+(* 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/.
+ *)
+
+
+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,t2,t1
+ | 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,t2,t1
+ | _ ->
+ 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_back_simpl_tac ~term ~status =
+ Tacticals.then_
+ ~start:(rewrite_back_tac ~term)
+ ~continuation:
+ (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~term:None)
+ ~status
+;;
+
+
+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
+ try
+ 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, [])) ; (* quale uguaglianza usare, eq o eqT ? *)
+ wty ;
+ what ;
+ with_what]))
+ ~continuations:[
+ T.then_
+ ~start:(rewrite_back_tac ~term:(C.Rel 1)) (* C.Name "dummy_for_replace" *)
+ ~continuation:(
+ ProofEngineStructuralRules.clear
+ ~hyp:(List.hd context)) ;
+(* (Some(C.Name "dummy_for_replace" , C.Def (CicTypeChecker.type_of_aux' metasenv context (C.Rel 1)) (* NOOOO!!!!! tipo di dummy *) )))) ; *)
+ T.id_tac]
+ ~status
+ else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
+ with (Failure "hd") -> raise (ProofEngineTypes.Fail "Replace: empty context")
+;;
+
+
+let reflexivity_tac =
+ IntroductionTactics.constructor_tac ~n:1
+;;
+
+
+let symmetry_tac ~status:(proof, goal) =
+ let module C = Cic in
+ let module R = CicReduction in
+ let module U = UriManager in
+ let (_,metasenv,_,_) = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+ match (R.whd context ty) with
+ (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
+ PrimitiveTactics.apply_tac ~status:(proof,goal)
+ ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/sym_eq.con", []))
+
+ | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
+ PrimitiveTactics.apply_tac ~status:(proof,goal)
+ ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic_Type/sym_eqT.con", []))
+
+ | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
+;;
+
+
+let transitivity_tac ~term ~status:((proof, goal) as status) =
+ let module C = Cic in
+ let module R = CicReduction in
+ let module U = UriManager in
+ let module T = Tacticals in
+ let (_,metasenv,_,_) = proof in
+ let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+ match (R.whd context ty) with
+ (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
+ T.thens
+ ~start:(PrimitiveTactics.apply_tac
+ ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/trans_eq.con", [])))
+ ~continuations:
+ [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac]
+ ~status
+
+ | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
+ T.thens
+ ~start:(PrimitiveTactics.apply_tac
+ ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic_Type/trans_eqT.con", [])))
+ ~continuations:
+ [T.id_tac ; T.id_tac ; PrimitiveTactics.exact_tac ~term]
+ ~status
+
+ | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
+;;
+
+