aboutsummaryrefslogtreecommitdiffhomepage
path: root/proofs/logic.ml
blob: 13a4e4ce31a5ad62a976598c80e9a523c8c7d64b (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
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

open Pp
open CErrors
open Util
open Names
open Nameops
open Term
open Constr
open Vars
open Termops
open Environ
open Reductionops
open Inductiveops
open Typing
open Proof_type
open Type_errors
open Retyping
open Misctypes

module NamedDecl = Context.Named.Declaration

type refiner_error =

  (* Errors raised by the refiner *)
  | BadType of constr * constr * constr
  | UnresolvedBindings of Name.t list
  | CannotApply of constr * constr
  | NotWellTyped of constr
  | NonLinearProof of constr
  | MetaInType of EConstr.constr

  (* Errors raised by the tactics *)
  | IntroNeedsProduct
  | DoesNotOccurIn of constr * Id.t
  | NoSuchHyp of Id.t

exception RefinerError of refiner_error

open Pretype_errors

(** FIXME: this is quite brittle. Why not accept any PretypeError? *)
let is_typing_error = function
| UnexpectedType (_, _) | NotProduct _
| VarNotFound _ | TypingError _ -> true
| _ -> false

let is_unification_error = function
| CannotUnify _ | CannotUnifyLocal _| CannotGeneralize _
| NoOccurrenceFound _ | CannotUnifyBindingType _
| ActualTypeNotCoercible _ | UnifOccurCheck _
| CannotFindWellTypedAbstraction _ | WrongAbstractionType _
| UnsolvableImplicit _| AbstractionOverMeta _
| UnsatisfiableConstraints _ -> true
| _ -> false

let catchable_exception = function
  | CErrors.UserError _ | TypeError _
  | RefinerError _ | Indrec.RecursionSchemeError _
  | Nametab.GlobalizationError _
  (* reduction errors *)
  | Tacred.ReductionTacticError _ -> true
  (* unification and typing errors *)
  | PretypeError(_,_, e) -> is_unification_error e || is_typing_error e 
  | _ -> false

let error_no_such_hypothesis id = raise (RefinerError (NoSuchHyp id))

(* Tells if the refiner should check that the submitted rules do not
   produce invalid subgoals *)
let check = ref false
let with_check = Flags.with_option check

(* [apply_to_hyp sign id f] splits [sign] into [tail::[id,_,_]::head] and
   returns [tail::(f head (id,_,_) (rev tail))] *)
let apply_to_hyp check sign id f =
  try apply_to_hyp sign id f
  with Hyp_not_found ->
    if check then error_no_such_hypothesis id
    else sign

let check_typability env sigma c =
  if !check then let _ = unsafe_type_of env sigma (EConstr.of_constr c) in ()

(************************************************************************)
(************************************************************************)
(* Implementation of the structural rules (moving and deleting
   hypotheses around) *)

(* The ClearBody tactic *)

(* Reordering of the context *)

(* faire le minimum d'echanges pour que l'ordre donne soit un *)
(* sous-ordre du resultat. Par exemple, 2 hyps non mentionnee ne sont *)
(* pas echangees. Choix: les hyps mentionnees ne peuvent qu'etre *)
(* reculees par rapport aux autres (faire le contraire!) *)

let mt_q = (Id.Map.empty,[])
let push_val y = function
    (_,[] as q) -> q
  | (m, (x,l)::q) -> (m, (x,Id.Set.add y l)::q)
let push_item x v (m,l) =
  (Id.Map.add x v m, (x,Id.Set.empty)::l)
let mem_q x (m,_) = Id.Map.mem x m
let find_q x (m,q) =
  let v = Id.Map.find x m in
  let m' = Id.Map.remove x m in
  let rec find accs acc = function
      [] -> raise Not_found
    | [(x',l)] ->
        if Id.equal x x' then ((v,Id.Set.union accs l),(m',List.rev acc))
        else raise Not_found
    | (x',l as i)::((x'',l'')::q as itl) ->
        if Id.equal x x' then
          ((v,Id.Set.union accs l),
           (m',List.rev acc@(x'',Id.Set.add x (Id.Set.union l l''))::q))
        else find (Id.Set.union l accs) (i::acc) itl in
  find Id.Set.empty [] q

let occur_vars_in_decl env sigma hyps d =
  if Id.Set.is_empty hyps then false else
    let ohyps = global_vars_set_of_decl env sigma d in
    Id.Set.exists (fun h -> Id.Set.mem h ohyps) hyps

let reorder_context env sigma sign ord =
  let ords = List.fold_right Id.Set.add ord Id.Set.empty in
  if not (Int.equal (List.length ord) (Id.Set.cardinal ords)) then
    user_err Pp.(str "Order list has duplicates");
  let rec step ord expected ctxt_head moved_hyps ctxt_tail =
    match ord with
      | [] -> List.rev ctxt_tail @ ctxt_head
      | top::ord' when mem_q top moved_hyps ->
          let ((d,h),mh) = find_q top moved_hyps in
          if occur_vars_in_decl env sigma h d then
            user_err ~hdr:"reorder_context"
              (str "Cannot move declaration " ++ Id.print top ++ spc() ++
              str "before " ++
              pr_sequence Id.print
                (Id.Set.elements (Id.Set.inter h
                  (global_vars_set_of_decl env sigma d))));
          step ord' expected ctxt_head mh (d::ctxt_tail)
      | _ ->
          (match ctxt_head with
            | [] -> error_no_such_hypothesis (List.hd ord)
            | d :: ctxt ->
                let x = NamedDecl.get_id d in
                if Id.Set.mem x expected then
                  step ord (Id.Set.remove x expected)
                    ctxt (push_item x d moved_hyps) ctxt_tail
                else
                  step ord expected
                    ctxt (push_val x moved_hyps) (d::ctxt_tail)) in
  step ord ords sign mt_q []

let reorder_val_context env sigma sign ord =
  let open EConstr in
  val_of_named_context (reorder_context env sigma (named_context_of_val sign) ord)




let check_decl_position env sigma sign d =
  let open EConstr in
  let x = NamedDecl.get_id d in
  let needed = global_vars_set_of_decl env sigma d in
  let deps = dependency_closure env sigma (named_context_of_val sign) needed in
  if Id.List.mem x deps then
    user_err ~hdr:"Logic.check_decl_position"
      (str "Cannot create self-referring hypothesis " ++ Id.print x);
  x::deps

(* Auxiliary functions for primitive MOVE tactic
 *
 * [move_hyp with_dep toleft (left,(hfrom,typfrom),right) hto] moves
 * hyp [hfrom] at location [hto] which belongs to the hyps on the
 * left side [left] of the full signature if [toleft=true] or to the hyps
 * on the right side [right] if [toleft=false].
 * If [with_dep] then dependent hypotheses are moved accordingly. *)

let move_location_eq m1 m2 = match m1, m2 with
| MoveAfter id1, MoveAfter id2 -> Id.equal id1 id2
| MoveBefore id1, MoveBefore id2 -> Id.equal id1 id2
| MoveLast, MoveLast -> true
| MoveFirst, MoveFirst -> true
| _ -> false

let split_sign hfrom hto l =
  let rec splitrec left toleft = function
    | [] -> error_no_such_hypothesis hfrom
    | d :: right ->
        let hyp = NamedDecl.get_id d in
      	if Id.equal hyp hfrom then
	  (left,right,d, toleft || move_location_eq hto MoveLast)
      	else
          let is_toleft = match hto with
          | MoveAfter h' | MoveBefore h' -> Id.equal hyp h'
          | _ -> false
          in
	  splitrec (d::left) (toleft || is_toleft)
	    right
  in
    splitrec [] false l

let hyp_of_move_location = function
  | MoveAfter id -> id
  | MoveBefore id -> id
  | _ -> assert false

let move_hyp sigma toleft (left,declfrom,right) hto =
  let env = Global.env() in
  let test_dep d d2 =
    if toleft
    then occur_var_in_decl env sigma (NamedDecl.get_id d2) d
    else occur_var_in_decl env sigma (NamedDecl.get_id d) d2
  in
  let rec moverec first middle = function
    | [] ->
	if match hto with MoveFirst | MoveLast -> false | _ -> true then
	  error_no_such_hypothesis (hyp_of_move_location hto);
	List.rev first @ List.rev middle
    | d :: _ as right when move_location_eq hto (MoveBefore (NamedDecl.get_id d)) ->
	List.rev first @ List.rev middle @ right
    | d :: right ->
        let hyp = NamedDecl.get_id d in
	let (first',middle') =
      	  if List.exists (test_dep d) middle then
	    if not (move_location_eq hto (MoveAfter hyp)) then
	      (first, d::middle)
            else
	      user_err ~hdr:"move_hyp" (str "Cannot move " ++ Id.print (NamedDecl.get_id declfrom) ++
	        Miscprint.pr_move_location Id.print hto ++
	        str (if toleft then ": it occurs in the type of " else ": it depends on ")
	        ++ Id.print hyp ++ str ".")
          else
	    (d::first, middle)
	in
      	if move_location_eq hto (MoveAfter hyp) then
	  List.rev first' @ List.rev middle' @ right
      	else
	  moverec first' middle' right
  in
  let open EConstr in
  if toleft then
    let right =
      List.fold_right push_named_context_val right empty_named_context_val in
    List.fold_left (fun sign d -> push_named_context_val d sign)
      right (moverec [] [declfrom] left)
  else
    let right =
      List.fold_right push_named_context_val
	(moverec [] [declfrom] right) empty_named_context_val in
    List.fold_left (fun sign d -> push_named_context_val d sign)
      right left

let move_hyp_in_named_context sigma hfrom hto sign =
  let open EConstr in
  let (left,right,declfrom,toleft) =
    split_sign hfrom hto (named_context_of_val sign) in
  move_hyp sigma toleft (left,declfrom,right) hto

let insert_decl_in_named_context sigma decl hto sign =
  let open EConstr in
  move_hyp sigma false ([],decl,named_context_of_val sign) hto

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


(************************************************************************)
(************************************************************************)
(* Implementation of the logical rules *)

(* Will only be used on terms given to the Refine rule which have meta
variables only in Application and Case *)

let error_unsupported_deep_meta c =
  user_err  (strbrk "Application of lemmas whose beta-iota normal " ++
    strbrk "form contains metavariables deep inside the term is not " ++
    strbrk "supported; try \"refine\" instead.")

let collect_meta_variables c =
  let rec collrec deep acc c = match kind c with
    | Meta mv -> if deep then error_unsupported_deep_meta () else mv::acc
    | Cast(c,_,_) -> collrec deep acc c
    | (App _| Case _) -> Constr.fold (collrec deep) acc c
    | Proj (_, c) -> collrec deep acc c
    | _ -> Constr.fold (collrec true) acc c
  in
  List.rev (collrec false [] c)

let check_meta_variables c =
  if not (List.distinct_f Int.compare (collect_meta_variables c)) then
    raise (RefinerError (NonLinearProof c))

let check_conv_leq_goal env sigma arg ty conclty =
  if !check then
    let evm, b = Reductionops.infer_conv env sigma (EConstr.of_constr ty) (EConstr.of_constr conclty) in
      if b then evm 
      else raise (RefinerError (BadType (arg,ty,conclty)))
  else sigma

exception Stop of EConstr.t list
let meta_free_prefix sigma a =
  try
    let a = Array.map EConstr.of_constr a in
    let _ = Array.fold_left (fun acc a -> 
      if occur_meta sigma a then raise (Stop acc)
      else a :: acc) [] a
    in a
  with Stop acc -> Array.rev_of_list acc

let goal_type_of env sigma c =
  if !check then
    let (sigma,t) = type_of env sigma (EConstr.of_constr c) in
    (sigma, EConstr.Unsafe.to_constr t)
  else (sigma, EConstr.Unsafe.to_constr (Retyping.get_type_of env sigma (EConstr.of_constr c)))

let rec mk_refgoals sigma goal goalacc conclty trm =
  let env = Goal.V82.env sigma goal in
  let hyps = Goal.V82.hyps sigma goal in
  let mk_goal hyps concl =
    Goal.V82.mk_goal sigma hyps concl (Goal.V82.extra sigma goal)
  in
    if (not !check) && not (occur_meta sigma (EConstr.of_constr trm)) then
      let t'ty = Retyping.get_type_of env sigma (EConstr.of_constr trm) in
      let t'ty = EConstr.Unsafe.to_constr t'ty in
      let sigma = check_conv_leq_goal env sigma trm t'ty conclty in
        (goalacc,t'ty,sigma,trm)
    else
      match kind trm with
      | Meta _ ->
	let conclty = nf_betaiota sigma (EConstr.of_constr conclty) in
	  if !check && occur_meta sigma conclty then
	    raise (RefinerError (MetaInType conclty));
	  let (gl,ev,sigma) = mk_goal hyps conclty in
	  let ev = EConstr.Unsafe.to_constr ev in
	  let conclty = EConstr.Unsafe.to_constr conclty in
	  gl::goalacc, conclty, sigma, ev

      | Cast (t,k, ty) ->
	check_typability env sigma ty;
        let sigma = check_conv_leq_goal env sigma trm ty conclty in
	let res = mk_refgoals sigma goal goalacc ty t in
	(** we keep the casts (in particular VMcast and NATIVEcast) except
	    when they are annotating metas *)
	if isMeta t then begin
	  assert (k != VMcast && k != NATIVEcast);
	  res
	end else
	  let (gls,cty,sigma,ans) = res in
          let ans = if ans == t then trm else mkCast(ans,k,ty) in
	  (gls,cty,sigma,ans)

      | App (f,l) ->
	let (acc',hdty,sigma,applicand) =
	  if is_template_polymorphic env sigma (EConstr.of_constr f) then
	    let ty = 
	      (* Template polymorphism of definitions and inductive types *)
	      let firstmeta = Array.findi (fun i x -> occur_meta sigma (EConstr.of_constr x)) l in
	      let args, _ = Option.cata (fun i -> CArray.chop i l) (l, [||]) firstmeta in
	        type_of_global_reference_knowing_parameters env sigma (EConstr.of_constr f) (Array.map EConstr.of_constr args)
	    in
	    let ty = EConstr.Unsafe.to_constr ty in
	      goalacc, ty, sigma, f
	  else
	    mk_hdgoals sigma goal goalacc f
	in
	let ((acc'',conclty',sigma), args) = mk_arggoals sigma goal acc' hdty l in
        let sigma = check_conv_leq_goal env sigma trm conclty' conclty in
        let ans = if applicand == f && args == l then trm else mkApp (applicand, args) in
        (acc'',conclty',sigma, ans)

      | Proj (p,c) ->
	let (acc',cty,sigma,c') = mk_hdgoals sigma goal goalacc c in
	let c = mkProj (p, c') in
	let ty = get_type_of env sigma (EConstr.of_constr c) in
	let ty = EConstr.Unsafe.to_constr ty in
	  (acc',ty,sigma,c)

      | Case (ci,p,c,lf) ->
	let (acc',lbrty,conclty',sigma,p',c') = mk_casegoals sigma goal goalacc p c in
	let sigma = check_conv_leq_goal env sigma trm conclty' conclty in
	let (acc'',sigma, rbranches) =
	  Array.fold_left2
            (fun (lacc,sigma,bacc) ty fi ->
	       let (r,_,s,b') = mk_refgoals sigma goal lacc ty fi in r,s,(b'::bacc))
            (acc',sigma,[]) lbrty lf
	in
        let lf' = Array.rev_of_list rbranches in
        let ans =
          if p' == p && c' == c && Array.equal (==) lf' lf then trm
          else mkCase (ci,p',c',lf')
        in
	(acc'',conclty',sigma, ans)

      | _ ->
	if occur_meta sigma (EConstr.of_constr trm) then
	  anomaly (Pp.str "refiner called with a meta in non app/case subterm.");
	let (sigma, t'ty) = goal_type_of env sigma trm in
	let sigma = check_conv_leq_goal env sigma trm t'ty conclty in
          (goalacc,t'ty,sigma, trm)

(* Same as mkREFGOALS but without knowing the type of the term. Therefore,
 * Metas should be casted. *)

and mk_hdgoals sigma goal goalacc trm =
  let env = Goal.V82.env sigma goal in
  let hyps = Goal.V82.hyps sigma goal in
  let mk_goal hyps concl = 
    Goal.V82.mk_goal sigma hyps concl (Goal.V82.extra sigma goal) in
  match kind trm with
    | Cast (c,_, ty) when isMeta c ->
	check_typability env sigma ty;
	let (gl,ev,sigma) = mk_goal hyps (nf_betaiota sigma (EConstr.of_constr ty)) in
	let ev = EConstr.Unsafe.to_constr ev in
	gl::goalacc,ty,sigma,ev

    | Cast (t,_, ty) ->
	check_typability env sigma ty;
	mk_refgoals sigma goal goalacc ty t

    | App (f,l) ->
	let (acc',hdty,sigma,applicand) =
	  if is_template_polymorphic env sigma (EConstr.of_constr f)
	  then
	    let l' = meta_free_prefix sigma l in
	   (goalacc,EConstr.Unsafe.to_constr (type_of_global_reference_knowing_parameters env sigma (EConstr.of_constr f) l'),sigma,f)
	  else mk_hdgoals sigma goal goalacc f
	in
	let ((acc'',conclty',sigma), args) = mk_arggoals sigma goal acc' hdty l in
        let ans = if applicand == f && args == l then trm else mkApp (applicand, args) in
	(acc'',conclty',sigma, ans)

    | Case (ci,p,c,lf) ->
	let (acc',lbrty,conclty',sigma,p',c') = mk_casegoals sigma goal goalacc p c in
	let (acc'',sigma,rbranches) =
	  Array.fold_left2
            (fun (lacc,sigma,bacc) ty fi ->
	       let (r,_,s,b') = mk_refgoals sigma goal lacc ty fi in r,s,(b'::bacc))
            (acc',sigma,[]) lbrty lf
	in
	let lf' = Array.rev_of_list rbranches in
	let ans =
          if p' == p && c' == c && Array.equal (==) lf' lf then trm
          else mkCase (ci,p',c',lf')
	in
	(acc'',conclty',sigma, ans)

    | Proj (p,c) ->
         let (acc',cty,sigma,c') = mk_hdgoals sigma goal goalacc c in
	 let c = mkProj (p, c') in
         let ty = get_type_of env sigma (EConstr.of_constr c) in
         let ty = EConstr.Unsafe.to_constr ty in
	   (acc',ty,sigma,c)

    | _ ->
	if !check && occur_meta sigma (EConstr.of_constr trm) then
	  anomaly (Pp.str "refine called with a dependent meta.");
        let (sigma, ty) = goal_type_of env sigma trm in
	goalacc, ty, sigma, trm

and mk_arggoals sigma goal goalacc funty allargs =
  let foldmap (goalacc, funty, sigma) harg =
    let t = whd_all (Goal.V82.env sigma goal) sigma (EConstr.of_constr funty) in
    let t = EConstr.Unsafe.to_constr t in
    let rec collapse t = match kind t with
    | LetIn (_, c1, _, b) -> collapse (subst1 c1 b)
    | _ -> t
    in
    let t = collapse t in
    match kind t with
    | Prod (_, c1, b) ->
      let (acc, hargty, sigma, arg) = mk_refgoals sigma goal goalacc c1 harg in
      (acc, subst1 harg b, sigma), arg
    | _ -> raise (RefinerError (CannotApply (t, harg)))
  in
  Array.smartfoldmap foldmap (goalacc, funty, sigma) allargs

and mk_casegoals sigma goal goalacc p c =
  let env = Goal.V82.env sigma goal in
  let (acc',ct,sigma,c') = mk_hdgoals sigma goal goalacc c in
  let ct = EConstr.of_constr ct in
  let (acc'',pt,sigma,p') = mk_hdgoals sigma goal acc' p in
  let ((ind, u), spec) =
    try Tacred.find_hnf_rectype env sigma ct
    with Not_found -> anomaly (Pp.str "mk_casegoals.") in
  let indspec = ((ind, EConstr.EInstance.kind sigma u), spec) in
  let (lbrty,conclty) = type_case_branches_with_names env sigma indspec p c in
  (acc'',lbrty,conclty,sigma,p',c')


let convert_hyp check sign sigma d =
  let id = NamedDecl.get_id d in
  let b = NamedDecl.get_value d in
  let env = Global.env() in
  let reorder = ref [] in
  let sign' =
    apply_to_hyp check sign id
      (fun _ d' _ ->
        let c = Option.map EConstr.of_constr (NamedDecl.get_value d') in
        let env = Global.env_of_context sign in
        if check && not (is_conv env sigma (NamedDecl.get_type d) (EConstr.of_constr (NamedDecl.get_type d'))) then
	  user_err ~hdr:"Logic.convert_hyp"
            (str "Incorrect change of the type of " ++ Id.print id ++ str ".");
        if check && not (Option.equal (is_conv env sigma) b c) then
	  user_err ~hdr:"Logic.convert_hyp"
            (str "Incorrect change of the body of "++ Id.print id ++ str ".");
       if check then reorder := check_decl_position env sigma sign d;
       map_named_decl EConstr.Unsafe.to_constr d) in
  reorder_val_context env sigma sign' !reorder



(************************************************************************)
(************************************************************************)
(* Primitive tactics are handled here *)

let prim_refiner r sigma goal =
  let cl = Goal.V82.concl sigma goal in
  match r with
    (* Logical rules *)
    | Refine c ->
        let cl = EConstr.Unsafe.to_constr cl in
	check_meta_variables c;
	let (sgl,cl',sigma,oterm) = mk_refgoals sigma goal [] cl c in
	let sgl = List.rev sgl in
	let sigma = Goal.V82.partial_solution sigma goal (EConstr.of_constr oterm) in
	  (sgl, sigma)