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+(* Copyright (C) 2002, HELM Team.
+ * 
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ * 
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+* 
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA  02111-1307, USA.
+ * 
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
+(* $Id$ *)
+
+exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
+exception NotAnInductiveTypeToEliminate
+
+let debug = false;; 
+let debug_print =
+ fun msg -> if debug then prerr_endline (Lazy.force msg) else ()
+
+
+let inside_obj = function
+    | Cic.InductiveDefinition (l,params, nleft, _) ->
+      (l,params,nleft)
+    | _ -> raise (Invalid_argument "Errore in inside_obj")
+
+let term_to_list = function
+	| Cic.Appl l -> l
+	| _ -> raise (Invalid_argument "Errore in term_to_list")
+
+
+let rec baseuri_of_term = function
+  | Cic.Appl l -> baseuri_of_term (List.hd l)  
+  | Cic.MutInd (baseuri, tyno, []) -> baseuri
+  | _ -> raise (Invalid_argument "baseuri_of_term")
+
+
+(* prende il numero dei parametri sinistri, la lista dei parametri, la lista 
+dei tipi dei parametri, il tipo del GOAL e costruisce il termine per la cut 
+ossia DX1 = DX1 -> ... DXn=DXn -> GOALTY *)
+
+let rec foo_cut nleft l param_ty_l body uri_of_eq = 
+ if nleft > 0 then foo_cut (nleft-1) (List.tl l)  (List.tl param_ty_l) body 
+  uri_of_eq
+ else 	match l with
+  | hd::tl -> Cic.Prod (Cic.Anonymous, Cic.Appl[Cic.MutInd (uri_of_eq  ,0,[]); 
+  (List.hd param_ty_l) ; hd; hd], foo_cut nleft 
+  (List.map (CicSubstitution.lift 1) tl) (List.tl param_ty_l) 
+  (CicSubstitution.lift 1 body) uri_of_eq )
+  | [] -> body
+ ;;
+
+(* da una catena di prod costruisce una lista dei termini che lo compongono.*)
+let rec list_of_prod term =
+match term with 
+ | Cic.Prod (Cic.Anonymous,src,tgt) -> [src] @ (list_of_prod tgt)
+ | _ -> [term]
+;;
+
+
+let rec cut_first n l =
+ if n>0 then  
+  match l with
+  | hd::tl -> cut_first (n-1) tl
+  | [] -> []
+  else l
+;;
+
+
+let rec cut_last l =
+match l with
+ | hd::tl when tl != [] -> hd:: (cut_last tl)
+ | _ -> []
+;;
+
+
+let foo_appl nleft nright_consno term uri =
+ let l = [] in
+ let a = ref l in
+ for n = 1 to nleft do
+	a := !a @ [(Cic.Implicit None)]
+ done;
+ a:= !a @ [term];
+ for n = 1 to nright_consno do
+	a := !a @ [(Cic.Implicit None)] 
+ done;
+ Cic.Appl ([Cic.Const(uri,[])] @ !a @ [Cic.Rel 1]) (*L'ipotesi e' sempre Rel 1. (?)  *)
+;;
+
+
+let rec foo_prod nright param_ty_l l l2 base_rel body uri_of_eq nleft termty 
+ isSetType term =
+  match param_ty_l with
+   | hd::tl -> Cic.Prod (
+    Cic.Anonymous, 
+    Cic.Appl[Cic.MutInd(uri_of_eq,0,[]); hd; (List.hd l); Cic.Rel base_rel],
+    foo_prod (nright-1) tl (List.map (CicSubstitution.lift 1) (List.tl l)) 
+     (List.map (CicSubstitution.lift 1) l2) 
+     base_rel (CicSubstitution.lift 1 body) 
+     uri_of_eq nleft (CicSubstitution.lift 1 termty)
+     isSetType (CicSubstitution.lift 1 term))
+   | [] -> ProofEngineReduction.replace_lifting 
+    ~equality:(ProofEngineReduction.alpha_equivalence)
+    ~what: (if isSetType 
+     then ((cut_first (1+nleft) (term_to_list termty) ) @ [term] ) 
+     else (cut_first (1+nleft) (term_to_list termty) ) )
+    ~with_what: (List.map (CicSubstitution.lift (-1)) l2)
+    ~where:body 
+(*TODO lo stesso sottotermine di body puo' essere sia sx che dx!*)
+;;
+
+let rec foo_lambda nright param_ty_l nright_ param_ty_l_ l l2 base_rel body 
+ uri_of_eq nleft termty isSetType ty_indty term =
+ (*assert nright >0 *)
+  match param_ty_l with
+   | hd::tl ->Cic.Lambda (
+    (Cic.Name ("lambda" ^ (string_of_int nright))),
+    hd, (* typ *)
+    foo_lambda (nright-1) tl nright_ param_ty_l_ 
+     (List.map (CicSubstitution.lift 1) l) 
+     (List.map (CicSubstitution.lift 1) (l2 @ [Cic.Rel 1])) 
+     base_rel (CicSubstitution.lift 1 body)  
+     uri_of_eq nleft 
+     (CicSubstitution.lift 1 termty)
+     isSetType ty_indty
+     (CicSubstitution.lift 1 term)) 
+   | [] when isSetType -> Cic.Lambda (
+    (Cic.Name ("lambda" ^ (string_of_int nright))),
+    (ProofEngineReduction.replace_lifting
+     ~equality:(ProofEngineReduction.alpha_equivalence)
+     ~what: (cut_first (1+nleft) (term_to_list termty) ) 
+     ~with_what: (List.map (CicSubstitution.lift (-1)) l2)
+     ~where:termty), (* tipo di H con i parametri destri sostituiti *)
+    foo_prod nright_ param_ty_l_ (List.map (CicSubstitution.lift 1) l)  
+     (List.map (CicSubstitution.lift 1) (l2 @ [Cic.Rel 1])) 
+     (base_rel+1) (CicSubstitution.lift 1 body)  
+     uri_of_eq nleft 
+     (CicSubstitution.lift 1 termty) isSetType
+     (CicSubstitution.lift 1 term))
+   | [] -> foo_prod nright_ param_ty_l_ l l2 base_rel body uri_of_eq nleft 
+    termty isSetType term
+;;
+
+let inversion_tac ~term =
+ let module T = CicTypeChecker in
+ let module R = CicReduction in
+ let module C = Cic in
+ let module P = PrimitiveTactics in
+ let module PET = ProofEngineTypes in
+ let module PEH = ProofEngineHelpers in
+ let inversion_tac ~term (proof, goal) =
+ let (_,metasenv,_,_) = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let (newproof, metasenv') = PEH.subst_meta_in_proof proof metano term [] in
+ let uri_of_eq = HelmLibraryObjects.Logic.eq_URI in
+
+ (* dall'indice che indentifica il goal nel metasenv, ritorna il suo tipo, che 
+ e' la terza componente della relativa congettura *)
+ let (_,_,body) = CicUtil.lookup_meta goal metasenv in
+ (* estrae il tipo del termine(ipotesi) oggetto di inversion, 
+ di solito un Cic.Appl *)
+ let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ let uri = baseuri_of_term termty in  
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ let l,params,nleft = inside_obj o in
+ let (_,_,typeno,_) =
+  match termty with
+   C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
+   | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
+    (uri,exp_named_subst,typeno,args)
+   | _ -> raise NotAnInductiveTypeToEliminate
+ in
+ let eliminator_uri =
+  let buri = UriManager.buri_of_uri uri in
+  let name =
+   match o with
+    C.InductiveDefinition (tys,_,_,_) ->
+     let (name,_,_,_) = List.nth tys typeno in
+     name
+    |_ -> assert false
+  in
+  let ext = "_ind" in
+  UriManager.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
+ in
+ (* il tipo del tipo induttivo da cui viene l'ipotesi oggetto di inversione *)
+ let (_,_,ty_indty,cons_list) = (List.hd l) in
+ (*la lista di Cic.term ricavata dal tipo del tipo induttivo. *)
+ let param_ty_l = list_of_prod ty_indty in
+ let consno = List.length cons_list in
+ let nright= (List.length param_ty_l)- (nleft+1) in 
+ let isSetType = ((Pervasives.compare 
+  (List.nth param_ty_l ((List.length param_ty_l)-1)) 
+  (Cic.Sort Cic.Prop)) != 0) 
+ in
+ (* eliminiamo la testa di termty, in quanto e' il nome del predicato e non un parametro.*)
+ let cut_term = foo_cut nleft (List.tl (term_to_list termty)) 
+  (list_of_prod ty_indty)  body uri_of_eq in
+ (* cut DXn=DXn \to GOAL *)
+ let proof1,gl1 = PET.apply_tactic (P.cut_tac cut_term) (proof,goal) in
+ (* apply Hcut ; reflexivity (su tutti i goals aperti da apply_tac) *)
+ let proof2, gl2 = PET.apply_tactic
+  (Tacticals.then_
+   ~start: (P.apply_tac (C.Rel 1)) (* apply Hcut *)
+   ~continuation: (EqualityTactics.reflexivity_tac)
+  ) (proof1, (List.hd gl1))
+ in          
+ (* apply (ledx_ind( lambda x. lambda y, ...)) *)
+ let (t1,metasenv,t3,t4) = proof2 in
+ let goal2 = List.hd (List.tl gl1) in
+ let (metano,context,_) = CicUtil.lookup_meta goal2 metasenv in
+ let cut_param_ty_l = (cut_first nleft (cut_last param_ty_l)) in
+ (* la lista dei soli parametri destri *)
+ let l= cut_first (1+nleft) (term_to_list termty) in
+ let lambda_t = foo_lambda nright cut_param_ty_l nright cut_param_ty_l l [] 
+  nright body uri_of_eq nleft termty isSetType ty_indty term in 
+ let t = foo_appl nleft (nright+consno) lambda_t eliminator_uri  in
+ debug_print (lazy ("Lambda_t: " ^ (CicPp.ppterm t)));
+ debug_print (lazy ("Term: " ^ (CicPp.ppterm termty)));
+ debug_print (lazy ("Body: " ^ (CicPp.ppterm body)));
+ debug_print (lazy ("Right param: " ^ (CicPp.ppterm (Cic.Appl l))));
+ 
+ let (ref_t,_,metasenv'',_) = CicRefine.type_of_aux' metasenv context t 
+  CicUniv.empty_ugraph 
+ in
+ let proof2 = (t1,metasenv'',t3,t4) in
+ let proof3,gl3 = PET.apply_tactic (P.apply_tac ref_t) (proof2, goal2) in
+ let new_goals = ProofEngineHelpers.compare_metasenvs
+  ~oldmetasenv:metasenv ~newmetasenv:metasenv''
+ in
+ let patched_new_goals =
+  let (_,metasenv''',_,_) = proof3 in
+  List.filter (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
+   new_goals @ gl3
+ in
+ (*prerr_endline ("METASENV: " ^ CicMetaSubst.ppmetasenv metasenv []); DEBUG*)
+ (proof3, patched_new_goals)
+in	
+ProofEngineTypes.mk_tactic (inversion_tac ~term)
+;;