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/.
30 module PET = ProofEngineTypes
31 module PER = ProofEngineReduction
32 module PEH = ProofEngineHelpers
33 module PESR = ProofEngineStructuralRules
34 module P = PrimitiveTactics
36 module R = CicReduction
37 module S = CicSubstitution
38 module TC = CicTypeChecker
39 module LO = LibraryObjects
40 module DTI = DoubleTypeInference
43 let rec rewrite ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status=
44 assert (wanted = None); (* this should be checked syntactically *)
45 let proof,goal = status in
46 let curi, metasenv, subst, pbo, pty, attrs = proof in
47 let (metano,context,gty) = CicUtil.lookup_meta goal metasenv in
52 (PET.mk_tactic (rewrite ~direction
53 ~pattern:(None,[he],None) equality))
54 (PET.mk_tactic (rewrite ~direction
55 ~pattern:(None,tl,concl_pat) (S.lift 1 equality)))
57 | [_] as hyps_pat when concl_pat <> None ->
60 (PET.mk_tactic (rewrite ~direction
61 ~pattern:(None,hyps_pat,None) equality))
62 (PET.mk_tactic (rewrite ~direction
63 ~pattern:(None,[],concl_pat) (S.lift 1 equality)))
66 let arg,dir2,tac,concl_pat,gty =
68 [] -> None,true,(fun ~term _ -> P.exact_tac term),concl_pat,gty
70 let arg,gty = ProofEngineHelpers.find_hyp name context in
71 let dummy = "dummy" in
76 [PESR.rename [name] [dummy];
78 ~mk_fresh_name_callback:(fun _ _ _ ~typ -> Cic.Name name) term;
80 ReductionTactics.change_tac
82 (None,[name,Cic.Implicit (Some `Hole)], None)
83 (ProofEngineTypes.const_lazy_term typ);
87 | _::_ -> assert false
90 CicTypeChecker.type_of_aux'
91 metasenv ~subst context gty CicUniv.oblivion_ugraph
93 let if_right_to_left do_not_change a b =
95 | `RightToLeft -> if do_not_change then a else b
96 | `LeftToRight -> if do_not_change then b else a
99 CicTypeChecker.type_of_aux' metasenv ~subst context equality
100 CicUniv.oblivion_ugraph in
101 let (ty_eq,metasenv',arguments,fresh_meta) =
102 TermUtil.saturate_term
103 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in
105 if List.length arguments = 0 then
108 C.Appl (equality :: arguments) in
109 (* t1x is t2 if we are rewriting in an hypothesis *)
110 let eq_ind, ty, t1, t2, t1x =
112 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
113 when LibraryObjects.is_eq_URI uri ->
117 if_right_to_left dir2
118 LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
120 if_right_to_left dir2
121 LibraryObjects.eq_rec_URI LibraryObjects.eq_rec_r_URI
123 if_right_to_left dir2
124 LibraryObjects.eq_rect_URI LibraryObjects.eq_rect_r_URI
126 let eq_ind = C.Const (ind_uri uri,[]) in
128 if_right_to_left true (eq_ind,ty,t2,t1,t2) (eq_ind,ty,t1,t2,t1)
130 if_right_to_left true (eq_ind,ty,t1,t2,t2) (eq_ind,ty,t2,t1,t1)
131 | _ -> raise (PET.Fail (lazy "Rewrite: argument is not a proof of an equality")) in
132 (* now we always do as if direction was `LeftToRight *)
134 FreshNamesGenerator.mk_fresh_name
135 ~subst metasenv' context C.Anonymous ~typ:ty in
136 let lifted_t1 = S.lift 1 t1x in
137 let lifted_gty = S.lift 1 gty in
138 let lifted_conjecture =
139 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
141 let lifted_concl_pat =
144 | Some term -> Some (S.lift 1 term) in
146 let distance = pred (List.length c - List.length context) in
147 S.lift distance lifted_t1, m, u),[],lifted_concl_pat
149 let subst,metasenv',ugraph,_,selected_terms_with_context =
150 ProofEngineHelpers.select
151 ~metasenv:metasenv' ~subst ~ugraph ~conjecture:lifted_conjecture
152 ~pattern:lifted_pattern in
153 let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in
155 (* Note: Rel 1 does not live in the context context_of_t *)
156 (* The replace_lifting_csc 0 function will take care of lifting it *)
157 (* to context_of_t *)
159 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
160 selected_terms_with_context ([],[]) in
161 let t1 = CicMetaSubst.apply_subst subst t1 in
162 let t2 = CicMetaSubst.apply_subst subst t2 in
163 let ty = CicMetaSubst.apply_subst subst ty in
164 let pbo = lazy (CicMetaSubst.apply_subst subst (Lazy.force pbo)) in
165 let pty = CicMetaSubst.apply_subst subst pty in
166 let equality = CicMetaSubst.apply_subst subst equality in
168 ProofEngineReduction.replace_lifting_csc 0
169 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
170 if lifted_gty = abstr_gty then
171 raise (ProofEngineTypes.Fail (lazy "nothing to do"));
172 let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
173 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
174 (* The argument is either a meta if we are rewriting in the conclusion
175 or the hypothesis if we are rewriting in an hypothesis *)
176 let metasenv',arg,newtyp =
179 let fresh_meta = CicMkImplicit.new_meta metasenv' subst in
180 let gty' = S.subst t2 abstr_gty in
182 CicMkImplicit.identity_relocation_list_for_metavariable context in
183 let metasenv' = (fresh_meta,context,gty')::metasenv' in
184 metasenv', C.Meta (fresh_meta,irl), Cic.Rel (-1) (* dummy term, never used *)
186 let gty' = S.subst t1 abstr_gty in
190 C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality]
194 PET.apply_tactic (tac ~term:exact_proof newtyp)
195 ((curi,metasenv',subst,pbo,pty, attrs),goal)
198 goals@(ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
199 ~newmetasenv:metasenv')
202 with (* FG: this should be PET.Fail _ *)
203 TC.TypeCheckerFailure m ->
204 let msg = lazy ("rewrite: "^ Lazy.force m) in
208 let rewrite_tac ~direction ~pattern equality names =
209 let _, hyps_pat, _ = pattern in
210 let froms = List.map fst hyps_pat in
211 let start = PET.mk_tactic (rewrite ~direction ~pattern equality) in
212 let continuation = PESR.rename ~froms ~tos:names in
213 if names = [] then start else T.then_ ~start ~continuation
216 let rewrite_simpl_tac ~direction ~pattern equality names =
218 ~start:(rewrite_tac ~direction ~pattern equality names)
220 (ReductionTactics.simpl_tac
221 ~pattern:(ProofEngineTypes.conclusion_pattern None))
223 let replace_tac ~(pattern: ProofEngineTypes.lazy_pattern) ~with_what =
224 let replace_tac ~(pattern: ProofEngineTypes.lazy_pattern) ~with_what status =
225 let _wanted, hyps_pat, concl_pat = pattern in
226 let (proof, goal) = status in
227 let uri,metasenv,subst,pbo,pty, attrs = proof in
228 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
229 assert (hyps_pat = []); (*CSC: not implemented yet *)
231 match LibraryObjects.eq_URI () with
233 | None -> raise (ProofEngineTypes.Fail (lazy "You need to register the default equality first. Please use the \"default\" command"))
235 let context_len = List.length context in
236 let subst,metasenv,u,_,selected_terms_with_context =
237 ProofEngineHelpers.select ~subst ~metasenv ~ugraph:CicUniv.oblivion_ugraph
238 ~conjecture ~pattern in
239 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
240 let with_what, metasenv, u = with_what context metasenv u in
241 let with_what = CicMetaSubst.apply_subst subst with_what in
242 let pbo = lazy (CicMetaSubst.apply_subst subst (Lazy.force pbo)) in
243 let pty = CicMetaSubst.apply_subst subst pty in
244 let status = (uri,metasenv,subst,pbo,pty, attrs),goal in
245 let ty_of_with_what,u =
246 CicTypeChecker.type_of_aux'
247 metasenv ~subst context with_what CicUniv.oblivion_ugraph in
249 match selected_terms_with_context with
250 [] -> raise (ProofEngineTypes.Fail (lazy "Replace: no term selected"))
253 (fun (context_of_t,t) ->
256 let context_of_t_len = List.length context_of_t in
257 if context_of_t_len = context_len then t
259 (let t_in_context,subst,metasenv' =
260 CicMetaSubst.delift_rels [] metasenv
261 (context_of_t_len - context_len) t
264 assert (metasenv = metasenv');
267 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
268 (*CSC: we could implement something stronger by completely changing
269 the semantics of the tactic *)
270 raise (ProofEngineTypes.Fail
271 (lazy "Replace: one of the selected terms is not closed")) in
272 let ty_of_t_in_context,u = (* TASSI: FIXME *)
273 CicTypeChecker.type_of_aux' metasenv ~subst context t_in_context
274 CicUniv.oblivion_ugraph in
275 let b,u = CicReduction.are_convertible ~metasenv ~subst context
276 ty_of_with_what ty_of_t_in_context u in
278 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
279 let pattern_for_t = None,[],Some concl_pat_for_t in
280 t_in_context,pattern_for_t
283 (ProofEngineTypes.Fail
284 (lazy "Replace: one of the selected terms and the term to be replaced with have not convertible types"))
286 let rec aux n whats (status : ProofEngineTypes.status) =
288 [] -> ProofEngineTypes.apply_tactic T.id_tac status
289 | (what,lazy_pattern)::tl ->
290 let what = S.lift n what in
291 let with_what = S.lift n with_what in
292 let ty_of_with_what = S.lift n ty_of_with_what in
293 ProofEngineTypes.apply_tactic
298 (C.MutInd (eq_URI, 0, [])) ;
306 ~direction:`LeftToRight ~pattern:lazy_pattern (C.Rel 1) [])
310 ProofEngineTypes.mk_tactic
311 (function ((proof,goal) as status) ->
312 let _,metasenv,_,_,_, _ = proof in
313 let _,context,_ = CicUtil.lookup_meta goal metasenv in
316 match List.hd context with
317 Some (Cic.Name name,_) -> [name]
319 with (Failure "hd") -> assert false
321 ProofEngineTypes.apply_tactic
322 (PESR.clear ~hyps) status))
323 ~continuation:(aux_tac (n + 1) tl));
326 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
327 aux 0 whats (status : ProofEngineTypes.status)
329 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
333 (* All these tacs do is applying the right constructor/theorem *)
335 let reflexivity_tac =
336 IntroductionTactics.constructor_tac ~n:1
340 let symmetry_tac (proof, goal) =
341 let (_,metasenv,_,_,_, _) = proof in
342 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
343 match (R.whd context ty) with
344 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
345 when LibraryObjects.is_eq_URI uri ->
346 ProofEngineTypes.apply_tactic
347 (PrimitiveTactics.apply_tac
348 ~term:(C.Const (LibraryObjects.sym_eq_URI uri, [])))
351 | _ -> raise (ProofEngineTypes.Fail (lazy "Symmetry failed"))
353 ProofEngineTypes.mk_tactic symmetry_tac
356 let transitivity_tac ~term =
357 let transitivity_tac ~term status =
358 let (proof, goal) = status in
359 let (_,metasenv,_,_,_, _) = proof in
360 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
361 match (R.whd context ty) with
362 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
363 when LibraryObjects.is_eq_URI uri ->
364 ProofEngineTypes.apply_tactic
366 ~start:(PrimitiveTactics.apply_tac
367 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
369 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
372 | _ -> raise (ProofEngineTypes.Fail (lazy "Transitivity failed"))
374 ProofEngineTypes.mk_tactic (transitivity_tac ~term)