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