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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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 (* $Id: destructTactic.ml 9774 2009-05-15 19:37:08Z sacerdot $ *)
29 open Continuationals.Stack
33 if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
39 "z" ^ string_of_int !i
43 let id = if id = "_" then fresh_name () else id in
44 CicNotationPt.Ident (id,None)
47 let rec mk_prods l t =
50 | hd::tl -> CicNotationPt.Binder (`Forall, (mk_id hd, None), mk_prods tl t)
57 | l -> CicNotationPt.Appl l
60 let rec iter f n acc =
62 else iter f (n-1) (f n acc)
65 let subst_metasenv_and_fix_names status =
66 let u,h,metasenv, subst,o = status#obj in
68 NCicUntrusted.map_obj_kind ~skip_body:true
69 (NCicUntrusted.apply_subst subst []) o
71 status#set_obj(u,h,NCicUntrusted.apply_subst_metasenv subst metasenv,subst,o)
74 (* input: nome della variabile riscritta
75 * output: lista dei nomi delle variabili il cui tipo dipende dall'input *)
76 let cascade_select_in_ctx ~subst ctx iname =
77 let lctx, rctx = HExtlib.split_nth (iname - 1) ctx in
78 let lctx = List.rev lctx in
79 let rec rm_last = function
81 | hd::tl -> hd::(rm_last tl)
84 let indices,_ = List.fold_left
85 (fun (acc,context) item ->
87 | n,(NCic.Decl s | NCic.Def (s,_))
88 when not (List.for_all (fun x -> NCicTypeChecker.does_not_occur ~subst context (x-1) x s) acc) ->
89 List.iter (fun m -> pp (lazy ("acc has " ^ (string_of_int m)))) acc;
90 pp (lazy ("acc occurs in the type of " ^ n));
91 (1::List.map ((+) 1) acc, item::context)
92 | _ -> (List.map ((+) 1) acc, item::context))
94 let indices = rm_last indices in
95 let res = List.map (fun n -> let s,_ = List.nth ctx (n-1) in s) indices in
96 List.iter (fun n -> pp (lazy n)) res;
97 pp (lazy (NCicPp.ppcontext ~metasenv:[] ~subst ctx));
101 let rec mk_fresh_name ctx firstch n =
102 let candidate = (String.make 1 firstch) ^ (string_of_int n) in
103 if (List.for_all (fun (s,_) -> s <> candidate) ctx) then candidate
104 else mk_fresh_name ctx firstch (n+1)
107 let arg_list nleft t =
108 let rec drop_prods n t =
111 | NCic.Prod (_,_,ta) -> drop_prods (n-1) ta
112 | _ -> raise (Failure "drop_prods")
114 let rec aux = function
115 | NCic.Prod (_,so,ta) -> so::aux ta
117 in aux (drop_prods nleft t)
120 let nargs it nleft consno =
121 pp (lazy (Printf.sprintf "nargs %d %d" nleft consno));
122 let _,indname,_,cl = it in
123 let _,_,t_k = List.nth cl consno in
124 List.length (arg_list nleft t_k) ;;
126 let default_pattern = "",0,(None,[],Some CicNotationPt.UserInput);;
128 (* returns the discrimination = injection+contradiction principle *)
129 (* FIXME: mi riservo di considerare tipi con parametri sx alla fine *)
131 let mk_discriminator it nleft status =
132 let _,indname,_,cl = it in
135 let mk_eq tys ts us es n =
136 (* eqty = Tn u0 e0...un-1 en-1 *)
138 (List.nth tys n :: iter (fun i acc ->
143 (* params = [T0;t0;...;Tn;tn;u0;e0;un-1;en-1] *)
144 let params = iter (fun i acc ->
146 List.nth ts i :: acc) n
149 List.nth es i:: acc) (n-1) []) in
150 mk_appl [mk_id "eq"; eqty;
151 mk_appl (mk_id ("R" ^ string_of_int n) :: params);
157 let _,name,_ = List.nth cl j in
161 let branch i j ts us =
162 let nargs = nargs it nleft i in
163 let es = List.map (fun x -> mk_id ("e" ^ string_of_int x)) (HExtlib.list_seq 0 nargs) in
165 (fun x -> CicNotationPt.Implicit (`Tagged ("T" ^ (string_of_int x))))
166 (HExtlib.list_seq 0 nargs) in
169 CicNotationPt.Binder (`Lambda, (mk_id ("x" ^ string_of_int i), None),
170 CicNotationPt.Binder (`Lambda, (mk_id ("p" ^ string_of_int i), None),
172 (mk_appl [mk_id "eq"; CicNotationPt.Implicit `JustOne;
173 mk_appl (mk_id (kname it i)::
174 List.map (fun x -> mk_id ("x" ^string_of_int x))
175 (HExtlib.list_seq 0 (List.length ts)));
176 mk_appl (mk_id (kname it j)::us)])]
178 (** CicNotationPt.Binder (`Lambda, (mk_id "e",
181 CicNotationPt.Implicit `JustOne;
182 mk_appl (mk_id (kname it i)::ts);
183 mk_appl (mk_id (kname it j)::us)])),
184 let ts = ts @ [mk_id "e"] in
187 CicNotationPt.Implicit `JustOne;
188 mk_appl (mk_id (kname it j)::us)] in
189 let us = us @ [refl2] in *)
190 CicNotationPt.Binder (`Forall, (mk_id "P", Some (CicNotationPt.Sort (`NType "1") )),
192 CicNotationPt.Binder (`Forall, (mk_id "_",
193 Some (iter (fun i acc ->
194 CicNotationPt.Binder (`Forall, (List.nth es i, Some (mk_eq tys ts us es i)), acc))
196 (** (CicNotationPt.Binder (`Forall, (mk_id "_",
197 Some (mk_eq tys ts us es nargs)),*)
198 (mk_id "P"))), mk_id "P")
202 let inner i ts = CicNotationPt.Case
204 (*Some (CicNotationPt.Binder (`Lambda, (mk_id "y",None),
205 CicNotationPt.Binder (`Forall, (mk_id "_", Some
206 (mk_appl [mk_id "eq";CicNotationPt.Implicit
207 `JustOne;(*CicNotationPt.Implicit `JustOne*)
208 mk_appl (mk_id (kname it i)::ts);mk_id "y"])),
209 CicNotationPt.Implicit `JustOne )))*)
213 let nargs_kty = nargs it nleft j in
214 let us = iter (fun m acc -> mk_id ("u" ^ (string_of_int m))::acc)
215 (nargs_kty - 1) [] in
217 iter (fun _ acc -> None::acc) (nargs_kty - 1) [] in
218 CicNotationPt.Pattern (kname it j,
220 List.combine us nones),
222 (HExtlib.list_seq 0 (List.length cl)))
224 let outer = CicNotationPt.Case
229 let nargs_kty = nargs it nleft i in
230 let ts = iter (fun m acc -> mk_id ("t" ^ (string_of_int m))::acc)
231 (nargs_kty - 1) [] in
233 iter (fun _ acc -> None::acc) (nargs_kty - 1) [] in
234 CicNotationPt.Pattern (kname it i,
236 List.combine ts nones),
238 (HExtlib.list_seq 0 (List.length cl))) in
239 let principle = CicNotationPt.Binder (`Lambda, (mk_id "x", (*Some (mk_id indname)*) None),
240 CicNotationPt.Binder (`Lambda, (mk_id "y", (*Some (mk_id indname)*) None), outer))
242 pp (lazy ("discriminator = " ^ (CicNotationPp.pp_term principle)));
247 let hd_of_term = function
248 | NCic.Appl (hd::_) -> hd
252 let name_of_rel ~context rel =
253 let s, _ = List.nth context (rel-1) in s
256 (* let lookup_in_ctx ~context n =
257 List.nth context ((List.length context) - n - 1)
260 let discriminate_tac ~context cur_eq status =
261 pp (lazy (Printf.sprintf "discriminate: equation %s" (name_of_rel ~context cur_eq)));
263 let dbranch it leftno consno =
264 pp (lazy (Printf.sprintf "dbranch %d %d" leftno consno));
265 let nlist = HExtlib.list_seq 0 (nargs it leftno consno) in
266 (* (\forall ...\forall P.\forall DH : ( ... = ... -> P). P) *)
267 let params = List.map (fun x -> NTactics.intro_tac ("a" ^ string_of_int x)) nlist in
268 NTactics.reduce_tac ~reduction:(`Normalize true) ~where:default_pattern::
270 NTactics.intro_tac "P";
271 NTactics.intro_tac "DH";
272 NTactics.apply_tac ("",0,mk_id "DH");
273 NTactics.apply_tac ("",0,mk_id "refl");
275 let dbranches it leftno =
276 pp (lazy (Printf.sprintf "dbranches %d" leftno));
278 let nbranches = List.length cl in
279 let branches = iter (fun n acc ->
280 let m = nbranches - n - 1 in
281 if m = 0 then acc @ (dbranch it leftno m)
282 else acc @ NTactics.shift_tac :: (dbranch it
285 if nbranches > 1 then
286 NTactics.branch_tac:: branches @ [NTactics.merge_tac]
290 let eq_name,(NCic.Decl s | NCic.Def (s,_)) = List.nth context (cur_eq-1) in
291 let _,ctx' = HExtlib.split_nth cur_eq context in
292 let status, s = NTacStatus.whd status ctx' (mk_cic_term ctx' s) in
293 let status, s = term_of_cic_term status s ctx' in
294 let status, leftno, it =
295 let it, t1, t2 = match s with
296 | NCic.Appl [_;it;t1;t2] -> it,t1,t2
297 | _ -> assert false in
298 (* XXX: serve? ho già fatto whd *)
299 let status, it = whd status ctx' (mk_cic_term ctx' it) in
300 let status, it = term_of_cic_term status it ctx' in
301 let _uri,indtyno,its = match it with
302 | NCic.Const (NReference.Ref (uri, NReference.Ind (_,indtyno,_)) as r)
303 | NCic.Appl (NCic.Const
304 (NReference.Ref (uri, NReference.Ind (_,indtyno,_)) as r)::_) ->
305 uri, indtyno, NCicEnvironment.get_checked_indtys r
306 | _ -> pp (lazy ("discriminate: indty =" ^ NCicPp.ppterm
307 ~metasenv:[] ~subst:[] ~context:[] it)) ; assert false in
308 let _,leftno,its,_,_ = its in
309 status, leftno, List.nth its indtyno
313 let _,_,arity,_ = it in
314 List.length (arg_list 0 arity) in
315 let _,itname,_,_ = it in
316 let params = List.map (fun x -> "a" ^ string_of_int x) (HExtlib.list_seq 1 (itnargs+1)) in
317 let print_tac s status = pp s ; status in
320 let status, discr = mk_discriminator it leftno status in
321 NTactics.cut_tac ("",0, mk_prods params (CicNotationPt.Binder (`Forall, (mk_id "x",
322 Some (mk_appl (List.map mk_id (itname::params)))),
323 CicNotationPt.Binder (`Forall, (mk_id "y", None),
324 CicNotationPt.Binder (`Forall, (mk_id "e",
325 Some (mk_appl [mk_id "eq";CicNotationPt.Implicit `JustOne; mk_id "x"; mk_id "y"])),
326 mk_appl [discr; mk_id "x"; mk_id "y"(*;mk_id "e"*)])))))
329 print_tac (lazy "ci sono");
330 NTactics.reduce_tac ~reduction:(`Normalize true) ~where:default_pattern]
331 @ List.map (fun x -> NTactics.intro_tac x) params @
332 [NTactics.intro_tac "x";
333 NTactics.intro_tac "y";
334 NTactics.intro_tac "Deq";
335 print_tac (lazy "ci sono 2");
336 NTactics.rewrite_tac ~dir:`RightToLeft ~what:("",0,mk_id "Deq") ~where:default_pattern;
337 NTactics.cases_tac ~what:("",0,mk_id "x") ~where:default_pattern]
338 @ dbranches it leftno @
340 print_tac (lazy "ci sono 3");
341 NTactics.intro_tac "#discriminate";
342 NTactics.apply_tac ("",0,mk_appl ([mk_id "#discriminate"]@
343 HExtlib.mk_list (CicNotationPt.Implicit `JustOne) (List.length params + 2) @
345 NTactics.reduce_tac ~reduction:(`Normalize true) ~where:default_pattern;
346 NTactics.clear_tac ["#discriminate"];
351 let subst_tac ~context ~dir cur_eq =
353 let eq_name,(NCic.Decl s | NCic.Def (s,_)) = List.nth context (cur_eq-1) in
354 let _,ctx' = HExtlib.split_nth cur_eq context in
355 let status, s = NTacStatus.whd status ctx' (mk_cic_term ctx' s) in
356 let status, s = term_of_cic_term status s ctx' in
357 pp (lazy (Printf.sprintf "subst: equation %s" eq_name));
358 let l, r = match s with
359 | NCic.Appl [_;_;t1;t2] -> t1,t2
360 | _ -> assert false in
361 let var = match dir with
363 | `RightToLeft -> r in
364 let var = match var with
366 | _ -> assert false in
367 let names_to_gen, _ =
368 cascade_select_in_ctx ~subst:(get_subst status) context (var+cur_eq) in
369 let names_to_gen = match names_to_gen with [] -> [] | _::tl -> tl in
371 NTactics.generalize_tac
372 ~where:("",0,(Some (mk_id x),[], Some CicNotationPt.UserInput)) in
373 NTactics.block_tac ((List.map gen_tac names_to_gen)@
374 [NTactics.clear_tac names_to_gen;
375 NTactics.rewrite_tac ~dir
376 ~what:("",0,mk_id eq_name) ~where:default_pattern;
377 NTactics.reduce_tac ~reduction:(`Normalize true)
378 ~where:default_pattern;
379 NTactics.clear_tac [eq_name]]@
380 (List.map NTactics.intro_tac (List.rev names_to_gen))) status
383 let clearid_tac ~context cur_eq =
385 let eq_name,(NCic.Decl s | NCic.Def (s,_)) = List.nth context (cur_eq-1) in
386 let _,ctx' = HExtlib.split_nth cur_eq context in
387 let status, s = NTacStatus.whd status ctx' (mk_cic_term ctx' s) in
388 let status, s = term_of_cic_term status s ctx' in
389 pp (lazy (Printf.sprintf "clearid: equation %s" eq_name));
390 let names_to_gen, _ =
391 cascade_select_in_ctx ~subst:(get_subst status) context cur_eq in
392 let names_to_gen = names_to_gen @ [eq_name] in
394 NTactics.generalize_tac
395 ~where:("",0,(Some (mk_id x),[], Some CicNotationPt.UserInput)) in
396 NTactics.block_tac ((List.map gen_tac names_to_gen)@
397 [NTactics.clear_tac names_to_gen;
398 NTactics.apply_tac ("",0, mk_appl [mk_id "streicherK";
399 CicNotationPt.Implicit `JustOne;
400 CicNotationPt.Implicit `JustOne;
401 CicNotationPt.Implicit `JustOne;
402 CicNotationPt.Implicit `JustOne]);
403 NTactics.reduce_tac ~reduction:(`Normalize true)
404 ~where:default_pattern] @
405 (let names_to_intro =
406 match List.rev names_to_gen with
409 List.map NTactics.intro_tac names_to_intro)) status
412 let get_ctx st goal =
413 ctx_of (get_goalty st goal)
416 (* = select + classify *)
417 let select_eq ctx acc status goal =
418 let classify ~subst ctx' l r =
419 (* FIXME: metasenv *)
420 if NCicReduction.are_convertible ~metasenv:[] ~subst ctx' l r
421 then status, `Identity
422 else status, (match hd_of_term l, hd_of_term r with
423 | NCic.Const (NReference.Ref (_,NReference.Con (_,ki,nleft)) as kref),
424 NCic.Const (NReference.Ref (_,NReference.Con (_,kj,_))) ->
425 if ki != kj then `Discriminate (0,true)
427 let rit = NReference.mk_indty true kref in
428 let _,_,its,_,itno = NCicEnvironment.get_checked_indtys rit in
429 let it = List.nth its itno in
430 let newprods = nargs it nleft (ki-1) in
431 `Discriminate (newprods, false)
433 when NCicTypeChecker.does_not_occur ~subst ctx' (j-1) j r ->
436 when NCicTypeChecker.does_not_occur ~subst ctx' (j-1) j l ->
438 | (NCic.Rel _, _ | _, NCic.Rel _ ) -> `Cycle
442 let index = List.length ctx - i in
443 pp (lazy ("provo classify di index = " ^string_of_int index));
444 match (List.nth ctx (index - 1)) with
445 | n, (NCic.Decl ty | NCic.Def (ty,_)) ->
446 (let _,ctx_ty = HExtlib.split_nth index ctx in
447 let status, ty = NTacStatus.whd status ctx_ty (mk_cic_term ctx_ty ty) in
448 let status, ty = term_of_cic_term status ty ctx_ty in
449 pp (lazy (Printf.sprintf "select_eq tries %s" (NCicPp.ppterm ~context:ctx_ty ~subst:[] ~metasenv:[] ty)));
451 | NCic.Appl [NCic.Const (NReference.Ref (u,_)) ;_;l;r] when NUri.name_of_uri u = "eq" ->
452 (let status, kind = classify ~subst:(get_subst status) ctx_ty l r in
455 let status, goalty = term_of_cic_term status (get_goalty status goal) ctx in
456 status, Some (List.length ctx - i), kind
457 | `Cycle | `Blob -> aux (i+1) (* XXX: skip cyclic/blob equations for now *)
459 if (List.for_all (fun x -> x <> n) acc) then
460 status, Some (List.length ctx - i), kind
463 with Failure _ | Invalid_argument _ -> status, None, `Blob
467 let rec destruct_tac0 nprods acc status goal =
468 let ctx = get_ctx status goal in
469 let subst = get_subst status in
470 let get_newgoal os ns ogoal =
471 let go, gc = NTactics.compare_statuses ~past:os ~present:ns in
472 let go' = ([ogoal] @- gc) @+ go in
473 match go' with [] -> assert false | g::_ -> g
475 let status, selection, kind = select_eq ctx acc status goal in
476 pp (lazy ("destruct: acc is " ^ String.concat "," acc ));
477 match selection, kind with
479 pp (lazy (Printf.sprintf "destruct: nprods is %d, no selection, context is %s" nprods (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
481 let status' = NTactics.exec (NTactics.intro_tac (mk_fresh_name ctx 'e' 0)) status goal in
482 destruct_tac0 (nprods-1) acc status' (get_newgoal status status' goal)
485 | Some cur_eq, `Discriminate (newprods,conflict) ->
486 pp (lazy (Printf.sprintf "destruct: discriminate - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
487 let status' = NTactics.exec (discriminate_tac ~context:ctx cur_eq) status goal in
488 if conflict then status'
489 else destruct_tac0 (nprods+newprods)
490 (name_of_rel ~context:ctx cur_eq::acc) status' (get_newgoal status status' goal)
491 | Some cur_eq, `Subst dir ->
492 pp (lazy (Printf.sprintf "destruct: subst - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
493 let status' = NTactics.exec (subst_tac ~context:ctx ~dir cur_eq) status goal in
494 pp (lazy (Printf.sprintf " ctx after subst = %s" (NCicPp.ppcontext ~metasenv:[] ~subst (get_ctx status' (get_newgoal status status' goal)))));
495 let eq_name,_ = List.nth ctx (cur_eq-1) in
496 destruct_tac0 nprods (List.filter (fun x -> x <> eq_name) acc) status' (get_newgoal status status' goal)
497 | Some cur_eq, `Identity ->
498 pp (lazy (Printf.sprintf "destruct: identity - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
499 let eq_name,_ = List.nth ctx (cur_eq-1) in
500 let status' = NTactics.exec (clearid_tac ~context:ctx cur_eq) status goal in
501 destruct_tac0 nprods (List.filter (fun x -> x <> eq_name) acc) status' (get_newgoal status status' goal)
502 | Some cur_eq, `Cycle -> (* TODO, should never happen *)
503 pp (lazy (Printf.sprintf "destruct: cycle - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
505 | Some cur_eq, `Blob ->
506 pp (lazy (Printf.sprintf "destruct: blob - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
510 let destruct_tac s = NTactics.distribute_tac (destruct_tac0 0 []) s;;