helm/ocaml/tactics/discriminationTactics.ml

   1 (* Copyright (C) 2002, HELM Team.
   2  *
   3  * This file is part of HELM, an Hypertextual, Electronic
   4  * Library of Mathematics, developed at the Computer Science
   5  * Department, University of Bologna, Italy.
   6  *
   7  * HELM is free software; you can redistribute it and/or
   8  * modify it under the terms of the GNU General Public License
   9  * as published by the Free Software Foundation; either version 2
  10  * of the License, or (at your option) any later version.
  11  *
  12  * HELM is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15  * GNU General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU General Public License
  18  * along with HELM; if not, write to the Free Software
  19  * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  20  * MA  02111-1307, USA.
  21  *
  22  * For details, see the HELM World-Wide-Web page,
  23  * http://cs.unibo.it/helm/.
  24  *)
  25
  26 open HelmLibraryObjects
  27
  28 let debug_print = fun _ -> ()
  29
  30 let rec injection_tac ~term =
  31  let injection_tac ~term status =
  32   let (proof, goal) = status in
  33   let module C = Cic in
  34   let module U = UriManager in
  35   let module P = PrimitiveTactics in
  36   let module T = Tacticals in
  37   let _,metasenv,_,_ = proof in
  38   let _,context,_ = CicUtil.lookup_meta goal metasenv in
  39   let termty,_ = (* TASSI: FIXME *)
  40     CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
  41     ProofEngineTypes.apply_tactic
  42       (match termty with
  43           (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
  44              when (U.eq equri Logic.eq_URI) -> (
  45            match tty with
  46               (C.MutInd (turi,typeno,exp_named_subst))
  47             | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> (
  48                    match t1,t2 with
  49                       ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
  50                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
  51                          when (uri1 = uri2) && (typeno1 = typeno2) &&
  52                               (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
  53                        (* raise (ProofEngineTypes.Fail "Injection: nothing to do") ; *) T.id_tac
  54                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
  55                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
  56                          when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
  57                        let rec traverse_list i l1 l2 =
  58                          match l1,l2 with
  59                             [],[] -> T.id_tac
  60                           | hd1::tl1,hd2::tl2 ->
  61                              T.then_
  62                               ~start:(injection1_tac ~i ~term)
  63                               ~continuation:(traverse_list (i+1) tl1 tl2)
  64                           | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???") ; T.id_tac
  65                        in traverse_list 1 applist1 applist2
  66                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
  67                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
  68                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
  69                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
  70                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
  71                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
  72                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
  73                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
  74                          when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
  75                        (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality but a discriminable one") ; *) T.id_tac
  76                     | _ -> (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality") ; *) T.id_tac
  77                    )
  78             | _ -> raise (ProofEngineTypes.Fail "Injection: not a projectable equality")
  79            )
  80         | _ -> raise (ProofEngineTypes.Fail "Injection: not an equation")
  81       ) status
  82  in
  83   ProofEngineTypes.mk_tactic (injection_tac ~term)
  84
  85 and injection1_tac ~term ~i =
  86  let injection1_tac ~term ~i status =
  87   let (proof, goal) = status in
  88   (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma differiscono (o potrebbero differire?) nell'i-esimo parametro del costruttore *)
  89    let module C = Cic in
  90    let module S = CicSubstitution in
  91    let module U = UriManager in
  92    let module P = PrimitiveTactics in
  93    let module T = Tacticals in
  94    let _,metasenv,_,_ = proof in
  95    let _,context,_ = CicUtil.lookup_meta goal metasenv in
  96    let termty,_ = (* TASSI: FIXME *)
  97      CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
  98      match termty with (* an equality *)
  99          (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
 100              when (U.eq equri Logic.eq_URI) -> (
 101            match tty with (* some inductive type *)
 102               (C.MutInd (turi,typeno,exp_named_subst))
 103             | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
 104                let t1',t2',consno = (* sono i due sottotermini che differiscono *)
 105                 match t1,t2 with
 106                    ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
 107                     (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
 108                       when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) -> (* controllo ridondante *)
 109                     (List.nth applist1 (i-1)),(List.nth applist2 (i-1)),consno2
 110                  | _ -> assert false
 111                in
 112                 let tty',_ =
 113                   CicTypeChecker.type_of_aux' metasenv context t1'
 114                     CicUniv.empty_ugraph  in
 115                 let pattern =
 116                       match fst(CicEnvironment.get_obj
 117                                   CicUniv.empty_ugraph turi ) with
 118                          C.InductiveDefinition (ind_type_list,_,nr_ind_params_dx,_)  ->
 119                           let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
 120                            let i_constr_id,_ = List.nth constructor_list (consno - 1) in
 121                             List.map
 122                              (function (id,cty) ->
 123                                let reduced_cty = CicReduction.whd context cty in
 124                                 let rec aux t k =
 125                                  match t with
 126                                     C.Prod (_,_,target) when (k <= nr_ind_params_dx) ->
 127                                      aux target (k+1)
 128                                   | C.Prod (binder,source,target) when (k > nr_ind_params_dx) ->
 129                                     let binder' =
 130                                       match binder with
 131                                          C.Name b -> C.Name b
 132                                        | C.Anonymous -> C.Name "y"
 133                                      in
 134                                       C.Lambda (binder',source,(aux target (k+1)))
 135                                   | _ ->
 136                                      let nr_param_constr = k - 1 - nr_ind_params_dx in
 137                                       if (id = i_constr_id)
 138                                        then C.Rel (nr_param_constr - i + 1)
 139                                        else S.lift (nr_param_constr + 1) t1' (* + 1 per liftare anche il lambda agguinto esternamente al case *)
 140                                 in aux reduced_cty 1
 141                              )
 142                              constructor_list
 143                        | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
 144                 in
 145                 ProofEngineTypes.apply_tactic
 146                  (T.thens
 147                   ~start:(P.cut_tac (C.Appl [(C.MutInd (equri,0,[])) ; tty' ; t1' ; t2']))
 148                   ~continuations:[
 149                     T.then_
 150                      ~start:(injection_tac ~term:(C.Rel 1))
 151                      ~continuation:T.id_tac (* !!! qui devo anche fare clear di term tranne al primo passaggio *)
 152                     ;
 153                     T.then_
 154                      ~start:(ProofEngineTypes.mk_tactic
 155                        (fun status ->
 156                          let (proof, goal) = status in
 157                          let _,metasenv,_,_ = proof in
 158                           let _,context,gty = CicUtil.lookup_meta goal metasenv in
 159                            let new_t1' =
 160                             match gty with
 161                                (C.Appl (C.MutInd (_,_,_)::arglist)) ->
 162                                 List.nth arglist 1
 163                              | _ -> raise (ProofEngineTypes.Fail "Injection: goal after cut is not correct")
 164                            in
 165                             ProofEngineTypes.apply_tactic
 166                             (P.change_tac
 167                                ~pattern:(ProofEngineTypes.conclusion_pattern (Some new_t1'))
 168                                (C.Appl [
 169                                  C.Lambda (
 170                                   C.Name "x", tty,
 171                                   C.MutCase (
 172                                    turi, typeno,
 173                                    (C.Lambda (
 174                                     (C.Name "x"),
 175                                     (S.lift 1 tty),
 176                                     (S.lift 2 tty'))),
 177                                    (C.Rel 1), pattern
 178                                   )
 179                                  );
 180                                  t1]
 181                                ))
 182                         status
 183                        ))
 184                      ~continuation:
 185                        (T.then_
 186                          ~start:
 187                            (EqualityTactics.rewrite_simpl_tac
 188                              ~direction:`LeftToRight
 189                              ~pattern:(ProofEngineTypes.conclusion_pattern None)
 190                              term)
 191                          ~continuation:EqualityTactics.reflexivity_tac
 192                        )
 193                    ])
 194                   status
 195             | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 196            )
 197         | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
 198  in
 199   ProofEngineTypes.mk_tactic (injection1_tac ~term ~i)
 200 ;;
 201
 202
 203
 204 exception TwoDifferentSubtermsFound of int
 205
 206 (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
 207 diversi *)
 208
 209 let discriminate'_tac ~term =
 210  let discriminate'_tac ~term status =
 211   let (proof, goal) = status in
 212   let module C = Cic in
 213   let module U = UriManager in
 214   let module P = PrimitiveTactics in
 215   let module T = Tacticals in
 216   let _,metasenv,_,_ = proof in
 217   let _,context,_ = CicUtil.lookup_meta goal metasenv in
 218   let termty,_ =
 219     CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
 220       match termty with
 221          (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
 222           when (U.eq equri Logic.eq_URI) -> (
 223            match tty with
 224               (C.MutInd (turi,typeno,exp_named_subst))
 225             | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
 226
 227                 let consno2 = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
 228                  try
 229                   let rec traverse t1 t2 =
 230                    match t1,t2 with
 231                       ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 232                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 233                          when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
 234                        0
 235                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
 236                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
 237                          when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
 238                        let rec traverse_list l1 l2 =
 239                          match l1,l2 with
 240                             [],[] -> 0
 241                           | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2
 242                           | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")
 243                        in traverse_list applist1 applist2
 244
 245                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 246                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 247                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 248                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
 249                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
 250                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 251                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
 252                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
 253                          when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
 254                        raise (TwoDifferentSubtermsFound consno2)
 255                     | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 256                   in traverse t1 t2
 257                  with (TwoDifferentSubtermsFound consno2) -> consno2
 258                 in
 259                  if consno2 = 0
 260                   then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
 261                   else
 262
 263                    let pattern =
 264                      (* a list of "True" except for the element in position consno2 which is "False" *)
 265                      match fst(CicEnvironment.get_obj
 266                                  CicUniv.empty_ugraph turi) with
 267                         C.InductiveDefinition (ind_type_list,_,nr_ind_params,_)  ->
 268                          let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
 269                           let false_constr_id,_ = List.nth constructor_list (consno2 - 1) in
 270                            List.map
 271                             (function (id,cty) ->
 272                               let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
 273                                let rec aux t k =
 274                                 match t with
 275                                    C.Prod (_,_,target) when (k <= nr_ind_params) ->
 276                                     aux target (k+1)
 277                                  | C.Prod (binder,source,target) when (k > nr_ind_params) ->
 278                                     C.Lambda (binder,source,(aux target (k+1)))
 279                                  | _ ->
 280                                     if (id = false_constr_id)
 281                                      then (C.MutInd(Logic.false_URI,0,[]))
 282                                      else (C.MutInd(Logic.true_URI,0,[]))
 283                                in aux red_ty 1
 284                             )
 285                             constructor_list
 286                       | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
 287                    in
 288
 289                     let (proof',goals') =
 290                      ProofEngineTypes.apply_tactic
 291                       (EliminationTactics.elim_type_tac
 292                        ~term:(C.MutInd(Logic.false_URI,0,[])))
 293                       status
 294                     in
 295                      (match goals' with
 296                          [goal'] ->
 297                           let _,metasenv',_,_ = proof' in
 298                            let _,context',gty' =
 299                              CicUtil.lookup_meta goal' metasenv'
 300                            in
 301                             ProofEngineTypes.apply_tactic
 302                             (T.then_
 303                              ~start:
 304                               (P.change_tac
 305                                ~pattern:(ProofEngineTypes.conclusion_pattern (Some gty'))
 306                                (C.Appl [
 307                                  C.Lambda (
 308                                   C.Name "x", tty,
 309                                   C.MutCase (
 310                                    turi, typeno,
 311                                    (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
 312                                    (C.Rel 1), pattern
 313                                   )
 314                                  );
 315                                  t2]
 316                                )
 317                               )
 318                              ~continuation:
 319                               (
 320                                  T.then_
 321                                    ~start:
 322                                      (EqualityTactics.rewrite_simpl_tac
 323                                        ~direction:`RightToLeft
 324                                        ~pattern:(ProofEngineTypes.conclusion_pattern None)
 325                                        term)
 326                                    ~continuation:(IntroductionTactics.constructor_tac ~n:1)
 327                               ))
 328                              (proof',goal')
 329                        | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
 330                      )
 331             | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 332            )
 333        | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
 334  in
 335   ProofEngineTypes.mk_tactic (discriminate'_tac ~term)
 336 ;;
 337
 338 let discriminate_tac ~term =
 339  let discriminate_tac ~term status =
 340   ProofEngineTypes.apply_tactic
 341   (Tacticals.then_
 342     ~start:(* (injection_tac ~term) *) Tacticals.id_tac
 343     ~continuation:(discriminate'_tac ~term)) (* NOOO!!! non term ma una (qualunque) delle nuove hyp introdotte da inject *)
 344    status
 345  in
 346   ProofEngineTypes.mk_tactic (discriminate_tac ~term)
 347 ;;
 348
 349
 350
 351 let decide_equality_tac =
 352 (* il goal e' un termine della forma t1=t2\/~t1=t2; la tattica decide se l'uguaglianza
 353 e' vera o no e lo risolve *)
 354   Tacticals.id_tac
 355 ;;
 356
 357
 358
 359 let compare_tac ~term = Tacticals.id_tac
 360  (*
 361 (* term is in the form t1=t2; the tactic leaves two goals: in the first you have to          *)
 362 (* demonstrate the goal with the additional hyp that t1=t2, in the second the hyp is ~t1=t2  *)
 363   let module C = Cic in
 364   let module U = UriManager in
 365   let module P = PrimitiveTactics in
 366   let module T = Tacticals in
 367    let _,metasenv,_,_ = proof in
 368     let _,context,gty = CicUtil.lookup_meta goal metasenv in
 369      let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
 370       match termty with
 371          (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
 372
 373           let term' = (* (t1=t2)\/~(t1=t2) *)
 374            C.Appl [
 375             (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ;
 376             term ;
 377             C.Appl [
 378              (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"), 1, [])) ;
 379              t1 ;
 380              C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
 381             ]
 382            ]
 383           in
 384             T.thens
 385                ~start:(P.cut_tac ~term:term')
 386                ~continuations:[
 387                  T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
 388                  decide_equality_tac]
 389                status
 390       | (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
 391           let term' = (* (t1=t2) \/ ~(t1=t2) *)
 392            C.Appl [
 393             (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ;
 394             term ;
 395             C.Appl [
 396              (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind"), 1, [])) ;
 397              t1 ;
 398              C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
 399             ]
 400            ]
 401           in
 402             T.thens
 403                ~start:(P.cut_tac ~term:term')
 404                ~continuations:[
 405                  T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
 406                  decide_equality_tac]
 407                status
 408       | _ -> raise (ProofEngineTypes.Fail "Compare: Not an equality")
 409 *)
 410 ;;
 411
 412
 413
 414 (* DISCRIMINTATE SENZA INJECTION
 415
 416 exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int)
 417
 418 let discriminate_tac ~term status =
 419   let module C = Cic in
 420   let module U = UriManager in
 421   let module P = PrimitiveTactics in
 422   let module T = Tacticals in
 423   let (proof, goal) = status in
 424    let _,metasenv,_,_ = proof in
 425     let _,context,_ = CicUtil.lookup_meta goal metasenv in
 426      let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
 427       match termty with
 428          (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
 429           when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"))
 430             or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> (
 431            match tty with
 432               (C.MutInd (turi,typeno,exp_named_subst))
 433             | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
 434
 435                 let (t1',t2',consno2') = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
 436                  try
 437                   let rec traverse t1 t2 =
 438 debug_print ("XXXX t1 " ^ CicPp.ppterm t1) ;
 439 debug_print ("XXXX t2 " ^ CicPp.ppterm t2) ;
 440                    match t1,t2 with
 441                       ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 442                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 443                          when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
 444                        t1,t2,0
 445                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
 446                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
 447                          when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
 448                        let rec traverse_list l1 l2 =
 449                          match l1,l2 with
 450                             [],[] -> t1,t2,0
 451                           | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2
 452                           | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")
 453                        in traverse_list applist1 applist2
 454
 455                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 456                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 457                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 458                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
 459                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
 460                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 461                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
 462                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
 463                          when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
 464                        raise (TwoDifferentSubtermsFound (t1,t2,consno2))
 465                     | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 466                   in traverse t1 t2
 467                  with (TwoDifferentSubtermsFound (t1,t2,consno2)) -> (t1,t2,consno2)
 468                 in
 469 debug_print ("XXXX consno2' " ^ (string_of_int consno2')) ;
 470                  if consno2' = 0
 471                   then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
 472                   else
 473
 474                    let pattern =
 475                      (* a list of "True" except for the element in position consno2' which is "False" *)
 476                      match fst(CicEnvironment.get_obj turi
 477                                  CicUniv.empty_ugraph) with
 478                         C.InductiveDefinition (ind_type_list,_,nr_ind_params)  ->
 479 debug_print ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno)) ;
 480                          let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
 481 debug_print ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2')) ;
 482                           let false_constr_id,_ = List.nth constructor_list (consno2' - 1) in
 483 debug_print ("XXXX nth funzionano ") ;
 484                            List.map
 485                             (function (id,cty) ->
 486                               let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
 487                                let rec aux t k =
 488                                 match t with
 489                                    C.Prod (_,_,target) when (k <= nr_ind_params) ->
 490                                     aux target (k+1)
 491                                  | C.Prod (binder,source,target) when (k > nr_ind_params) ->
 492                                     C.Lambda (binder,source,(aux target (k+1)))
 493                                  | _ ->
 494                                     if (id = false_constr_id)
 495                                      then (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [])
 496                                      else (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/True.ind") 0 [])
 497                                in aux red_ty 1
 498                             )
 499                             constructor_list
 500                       | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
 501                    in
 502
 503                     let (proof',goals') =
 504                      EliminationTactics.elim_type_tac
 505                       ~term:(C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] )
 506                       status
 507                     in
 508                      (match goals' with
 509                          [goal'] ->
 510                           let _,metasenv',_,_ = proof' in
 511                            let _,context',gty' =
 512                              CicUtil.lookup_meta goal' metasenv'
 513                            in
 514                             T.then_
 515                              ~start:
 516                               (P.change_tac
 517                                ~what:gty'
 518                                ~with_what:
 519                                 (C.Appl [
 520                                   C.Lambda (
 521                                    C.Name "x", tty,
 522                                    C.MutCase (
 523                                     turi, typeno,
 524                                     (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
 525                                     (C.Rel 1), pattern
 526                                    )
 527                                   );
 528                                   t2']
 529                                 )
 530                               )
 531                              ~continuation:
 532                               (
 533 debug_print ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])));
 534 debug_print ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])) ;
 535 debug_print ("XXXX equri: " ^ U.string_of_uri equri) ;
 536 debug_print ("XXXX tty : " ^ CicPp.ppterm tty) ;
 537 debug_print ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ;
 538 debug_print ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
 539 if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> tty then debug_print ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ;
 540 if (CicTypeChecker.type_of_aux' metasenv' context' t2') <> tty then debug_print ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
 541 if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> (CicTypeChecker.type_of_aux' metasenv' context' t2')
 542  then debug_print ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux'
 543  metasenv' context' t1')) ; debug_print ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
 544
 545                                let termty' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t1 ~with_what:t1' ~where:termty in
 546                                 let termty'' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t2 ~with_what:t2' ~where:termty' in
 547
 548 debug_print ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term));
 549                                  T.then_
 550                                    ~start:(EqualityTactics.rewrite_back_simpl_tac ~term:term)
 551                                    ~continuation:(IntroductionTactics.constructor_tac ~n:1)
 552                               )
 553                              (proof',goal')
 554                        | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
 555                      )
 556             | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 557            )
 558        | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
 559 ;;
 560
 561 *)
 562
 563
 564