aboutsummaryrefslogtreecommitdiffhomepage
path: root/tactics/hipattern.ml
blob: 15b40b42d15d3bededc88d558c018e31fcd7c36a (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
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
(*   \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 Term
open Termops
open EConstr
open Inductiveops
open Constr_matching
open Coqlib
open Declarations
open Tacmach.New
open Context.Rel.Declaration

module RelDecl = Context.Rel.Declaration

(* I implemented the following functions which test whether a term t
   is an inductive but non-recursive type, a general conjuction, a
   general disjunction, or a type with no constructors.

   They are more general than matching with or_term, and_term, etc,
   since they do not depend on the name of the type. Hence, they
   also work on ad-hoc disjunctions introduced by the user.

  -- Eduardo (6/8/97). *)

type 'a matching_function = Evd.evar_map -> EConstr.constr -> 'a option

type testing_function  = Evd.evar_map -> EConstr.constr -> bool

let mkmeta n = Nameops.make_ident "X" (Some n)
let meta1 = mkmeta 1
let meta2 = mkmeta 2
let meta3 = mkmeta 3

let op2bool = function Some _ -> true | None -> false

let match_with_non_recursive_type sigma t =
  match EConstr.kind sigma t with
    | App _ ->
        let (hdapp,args) = decompose_app sigma t in
        (match EConstr.kind sigma hdapp with
           | Ind (ind,u) ->
               if (Global.lookup_mind (fst ind)).mind_finite == Decl_kinds.CoFinite then
		 Some (hdapp,args)
	       else
		 None
           | _ -> None)
    | _ -> None

let is_non_recursive_type sigma t = op2bool (match_with_non_recursive_type sigma t)

(* Test dependencies *)

(* NB: we consider also the let-in case in the following function,
   since they may appear in types of inductive constructors (see #2629) *)

let rec has_nodep_prod_after n sigma c =
  match EConstr.kind sigma c with
    | Prod (_,_,b) | LetIn (_,_,_,b) ->
	( n>0 || Vars.noccurn sigma 1 b)
	&& (has_nodep_prod_after (n-1) sigma b)
    | _            -> true

let has_nodep_prod sigma c = has_nodep_prod_after 0 sigma c

(* A general conjunctive type is a non-recursive with-no-indices inductive
   type with only one constructor and no dependencies between argument;
   it is strict if it has the form
   "Inductive I A1 ... An := C (_:A1) ... (_:An)" *)

(* style: None = record; Some false = conjunction; Some true = strict conj *)

let is_strict_conjunction = function
| Some true -> true
| _ -> false

let is_lax_conjunction = function
| Some false -> true
| _ -> false

let prod_assum sigma t = fst (decompose_prod_assum sigma t)

let match_with_one_constructor sigma style onlybinary allow_rec t =
  let (hdapp,args) = decompose_app sigma t in
  let res = match EConstr.kind sigma hdapp with
  | Ind ind ->
      let (mib,mip) = Global.lookup_inductive (fst ind) in
      if Int.equal (Array.length mip.mind_consnames) 1
	&& (allow_rec || not (mis_is_recursive (fst ind,mib,mip)))
        && (Int.equal mip.mind_nrealargs 0)
      then
	if is_strict_conjunction style (* strict conjunction *) then
	  let ctx =
	    (prod_assum sigma (snd
	      (decompose_prod_n_assum sigma mib.mind_nparams (EConstr.of_constr mip.mind_nf_lc.(0))))) in
	  if
	    List.for_all
	      (fun decl -> let c = RelDecl.get_type decl in
	                   is_local_assum decl &&
			   isRel sigma c &&
                           Int.equal (destRel sigma c) mib.mind_nparams) ctx
	  then
	    Some (hdapp,args)
	  else None
	else
	  let ctyp = Termops.prod_applist sigma (EConstr.of_constr mip.mind_nf_lc.(0)) args in
	  let cargs = List.map RelDecl.get_type (prod_assum sigma ctyp) in
	  if not (is_lax_conjunction style) || has_nodep_prod sigma ctyp then
	    (* Record or non strict conjunction *)
	    Some (hdapp,List.rev cargs)
	  else
	      None
      else
	None
  | _ -> None in
  match res with
  | Some (hdapp, args) when not onlybinary -> res
  | Some (hdapp, [_; _]) -> res
  | _ -> None

let match_with_conjunction ?(strict=false) ?(onlybinary=false) sigma t =
  match_with_one_constructor sigma (Some strict) onlybinary false t

let match_with_record sigma t =
  match_with_one_constructor sigma None false false t

let is_conjunction ?(strict=false) ?(onlybinary=false) sigma t =
  op2bool (match_with_conjunction sigma ~strict ~onlybinary t)

let is_record sigma t =
  op2bool (match_with_record sigma t)

let match_with_tuple sigma t =
  let t = match_with_one_constructor sigma None false true t in
  Option.map (fun (hd,l) ->
    let ind = destInd sigma hd in
    let ind = on_snd (fun u -> EInstance.kind sigma u) ind in
    let (mib,mip) = Global.lookup_pinductive ind in
    let isrec = mis_is_recursive (fst ind,mib,mip) in
    (hd,l,isrec)) t

let is_tuple sigma t =
  op2bool (match_with_tuple sigma t)

(* A general disjunction type is a non-recursive with-no-indices inductive
   type with of which all constructors have a single argument;
   it is strict if it has the form
   "Inductive I A1 ... An := C1 (_:A1) | ... | Cn : (_:An)" *)

let test_strict_disjunction n lc =
  let open Term in
  Array.for_all_i (fun i c ->
    match (prod_assum (snd (decompose_prod_n_assum n c))) with
    | [LocalAssum (_,c)] -> isRel c && Int.equal (destRel c) (n - i)
    | _ -> false) 0 lc

let match_with_disjunction ?(strict=false) ?(onlybinary=false) sigma t =
  let (hdapp,args) = decompose_app sigma t in
  let res = match EConstr.kind sigma hdapp with
  | Ind (ind,u)  ->
      let car = constructors_nrealargs ind in
      let (mib,mip) = Global.lookup_inductive ind in
      if Array.for_all (fun ar -> Int.equal ar 1) car
	&& not (mis_is_recursive (ind,mib,mip))
        && (Int.equal mip.mind_nrealargs 0)
      then
	if strict then
	  if test_strict_disjunction mib.mind_nparams mip.mind_nf_lc then
	    Some (hdapp,args)
	  else
	    None
	else
	  let cargs =
	    Array.map (fun ar -> pi2 (destProd sigma (prod_applist sigma (EConstr.of_constr ar) args)))
	      mip.mind_nf_lc in
	  Some (hdapp,Array.to_list cargs)
      else
	None
  | _ -> None in
  match res with
  | Some (hdapp,args) when not onlybinary -> res
  | Some (hdapp,[_; _]) -> res
  | _ -> None

let is_disjunction ?(strict=false) ?(onlybinary=false) sigma t =
  op2bool (match_with_disjunction ~strict ~onlybinary sigma t)

(* An empty type is an inductive type, possible with indices, that has no
   constructors *)

let match_with_empty_type sigma t =
  let (hdapp,args) = decompose_app sigma t in
  match EConstr.kind sigma hdapp with
    | Ind (ind, _) ->
        let (mib,mip) = Global.lookup_inductive ind in
        let nconstr = Array.length mip.mind_consnames in
	if Int.equal nconstr 0 then Some hdapp else None
    | _ ->  None

let is_empty_type sigma t = op2bool (match_with_empty_type sigma t)

(* This filters inductive types with one constructor with no arguments;
   Parameters and indices are allowed *)

let match_with_unit_or_eq_type sigma t =
  let (hdapp,args) = decompose_app sigma t in
  match EConstr.kind sigma hdapp with
    | Ind (ind , _) ->
        let (mib,mip) = Global.lookup_inductive ind in
        let constr_types = mip.mind_nf_lc in
        let nconstr = Array.length mip.mind_consnames in
        let zero_args c = Int.equal (nb_prod sigma (EConstr.of_constr c)) mib.mind_nparams in
	if Int.equal nconstr 1 && zero_args constr_types.(0) then
	  Some hdapp
	else
	  None
    | _ -> None

let is_unit_or_eq_type sigma t = op2bool (match_with_unit_or_eq_type sigma t)

(* A unit type is an inductive type with no indices but possibly
   (useless) parameters, and that has no arguments in its unique
   constructor *)

let is_unit_type sigma t =
  match match_with_conjunction sigma t with
  | Some (_,[]) -> true
  | _ -> false

(* Checks if a given term is an application of an
   inductive binary relation R, so that R has only one constructor
   establishing its reflexivity.  *)

type equation_kind =
  | MonomorphicLeibnizEq of constr * constr
  | PolymorphicLeibnizEq of constr * constr * constr
  | HeterogenousEq of constr * constr * constr * constr

exception NoEquationFound

open Glob_term
open Decl_kinds
open Evar_kinds

let mkPattern c = snd (Patternops.pattern_of_glob_constr c)
let mkGApp f args = GApp (Loc.ghost, f, args)
let mkGHole =
  GHole (Loc.ghost, QuestionMark (Define false), Misctypes.IntroAnonymous, None)
let mkGProd id c1 c2 =
  GProd (Loc.ghost, Name (Id.of_string id), Explicit, c1, c2)
let mkGArrow c1 c2 =
  GProd (Loc.ghost, Anonymous, Explicit, c1, c2)
let mkGVar id = GVar (Loc.ghost, Id.of_string id)
let mkGPatVar id = GPatVar(Loc.ghost, (false, Id.of_string id))
let mkGRef r = GRef (Loc.ghost, Lazy.force r, None)
let mkGAppRef r args = mkGApp (mkGRef r) args

(** forall x : _, _ x x *)
let coq_refl_leibniz1_pattern =
  mkPattern (mkGProd "x" mkGHole (mkGApp mkGHole [mkGVar "x"; mkGVar "x";]))

(** forall A:_, forall x:A, _ A x x *)
let coq_refl_leibniz2_pattern =
  mkPattern (mkGProd "A" mkGHole (mkGProd "x" (mkGVar "A")
    (mkGApp mkGHole [mkGVar "A"; mkGVar "x"; mkGVar "x";])))

(** forall A:_, forall x:A, _ A x A x *)
let coq_refl_jm_pattern       =
  mkPattern (mkGProd "A" mkGHole (mkGProd "x" (mkGVar "A")
    (mkGApp mkGHole [mkGVar "A"; mkGVar "x"; mkGVar "A"; mkGVar "x";])))

open Globnames

let is_matching sigma x y = is_matching (Global.env ()) sigma x y
let matches sigma x y = matches (Global.env ()) sigma x y

let match_with_equation sigma t =
  if not (isApp sigma t) then raise NoEquationFound;
  let (hdapp,args) = destApp sigma t in
  match EConstr.kind sigma hdapp with
  | Ind (ind,u) ->
      if eq_gr (IndRef ind) glob_eq then
	Some (build_coq_eq_data()),hdapp,
	PolymorphicLeibnizEq(args.(0),args.(1),args.(2))
      else if eq_gr (IndRef ind) glob_identity then
	Some (build_coq_identity_data()),hdapp,
	PolymorphicLeibnizEq(args.(0),args.(1),args.(2))
      else if eq_gr (IndRef ind) glob_jmeq then
	Some (build_coq_jmeq_data()),hdapp,
	HeterogenousEq(args.(0),args.(1),args.(2),args.(3))
      else
        let (mib,mip) = Global.lookup_inductive ind in
        let constr_types = mip.mind_nf_lc in
        let nconstr = Array.length mip.mind_consnames in
	if Int.equal nconstr 1 then
          if is_matching sigma coq_refl_leibniz1_pattern (EConstr.of_constr constr_types.(0)) then
	    None, hdapp, MonomorphicLeibnizEq(args.(0),args.(1))
	  else if is_matching sigma coq_refl_leibniz2_pattern (EConstr.of_constr constr_types.(0)) then
	    None, hdapp, PolymorphicLeibnizEq(args.(0),args.(1),args.(2))
	  else if is_matching sigma coq_refl_jm_pattern (EConstr.of_constr constr_types.(0)) then
	    None, hdapp, HeterogenousEq(args.(0),args.(1),args.(2),args.(3))
	  else raise NoEquationFound
        else raise NoEquationFound
    | _ -> raise NoEquationFound

(* Note: An "equality type" is any type with a single argument-free
   constructor: it captures eq, eq_dep, JMeq, eq_true, etc. but also
   True/unit which is the degenerate equality type (isomorphic to ()=());
   in particular, True/unit are provable by "reflexivity" *)

let is_inductive_equality ind =
  let (mib,mip) = Global.lookup_inductive ind in
  let nconstr = Array.length mip.mind_consnames in
  Int.equal nconstr 1 && Int.equal (constructor_nrealargs (ind,1)) 0

let match_with_equality_type sigma t =
  let (hdapp,args) = decompose_app sigma t in
  match EConstr.kind sigma hdapp with
  | Ind (ind,_) when is_inductive_equality ind -> Some (hdapp,args)
  | _ -> None

let is_equality_type sigma t = op2bool (match_with_equality_type sigma t)

(* Arrows/Implication/Negation *)

(** X1 -> X2 **)
let coq_arrow_pattern = mkPattern (mkGArrow (mkGPatVar "X1") (mkGPatVar "X2"))

let match_arrow_pattern sigma t =
  let result = matches sigma coq_arrow_pattern t in
  match Id.Map.bindings result with
    | [(m1,arg);(m2,mind)] ->
      assert (Id.equal m1 meta1 && Id.equal m2 meta2); (arg, mind)
    | _ -> anomaly (Pp.str "Incorrect pattern matching")

let match_with_imp_term sigma c =
  match EConstr.kind sigma c with
    | Prod (_,a,b) when Vars.noccurn sigma 1 b -> Some (a,b)
    | _              -> None

let is_imp_term sigma c = op2bool (match_with_imp_term sigma c)

let match_with_nottype sigma t =
  try
    let (arg,mind) = match_arrow_pattern sigma t in
    if is_empty_type sigma mind then Some (mind,arg) else None
  with PatternMatchingFailure -> None

let is_nottype sigma t = op2bool (match_with_nottype sigma t)

(* Forall *)

let match_with_forall_term sigma c=
  match EConstr.kind sigma c with
    | Prod (nam,a,b) -> Some (nam,a,b)
    | _            -> None

let is_forall_term sigma c = op2bool (match_with_forall_term sigma c)

let match_with_nodep_ind sigma t =
  let (hdapp,args) = decompose_app sigma t in
    match EConstr.kind sigma hdapp with
      | Ind (ind, _)  ->
          let (mib,mip) = Global.lookup_inductive ind in
	    if Array.length (mib.mind_packets)>1 then None else
	      let nodep_constr c = has_nodep_prod_after mib.mind_nparams sigma (EConstr.of_constr c) in
		if Array.for_all nodep_constr mip.mind_nf_lc then
		  let params=
		    if Int.equal mip.mind_nrealargs 0 then args else
		      fst (List.chop mib.mind_nparams args) in
		    Some (hdapp,params,mip.mind_nrealargs)
		else
		  None
      | _ -> None

let is_nodep_ind sigma t = op2bool (match_with_nodep_ind sigma t)

let match_with_sigma_type sigma t =
  let (hdapp,args) = decompose_app sigma t in
  match EConstr.kind sigma hdapp with
    | Ind (ind, _) ->
        let (mib,mip) = Global.lookup_inductive ind in
          if Int.equal (Array.length (mib.mind_packets)) 1 &&
	    (Int.equal mip.mind_nrealargs 0) &&
	    (Int.equal (Array.length mip.mind_consnames)1) &&
	    has_nodep_prod_after (mib.mind_nparams+1) sigma (EConstr.of_constr mip.mind_nf_lc.(0)) then
	      (*allowing only 1 existential*)
	      Some (hdapp,args)
	  else
	    None
    | _ -> None

let is_sigma_type sigma t = op2bool (match_with_sigma_type sigma t)

(***** Destructing patterns bound to some theory *)

let rec first_match matcher = function
  | [] -> raise PatternMatchingFailure
  | (pat,check,build_set)::l when check () ->
      (try (build_set (),matcher pat)
       with PatternMatchingFailure -> first_match matcher l)
  | _::l -> first_match matcher l

(*** Equality *)

let match_eq sigma eqn (ref, hetero) =
  let ref =
    try Lazy.force ref
    with e when CErrors.noncritical e -> raise PatternMatchingFailure
  in
  match EConstr.kind sigma eqn with
  | App (c, [|t; x; y|]) ->
    if not hetero && Termops.is_global sigma ref c then PolymorphicLeibnizEq (t, x, y)
    else raise PatternMatchingFailure
  | App (c, [|t; x; t'; x'|]) ->
    if hetero && Termops.is_global sigma ref c then HeterogenousEq (t, x, t', x')
    else raise PatternMatchingFailure
  | _ -> raise PatternMatchingFailure

let no_check () = true
let check_jmeq_loaded () = Library.library_is_loaded Coqlib.jmeq_module

let equalities =
  [(coq_eq_ref, false), no_check, build_coq_eq_data;
   (coq_jmeq_ref, true), check_jmeq_loaded, build_coq_jmeq_data;
   (coq_identity_ref, false), no_check, build_coq_identity_data]

let find_eq_data sigma eqn = (* fails with PatternMatchingFailure *)
  let d,k = first_match (match_eq sigma eqn) equalities in
  let hd,u = destInd sigma (fst (destApp sigma eqn)) in
    d,u,k

let extract_eq_args gl = function
  | MonomorphicLeibnizEq (e1,e2) ->
      let t = pf_unsafe_type_of gl e1 in (t,e1,e2)
  | PolymorphicLeibnizEq (t,e1,e2) -> (t,e1,e2)
  | HeterogenousEq (t1,e1,t2,e2) ->
      if pf_conv_x gl t1 t2 then (t1,e1,e2)
      else raise PatternMatchingFailure

let find_eq_data_decompose gl eqn =
  let (lbeq,u,eq_args) = find_eq_data (project gl) eqn in
  (lbeq,u,extract_eq_args gl eq_args)

let find_this_eq_data_decompose gl eqn =
  let (lbeq,u,eq_args) =
    try (*first_match (match_eq eqn) inversible_equalities*)
      find_eq_data (project gl) eqn
    with PatternMatchingFailure ->
      user_err  (str "No primitive equality found.") in
  let eq_args =
    try extract_eq_args gl eq_args
    with PatternMatchingFailure ->
      error "Don't know what to do with JMeq on arguments not of same type." in
  (lbeq,u,eq_args)

let match_eq_nf gls eqn (ref, hetero) =
  let n = if hetero then 4 else 3 in
  let args = List.init n (fun i -> mkGPatVar ("X" ^ string_of_int (i + 1))) in
  let pat = mkPattern (mkGAppRef ref args) in
  match Id.Map.bindings (pf_matches gls pat eqn) with
    | [(m1,t);(m2,x);(m3,y)] ->
        assert (Id.equal m1 meta1 && Id.equal m2 meta2 && Id.equal m3 meta3);
	(t,pf_whd_all gls x,pf_whd_all gls y)
    | _ -> anomaly ~label:"match_eq" (Pp.str "an eq pattern should match 3 terms")

let dest_nf_eq gls eqn =
  try
    snd (first_match (match_eq_nf gls eqn) equalities)
  with PatternMatchingFailure ->
    error "Not an equality."

(*** Sigma-types *)

let match_sigma sigma ex =
  match EConstr.kind sigma ex with
  | App (f, [| a; p; car; cdr |]) when Termops.is_global sigma (Lazy.force coq_exist_ref) f -> 
      build_sigma (), (snd (destConstruct sigma f), a, p, car, cdr)
  | App (f, [| a; p; car; cdr |]) when Termops.is_global sigma (Lazy.force coq_existT_ref) f -> 
    build_sigma_type (), (snd (destConstruct sigma f), a, p, car, cdr)
  | _ -> raise PatternMatchingFailure
    
let find_sigma_data_decompose ex = (* fails with PatternMatchingFailure *)
  match_sigma ex

(* Pattern "(sig ?1 ?2)" *)
let coq_sig_pattern =
  lazy (mkPattern (mkGAppRef coq_sig_ref [mkGPatVar "X1"; mkGPatVar "X2"]))

let match_sigma sigma t =
  match Id.Map.bindings (matches sigma (Lazy.force coq_sig_pattern) t) with
    | [(_,a); (_,p)] -> (a,p)
    | _ -> anomaly (Pp.str "Unexpected pattern")

let is_matching_sigma sigma t = is_matching sigma (Lazy.force coq_sig_pattern) t

(*** Decidable equalities *)

(* The expected form of the goal for the tactic Decide Equality *)

(* Pattern "{<?1>x=y}+{~(<?1>x=y)}" *)
(* i.e. "(sumbool (eq ?1 x y) ~(eq ?1 x y))" *)

let coq_eqdec ~sum ~rev =
  lazy (
    let eqn = mkGAppRef coq_eq_ref (List.map mkGPatVar ["X1"; "X2"; "X3"]) in
    let args = [eqn; mkGAppRef coq_not_ref [eqn]] in
    let args = if rev then List.rev args else args in
    mkPattern (mkGAppRef sum args)
  )

(** { ?X2 = ?X3 :> ?X1 } + { ~ ?X2 = ?X3 :> ?X1 } *)
let coq_eqdec_inf_pattern = coq_eqdec ~sum:coq_sumbool_ref ~rev:false

(** { ~ ?X2 = ?X3 :> ?X1 } + { ?X2 = ?X3 :> ?X1 } *)
let coq_eqdec_inf_rev_pattern = coq_eqdec ~sum:coq_sumbool_ref ~rev:true

(** %coq_or_ref (?X2 = ?X3 :> ?X1) (~ ?X2 = ?X3 :> ?X1) *)
let coq_eqdec_pattern = coq_eqdec ~sum:coq_or_ref ~rev:false

(** %coq_or_ref (~ ?X2 = ?X3 :> ?X1) (?X2 = ?X3 :> ?X1) *)
let coq_eqdec_rev_pattern = coq_eqdec ~sum:coq_or_ref ~rev:true

let op_or = coq_or_ref
let op_sum = coq_sumbool_ref

let match_eqdec sigma t =
  let eqonleft,op,subst =
    try true,op_sum,matches sigma (Lazy.force coq_eqdec_inf_pattern) t
    with PatternMatchingFailure ->
    try false,op_sum,matches sigma (Lazy.force coq_eqdec_inf_rev_pattern) t
    with PatternMatchingFailure ->
    try true,op_or,matches sigma (Lazy.force coq_eqdec_pattern) t
    with PatternMatchingFailure ->
        false,op_or,matches sigma (Lazy.force coq_eqdec_rev_pattern) t in
  match Id.Map.bindings subst with
  | [(_,typ);(_,c1);(_,c2)] ->
      eqonleft, EConstr.of_constr (Universes.constr_of_global (Lazy.force op)), c1, c2, typ
  | _ -> anomaly (Pp.str "Unexpected pattern")

(* Patterns "~ ?" and "? -> False" *)
let coq_not_pattern = lazy (mkPattern (mkGAppRef coq_not_ref [mkGHole]))
let coq_imp_False_pattern = lazy (mkPattern (mkGArrow mkGHole (mkGRef coq_False_ref)))

let is_matching_not sigma t = is_matching sigma (Lazy.force coq_not_pattern) t
let is_matching_imp_False sigma t = is_matching sigma (Lazy.force coq_imp_False_pattern) t

(* Remark: patterns that have references to the standard library must
   be evaluated lazily (i.e. at the time they are used, not a the time
   coqtop starts) *)