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 ~direction ~pattern equality =
28 let rewrite_tac ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status
31 let module U = UriManager in
32 let module PET = ProofEngineTypes in
33 let module PER = ProofEngineReduction in
34 let module PEH = ProofEngineHelpers in
35 let module PT = PrimitiveTactics in
36 let module HLO = HelmLibraryObjects in
37 assert (wanted = None); (* this should be checked syntactically *)
38 assert (hyps_pat = []); (*CSC: not implemented yet! *)
39 let proof,goal = status in
40 let if_right_to_left a b =
45 let curi, metasenv, pbo, pty = proof in
46 let (metano,context,gty) as conjecture = CicUtil.lookup_meta goal metasenv in
47 let eq_uri = HLO.Logic.eq_URI in
49 CicTypeChecker.type_of_aux' metasenv context equality
52 let eq_ind, ty, t1, t2 =
54 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2] when U.eq uri eq_uri ->
56 C.Const (if_right_to_left HLO.Logic.eq_ind_URI HLO.Logic.eq_ind_r_URI,[])
58 if_right_to_left (eq_ind, ty, t2, t1) (eq_ind, ty, t1, t2)
59 | _ -> raise (PET.Fail "Rewrite: argument is not a proof of an equality") in
60 (* now we always do as if direction was `LeftToRight *)
62 FreshNamesGenerator.mk_fresh_name
63 ~subst:[] metasenv context C.Anonymous ~typ:ty in
64 let lifted_t1 = CicSubstitution.lift 1 t1 in
65 let lifted_gty = CicSubstitution.lift 1 gty in
66 let lifted_conjecture =
67 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
68 let lifted_pattern = Some lifted_t1,[],CicSubstitution.lift 1 concl_pat in
69 let _,selected_terms_with_context =
70 ProofEngineHelpers.select
71 ~metasenv ~conjecture:lifted_conjecture ~pattern:lifted_pattern in
73 (* Note: Rel 1 does not live in the context context_of_t *)
74 (* The replace_lifting_csc_0 function will take care of lifting it *)
77 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
78 selected_terms_with_context ([],[]) in
80 ProofEngineReduction.replace_lifting_csc 0
81 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
82 let gty' = CicSubstitution.subst t2 abstr_gty in
83 let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
84 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
85 let metasenv' = (fresh_meta,context,gty')::metasenv in
86 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
88 C.Appl [eq_ind ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]
92 (PT.exact_tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal)
94 assert (List.length goals = 0) ;
97 ProofEngineTypes.mk_tactic (rewrite_tac ~direction ~pattern equality)
100 let rewrite_simpl_tac ~direction ~pattern equality =
101 let rewrite_simpl_tac ~direction ~pattern equality status =
102 ProofEngineTypes.apply_tactic
104 ~start:(rewrite_tac ~direction ~pattern equality)
106 (ReductionTactics.simpl_tac
107 ~pattern:(ProofEngineTypes.conclusion_pattern None)))
110 ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
113 let replace_tac ~pattern ~with_what =
115 let replace_tac ~pattern ~with_what status =
116 let (proof, goal) = status in
117 let module C = Cic in
118 let module U = UriManager in
119 let module P = PrimitiveTactics in
120 let module T = Tacticals in
121 let _,metasenv,_,_ = proof in
122 let _,context,_ = CicUtil.lookup_meta goal metasenv in
123 let wty,u = (* TASSI: FIXME *)
124 CicTypeChecker.type_of_aux' metasenv context what CicUniv.empty_ugraph in
125 let wwty,_ = CicTypeChecker.type_of_aux' metasenv context with_what u in
128 ProofEngineTypes.apply_tactic
133 (C.MutInd (HelmLibraryObjects.Logic.eq_URI, 0, [])) ;
139 T.then_ ~start:(rewrite_simpl_tac ~term:(C.Rel 1) ())
141 ProofEngineStructuralRules.clear
142 ~hyp:(List.hd context)) ;
145 else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
146 with (Failure "hd") ->
147 raise (ProofEngineTypes.Fail "Replace: empty context")
149 ProofEngineTypes.mk_tactic (replace_tac ~what ~with_what)
154 (* All these tacs do is applying the right constructor/theorem *)
156 let reflexivity_tac =
157 IntroductionTactics.constructor_tac ~n:1
161 let symmetry_tac (proof, goal) =
162 let module C = Cic in
163 let module R = CicReduction in
164 let module U = UriManager in
165 let (_,metasenv,_,_) = proof in
166 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
167 match (R.whd context ty) with
168 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
169 when (U.eq uri HelmLibraryObjects.Logic.eq_URI) ->
170 ProofEngineTypes.apply_tactic
171 (PrimitiveTactics.apply_tac
172 ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, [])))
175 | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
177 ProofEngineTypes.mk_tactic symmetry_tac
180 let transitivity_tac ~term =
181 let transitivity_tac ~term status =
182 let (proof, goal) = status in
183 let module C = Cic in
184 let module R = CicReduction in
185 let module U = UriManager in
186 let module T = Tacticals in
187 let (_,metasenv,_,_) = proof in
188 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
189 match (R.whd context ty) with
190 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
191 when (uri = HelmLibraryObjects.Logic.eq_URI) ->
192 ProofEngineTypes.apply_tactic
194 ~start:(PrimitiveTactics.apply_tac
195 ~term: (C.Const (HelmLibraryObjects.Logic.trans_eq_URI, [])))
197 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
200 | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
202 ProofEngineTypes.mk_tactic (transitivity_tac ~term)