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.
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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/.
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) equality)
49 | [_] as hyps_pat when concl_pat <> None ->
52 (rewrite_tac ~direction
53 ~pattern:(None,hyps_pat,None) equality)
54 (rewrite_tac ~direction ~pattern:(None,[],concl_pat) equality)
57 let arg,dir2,tac,concl_pat,gty =
59 [] -> None,true,(fun ~term _ -> PT.exact_tac term),concl_pat,gty
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! But does this make any sense?*)
67 | _::tl -> find_hyp (n+1) tl
69 let arg,gty = find_hyp 1 context in
70 let dummy = "dummy" in
75 [ProofEngineStructuralRules.rename name dummy;
77 ~mk_fresh_name_callback:(fun _ _ _ ~typ -> Cic.Name name) term;
78 ProofEngineStructuralRules.clearbody name;
79 ReductionTactics.change_tac
81 (None,[name,Cic.Implicit (Some `Hole)], None)
82 (ProofEngineTypes.const_lazy_term typ);
83 ProofEngineStructuralRules.clear dummy
86 | _::_ -> assert false
88 let if_right_to_left do_not_change a b =
90 | `RightToLeft -> if do_not_change then a else b
91 | `LeftToRight -> if do_not_change then b else a
94 CicTypeChecker.type_of_aux' metasenv context equality
95 CicUniv.empty_ugraph in
96 let (ty_eq,metasenv',arguments,fresh_meta) =
97 ProofEngineHelpers.saturate_term
98 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in
100 if List.length arguments = 0 then
103 C.Appl (equality :: arguments) in
104 (* t1x is t2 if we are rewriting in an hypothesis *)
105 let eq_ind, ty, t1, t2, t1x =
107 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
108 when LibraryObjects.is_eq_URI uri ->
110 if_right_to_left dir2
111 LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
113 let eq_ind = C.Const (ind_uri uri,[]) in
115 if_right_to_left true (eq_ind,ty,t2,t1,t2) (eq_ind,ty,t1,t2,t1)
117 if_right_to_left true (eq_ind,ty,t1,t2,t2) (eq_ind,ty,t2,t1,t1)
118 | _ -> raise (PET.Fail (lazy "Rewrite: argument is not a proof of an equality")) in
119 (* now we always do as if direction was `LeftToRight *)
121 FreshNamesGenerator.mk_fresh_name
122 ~subst:[] metasenv' context C.Anonymous ~typ:ty in
123 let lifted_t1 = CicSubstitution.lift 1 t1x in
124 let lifted_gty = CicSubstitution.lift 1 gty in
125 let lifted_conjecture =
126 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
128 let lifted_concl_pat =
131 | Some term -> Some (CicSubstitution.lift 1 term) in
132 Some (fun _ m u -> lifted_t1, m, u),[],lifted_concl_pat
134 let subst,metasenv',ugraph,_,selected_terms_with_context =
135 ProofEngineHelpers.select
136 ~metasenv:metasenv' ~ugraph ~conjecture:lifted_conjecture
137 ~pattern:lifted_pattern in
138 let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in
140 (* Note: Rel 1 does not live in the context context_of_t *)
141 (* The replace_lifting_csc 0 function will take care of lifting it *)
142 (* to context_of_t *)
144 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
145 selected_terms_with_context ([],[]) in
146 let t1 = CicMetaSubst.apply_subst subst t1 in
147 let t2 = CicMetaSubst.apply_subst subst t2 in
148 let ty = CicMetaSubst.apply_subst subst ty in
149 let equality = CicMetaSubst.apply_subst subst equality in
151 ProofEngineReduction.replace_lifting_csc 0
152 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
153 let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
154 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
155 (* The argument is either a meta if we are rewriting in the conclusion
156 or the hypothesis if we are rewriting in an hypothesis *)
157 let metasenv',arg,newtyp =
160 let gty' = CicSubstitution.subst t2 abstr_gty in
162 CicMkImplicit.identity_relocation_list_for_metavariable context in
163 let metasenv' = (fresh_meta,context,gty')::metasenv' in
164 metasenv', C.Meta (fresh_meta,irl), Cic.Rel (-1) (* dummy term, never used *)
166 let gty' = CicSubstitution.subst t1 abstr_gty in
170 C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality]
174 (tac ~term:exact_proof newtyp) ((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: ProofEngineTypes.lazy_pattern) ~with_what =
199 let replace_tac ~(pattern: ProofEngineTypes.lazy_pattern) ~with_what status =
200 let _wanted, hyps_pat, concl_pat = pattern in
201 let (proof, goal) = status in
202 let module C = Cic in
203 let module U = UriManager in
204 let module P = PrimitiveTactics in
205 let module T = Tacticals in
206 let uri,metasenv,pbo,pty = proof in
207 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
208 assert (hyps_pat = []); (*CSC: not implemented yet *)
210 match LibraryObjects.eq_URI () with
212 | None -> raise (ProofEngineTypes.Fail (lazy "You need to register the default equality first. Please use the \"default\" command"))
214 let context_len = List.length context in
215 let subst,metasenv,u,_,selected_terms_with_context =
216 ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.empty_ugraph
217 ~conjecture ~pattern in
218 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
219 let with_what, metasenv, u = with_what context metasenv u in
220 let with_what = CicMetaSubst.apply_subst subst with_what in
221 let pbo = CicMetaSubst.apply_subst subst pbo in
222 let pty = CicMetaSubst.apply_subst subst pty in
223 let status = (uri,metasenv,pbo,pty),goal in
224 let ty_of_with_what,u =
225 CicTypeChecker.type_of_aux'
226 metasenv context with_what CicUniv.empty_ugraph in
228 match selected_terms_with_context with
229 [] -> raise (ProofEngineTypes.Fail (lazy "Replace: no term selected"))
232 (fun (context_of_t,t) ->
235 let context_of_t_len = List.length context_of_t in
236 if context_of_t_len = context_len then t
238 (let t_in_context,subst,metasenv' =
239 CicMetaSubst.delift_rels [] metasenv
240 (context_of_t_len - context_len) t
243 assert (metasenv = metasenv');
246 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
247 (*CSC: we could implement something stronger by completely changing
248 the semantics of the tactic *)
249 raise (ProofEngineTypes.Fail
250 (lazy "Replace: one of the selected terms is not closed")) in
251 let ty_of_t_in_context,u = (* TASSI: FIXME *)
252 CicTypeChecker.type_of_aux' metasenv context t_in_context
253 CicUniv.empty_ugraph in
254 let b,u = CicReduction.are_convertible ~metasenv context
255 ty_of_with_what ty_of_t_in_context u in
257 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
258 let pattern_for_t = None,[],Some concl_pat_for_t in
259 t_in_context,pattern_for_t
262 (ProofEngineTypes.Fail
263 (lazy "Replace: one of the selected terms and the term to be replaced with have not convertible types"))
265 let rec aux n whats status =
267 [] -> ProofEngineTypes.apply_tactic T.id_tac status
268 | (what,lazy_pattern)::tl ->
269 let what = CicSubstitution.lift n what in
270 let with_what = CicSubstitution.lift n with_what in
271 let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in
272 ProofEngineTypes.apply_tactic
277 (C.MutInd (eq_URI, 0, [])) ;
284 rewrite_tac ~direction:`LeftToRight ~pattern:lazy_pattern (C.Rel 1))
288 ProofEngineTypes.mk_tactic
289 (function ((proof,goal) as status) ->
290 let _,metasenv,_,_ = proof in
291 let _,context,_ = CicUtil.lookup_meta goal metasenv in
294 match List.hd context with
295 Some (Cic.Name name,_) -> name
297 with (Failure "hd") -> assert false
299 ProofEngineTypes.apply_tactic
300 (ProofEngineStructuralRules.clear ~hyp) status))
301 ~continuation:(aux_tac (n + 1) tl));
304 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
307 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
311 (* All these tacs do is applying the right constructor/theorem *)
313 let reflexivity_tac =
314 IntroductionTactics.constructor_tac ~n:1
318 let symmetry_tac (proof, goal) =
319 let module C = Cic in
320 let module R = CicReduction in
321 let module U = UriManager in
322 let (_,metasenv,_,_) = proof in
323 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
324 match (R.whd context ty) with
325 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
326 when LibraryObjects.is_eq_URI uri ->
327 ProofEngineTypes.apply_tactic
328 (PrimitiveTactics.apply_tac
329 ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
332 | _ -> raise (ProofEngineTypes.Fail (lazy "Symmetry failed"))
334 ProofEngineTypes.mk_tactic symmetry_tac
337 let transitivity_tac ~term =
338 let transitivity_tac ~term status =
339 let (proof, goal) = status in
340 let module C = Cic in
341 let module R = CicReduction in
342 let module U = UriManager in
343 let module T = Tacticals in
344 let (_,metasenv,_,_) = proof in
345 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
346 match (R.whd context ty) with
347 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
348 when LibraryObjects.is_eq_URI uri ->
349 ProofEngineTypes.apply_tactic
351 ~start:(PrimitiveTactics.apply_tac
352 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
354 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
357 | _ -> raise (ProofEngineTypes.Fail (lazy "Transitivity failed"))
359 ProofEngineTypes.mk_tactic (transitivity_tac ~term)