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                                ~what:new_t1'
 168                                ~pattern:([],None)
 169                                ~with_what:
 170                                  (C.Appl [
 171                                    C.Lambda (
 172                                     C.Name "x", tty,
 173                                     C.MutCase (
 174                                      turi, typeno,
 175                                      (C.Lambda (
 176                                       (C.Name "x"),
 177                                       (S.lift 1 tty),
 178                                       (S.lift 2 tty'))),
 179                                      (C.Rel 1), pattern
 180                                     )
 181                                    );
 182                                    t1]
 183                                  ))
 184                         status
 185                        ))
 186                      ~continuation:
 187                        (T.then_
 188                          ~start:(EqualityTactics.rewrite_simpl_tac ~term ())
 189                          ~continuation:EqualityTactics.reflexivity_tac
 190                        )
 191                    ])
 192                   status
 193             | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 194            )
 195         | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
 196  in
 197   ProofEngineTypes.mk_tactic (injection1_tac ~term ~i)
 198 ;;
 199
 200
 201
 202 exception TwoDifferentSubtermsFound of int
 203
 204 (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
 205 diversi *)
 206
 207 let discriminate'_tac ~term =
 208  let discriminate'_tac ~term status =
 209   let (proof, goal) = status in
 210   let module C = Cic in
 211   let module U = UriManager in
 212   let module P = PrimitiveTactics in
 213   let module T = Tacticals in
 214   let _,metasenv,_,_ = proof in
 215   let _,context,_ = CicUtil.lookup_meta goal metasenv in
 216   let termty,_ =
 217     CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
 218       match termty with
 219          (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
 220           when (U.eq equri Logic.eq_URI) -> (
 221            match tty with
 222               (C.MutInd (turi,typeno,exp_named_subst))
 223             | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
 224
 225                 let consno2 = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
 226                  try
 227                   let rec traverse t1 t2 =
 228                    match t1,t2 with
 229                       ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 230                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 231                          when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
 232                        0
 233                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
 234                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
 235                          when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
 236                        let rec traverse_list l1 l2 =
 237                          match l1,l2 with
 238                             [],[] -> 0
 239                           | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2
 240                           | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")
 241                        in traverse_list applist1 applist2
 242
 243                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 244                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 245                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 246                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
 247                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
 248                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 249                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
 250                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
 251                          when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
 252                        raise (TwoDifferentSubtermsFound consno2)
 253                     | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 254                   in traverse t1 t2
 255                  with (TwoDifferentSubtermsFound consno2) -> consno2
 256                 in
 257                  if consno2 = 0
 258                   then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
 259                   else
 260
 261                    let pattern =
 262                      (* a list of "True" except for the element in position consno2 which is "False" *)
 263                      match fst(CicEnvironment.get_obj
 264                                  CicUniv.empty_ugraph turi) with
 265                         C.InductiveDefinition (ind_type_list,_,nr_ind_params,_)  ->
 266                          let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
 267                           let false_constr_id,_ = List.nth constructor_list (consno2 - 1) in
 268                            List.map
 269                             (function (id,cty) ->
 270                               let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
 271                                let rec aux t k =
 272                                 match t with
 273                                    C.Prod (_,_,target) when (k <= nr_ind_params) ->
 274                                     aux target (k+1)
 275                                  | C.Prod (binder,source,target) when (k > nr_ind_params) ->
 276                                     C.Lambda (binder,source,(aux target (k+1)))
 277                                  | _ ->
 278                                     if (id = false_constr_id)
 279                                      then (C.MutInd(Logic.false_URI,0,[]))
 280                                      else (C.MutInd(Logic.true_URI,0,[]))
 281                                in aux red_ty 1
 282                             )
 283                             constructor_list
 284                       | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
 285                    in
 286
 287                     let (proof',goals') =
 288                      ProofEngineTypes.apply_tactic
 289                       (EliminationTactics.elim_type_tac
 290                        ~term:(C.MutInd(Logic.false_URI,0,[])))
 291                       status
 292                     in
 293                      (match goals' with
 294                          [goal'] ->
 295                           let _,metasenv',_,_ = proof' in
 296                            let _,context',gty' =
 297                              CicUtil.lookup_meta goal' metasenv'
 298                            in
 299                             ProofEngineTypes.apply_tactic
 300                             (T.then_
 301                              ~start:
 302                               (P.change_tac
 303                                ~what:gty'
 304                                ~pattern:([],None)
 305                                ~with_what:
 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:(EqualityTactics.rewrite_back_simpl_tac
 322                                    ~term ())
 323                                    ~continuation:(IntroductionTactics.constructor_tac ~n:1)
 324                               ))
 325                              (proof',goal')
 326                        | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
 327                      )
 328             | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 329            )
 330        | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
 331  in
 332   ProofEngineTypes.mk_tactic (discriminate'_tac ~term)
 333 ;;
 334
 335 let discriminate_tac ~term =
 336  let discriminate_tac ~term status =
 337   ProofEngineTypes.apply_tactic
 338   (Tacticals.then_
 339     ~start:(* (injection_tac ~term) *) Tacticals.id_tac
 340     ~continuation:(discriminate'_tac ~term)) (* NOOO!!! non term ma una (qualunque) delle nuove hyp introdotte da inject *)
 341    status
 342  in
 343   ProofEngineTypes.mk_tactic (discriminate_tac ~term)
 344 ;;
 345
 346
 347
 348 let decide_equality_tac =
 349 (* il goal e' un termine della forma t1=t2\/~t1=t2; la tattica decide se l'uguaglianza
 350 e' vera o no e lo risolve *)
 351   Tacticals.id_tac
 352 ;;
 353
 354
 355
 356 let compare_tac ~term = Tacticals.id_tac
 357  (*
 358 (* term is in the form t1=t2; the tactic leaves two goals: in the first you have to          *)
 359 (* demonstrate the goal with the additional hyp that t1=t2, in the second the hyp is ~t1=t2  *)
 360   let module C = Cic in
 361   let module U = UriManager in
 362   let module P = PrimitiveTactics in
 363   let module T = Tacticals in
 364    let _,metasenv,_,_ = proof in
 365     let _,context,gty = CicUtil.lookup_meta goal metasenv in
 366      let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
 367       match termty with
 368          (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
 369
 370           let term' = (* (t1=t2)\/~(t1=t2) *)
 371            C.Appl [
 372             (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ;
 373             term ;
 374             C.Appl [
 375              (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"), 1, [])) ;
 376              t1 ;
 377              C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
 378             ]
 379            ]
 380           in
 381             T.thens
 382                ~start:(P.cut_tac ~term:term')
 383                ~continuations:[
 384                  T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
 385                  decide_equality_tac]
 386                status
 387       | (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
 388           let term' = (* (t1=t2) \/ ~(t1=t2) *)
 389            C.Appl [
 390             (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ;
 391             term ;
 392             C.Appl [
 393              (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind"), 1, [])) ;
 394              t1 ;
 395              C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
 396             ]
 397            ]
 398           in
 399             T.thens
 400                ~start:(P.cut_tac ~term:term')
 401                ~continuations:[
 402                  T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
 403                  decide_equality_tac]
 404                status
 405       | _ -> raise (ProofEngineTypes.Fail "Compare: Not an equality")
 406 *)
 407 ;;
 408
 409
 410
 411 (* DISCRIMINTATE SENZA INJECTION
 412
 413 exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int)
 414
 415 let discriminate_tac ~term status =
 416   let module C = Cic in
 417   let module U = UriManager in
 418   let module P = PrimitiveTactics in
 419   let module T = Tacticals in
 420   let (proof, goal) = status in
 421    let _,metasenv,_,_ = proof in
 422     let _,context,_ = CicUtil.lookup_meta goal metasenv in
 423      let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
 424       match termty with
 425          (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
 426           when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"))
 427             or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> (
 428            match tty with
 429               (C.MutInd (turi,typeno,exp_named_subst))
 430             | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
 431
 432                 let (t1',t2',consno2') = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
 433                  try
 434                   let rec traverse t1 t2 =
 435 debug_print ("XXXX t1 " ^ CicPp.ppterm t1) ;
 436 debug_print ("XXXX t2 " ^ CicPp.ppterm t2) ;
 437                    match t1,t2 with
 438                       ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 439                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 440                          when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
 441                        t1,t2,0
 442                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
 443                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
 444                          when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
 445                        let rec traverse_list l1 l2 =
 446                          match l1,l2 with
 447                             [],[] -> t1,t2,0
 448                           | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2
 449                           | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")
 450                        in traverse_list applist1 applist2
 451
 452                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 453                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 454                     | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
 455                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
 456                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
 457                        (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
 458                     | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
 459                        (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
 460                          when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
 461                        raise (TwoDifferentSubtermsFound (t1,t2,consno2))
 462                     | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 463                   in traverse t1 t2
 464                  with (TwoDifferentSubtermsFound (t1,t2,consno2)) -> (t1,t2,consno2)
 465                 in
 466 debug_print ("XXXX consno2' " ^ (string_of_int consno2')) ;
 467                  if consno2' = 0
 468                   then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
 469                   else
 470
 471                    let pattern =
 472                      (* a list of "True" except for the element in position consno2' which is "False" *)
 473                      match fst(CicEnvironment.get_obj turi
 474                                  CicUniv.empty_ugraph) with
 475                         C.InductiveDefinition (ind_type_list,_,nr_ind_params)  ->
 476 debug_print ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno)) ;
 477                          let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
 478 debug_print ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2')) ;
 479                           let false_constr_id,_ = List.nth constructor_list (consno2' - 1) in
 480 debug_print ("XXXX nth funzionano ") ;
 481                            List.map
 482                             (function (id,cty) ->
 483                               let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
 484                                let rec aux t k =
 485                                 match t with
 486                                    C.Prod (_,_,target) when (k <= nr_ind_params) ->
 487                                     aux target (k+1)
 488                                  | C.Prod (binder,source,target) when (k > nr_ind_params) ->
 489                                     C.Lambda (binder,source,(aux target (k+1)))
 490                                  | _ ->
 491                                     if (id = false_constr_id)
 492                                      then (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [])
 493                                      else (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/True.ind") 0 [])
 494                                in aux red_ty 1
 495                             )
 496                             constructor_list
 497                       | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
 498                    in
 499
 500                     let (proof',goals') =
 501                      EliminationTactics.elim_type_tac
 502                       ~term:(C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] )
 503                       status
 504                     in
 505                      (match goals' with
 506                          [goal'] ->
 507                           let _,metasenv',_,_ = proof' in
 508                            let _,context',gty' =
 509                              CicUtil.lookup_meta goal' metasenv'
 510                            in
 511                             T.then_
 512                              ~start:
 513                               (P.change_tac
 514                                ~what:gty'
 515                                ~with_what:
 516                                 (C.Appl [
 517                                   C.Lambda (
 518                                    C.Name "x", tty,
 519                                    C.MutCase (
 520                                     turi, typeno,
 521                                     (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
 522                                     (C.Rel 1), pattern
 523                                    )
 524                                   );
 525                                   t2']
 526                                 )
 527                               )
 528                              ~continuation:
 529                               (
 530 debug_print ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])));
 531 debug_print ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])) ;
 532 debug_print ("XXXX equri: " ^ U.string_of_uri equri) ;
 533 debug_print ("XXXX tty : " ^ CicPp.ppterm tty) ;
 534 debug_print ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ;
 535 debug_print ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
 536 if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> tty then debug_print ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ;
 537 if (CicTypeChecker.type_of_aux' metasenv' context' t2') <> tty then debug_print ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
 538 if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> (CicTypeChecker.type_of_aux' metasenv' context' t2')
 539  then debug_print ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux'
 540  metasenv' context' t1')) ; debug_print ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
 541
 542                                let termty' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t1 ~with_what:t1' ~where:termty in
 543                                 let termty'' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t2 ~with_what:t2' ~where:termty' in
 544
 545 debug_print ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term));
 546                                  T.then_
 547                                    ~start:(EqualityTactics.rewrite_back_simpl_tac ~term:term)
 548                                    ~continuation:(IntroductionTactics.constructor_tac ~n:1)
 549                               )
 550                              (proof',goal')
 551                        | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
 552                      )
 553             | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
 554            )
 555        | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
 556 ;;
 557
 558 *)
 559
 560
 561