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
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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.
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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/.
26 let rewrite_tac ~direction ~pattern equality =
27 let rewrite_tac ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status
30 let module U = UriManager in
31 let module PET = ProofEngineTypes in
32 let module PER = ProofEngineReduction in
33 let module PEH = ProofEngineHelpers in
34 let module PT = PrimitiveTactics in
35 assert (wanted = None); (* this should be checked syntactically *)
36 assert (hyps_pat = []); (*CSC: not implemented yet! *)
37 let proof,goal = status in
38 let if_right_to_left a b =
43 let curi, metasenv, pbo, pty = proof in
44 let (metano,context,gty) as conjecture = CicUtil.lookup_meta goal metasenv in
46 CicTypeChecker.type_of_aux' metasenv context equality
47 CicUniv.empty_ugraph in
48 let (ty_eq,metasenv',arguments,fresh_meta) =
49 ProofEngineHelpers.saturate_term
50 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in
52 if List.length arguments = 0 then
55 C.Appl (equality :: arguments) in
56 let eq_ind, ty, t1, t2 =
58 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
59 when LibraryObjects.is_eq_URI uri ->
61 if_right_to_left LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
63 let eq_ind = C.Const (ind_uri uri,[]) in
64 if_right_to_left (eq_ind, ty, t2, t1) (eq_ind, ty, t1, t2)
65 | _ -> raise (PET.Fail "Rewrite: argument is not a proof of an equality") in
66 (* now we always do as if direction was `LeftToRight *)
68 FreshNamesGenerator.mk_fresh_name
69 ~subst:[] metasenv' context C.Anonymous ~typ:ty in
70 let lifted_t1 = CicSubstitution.lift 1 t1 in
71 let lifted_gty = CicSubstitution.lift 1 gty in
72 let lifted_conjecture =
73 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
75 Some (fun _ m u -> lifted_t1, m, u),[],CicSubstitution.lift 1 concl_pat
77 let subst,metasenv',ugraph,_,selected_terms_with_context =
78 ProofEngineHelpers.select
79 ~metasenv:metasenv' ~ugraph ~conjecture:lifted_conjecture
80 ~pattern:lifted_pattern in
81 let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in
83 (* Note: Rel 1 does not live in the context context_of_t *)
84 (* The replace_lifting_csc_0 function will take care of lifting it *)
87 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
88 selected_terms_with_context ([],[]) in
90 ProofEngineReduction.replace_lifting_csc 0
91 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
92 let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
93 let t1 = CicMetaSubst.apply_subst subst t1 in
94 let t2 = CicMetaSubst.apply_subst subst t2 in
95 let equality = CicMetaSubst.apply_subst subst equality in
96 let gty' = CicSubstitution.subst t2 abstr_gty in
97 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
98 let metasenv' = (fresh_meta,context,gty')::metasenv' in
99 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
101 C.Appl [eq_ind ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]
105 (PT.exact_tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal)
107 assert (List.length goals = 0) ;
109 ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
110 ~newmetasenv:metasenv'
114 ProofEngineTypes.mk_tactic (rewrite_tac ~direction ~pattern equality)
117 let rewrite_simpl_tac ~direction ~pattern equality =
118 let rewrite_simpl_tac ~direction ~pattern equality status =
119 ProofEngineTypes.apply_tactic
121 ~start:(rewrite_tac ~direction ~pattern equality)
123 (ReductionTactics.simpl_tac
124 ~pattern:(ProofEngineTypes.conclusion_pattern None)))
127 ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
130 let replace_tac ~pattern ~with_what =
131 let replace_tac ~pattern:(wanted,hyps_pat,concl_pat) ~with_what status =
132 let (proof, goal) = status in
133 let module C = Cic in
134 let module U = UriManager in
135 let module P = PrimitiveTactics in
136 let module T = Tacticals in
137 let uri,metasenv,pbo,pty = proof in
138 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
139 assert (hyps_pat = []); (*CSC: not implemented yet *)
140 let context_len = List.length context in
141 let subst,metasenv,u,_,selected_terms_with_context =
142 ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.empty_ugraph
143 ~conjecture ~pattern in
144 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
145 let with_what, metasenv, u = with_what context metasenv u in
146 let with_what = CicMetaSubst.apply_subst subst with_what in
147 let pbo = CicMetaSubst.apply_subst subst pbo in
148 let pty = CicMetaSubst.apply_subst subst pty in
149 let status = (uri,metasenv,pbo,pty),goal in
150 let ty_of_with_what,u =
151 CicTypeChecker.type_of_aux'
152 metasenv context with_what CicUniv.empty_ugraph in
154 match selected_terms_with_context with
155 [] -> raise (ProofEngineTypes.Fail "Replace: no term selected")
158 (fun (context_of_t,t) ->
161 let context_of_t_len = List.length context_of_t in
162 if context_of_t_len = context_len then t
164 (let t_in_context,subst,metasenv' =
165 CicMetaSubst.delift_rels [] metasenv
166 (context_of_t_len - context_len) t
169 assert (metasenv = metasenv');
172 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
173 (*CSC: we could implement something stronger by completely changing
174 the semantics of the tactic *)
175 raise (ProofEngineTypes.Fail
176 "Replace: one of the selected terms is not closed") in
177 let ty_of_t_in_context,u = (* TASSI: FIXME *)
178 CicTypeChecker.type_of_aux' metasenv context t_in_context
179 CicUniv.empty_ugraph in
180 let b,u = CicReduction.are_convertible ~metasenv context
181 ty_of_with_what ty_of_t_in_context u in
183 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
184 let pattern_for_t = None,[],concl_pat_for_t in
185 t_in_context,pattern_for_t
188 (ProofEngineTypes.Fail
189 "Replace: one of the selected terms and the term to be replaced with have not convertible types")
191 let rec aux n whats status =
193 [] -> ProofEngineTypes.apply_tactic T.id_tac status
194 | (what,pattern)::tl ->
195 let what = CicSubstitution.lift n what in
196 let with_what = CicSubstitution.lift n with_what in
197 let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in
198 ProofEngineTypes.apply_tactic
203 (C.MutInd (LibraryObjects.eq_URI (), 0, [])) ;
210 rewrite_tac ~direction:`LeftToRight ~pattern (C.Rel 1))
214 ProofEngineTypes.mk_tactic
215 (function ((proof,goal) as status) ->
216 let _,metasenv,_,_ = proof in
217 let _,context,_ = CicUtil.lookup_meta goal metasenv in
220 match List.hd context with
221 Some (Cic.Name name,_) -> name
223 with (Failure "hd") -> assert false
225 ProofEngineTypes.apply_tactic
226 (ProofEngineStructuralRules.clear ~hyp) status))
227 ~continuation:(aux_tac (n + 1) tl));
230 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
233 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
237 (* All these tacs do is applying the right constructor/theorem *)
239 let reflexivity_tac =
240 IntroductionTactics.constructor_tac ~n:1
244 let symmetry_tac (proof, goal) =
245 let module C = Cic in
246 let module R = CicReduction in
247 let module U = UriManager in
248 let (_,metasenv,_,_) = proof in
249 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
250 match (R.whd context ty) with
251 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
252 when LibraryObjects.is_eq_URI uri ->
253 ProofEngineTypes.apply_tactic
254 (PrimitiveTactics.apply_tac
255 ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
258 | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
260 ProofEngineTypes.mk_tactic symmetry_tac
263 let transitivity_tac ~term =
264 let transitivity_tac ~term status =
265 let (proof, goal) = status in
266 let module C = Cic in
267 let module R = CicReduction in
268 let module U = UriManager in
269 let module T = Tacticals in
270 let (_,metasenv,_,_) = proof in
271 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
272 match (R.whd context ty) with
273 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
274 when LibraryObjects.is_eq_URI uri ->
275 ProofEngineTypes.apply_tactic
277 ~start:(PrimitiveTactics.apply_tac
278 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
280 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
283 | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
285 ProofEngineTypes.mk_tactic (transitivity_tac ~term)