+
+let rewrite_tac ~term:equality ~status:(proof,goal) =
+ let module C = Cic in
+ let module U = UriManager in
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
+ let eq_ind_r,ty,t1,t2 =
+ match CicTypeChecker.type_of_aux' metasenv context equality with
+ C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
+ when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
+ let eq_ind_r =
+ C.Const
+ (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind_r.con",[])
+ in
+ eq_ind_r,ty,t1,t2
+ | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
+ when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
+ let eqT_ind_r =
+ C.Const
+ (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind_r.con",[])
+ in
+ eqT_ind_r,ty,t1,t2
+ | _ ->
+ raise
+ (ProofEngineTypes.Fail
+ "Rewrite: the argument is not a proof of an equality")
+ in
+ let pred =
+ let gty' = CicSubstitution.lift 1 gty in
+ let t1' = CicSubstitution.lift 1 t1 in
+ let gty'' =
+ ProofEngineReduction.replace_lifting
+ ~equality:ProofEngineReduction.alpha_equivalence
+ ~what:t1' ~with_what:(C.Rel 1) ~where:gty'
+ in
+ C.Lambda (C.Name "dummy_for_rewrite", ty, gty'')
+ in
+prerr_endline ("#### Sintetizzato: " ^ CicPp.ppterm pred);
+ let fresh_meta = ProofEngineHelpers.new_meta proof in
+ let irl =
+ ProofEngineHelpers.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
+
+ let (proof',goals) =
+ PrimitiveTactics.exact_tac
+ ~term:(C.Appl
+ [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
+ ~status:((curi,metasenv',pbo,pty),goal)
+ in
+ assert (List.length goals = 0) ;
+ (proof',[fresh_meta])
+;;
+
+
+let rewrite_simpl_tac ~term ~status =
+ Tacticals.then_ ~start:(rewrite_tac ~term)
+ ~continuation:
+ (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~term:None)
+ ~status
+;;
+
+
+let rewrite_back_tac ~term:equality ~status:(proof,goal) =
+ let module C = Cic in
+ let module U = UriManager in
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
+ let eq_ind_r,ty,t1,t2 =
+ match CicTypeChecker.type_of_aux' metasenv context equality with
+ C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
+ when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
+ let eq_ind_r =
+ C.Const
+ (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind.con",[])
+ in
+ eq_ind_r,ty,t1,t2
+ | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
+ when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
+ let eqT_ind_r =
+ C.Const
+ (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind.con",[])
+ in
+ eqT_ind_r,ty,t1,t2
+ | _ ->
+ raise
+ (ProofEngineTypes.Fail
+ "Rewrite: the argument is not a proof of an equality")
+ in
+ let pred =
+ let gty' = CicSubstitution.lift 1 gty in
+ let t1' = CicSubstitution.lift 1 t1 in
+ let gty'' =
+ ProofEngineReduction.replace_lifting
+ ~equality:ProofEngineReduction.alpha_equivalence
+ ~what:t1' ~with_what:(C.Rel 1) ~where:gty'
+ in
+ C.Lambda (C.Name "dummy_for_rewrite", ty, gty'')
+ in
+prerr_endline ("#### Sintetizzato: " ^ CicPp.ppterm pred);
+ let fresh_meta = ProofEngineHelpers.new_meta proof in
+ let irl =
+ ProofEngineHelpers.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
+
+ let (proof',goals) =
+ PrimitiveTactics.exact_tac
+ ~term:(C.Appl
+ [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
+ ~status:((curi,metasenv',pbo,pty),goal)
+ in
+ assert (List.length goals = 0) ;
+ (proof',[fresh_meta])
+
+;;
+
+
+let replace_tac ~what ~with_what ~status:((proof, goal) as status) =
+ let module C = Cic in
+ let module U = UriManager in
+ let module P = PrimitiveTactics in
+ let module T = Tacticals in
+ let _,metasenv,_,_ = proof in
+ let _,context,_ = List.find (function (m,_,_) -> m=goal) metasenv in
+ let wty = CicTypeChecker.type_of_aux' metasenv context what in
+ if (wty = (CicTypeChecker.type_of_aux' metasenv context with_what))
+ then T.thens
+ ~start:(P.cut_tac ~term:(C.Appl [(C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"), 0, [])) ; wty ; what ; with_what]))
+ (* quale uguaglianza usare, eq o eqT ? *)
+ ~continuations:[
+ T.then_
+ ~start:(P.intros_tac ~name:"dummy_for_replace")
+ ~continuation:(T.then_
+ ~start:(rewrite_back_tac ~term:(C.Rel 1)) (* C.Name "dummy_for_replace" *)
+ ~continuation:(ProofEngineStructuralRules.clear
+ ~hyp:(Some((C.Name "dummy_for_replace") , (C.Def C.Implicit) (* NO!! tipo di dummy *) ))
+ )
+ ) ;
+ T.id_tac]
+ ~status
+ else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
+;;
+