
  if not (Locusops.clause_with_generic_occurrences cls) then
    user_err (str "\"at\" clause not supported.");
  match List.fold_left (fun (ids, csts) dbname ->
    let db = try searchtable_map dbname
      with Not_found -> raise (UnknownDatabase dbname)
    in
    let (db_ids, db_csts) = Hint_db.unfolds db in
    (Id.Set.fold cons db_ids ids, Cset.fold cons db_csts csts)) ([], []) db
  with
  | (ids, csts) -> Proofview.Goal.enter begin fun gl ->
      let cls = concrete_clause_of (fun () -> Tacmach.pf_ids_of_hyps gl) cls in
      let tac = autounfolds ids csts gl in
      Tacticals.tclMAP (function
      | OnHyp (id, _, where) -> tac (Some (id, where))
      | OnConcl _ -> tac None) cls
    end
  | exception UnknownDatabase dbname -> Tacticals.tclZEROMSG (str "Unknown database " ++ str dbname)

let autounfold_tac db cls =
  Proofview.tclUNIT () >>= fun () ->
  let dbs = match db with
  | None -> String.Set.elements (current_db_names ())
  | Some [] -> ["core"]
  | Some l -> l
  in
  autounfold dbs cls

let unfold_head env sigma (ids, csts) c =
  let rec aux c =
    match EConstr.kind sigma c with
    | Var id when Id.Set.mem id ids ->
        (match Environ.named_body id env with
        | Some b -> true, EConstr.of_constr b
        | None -> false, c)
    | Const (cst, u) when Cset.mem cst csts ->
        let u = EInstance.kind sigma u in
        true, EConstr.of_constr (Environ.constant_value_in env (cst, u))
    | App (f, args) ->
        (match aux f with
        | true, f' -> true, Reductionops.whd_betaiota env sigma (mkApp (f', args))
        | false, _ ->
            let done_, args' =
              Array.fold_left_i (fun i (done_, acc) arg ->
                if done_ then done_, arg :: acc
                else match aux arg with
                | true, arg' -> true, arg' :: acc
                | false, arg' -> false, arg :: acc)
                (false, []) args
            in
              if done_ then true, mkApp (f, Array.of_list (List.rev args'))
              else false, c)
    | _ ->
        let done_ = ref false in
        let c' = EConstr.map sigma (fun c ->
          if !done_ then c else
            let x, c' = aux c in
              done_ := x; c') c
        in !done_, c'
  in aux c

let autounfold_one db cl =
  Proofview.Goal.enter begin fun gl ->
  let env = Proofview.Goal.env gl in
  let sigma = Tacmach.project gl in
  let concl = Proofview.Goal.concl gl in
  let st =
    List.fold_left (fun (i,c) dbname ->
      let db = try searchtable_map dbname
        with Not_found -> user_err (str "Unknown database " ++ str dbname ++ str ".")
      in
      let (ids, csts) = Hint_db.unfolds db in
        (Id.Set.union ids i, Cset.union csts c)) (Id.Set.empty, Cset.empty) db
  in
  let did, c' = unfold_head env sigma st
    (match cl with Some (id, _) -> Tacmach.pf_get_hyp_typ id gl | None -> concl)
  in
    if did then
      match cl with
      | Some hyp -> change_in_hyp ~check:true None (make_change_arg c') hyp
      | None -> convert_concl ~cast:false ~check:false c' DEFAULTcast
    else
      let info = Exninfo.reify () in
      Tacticals.tclFAIL ~info (str "Nothing to unfold")
  end