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 rec 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 curi, metasenv, pbo, pty = proof in
39 let (metano,context,gty) as conjecture = CicUtil.lookup_meta goal metasenv in
44 (rewrite_tac ~direction
45 ~pattern:(None,[he],Cic.Implicit None) equality)
46 (rewrite_tac ~direction ~pattern:(None,tl,concl_pat) equality)
48 | [_] as hyps_pat when concl_pat <> Cic.Implicit None ->
51 (rewrite_tac ~direction
52 ~pattern:(None,hyps_pat,Cic.Implicit None) equality)
53 (rewrite_tac ~direction ~pattern:(None,[],concl_pat) equality)
56 let arg,dir2,tac,concl_pat,gty =
58 [] -> None,true,PT.exact_tac,concl_pat,gty
60 (*CSC: bug here; I am ignoring the concl_pat *)
64 | Some (Cic.Name s,Cic.Decl ty)::_ when name = s ->
65 Cic.Rel n, CicSubstitution.lift n ty
66 | Some (Cic.Name s,Cic.Def _)::_ -> assert false (*CSC: not implemented yet!*)
67 | _::tl -> find_hyp (n+1) tl
69 let arg,gty = find_hyp 1 context in
70 let last_hyp_name_of_status (proof,goal) =
71 let curi, metasenv, pbo, pty = proof in
72 let metano,context,gty = CicUtil.lookup_meta goal metasenv in
74 (Some (Cic.Name s,_))::_ -> s
77 let dummy = "dummy" in
82 [ProofEngineStructuralRules.rename name dummy;
84 ~mk_fresh_name_callback:(fun _ _ _ ~typ -> Cic.Name name) term;
85 ProofEngineStructuralRules.clearbody name;
86 ReductionTactics.simpl_tac
88 (None,[name,Cic.Implicit (Some `Hole)],Cic.Implicit None);
89 ProofEngineStructuralRules.clear dummy
92 | _::_ -> assert false
94 let if_right_to_left do_not_change a b =
96 | `RightToLeft -> if do_not_change then a else b
97 | `LeftToRight -> if do_not_change then b else a
100 CicTypeChecker.type_of_aux' metasenv context equality
101 CicUniv.empty_ugraph in
102 let (ty_eq,metasenv',arguments,fresh_meta) =
103 ProofEngineHelpers.saturate_term
104 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in
106 if List.length arguments = 0 then
109 C.Appl (equality :: arguments) in
110 (* t1x is t2 if we are rewriting in an hypothesis *)
111 let eq_ind, ty, t1, t2, t1x =
113 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
114 when LibraryObjects.is_eq_URI uri ->
116 if_right_to_left dir2
117 LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
119 let eq_ind = C.Const (ind_uri uri,[]) in
121 if_right_to_left true (eq_ind,ty,t2,t1,t2) (eq_ind,ty,t1,t2,t1)
123 if_right_to_left true (eq_ind,ty,t1,t2,t2) (eq_ind,ty,t2,t1,t1)
124 | _ -> raise (PET.Fail (lazy "Rewrite: argument is not a proof of an equality")) in
125 (* now we always do as if direction was `LeftToRight *)
127 FreshNamesGenerator.mk_fresh_name
128 ~subst:[] metasenv' context C.Anonymous ~typ:ty in
129 let lifted_t1 = CicSubstitution.lift 1 t1x in
130 let lifted_gty = CicSubstitution.lift 1 gty in
131 let lifted_conjecture =
132 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
134 Some (fun _ m u -> lifted_t1, m, u),[],CicSubstitution.lift 1 concl_pat
136 let subst,metasenv',ugraph,_,selected_terms_with_context =
137 ProofEngineHelpers.select
138 ~metasenv:metasenv' ~ugraph ~conjecture:lifted_conjecture
139 ~pattern:lifted_pattern in
140 let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in
142 (* Note: Rel 1 does not live in the context context_of_t *)
143 (* The replace_lifting_csc 0 function will take care of lifting it *)
144 (* to context_of_t *)
146 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
147 selected_terms_with_context ([],[]) in
148 let t1 = CicMetaSubst.apply_subst subst t1 in
149 let t2 = CicMetaSubst.apply_subst subst t2 in
150 let equality = CicMetaSubst.apply_subst subst equality in
152 ProofEngineReduction.replace_lifting_csc 0
153 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
154 let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
155 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
156 (* The argument is either a meta if we are rewriting in the conclusion
157 or the hypothesis if we are rewriting in an hypothesis *)
161 let gty' = CicSubstitution.subst t2 abstr_gty in
163 CicMkImplicit.identity_relocation_list_for_metavariable context in
164 let metasenv' = (fresh_meta,context,gty')::metasenv' in
165 metasenv', C.Meta (fresh_meta,irl)
170 C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality]
174 (tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal)
177 goals@(ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
178 ~newmetasenv:metasenv')
182 ProofEngineTypes.mk_tactic (_rewrite_tac ~direction ~pattern equality)
185 let rewrite_simpl_tac ~direction ~pattern equality =
186 let rewrite_simpl_tac ~direction ~pattern equality status =
187 ProofEngineTypes.apply_tactic
189 ~start:(rewrite_tac ~direction ~pattern equality)
191 (ReductionTactics.simpl_tac
192 ~pattern:(ProofEngineTypes.conclusion_pattern None)))
195 ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
198 let replace_tac ~pattern ~with_what =
199 let replace_tac ~pattern:(wanted,hyps_pat,concl_pat) ~with_what status =
200 let (proof, goal) = status in
201 let module C = Cic in
202 let module U = UriManager in
203 let module P = PrimitiveTactics in
204 let module T = Tacticals in
205 let uri,metasenv,pbo,pty = proof in
206 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
207 assert (hyps_pat = []); (*CSC: not implemented yet *)
208 let context_len = List.length context in
209 let subst,metasenv,u,_,selected_terms_with_context =
210 ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.empty_ugraph
211 ~conjecture ~pattern in
212 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
213 let with_what, metasenv, u = with_what context metasenv u in
214 let with_what = CicMetaSubst.apply_subst subst with_what in
215 let pbo = CicMetaSubst.apply_subst subst pbo in
216 let pty = CicMetaSubst.apply_subst subst pty in
217 let status = (uri,metasenv,pbo,pty),goal in
218 let ty_of_with_what,u =
219 CicTypeChecker.type_of_aux'
220 metasenv context with_what CicUniv.empty_ugraph in
222 match selected_terms_with_context with
223 [] -> raise (ProofEngineTypes.Fail (lazy "Replace: no term selected"))
226 (fun (context_of_t,t) ->
229 let context_of_t_len = List.length context_of_t in
230 if context_of_t_len = context_len then t
232 (let t_in_context,subst,metasenv' =
233 CicMetaSubst.delift_rels [] metasenv
234 (context_of_t_len - context_len) t
237 assert (metasenv = metasenv');
240 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
241 (*CSC: we could implement something stronger by completely changing
242 the semantics of the tactic *)
243 raise (ProofEngineTypes.Fail
244 (lazy "Replace: one of the selected terms is not closed")) in
245 let ty_of_t_in_context,u = (* TASSI: FIXME *)
246 CicTypeChecker.type_of_aux' metasenv context t_in_context
247 CicUniv.empty_ugraph in
248 let b,u = CicReduction.are_convertible ~metasenv context
249 ty_of_with_what ty_of_t_in_context u in
251 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
252 let pattern_for_t = None,[],concl_pat_for_t in
253 t_in_context,pattern_for_t
256 (ProofEngineTypes.Fail
257 (lazy "Replace: one of the selected terms and the term to be replaced with have not convertible types"))
259 let rec aux n whats status =
261 [] -> ProofEngineTypes.apply_tactic T.id_tac status
262 | (what,pattern)::tl ->
263 let what = CicSubstitution.lift n what in
264 let with_what = CicSubstitution.lift n with_what in
265 let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in
266 ProofEngineTypes.apply_tactic
271 (C.MutInd (LibraryObjects.eq_URI (), 0, [])) ;
278 rewrite_tac ~direction:`LeftToRight ~pattern (C.Rel 1))
282 ProofEngineTypes.mk_tactic
283 (function ((proof,goal) as status) ->
284 let _,metasenv,_,_ = proof in
285 let _,context,_ = CicUtil.lookup_meta goal metasenv in
288 match List.hd context with
289 Some (Cic.Name name,_) -> name
291 with (Failure "hd") -> assert false
293 ProofEngineTypes.apply_tactic
294 (ProofEngineStructuralRules.clear ~hyp) status))
295 ~continuation:(aux_tac (n + 1) tl));
298 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
301 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
305 (* All these tacs do is applying the right constructor/theorem *)
307 let reflexivity_tac =
308 IntroductionTactics.constructor_tac ~n:1
312 let symmetry_tac (proof, goal) =
313 let module C = Cic in
314 let module R = CicReduction in
315 let module U = UriManager in
316 let (_,metasenv,_,_) = proof in
317 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
318 match (R.whd context ty) with
319 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
320 when LibraryObjects.is_eq_URI uri ->
321 ProofEngineTypes.apply_tactic
322 (PrimitiveTactics.apply_tac
323 ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
326 | _ -> raise (ProofEngineTypes.Fail (lazy "Symmetry failed"))
328 ProofEngineTypes.mk_tactic symmetry_tac
331 let transitivity_tac ~term =
332 let transitivity_tac ~term status =
333 let (proof, goal) = status in
334 let module C = Cic in
335 let module R = CicReduction in
336 let module U = UriManager in
337 let module T = Tacticals in
338 let (_,metasenv,_,_) = proof in
339 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
340 match (R.whd context ty) with
341 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
342 when LibraryObjects.is_eq_URI uri ->
343 ProofEngineTypes.apply_tactic
345 ~start:(PrimitiveTactics.apply_tac
346 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
348 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
351 | _ -> raise (ProofEngineTypes.Fail (lazy "Transitivity failed"))
353 ProofEngineTypes.mk_tactic (transitivity_tac ~term)