1 (* Copyright (C) 2002, HELM Team.
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.
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.
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.
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,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
27 let rewrite_tac ~term:equality (proof,goal) =
29 let module U = UriManager in
30 let curi,metasenv,pbo,pty = proof in
31 let metano,context,gty = CicUtil.lookup_meta goal metasenv in
32 let eq_ind_r,ty,t1,t2 =
33 match CicTypeChecker.type_of_aux' metasenv context equality with
34 C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
35 when U.eq uri HelmLibraryObjects.Logic.eq_URI ->
38 (HelmLibraryObjects.Logic.eq_ind_r_URI,[])
43 (ProofEngineTypes.Fail
44 "Rewrite: the argument is not a proof of an equality")
47 let gty' = CicSubstitution.lift 1 gty in
48 let t1' = CicSubstitution.lift 1 t1 in
50 ProofEngineReduction.replace_lifting
51 ~equality:ProofEngineReduction.alpha_equivalence
52 ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
55 (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty,
58 let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
59 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
60 let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
63 PrimitiveTactics.exact_tac
65 [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
66 ((curi,metasenv',pbo,pty),goal)
68 assert (List.length goals = 0) ;
73 let rewrite_simpl_tac ~term status =
75 ~start:(rewrite_tac ~term)
77 (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)
82 let rewrite_back_tac ~term:equality (proof,goal) =
84 let module U = UriManager in
85 let curi,metasenv,pbo,pty = proof in
86 let metano,context,gty = CicUtil.lookup_meta goal metasenv in
87 let eq_ind_r,ty,t1,t2 =
88 match CicTypeChecker.type_of_aux' metasenv context equality with
89 C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
90 when U.eq uri HelmLibraryObjects.Logic.eq_URI ->
92 C.Const (HelmLibraryObjects.Logic.eq_ind_URI,[])
97 (ProofEngineTypes.Fail
98 "Rewrite: the argument is not a proof of an equality")
101 let gty' = CicSubstitution.lift 1 gty in
102 let t1' = CicSubstitution.lift 1 t1 in
104 ProofEngineReduction.replace_lifting
105 ~equality:ProofEngineReduction.alpha_equivalence
106 ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
109 (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty,
112 let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
114 CicMkImplicit.identity_relocation_list_for_metavariable context in
115 let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
118 PrimitiveTactics.exact_tac
120 [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
121 ((curi,metasenv',pbo,pty),goal)
123 assert (List.length goals = 0) ;
124 (proof',[fresh_meta])
129 let rewrite_back_simpl_tac ~term status =
131 ~start:(rewrite_back_tac ~term)
133 (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)
138 let replace_tac ~what ~with_what status =
139 let (proof, goal) = status in
140 let module C = Cic in
141 let module U = UriManager in
142 let module P = PrimitiveTactics in
143 let module T = Tacticals in
144 let _,metasenv,_,_ = proof in
145 let _,context,_ = CicUtil.lookup_meta goal metasenv in
146 let wty = CicTypeChecker.type_of_aux' metasenv context what in
148 if (wty = (CicTypeChecker.type_of_aux' metasenv context with_what))
154 (C.MutInd (HelmLibraryObjects.Logic.eq_URI, 0, [])) ;
160 ~start:(rewrite_simpl_tac ~term:(C.Rel 1))
162 ProofEngineStructuralRules.clear
163 ~hyp:(List.hd context)) ;
166 else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
167 with (Failure "hd") -> raise (ProofEngineTypes.Fail "Replace: empty context")
171 (* All these tacs do is applying the right constructor/theorem *)
173 let reflexivity_tac =
174 IntroductionTactics.constructor_tac ~n:1
178 let symmetry_tac (proof, goal) =
179 let module C = Cic in
180 let module R = CicReduction in
181 let module U = UriManager in
182 let (_,metasenv,_,_) = proof in
183 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
184 match (R.whd context ty) with
185 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri HelmLibraryObjects.Logic.eq_URI) ->
186 PrimitiveTactics.apply_tac (proof,goal)
187 ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, []))
189 | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
193 let transitivity_tac ~term status =
194 let (proof, goal) = status in
195 let module C = Cic in
196 let module R = CicReduction in
197 let module U = UriManager in
198 let module T = Tacticals in
199 let (_,metasenv,_,_) = proof in
200 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
201 match (R.whd context ty) with
202 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = HelmLibraryObjects.Logic.eq_URI) ->
204 ~start:(PrimitiveTactics.apply_tac
205 ~term: (C.Const (HelmLibraryObjects.Logic.trans_eq_URI, [])))
207 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac]
210 | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")