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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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/.
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 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
74 let lifted_pattern = Some lifted_t1,[],CicSubstitution.lift 1 concl_pat in
75 let subst,metasenv',ugraph,_,selected_terms_with_context =
76 ProofEngineHelpers.select
77 ~metasenv:metasenv' ~ugraph ~conjecture:lifted_conjecture
78 ~pattern:lifted_pattern in
79 let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in
81 (* Note: Rel 1 does not live in the context context_of_t *)
82 (* The replace_lifting_csc_0 function will take care of lifting it *)
85 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
86 selected_terms_with_context ([],[]) in
88 ProofEngineReduction.replace_lifting_csc 0
89 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
90 let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
91 let t1 = CicMetaSubst.apply_subst subst t1 in
92 let t2 = CicMetaSubst.apply_subst subst t2 in
93 let equality = CicMetaSubst.apply_subst subst equality in
94 let gty' = CicSubstitution.subst t2 abstr_gty in
95 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
96 let metasenv' = (fresh_meta,context,gty')::metasenv' in
97 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
99 C.Appl [eq_ind ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]
103 (PT.exact_tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal)
105 assert (List.length goals = 0) ;
107 ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
108 ~newmetasenv:metasenv'
112 ProofEngineTypes.mk_tactic (rewrite_tac ~direction ~pattern equality)
115 let rewrite_simpl_tac ~direction ~pattern equality =
116 let rewrite_simpl_tac ~direction ~pattern equality status =
117 ProofEngineTypes.apply_tactic
119 ~start:(rewrite_tac ~direction ~pattern equality)
121 (ReductionTactics.simpl_tac
122 ~pattern:(ProofEngineTypes.conclusion_pattern None)))
125 ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
128 let replace_tac ~pattern ~with_what =
129 let replace_tac ~pattern:(wanted,hyps_pat,concl_pat) ~with_what status =
130 let (proof, goal) = status in
131 let module C = Cic in
132 let module U = UriManager in
133 let module P = PrimitiveTactics in
134 let module T = Tacticals in
135 let uri,metasenv,pbo,pty = proof in
136 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
137 assert (hyps_pat = []); (*CSC: not implemented yet *)
138 let context_len = List.length context in
139 let subst,metasenv,u,_,selected_terms_with_context =
140 ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.empty_ugraph
141 ~conjecture ~pattern in
142 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
143 let with_what = CicMetaSubst.apply_subst subst with_what in
144 let pbo = CicMetaSubst.apply_subst subst pbo in
145 let pty = CicMetaSubst.apply_subst subst pty in
146 let status = (uri,metasenv,pbo,pty),goal in
147 let ty_of_with_what,u =
148 CicTypeChecker.type_of_aux'
149 metasenv context with_what CicUniv.empty_ugraph in
151 match selected_terms_with_context with
152 [] -> raise (ProofEngineTypes.Fail "Replace: no term selected")
155 (fun (context_of_t,t) ->
158 let context_of_t_len = List.length context_of_t in
159 if context_of_t_len = context_len then t
161 (let t_in_context,subst,metasenv' =
162 CicMetaSubst.delift_rels [] metasenv
163 (context_of_t_len - context_len) t
166 assert (metasenv = metasenv');
169 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
170 (*CSC: we could implement something stronger by completely changing
171 the semantics of the tactic *)
172 raise (ProofEngineTypes.Fail
173 "Replace: one of the selected terms is not closed") in
174 let ty_of_t_in_context,u = (* TASSI: FIXME *)
175 CicTypeChecker.type_of_aux' metasenv context t_in_context
176 CicUniv.empty_ugraph in
177 let b,u = CicReduction.are_convertible ~metasenv context
178 ty_of_with_what ty_of_t_in_context u in
180 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
181 let pattern_for_t = None,[],concl_pat_for_t in
182 t_in_context,pattern_for_t
185 (ProofEngineTypes.Fail
186 "Replace: one of the selected terms and the term to be replaced with have not convertible types")
188 let rec aux n whats status =
190 [] -> ProofEngineTypes.apply_tactic T.id_tac status
191 | (what,pattern)::tl ->
192 let what = CicSubstitution.lift n what in
193 let with_what = CicSubstitution.lift n with_what in
194 let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in
195 ProofEngineTypes.apply_tactic
200 (C.MutInd (LibraryObjects.eq_URI (), 0, [])) ;
207 rewrite_tac ~direction:`LeftToRight ~pattern (C.Rel 1))
211 ProofEngineTypes.mk_tactic
212 (function ((proof,goal) as status) ->
213 let _,metasenv,_,_ = proof in
214 let _,context,_ = CicUtil.lookup_meta goal metasenv in
217 match List.hd context with
218 Some (Cic.Name name,_) -> name
220 with (Failure "hd") -> assert false
222 ProofEngineTypes.apply_tactic
223 (ProofEngineStructuralRules.clear ~hyp) status))
224 ~continuation:(aux_tac (n + 1) tl));
227 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
230 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
234 (* All these tacs do is applying the right constructor/theorem *)
236 let reflexivity_tac =
237 IntroductionTactics.constructor_tac ~n:1
241 let symmetry_tac (proof, goal) =
242 let module C = Cic in
243 let module R = CicReduction in
244 let module U = UriManager in
245 let (_,metasenv,_,_) = proof in
246 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
247 match (R.whd context ty) with
248 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
249 when LibraryObjects.is_eq_URI uri ->
250 ProofEngineTypes.apply_tactic
251 (PrimitiveTactics.apply_tac
252 ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
255 | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
257 ProofEngineTypes.mk_tactic symmetry_tac
260 let transitivity_tac ~term =
261 let transitivity_tac ~term status =
262 let (proof, goal) = status in
263 let module C = Cic in
264 let module R = CicReduction in
265 let module U = UriManager in
266 let module T = Tacticals in
267 let (_,metasenv,_,_) = proof in
268 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
269 match (R.whd context ty) with
270 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
271 when LibraryObjects.is_eq_URI uri ->
272 ProofEngineTypes.apply_tactic
274 ~start:(PrimitiveTactics.apply_tac
275 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
277 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
280 | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
282 ProofEngineTypes.mk_tactic (transitivity_tac ~term)