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/.
28 let rec rewrite_tac ~direction ~(pattern: ProofEngineTypes.lazy_pattern) equality =
29 let _rewrite_tac ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status
32 let module U = UriManager in
33 let module PET = ProofEngineTypes in
34 let module PER = ProofEngineReduction in
35 let module PEH = ProofEngineHelpers in
36 let module PT = PrimitiveTactics in
37 assert (wanted = None); (* this should be checked syntactically *)
38 let proof,goal = status in
39 let curi, metasenv, pbo, pty = proof in
40 let (metano,context,gty) = CicUtil.lookup_meta goal metasenv in
45 (rewrite_tac ~direction
46 ~pattern:(None,[he],None) equality)
47 (rewrite_tac ~direction ~pattern:(None,tl,concl_pat)
48 (CicSubstitution.lift 1 equality))
50 | [_] as hyps_pat when concl_pat <> None ->
53 (rewrite_tac ~direction
54 ~pattern:(None,hyps_pat,None) equality)
55 (rewrite_tac ~direction ~pattern:(None,[],concl_pat)
56 (CicSubstitution.lift 1 equality))
59 let arg,dir2,tac,concl_pat,gty =
61 [] -> None,true,(fun ~term _ -> PT.exact_tac term),concl_pat,gty
66 | Some (Cic.Name s,Cic.Decl ty)::_ when name = s ->
67 Cic.Rel n, CicSubstitution.lift n ty
68 | Some (Cic.Name s,Cic.Def _)::_ -> assert false (*CSC: not implemented yet! But does this make any sense?*)
69 | _::tl -> find_hyp (n+1) tl
71 let arg,gty = find_hyp 1 context in
72 let dummy = "dummy" in
77 [ProofEngineStructuralRules.rename name dummy;
79 ~mk_fresh_name_callback:(fun _ _ _ ~typ -> Cic.Name name) term;
80 ProofEngineStructuralRules.clearbody name;
81 ReductionTactics.change_tac
83 (None,[name,Cic.Implicit (Some `Hole)], None)
84 (ProofEngineTypes.const_lazy_term typ);
85 ProofEngineStructuralRules.clear [dummy]
88 | _::_ -> assert false
90 let if_right_to_left do_not_change a b =
92 | `RightToLeft -> if do_not_change then a else b
93 | `LeftToRight -> if do_not_change then b else a
96 CicTypeChecker.type_of_aux' metasenv context equality
97 CicUniv.empty_ugraph in
98 let (ty_eq,metasenv',arguments,fresh_meta) =
99 ProofEngineHelpers.saturate_term
100 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in
102 if List.length arguments = 0 then
105 C.Appl (equality :: arguments) in
106 (* t1x is t2 if we are rewriting in an hypothesis *)
107 let eq_ind, ty, t1, t2, t1x =
109 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
110 when LibraryObjects.is_eq_URI uri ->
112 if_right_to_left dir2
113 LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
115 let eq_ind = C.Const (ind_uri uri,[]) in
117 if_right_to_left true (eq_ind,ty,t2,t1,t2) (eq_ind,ty,t1,t2,t1)
119 if_right_to_left true (eq_ind,ty,t1,t2,t2) (eq_ind,ty,t2,t1,t1)
120 | _ -> raise (PET.Fail (lazy "Rewrite: argument is not a proof of an equality")) in
121 (* now we always do as if direction was `LeftToRight *)
123 FreshNamesGenerator.mk_fresh_name
124 ~subst:[] metasenv' context C.Anonymous ~typ:ty in
125 let lifted_t1 = CicSubstitution.lift 1 t1x in
126 let lifted_gty = CicSubstitution.lift 1 gty in
127 let lifted_conjecture =
128 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
130 let lifted_concl_pat =
133 | Some term -> Some (CicSubstitution.lift 1 term) in
134 Some (fun _ m u -> lifted_t1, m, u),[],lifted_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 ty = CicMetaSubst.apply_subst subst ty in
151 let pbo = CicMetaSubst.apply_subst subst pbo in
152 let pty = CicMetaSubst.apply_subst subst pty in
153 let equality = CicMetaSubst.apply_subst subst equality in
155 ProofEngineReduction.replace_lifting_csc 0
156 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
157 let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
158 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
159 (* The argument is either a meta if we are rewriting in the conclusion
160 or the hypothesis if we are rewriting in an hypothesis *)
161 let metasenv',arg,newtyp =
164 let gty' = CicSubstitution.subst t2 abstr_gty in
166 CicMkImplicit.identity_relocation_list_for_metavariable context in
167 let metasenv' = (fresh_meta,context,gty')::metasenv' in
168 metasenv', C.Meta (fresh_meta,irl), Cic.Rel (-1) (* dummy term, never used *)
170 let gty' = CicSubstitution.subst t1 abstr_gty in
174 C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality]
178 (tac ~term:exact_proof newtyp) ((curi,metasenv',pbo,pty),goal)
181 goals@(ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
182 ~newmetasenv:metasenv')
186 ProofEngineTypes.mk_tactic (_rewrite_tac ~direction ~pattern equality)
189 let rewrite_simpl_tac ~direction ~pattern equality =
190 let rewrite_simpl_tac ~direction ~pattern equality status =
191 ProofEngineTypes.apply_tactic
193 ~start:(rewrite_tac ~direction ~pattern equality)
195 (ReductionTactics.simpl_tac
196 ~pattern:(ProofEngineTypes.conclusion_pattern None)))
199 ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
202 let replace_tac ~(pattern: ProofEngineTypes.lazy_pattern) ~with_what =
203 let replace_tac ~(pattern: ProofEngineTypes.lazy_pattern) ~with_what status =
204 let _wanted, hyps_pat, concl_pat = pattern in
205 let (proof, goal) = status in
206 let module C = Cic in
207 let module U = UriManager in
208 let module P = PrimitiveTactics in
209 let module T = Tacticals in
210 let uri,metasenv,pbo,pty = proof in
211 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
212 assert (hyps_pat = []); (*CSC: not implemented yet *)
214 match LibraryObjects.eq_URI () with
216 | None -> raise (ProofEngineTypes.Fail (lazy "You need to register the default equality first. Please use the \"default\" command"))
218 let context_len = List.length context in
219 let subst,metasenv,u,_,selected_terms_with_context =
220 ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.empty_ugraph
221 ~conjecture ~pattern in
222 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
223 let with_what, metasenv, u = with_what context metasenv u in
224 let with_what = CicMetaSubst.apply_subst subst with_what in
225 let pbo = CicMetaSubst.apply_subst subst pbo in
226 let pty = CicMetaSubst.apply_subst subst pty in
227 let status = (uri,metasenv,pbo,pty),goal in
228 let ty_of_with_what,u =
229 CicTypeChecker.type_of_aux'
230 metasenv context with_what CicUniv.empty_ugraph in
232 match selected_terms_with_context with
233 [] -> raise (ProofEngineTypes.Fail (lazy "Replace: no term selected"))
236 (fun (context_of_t,t) ->
239 let context_of_t_len = List.length context_of_t in
240 if context_of_t_len = context_len then t
242 (let t_in_context,subst,metasenv' =
243 CicMetaSubst.delift_rels [] metasenv
244 (context_of_t_len - context_len) t
247 assert (metasenv = metasenv');
250 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
251 (*CSC: we could implement something stronger by completely changing
252 the semantics of the tactic *)
253 raise (ProofEngineTypes.Fail
254 (lazy "Replace: one of the selected terms is not closed")) in
255 let ty_of_t_in_context,u = (* TASSI: FIXME *)
256 CicTypeChecker.type_of_aux' metasenv context t_in_context
257 CicUniv.empty_ugraph in
258 let b,u = CicReduction.are_convertible ~metasenv context
259 ty_of_with_what ty_of_t_in_context u in
261 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
262 let pattern_for_t = None,[],Some concl_pat_for_t in
263 t_in_context,pattern_for_t
266 (ProofEngineTypes.Fail
267 (lazy "Replace: one of the selected terms and the term to be replaced with have not convertible types"))
269 let rec aux n whats status =
271 [] -> ProofEngineTypes.apply_tactic T.id_tac status
272 | (what,lazy_pattern)::tl ->
273 let what = CicSubstitution.lift n what in
274 let with_what = CicSubstitution.lift n with_what in
275 let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in
276 ProofEngineTypes.apply_tactic
281 (C.MutInd (eq_URI, 0, [])) ;
288 rewrite_tac ~direction:`LeftToRight ~pattern:lazy_pattern (C.Rel 1))
292 ProofEngineTypes.mk_tactic
293 (function ((proof,goal) as status) ->
294 let _,metasenv,_,_ = proof in
295 let _,context,_ = CicUtil.lookup_meta goal metasenv in
298 match List.hd context with
299 Some (Cic.Name name,_) -> [name]
301 with (Failure "hd") -> assert false
303 ProofEngineTypes.apply_tactic
304 (ProofEngineStructuralRules.clear ~hyps) status))
305 ~continuation:(aux_tac (n + 1) tl));
308 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
311 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
315 (* All these tacs do is applying the right constructor/theorem *)
317 let reflexivity_tac =
318 IntroductionTactics.constructor_tac ~n:1
322 let symmetry_tac (proof, goal) =
323 let module C = Cic in
324 let module R = CicReduction in
325 let module U = UriManager in
326 let (_,metasenv,_,_) = proof in
327 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
328 match (R.whd context ty) with
329 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
330 when LibraryObjects.is_eq_URI uri ->
331 ProofEngineTypes.apply_tactic
332 (PrimitiveTactics.apply_tac
333 ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
336 | _ -> raise (ProofEngineTypes.Fail (lazy "Symmetry failed"))
338 ProofEngineTypes.mk_tactic symmetry_tac
341 let transitivity_tac ~term =
342 let transitivity_tac ~term status =
343 let (proof, goal) = status in
344 let module C = Cic in
345 let module R = CicReduction in
346 let module U = UriManager in
347 let module T = Tacticals in
348 let (_,metasenv,_,_) = proof in
349 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
350 match (R.whd context ty) with
351 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
352 when LibraryObjects.is_eq_URI uri ->
353 ProofEngineTypes.apply_tactic
355 ~start:(PrimitiveTactics.apply_tac
356 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
358 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
361 | _ -> raise (ProofEngineTypes.Fail (lazy "Transitivity failed"))
363 ProofEngineTypes.mk_tactic (transitivity_tac ~term)