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/.
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 curi, metasenv, pbo, pty = proof in
39 let (metano,context,gty) as conjecture = CicUtil.lookup_meta goal metasenv in
40 let arg,dir2,tac,concl_pat,gty =
42 [] -> None,true,PT.exact_tac,concl_pat,gty
44 (*CSC: bug here; I am ignoring the concl_pat *)
48 | Some (Cic.Name s,Cic.Decl ty)::_ when name = s ->
49 Cic.Rel n, CicSubstitution.lift n ty
50 | Some (Cic.Name s,Cic.Def _)::_ -> assert false (*CSC: not implemented yet!*)
51 | _::tl -> find_hyp (n+1) tl
53 let arg,gty = find_hyp 1 context in
54 let last_hyp_name_of_status (proof,goal) =
55 let curi, metasenv, pbo, pty = proof in
56 let metano,context,gty = CicUtil.lookup_meta goal metasenv in
58 (Some (Cic.Name s,_))::_ -> s
66 PET.mk_tactic (fun status ->
68 (ProofEngineStructuralRules.clearbody
69 (last_hyp_name_of_status status)) status);
70 PET.mk_tactic (fun status ->
71 let hyp = last_hyp_name_of_status status in
73 (ReductionTactics.simpl_tac
75 (None,[hyp,Cic.Implicit (Some `Hole)],Cic.Implicit None))
77 ProofEngineStructuralRules.clear name;
78 PET.mk_tactic (fun status ->
79 let hyp = last_hyp_name_of_status status in
81 (ProofEngineStructuralRules.rename hyp name) status)
84 | _ -> assert false (*CSC: not implemented yet!*)
86 let if_right_to_left do_not_change a b =
88 | `RightToLeft -> if do_not_change then a else b
89 | `LeftToRight -> if do_not_change then b else a
92 CicTypeChecker.type_of_aux' metasenv context equality
93 CicUniv.empty_ugraph in
94 let (ty_eq,metasenv',arguments,fresh_meta) =
95 ProofEngineHelpers.saturate_term
96 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in
98 if List.length arguments = 0 then
101 C.Appl (equality :: arguments) in
102 (* t1x is t2 if we are rewriting in an hypothesis *)
103 let eq_ind, ty, t1, t2, t1x =
105 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
106 when LibraryObjects.is_eq_URI uri ->
108 if_right_to_left dir2
109 LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
111 let eq_ind = C.Const (ind_uri uri,[]) in
113 if_right_to_left true (eq_ind,ty,t2,t1,t2) (eq_ind,ty,t1,t2,t1)
115 if_right_to_left true (eq_ind,ty,t1,t2,t2) (eq_ind,ty,t2,t1,t1)
116 | _ -> raise (PET.Fail (lazy "Rewrite: argument is not a proof of an equality")) in
117 (* now we always do as if direction was `LeftToRight *)
119 FreshNamesGenerator.mk_fresh_name
120 ~subst:[] metasenv' context C.Anonymous ~typ:ty in
121 let lifted_t1 = CicSubstitution.lift 1 t1x in
122 let lifted_gty = CicSubstitution.lift 1 gty in
123 let lifted_conjecture =
124 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
126 Some (fun _ m u -> lifted_t1, m, u),[],CicSubstitution.lift 1 concl_pat
128 let subst,metasenv',ugraph,_,selected_terms_with_context =
129 ProofEngineHelpers.select
130 ~metasenv:metasenv' ~ugraph ~conjecture:lifted_conjecture
131 ~pattern:lifted_pattern in
132 let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in
134 (* Note: Rel 1 does not live in the context context_of_t *)
135 (* The replace_lifting_csc 0 function will take care of lifting it *)
136 (* to context_of_t *)
138 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
139 selected_terms_with_context ([],[]) in
140 let t1 = CicMetaSubst.apply_subst subst t1 in
141 let t2 = CicMetaSubst.apply_subst subst t2 in
142 let equality = CicMetaSubst.apply_subst subst equality in
144 ProofEngineReduction.replace_lifting_csc 0
145 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
146 let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
147 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
148 (* The argument is either a meta if we are rewriting in the conclusion
149 or the hypothesis if we are rewriting in an hypothesis *)
153 let gty' = CicSubstitution.subst t2 abstr_gty in
155 CicMkImplicit.identity_relocation_list_for_metavariable context in
156 let metasenv' = (fresh_meta,context,gty')::metasenv' in
157 metasenv', C.Meta (fresh_meta,irl)
162 C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality]
166 (tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal)
169 goals@(ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
170 ~newmetasenv:metasenv')
174 ProofEngineTypes.mk_tactic (rewrite_tac ~direction ~pattern equality)
177 let rewrite_simpl_tac ~direction ~pattern equality =
178 let rewrite_simpl_tac ~direction ~pattern equality status =
179 ProofEngineTypes.apply_tactic
181 ~start:(rewrite_tac ~direction ~pattern equality)
183 (ReductionTactics.simpl_tac
184 ~pattern:(ProofEngineTypes.conclusion_pattern None)))
187 ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
190 let replace_tac ~pattern ~with_what =
191 let replace_tac ~pattern:(wanted,hyps_pat,concl_pat) ~with_what status =
192 let (proof, goal) = status in
193 let module C = Cic in
194 let module U = UriManager in
195 let module P = PrimitiveTactics in
196 let module T = Tacticals in
197 let uri,metasenv,pbo,pty = proof in
198 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
199 assert (hyps_pat = []); (*CSC: not implemented yet *)
200 let context_len = List.length context in
201 let subst,metasenv,u,_,selected_terms_with_context =
202 ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.empty_ugraph
203 ~conjecture ~pattern in
204 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
205 let with_what, metasenv, u = with_what context metasenv u in
206 let with_what = CicMetaSubst.apply_subst subst with_what in
207 let pbo = CicMetaSubst.apply_subst subst pbo in
208 let pty = CicMetaSubst.apply_subst subst pty in
209 let status = (uri,metasenv,pbo,pty),goal in
210 let ty_of_with_what,u =
211 CicTypeChecker.type_of_aux'
212 metasenv context with_what CicUniv.empty_ugraph in
214 match selected_terms_with_context with
215 [] -> raise (ProofEngineTypes.Fail (lazy "Replace: no term selected"))
218 (fun (context_of_t,t) ->
221 let context_of_t_len = List.length context_of_t in
222 if context_of_t_len = context_len then t
224 (let t_in_context,subst,metasenv' =
225 CicMetaSubst.delift_rels [] metasenv
226 (context_of_t_len - context_len) t
229 assert (metasenv = metasenv');
232 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
233 (*CSC: we could implement something stronger by completely changing
234 the semantics of the tactic *)
235 raise (ProofEngineTypes.Fail
236 (lazy "Replace: one of the selected terms is not closed")) in
237 let ty_of_t_in_context,u = (* TASSI: FIXME *)
238 CicTypeChecker.type_of_aux' metasenv context t_in_context
239 CicUniv.empty_ugraph in
240 let b,u = CicReduction.are_convertible ~metasenv context
241 ty_of_with_what ty_of_t_in_context u in
243 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
244 let pattern_for_t = None,[],concl_pat_for_t in
245 t_in_context,pattern_for_t
248 (ProofEngineTypes.Fail
249 (lazy "Replace: one of the selected terms and the term to be replaced with have not convertible types"))
251 let rec aux n whats status =
253 [] -> ProofEngineTypes.apply_tactic T.id_tac status
254 | (what,pattern)::tl ->
255 let what = CicSubstitution.lift n what in
256 let with_what = CicSubstitution.lift n with_what in
257 let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in
258 ProofEngineTypes.apply_tactic
263 (C.MutInd (LibraryObjects.eq_URI (), 0, [])) ;
270 rewrite_tac ~direction:`LeftToRight ~pattern (C.Rel 1))
274 ProofEngineTypes.mk_tactic
275 (function ((proof,goal) as status) ->
276 let _,metasenv,_,_ = proof in
277 let _,context,_ = CicUtil.lookup_meta goal metasenv in
280 match List.hd context with
281 Some (Cic.Name name,_) -> name
283 with (Failure "hd") -> assert false
285 ProofEngineTypes.apply_tactic
286 (ProofEngineStructuralRules.clear ~hyp) status))
287 ~continuation:(aux_tac (n + 1) tl));
290 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
293 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
297 (* All these tacs do is applying the right constructor/theorem *)
299 let reflexivity_tac =
300 IntroductionTactics.constructor_tac ~n:1
304 let symmetry_tac (proof, goal) =
305 let module C = Cic in
306 let module R = CicReduction in
307 let module U = UriManager in
308 let (_,metasenv,_,_) = proof in
309 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
310 match (R.whd context ty) with
311 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
312 when LibraryObjects.is_eq_URI uri ->
313 ProofEngineTypes.apply_tactic
314 (PrimitiveTactics.apply_tac
315 ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
318 | _ -> raise (ProofEngineTypes.Fail (lazy "Symmetry failed"))
320 ProofEngineTypes.mk_tactic symmetry_tac
323 let transitivity_tac ~term =
324 let transitivity_tac ~term status =
325 let (proof, goal) = status in
326 let module C = Cic in
327 let module R = CicReduction in
328 let module U = UriManager in
329 let module T = Tacticals in
330 let (_,metasenv,_,_) = proof in
331 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
332 match (R.whd context ty) with
333 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
334 when LibraryObjects.is_eq_URI uri ->
335 ProofEngineTypes.apply_tactic
337 ~start:(PrimitiveTactics.apply_tac
338 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
340 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
343 | _ -> raise (ProofEngineTypes.Fail (lazy "Transitivity failed"))
345 ProofEngineTypes.mk_tactic (transitivity_tac ~term)