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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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/.
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
42 let rec rewrite_tac ~direction ~(pattern: ProofEngineTypes.lazy_pattern) equality =
43 let _rewrite_tac ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status
45 assert (wanted = None); (* this should be checked syntactically *)
46 let proof,goal = status in
47 let curi, metasenv, pbo, pty = proof in
48 let (metano,context,gty) = CicUtil.lookup_meta goal metasenv in
53 (rewrite_tac ~direction
54 ~pattern:(None,[he],None) equality)
55 (rewrite_tac ~direction ~pattern:(None,tl,concl_pat)
58 | [_] as hyps_pat when concl_pat <> None ->
61 (rewrite_tac ~direction
62 ~pattern:(None,hyps_pat,None) equality)
63 (rewrite_tac ~direction ~pattern:(None,[],concl_pat)
67 let arg,dir2,tac,concl_pat,gty =
69 [] -> None,true,(fun ~term _ -> P.exact_tac term),concl_pat,gty
74 | Some (Cic.Name s,Cic.Decl ty)::_ when name = s ->
75 Cic.Rel n, S.lift n ty
76 | Some (Cic.Name s,Cic.Def _)::_ -> assert false (*CSC: not implemented yet! But does this make any sense?*)
77 | _::tl -> find_hyp (n+1) tl
79 let arg,gty = find_hyp 1 context in
80 let dummy = "dummy" in
85 [ProofEngineStructuralRules.rename name dummy;
87 ~mk_fresh_name_callback:(fun _ _ _ ~typ -> Cic.Name name) term;
88 ProofEngineStructuralRules.clearbody name;
89 ReductionTactics.change_tac
91 (None,[name,Cic.Implicit (Some `Hole)], None)
92 (ProofEngineTypes.const_lazy_term typ);
93 ProofEngineStructuralRules.clear [dummy]
96 | _::_ -> assert false
98 let if_right_to_left do_not_change a b =
100 | `RightToLeft -> if do_not_change then a else b
101 | `LeftToRight -> if do_not_change then b else a
104 CicTypeChecker.type_of_aux' metasenv context equality
105 CicUniv.empty_ugraph in
106 let (ty_eq,metasenv',arguments,fresh_meta) =
107 ProofEngineHelpers.saturate_term
108 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in
110 if List.length arguments = 0 then
113 C.Appl (equality :: arguments) in
114 (* t1x is t2 if we are rewriting in an hypothesis *)
115 let eq_ind, ty, t1, t2, t1x =
117 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
118 when LibraryObjects.is_eq_URI uri ->
120 if_right_to_left dir2
121 LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
123 let eq_ind = C.Const (ind_uri uri,[]) in
125 if_right_to_left true (eq_ind,ty,t2,t1,t2) (eq_ind,ty,t1,t2,t1)
127 if_right_to_left true (eq_ind,ty,t1,t2,t2) (eq_ind,ty,t2,t1,t1)
128 | _ -> raise (PET.Fail (lazy "Rewrite: argument is not a proof of an equality")) in
129 (* now we always do as if direction was `LeftToRight *)
131 FreshNamesGenerator.mk_fresh_name
132 ~subst:[] metasenv' context C.Anonymous ~typ:ty in
133 let lifted_t1 = S.lift 1 t1x in
134 let lifted_gty = S.lift 1 gty in
135 let lifted_conjecture =
136 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
138 let lifted_concl_pat =
141 | Some term -> Some (S.lift 1 term) in
142 Some (fun _ m u -> lifted_t1, m, u),[],lifted_concl_pat
144 let subst,metasenv',ugraph,_,selected_terms_with_context =
145 ProofEngineHelpers.select
146 ~metasenv:metasenv' ~ugraph ~conjecture:lifted_conjecture
147 ~pattern:lifted_pattern in
148 let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in
150 (* Note: Rel 1 does not live in the context context_of_t *)
151 (* The replace_lifting_csc 0 function will take care of lifting it *)
152 (* to context_of_t *)
154 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
155 selected_terms_with_context ([],[]) in
156 let t1 = CicMetaSubst.apply_subst subst t1 in
157 let t2 = CicMetaSubst.apply_subst subst t2 in
158 let ty = CicMetaSubst.apply_subst subst ty in
159 let pbo = CicMetaSubst.apply_subst subst pbo in
160 let pty = CicMetaSubst.apply_subst subst pty in
161 let equality = CicMetaSubst.apply_subst subst equality in
163 ProofEngineReduction.replace_lifting_csc 0
164 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
165 let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
166 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
167 (* The argument is either a meta if we are rewriting in the conclusion
168 or the hypothesis if we are rewriting in an hypothesis *)
169 let metasenv',arg,newtyp =
172 let gty' = S.subst t2 abstr_gty in
174 CicMkImplicit.identity_relocation_list_for_metavariable context in
175 let metasenv' = (fresh_meta,context,gty')::metasenv' in
176 metasenv', C.Meta (fresh_meta,irl), Cic.Rel (-1) (* dummy term, never used *)
178 let gty' = S.subst t1 abstr_gty in
182 C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality]
187 (tac ~term:exact_proof newtyp) ((curi,metasenv',pbo,pty),goal)
190 goals@(ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
191 ~newmetasenv:metasenv')
194 with (* FG: this should be PET.Fail _ *)
195 TC.TypeCheckerFailure _ ->
196 let msg = lazy "rewrite: nothing to rewrite" in
199 ProofEngineTypes.mk_tactic (_rewrite_tac ~direction ~pattern equality)
202 let rewrite_simpl_tac ~direction ~pattern equality =
203 let rewrite_simpl_tac ~direction ~pattern equality status =
204 ProofEngineTypes.apply_tactic
206 ~start:(rewrite_tac ~direction ~pattern equality)
208 (ReductionTactics.simpl_tac
209 ~pattern:(ProofEngineTypes.conclusion_pattern None)))
212 ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
215 let replace_tac ~(pattern: ProofEngineTypes.lazy_pattern) ~with_what =
216 let replace_tac ~(pattern: ProofEngineTypes.lazy_pattern) ~with_what status =
217 let _wanted, hyps_pat, concl_pat = pattern in
218 let (proof, goal) = status in
219 let uri,metasenv,pbo,pty = proof in
220 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
221 assert (hyps_pat = []); (*CSC: not implemented yet *)
223 match LibraryObjects.eq_URI () with
225 | None -> raise (ProofEngineTypes.Fail (lazy "You need to register the default equality first. Please use the \"default\" command"))
227 let context_len = List.length context in
228 let subst,metasenv,u,_,selected_terms_with_context =
229 ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.empty_ugraph
230 ~conjecture ~pattern in
231 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
232 let with_what, metasenv, u = with_what context metasenv u in
233 let with_what = CicMetaSubst.apply_subst subst with_what in
234 let pbo = CicMetaSubst.apply_subst subst pbo in
235 let pty = CicMetaSubst.apply_subst subst pty in
236 let status = (uri,metasenv,pbo,pty),goal in
237 let ty_of_with_what,u =
238 CicTypeChecker.type_of_aux'
239 metasenv context with_what CicUniv.empty_ugraph in
241 match selected_terms_with_context with
242 [] -> raise (ProofEngineTypes.Fail (lazy "Replace: no term selected"))
245 (fun (context_of_t,t) ->
248 let context_of_t_len = List.length context_of_t in
249 if context_of_t_len = context_len then t
251 (let t_in_context,subst,metasenv' =
252 CicMetaSubst.delift_rels [] metasenv
253 (context_of_t_len - context_len) t
256 assert (metasenv = metasenv');
259 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
260 (*CSC: we could implement something stronger by completely changing
261 the semantics of the tactic *)
262 raise (ProofEngineTypes.Fail
263 (lazy "Replace: one of the selected terms is not closed")) in
264 let ty_of_t_in_context,u = (* TASSI: FIXME *)
265 CicTypeChecker.type_of_aux' metasenv context t_in_context
266 CicUniv.empty_ugraph in
267 let b,u = CicReduction.are_convertible ~metasenv context
268 ty_of_with_what ty_of_t_in_context u in
270 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
271 let pattern_for_t = None,[],Some concl_pat_for_t in
272 t_in_context,pattern_for_t
275 (ProofEngineTypes.Fail
276 (lazy "Replace: one of the selected terms and the term to be replaced with have not convertible types"))
278 let rec aux n whats status =
280 [] -> ProofEngineTypes.apply_tactic T.id_tac status
281 | (what,lazy_pattern)::tl ->
282 let what = S.lift n what in
283 let with_what = S.lift n with_what in
284 let ty_of_with_what = S.lift n ty_of_with_what in
285 ProofEngineTypes.apply_tactic
290 (C.MutInd (eq_URI, 0, [])) ;
297 rewrite_tac ~direction:`LeftToRight ~pattern:lazy_pattern (C.Rel 1))
301 ProofEngineTypes.mk_tactic
302 (function ((proof,goal) as status) ->
303 let _,metasenv,_,_ = proof in
304 let _,context,_ = CicUtil.lookup_meta goal metasenv in
307 match List.hd context with
308 Some (Cic.Name name,_) -> [name]
310 with (Failure "hd") -> assert false
312 ProofEngineTypes.apply_tactic
313 (ProofEngineStructuralRules.clear ~hyps) status))
314 ~continuation:(aux_tac (n + 1) tl));
317 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
320 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
324 (* All these tacs do is applying the right constructor/theorem *)
326 let reflexivity_tac =
327 IntroductionTactics.constructor_tac ~n:1
331 let symmetry_tac (proof, goal) =
332 let (_,metasenv,_,_) = proof in
333 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
334 match (R.whd context ty) with
335 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
336 when LibraryObjects.is_eq_URI uri ->
337 ProofEngineTypes.apply_tactic
338 (PrimitiveTactics.apply_tac
339 ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
342 | _ -> raise (ProofEngineTypes.Fail (lazy "Symmetry failed"))
344 ProofEngineTypes.mk_tactic symmetry_tac
347 let transitivity_tac ~term =
348 let transitivity_tac ~term status =
349 let (proof, goal) = status in
350 let (_,metasenv,_,_) = proof in
351 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
352 match (R.whd context ty) with
353 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
354 when LibraryObjects.is_eq_URI uri ->
355 ProofEngineTypes.apply_tactic
357 ~start:(PrimitiveTactics.apply_tac
358 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
360 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
363 | _ -> raise (ProofEngineTypes.Fail (lazy "Transitivity failed"))
365 ProofEngineTypes.mk_tactic (transitivity_tac ~term)
368 (* FG: subst tactic *********************************************************)
370 (* FG: This should be replaced by T.try_tactic *)
371 let try_tactic ~tactic =
372 let try_tactic status =
373 try PET.apply_tactic tactic status with
374 | PET.Fail _ -> PET.apply_tactic T.id_tac status
376 PET.mk_tactic try_tactic
378 let rec lift_rewrite_tac ~context ~direction ~pattern equality =
379 let lift_rewrite_tac status =
380 let (proof, goal) = status in
381 let (_, metasenv, _, _) = proof in
382 let _, new_context, _ = CicUtil.lookup_meta goal metasenv in
383 let n = List.length new_context - List.length context in
384 let equality = if n > 0 then S.lift n equality else equality in
385 PET.apply_tactic (rewrite_tac ~direction ~pattern equality) status
387 PET.mk_tactic lift_rewrite_tac
390 let msg0 = lazy "Subst: not found in context"
391 let msg1 = lazy "Subst: not a simple equality"
392 let msg2 = lazy "Subst: recursive equation"
395 let hole = C.Implicit (Some `Hole) in
396 let subst_tac status =
397 let (proof, goal) = status in
398 let (_, metasenv, _, _) = proof in
399 let _, context, _ = CicUtil.lookup_meta goal metasenv in
400 let what = match PEH.get_rel context hyp with
402 | None -> raise (PET.Fail msg0)
404 let ty, _ = TC.type_of_aux' metasenv context what CicUniv.empty_ugraph in
405 let direction, i, t = match ty with
406 | (C.Appl [(C.MutInd (uri, 0, [])); _; C.Rel i; t])
407 when LO.is_eq_URI uri -> `LeftToRight, i, t
408 | (C.Appl [(C.MutInd (uri, 0, [])); _; t; C.Rel i])
409 when LO.is_eq_URI uri -> `RightToLeft, i, t
410 | _ -> raise (PET.Fail msg1)
412 let rewrite pattern =
413 let tactic = lift_rewrite_tac ~context ~direction ~pattern what in
416 let var = match PEH.get_name context i with
418 | None -> raise (PET.Fail msg0)
420 if DTI.does_not_occur i t then () else raise (PET.Fail msg2);
421 let map self = function
422 | Some (C.Name s, _) when s <> self ->
423 Some (rewrite (None, [(s, hole)], None))
426 let rew_hips = PEH.list_rev_map_filter (map hyp) context in
427 let rew_concl = rewrite (None, [], Some hole) in
428 let clear = PESR.clear ~hyps:[hyp; var] in
429 let tactics = List.rev_append (rew_concl :: rew_hips) [clear] in
430 PET.apply_tactic (T.seq ~tactics) status
432 PET.mk_tactic subst_tac
435 let subst hyp = try_tactic ~tactic:(subst_tac hyp) in
437 | Some (C.Name s, _) -> Some (subst s)
440 let subst_tac status =
441 let (proof, goal) = status in
442 let (_, metasenv, _, _) = proof in
443 let _, context, _ = CicUtil.lookup_meta goal metasenv in
444 let tactics = PEH.list_rev_map_filter map context in
445 PET.apply_tactic (T.seq ~tactics) status
447 PET.mk_tactic subst_tac