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
10 * of the License, or (at your option) any later version.
12 * HELM is distributed in the hope that it will be useful,
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.
17 * You should have received a copy of the GNU General Public License
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 *)
130 let mk_discriminator it ~use_jmeq nleft xyty status =
131 let _,indname,_,cl = it in
134 let mk_eq tys ts us es n =
136 mk_appl [mk_id "jmeq";
137 CicNotationPt.Implicit `JustOne; List.nth ts n;
138 CicNotationPt.Implicit `JustOne; List.nth us n]
140 (* eqty = Tn u0 e0...un-1 en-1 *)
142 (List.nth tys n :: iter (fun i acc ->
147 (* params = [T0;t0;...;Tn;tn;u0;e0;un-1;en-1] *)
148 let params = iter (fun i acc ->
150 List.nth ts i :: acc) n
153 List.nth es i:: acc) (n-1) []) in
154 mk_appl [mk_id "eq"; eqty;
155 mk_appl (mk_id ("R" ^ string_of_int n) :: params);
162 let _,name,_ = List.nth cl j in
166 let branch i j ts us =
167 let nargs = nargs it nleft i in
168 let es = List.map (fun x -> mk_id ("e" ^ string_of_int x)) (HExtlib.list_seq 0 nargs) in
172 CicNotationPt.Binder (`Lambda, (mk_id ("x" ^ string_of_int i), None),
173 CicNotationPt.Binder (`Lambda, (mk_id ("p" ^ string_of_int i), None),
175 (CicNotationPt.Implicit (`Tagged ("T" ^ (string_of_int x)))))
176 (HExtlib.list_seq 0 nargs) in
179 CicNotationPt.Binder (`Lambda, (mk_id ("x" ^ string_of_int i), None),
180 CicNotationPt.Binder (`Lambda, (mk_id ("p" ^ string_of_int i), None),
182 (mk_appl [mk_id "eq"; CicNotationPt.Implicit `JustOne;
183 mk_appl (mk_id (kname it i)::
184 List.map (fun x -> mk_id ("x" ^string_of_int x))
185 (HExtlib.list_seq 0 (List.length ts)));
186 mk_appl (mk_id (kname it j)::us)])]
188 (** CicNotationPt.Binder (`Lambda, (mk_id "e",
191 CicNotationPt.Implicit `JustOne;
192 mk_appl (mk_id (kname it i)::ts);
193 mk_appl (mk_id (kname it j)::us)])),
194 let ts = ts @ [mk_id "e"] in
197 CicNotationPt.Implicit `JustOne;
198 mk_appl (mk_id (kname it j)::us)] in
199 let us = us @ [refl2] in *)
200 CicNotationPt.Binder (`Forall, (mk_id "P", Some (CicNotationPt.Sort (`NType "1") )),
202 CicNotationPt.Binder (`Forall, (mk_id "_",
203 Some (iter (fun i acc ->
204 CicNotationPt.Binder (`Forall, (List.nth es i, Some (mk_eq tys ts us es i)), acc))
206 (** (CicNotationPt.Binder (`Forall, (mk_id "_",
207 Some (mk_eq tys ts us es nargs)),*)
208 (mk_id "P"))), mk_id "P")
212 let inner i ts = CicNotationPt.Case
214 (*Some (CicNotationPt.Binder (`Lambda, (mk_id "y",None),
215 CicNotationPt.Binder (`Forall, (mk_id "_", Some
216 (mk_appl [mk_id "eq";CicNotationPt.Implicit
217 `JustOne;(*CicNotationPt.Implicit `JustOne*)
218 mk_appl (mk_id (kname it i)::ts);mk_id "y"])),
219 CicNotationPt.Implicit `JustOne )))*)
223 let nargs_kty = nargs it nleft j in
224 let us = iter (fun m acc -> mk_id ("u" ^ (string_of_int m))::acc)
225 (nargs_kty - 1) [] in
227 iter (fun _ acc -> None::acc) (nargs_kty - 1) [] in
228 CicNotationPt.Pattern (kname it j,
230 List.combine us nones),
232 (HExtlib.list_seq 0 (List.length cl)))
234 let outer = CicNotationPt.Case
239 let nargs_kty = nargs it nleft i in
240 let ts = iter (fun m acc -> mk_id ("t" ^ (string_of_int m))::acc)
241 (nargs_kty - 1) [] in
243 iter (fun _ acc -> None::acc) (nargs_kty - 1) [] in
244 CicNotationPt.Pattern (kname it i,
246 List.combine ts nones),
248 (HExtlib.list_seq 0 (List.length cl))) in
249 let principle = CicNotationPt.Binder (`Lambda, (mk_id "x", Some xyty),
250 CicNotationPt.Binder (`Lambda, (mk_id "y", Some xyty), outer))
252 pp (lazy ("discriminator = " ^ (CicNotationPp.pp_term principle)));
257 let hd_of_term = function
258 | NCic.Appl (hd::_) -> hd
262 let name_of_rel ~context rel =
263 let s, _ = List.nth context (rel-1) in s
266 (* let lookup_in_ctx ~context n =
267 List.nth context ((List.length context) - n - 1)
270 let discriminate_tac ~context cur_eq status =
271 pp (lazy (Printf.sprintf "discriminate: equation %s" (name_of_rel ~context cur_eq)));
273 let dbranch it ~use_jmeq leftno consno =
274 let refl_id = mk_id (if use_jmeq then "refl_jmeq" else "refl") in
275 pp (lazy (Printf.sprintf "dbranch %d %d" leftno consno));
276 let nlist = HExtlib.list_seq 0 (nargs it leftno consno) in
277 (* (\forall ...\forall P.\forall DH : ( ... = ... -> P). P) *)
278 let params = List.map (fun x -> NTactics.intro_tac ("a" ^ string_of_int x)) nlist in
279 NTactics.reduce_tac ~reduction:(`Normalize true) ~where:default_pattern::
281 NTactics.intro_tac "P";
282 NTactics.intro_tac "DH";
283 NTactics.apply_tac ("",0,mk_id "DH");
284 NTactics.apply_tac ("",0,refl_id); (* well, it works even if no goal is selected after applying DH... *)
286 let dbranches it ~use_jmeq leftno =
287 pp (lazy (Printf.sprintf "dbranches %d" leftno));
289 let nbranches = List.length cl in
290 let branches = iter (fun n acc ->
291 let m = nbranches - n - 1 in
292 if m = 0 then acc @ (dbranch it ~use_jmeq leftno m)
293 else acc @ NTactics.shift_tac :: (dbranch it ~use_jmeq
296 if nbranches > 1 then
297 NTactics.branch_tac ~force:false:: branches @ [NTactics.merge_tac]
301 let eq_name,(NCic.Decl s | NCic.Def (s,_)) = List.nth context (cur_eq-1) in
302 let _,ctx' = HExtlib.split_nth cur_eq context in
303 let status, s = NTacStatus.whd status ctx' (mk_cic_term ctx' s) in
304 let status, s = term_of_cic_term status s ctx' in
305 let status, leftno, it, use_jmeq =
306 let it, t1, t2, use_jmeq = match s with
307 | NCic.Appl [_;it;t1;t2] -> it,t1,t2,false
308 | NCic.Appl [_;it;t1;_;t2] -> it,t1,t2,true
309 | _ -> assert false in
310 (* XXX: serve? ho già fatto whd *)
311 let status, it = whd status ctx' (mk_cic_term ctx' it) in
312 let status, it = term_of_cic_term status it ctx' in
313 let _uri,indtyno,its = match it with
314 | NCic.Const (NReference.Ref (uri, NReference.Ind (_,indtyno,_)) as r)
315 | NCic.Appl (NCic.Const
316 (NReference.Ref (uri, NReference.Ind (_,indtyno,_)) as r)::_) ->
317 uri, indtyno, NCicEnvironment.get_checked_indtys r
318 | _ -> pp (lazy ("discriminate: indty =" ^ NCicPp.ppterm
319 ~metasenv:[] ~subst:[] ~context:[] it)) ; assert false in
320 let _,leftno,its,_,_ = its in
321 status, leftno, List.nth its indtyno, use_jmeq
325 let _,_,arity,_ = it in
326 List.length (arg_list 0 arity) in
327 let _,itname,_,_ = it in
328 let params = List.map (fun x -> "a" ^ string_of_int x) (HExtlib.list_seq 1 (itnargs+1)) in
329 let xyty = mk_appl (List.map mk_id (itname::params)) in
330 let print_tac s status = pp s ; status in
333 let status, discr = mk_discriminator it ~use_jmeq leftno xyty status in
334 let cut_term = mk_prods params (CicNotationPt.Binder (`Forall, (mk_id "x",
336 CicNotationPt.Binder (`Forall, (mk_id "y", Some xyty),
337 CicNotationPt.Binder (`Forall, (mk_id "e",
338 Some (mk_appl [mk_id "eq";CicNotationPt.Implicit `JustOne; mk_id "x"; mk_id "y"])),
339 mk_appl [discr; mk_id "x"; mk_id "y"(*;mk_id "e"*)])))) in
340 let status = print_tac (lazy ("cut_term = "^ CicNotationPp.pp_term cut_term)) status in
341 NTactics.cut_tac ("",0, cut_term)
344 print_tac (lazy "ci sono");
345 NTactics.reduce_tac ~reduction:(`Normalize true) ~where:default_pattern]
346 @ List.map (fun x -> NTactics.intro_tac x) params @
347 [NTactics.intro_tac "x";
348 NTactics.intro_tac "y";
349 NTactics.intro_tac "Deq";
350 print_tac (lazy "ci sono 2");
351 NTactics.rewrite_tac ~dir:`RightToLeft ~what:("",0,mk_id "Deq") ~where:default_pattern;
352 NTactics.cases_tac ~what:("",0,mk_id "x") ~where:default_pattern]
353 @ dbranches it ~use_jmeq leftno @
355 print_tac (lazy "ci sono 3");
356 NTactics.intro_tac "#discriminate";
357 NTactics.apply_tac ("",0,mk_appl ([mk_id "#discriminate"]@
358 HExtlib.mk_list (CicNotationPt.Implicit `JustOne) (List.length params + 2) @
360 NTactics.reduce_tac ~reduction:(`Normalize true) ~where:default_pattern;
361 NTactics.clear_tac ["#discriminate"];
362 NTactics.merge_tac; print_tac (lazy "the end of discriminate")]
366 let subst_tac ~context ~dir cur_eq =
368 let eq_name,(NCic.Decl s | NCic.Def (s,_)) = List.nth context (cur_eq-1) in
369 let _,ctx' = HExtlib.split_nth cur_eq context in
370 let status, s = NTacStatus.whd status ctx' (mk_cic_term ctx' s) in
371 let status, s = term_of_cic_term status s ctx' in
372 pp (lazy (Printf.sprintf "subst: equation %s" eq_name));
373 let l, r = match s with
374 | NCic.Appl [_;_;t1;t2] | NCic.Appl [_;_;t1;_;t2] -> t1,t2
375 | _ -> assert false in
376 let var = match dir with
378 | `RightToLeft -> r in
379 (* let var = match var with
381 | _ -> assert false in *)
382 let names_to_gen, _ =
385 cascade_select_in_ctx ~subst:(get_subst status) context (var+cur_eq)
386 | _ -> cascade_select_in_ctx ~subst:(get_subst status) context cur_eq in
387 let names_to_gen = List.filter (fun n -> n <> eq_name) names_to_gen in
389 NTactics.generalize_tac
390 ~where:("",0,(Some (mk_id x),[], Some CicNotationPt.UserInput)) in
391 NTactics.block_tac ((List.map gen_tac names_to_gen)@
392 [NTactics.clear_tac names_to_gen;
393 NTactics.rewrite_tac ~dir
394 ~what:("",0,mk_id eq_name) ~where:default_pattern;
395 NTactics.reduce_tac ~reduction:(`Normalize true)
396 ~where:default_pattern;
397 NTactics.clear_tac [eq_name]]@
398 (List.map NTactics.intro_tac (List.rev names_to_gen))) status
401 let clearid_tac ~context cur_eq =
403 let eq_name,(NCic.Decl s | NCic.Def (s,_)) = List.nth context (cur_eq-1) in
404 let _,ctx' = HExtlib.split_nth cur_eq context in
405 let status, s = NTacStatus.whd status ctx' (mk_cic_term ctx' s) in
406 let status, s = term_of_cic_term status s ctx' in
409 | NCic.Appl [_;_;_;_] -> mk_id "streicherK"
410 | NCic.Appl [_;_;_;_;_] -> mk_id "streicherKjmeq"
413 pp (lazy (Printf.sprintf "clearid: equation %s" eq_name));
414 let names_to_gen, _ =
415 cascade_select_in_ctx ~subst:(get_subst status) context cur_eq in
416 let names_to_gen = names_to_gen @ [eq_name] in
418 NTactics.generalize_tac
419 ~where:("",0,(Some (mk_id x),[], Some CicNotationPt.UserInput)) in
420 NTactics.block_tac ((List.map gen_tac names_to_gen)@
421 [NTactics.clear_tac names_to_gen;
422 NTactics.apply_tac ("",0, mk_appl [streicher_id;
423 CicNotationPt.Implicit `JustOne;
424 CicNotationPt.Implicit `JustOne;
425 CicNotationPt.Implicit `JustOne;
426 CicNotationPt.Implicit `JustOne]);
427 NTactics.reduce_tac ~reduction:(`Normalize true)
428 ~where:default_pattern] @
429 (let names_to_intro =
430 match List.rev names_to_gen with
433 List.map NTactics.intro_tac names_to_intro)) status
436 let get_ctx st goal =
437 ctx_of (get_goalty st goal)
440 (* = select + classify *)
441 let select_eq ctx acc status goal =
442 let classify ~subst ctx' l r =
443 (* FIXME: metasenv *)
444 if NCicReduction.are_convertible ~metasenv:[] ~subst ctx' l r
445 then status, `Identity
446 else status, (match hd_of_term l, hd_of_term r with
447 | NCic.Const (NReference.Ref (_,NReference.Con (_,ki,nleft)) as kref),
448 NCic.Const (NReference.Ref (_,NReference.Con (_,kj,_))) ->
449 if ki != kj then `Discriminate (0,true)
451 let rit = NReference.mk_indty true kref in
452 let _,_,its,_,itno = NCicEnvironment.get_checked_indtys rit in
453 let it = List.nth its itno in
454 let newprods = nargs it nleft (ki-1) in
455 `Discriminate (newprods, false)
457 when NCicTypeChecker.does_not_occur ~subst ctx' (j-1) j r
458 && l = NCic.Rel j -> `Subst `LeftToRight
460 when NCicTypeChecker.does_not_occur ~subst ctx' (j-1) j l
461 && r = NCic.Rel j -> `Subst `RightToLeft
462 | (NCic.Rel _, _ | _, NCic.Rel _ ) -> `Cycle (* could be a blob too... *)
466 let index = List.length ctx - i in
467 pp (lazy ("provo classify di index = " ^string_of_int index));
468 match (List.nth ctx (index - 1)) with
469 | n, (NCic.Decl ty | NCic.Def (ty,_)) ->
470 (let _,ctx_ty = HExtlib.split_nth index ctx in
471 let status, ty = NTacStatus.whd status ctx_ty (mk_cic_term ctx_ty ty) in
472 let status, ty = term_of_cic_term status ty ctx_ty in
473 pp (lazy (Printf.sprintf "select_eq tries %s" (NCicPp.ppterm ~context:ctx_ty ~subst:[] ~metasenv:[] ty)));
474 let status, kind = match ty with
475 | NCic.Appl [NCic.Const (NReference.Ref (u,_)) ;_;l;r]
476 when NUri.name_of_uri u = "eq" ->
477 classify ~subst:(get_subst status) ctx_ty l r
478 | NCic.Appl [NCic.Const (NReference.Ref (u,_)) ;lty;l;rty;r]
479 when NUri.name_of_uri u = "jmeq" &&
480 NCicReduction.are_convertible ~metasenv:[]
481 ~subst:(get_subst status) ctx_ty lty rty
482 -> classify ~subst:(get_subst status) ctx_ty l r
483 | _ -> status, `NonEq
486 let status, goalty = term_of_cic_term status (get_goalty status goal) ctx in
487 status, Some (List.length ctx - i), kind
488 | `Cycle | `Blob | `NonEq -> aux (i+1) (* XXX: skip cyclic/blob equations for now *)
490 if (List.for_all (fun x -> x <> n) acc) then
491 status, Some (List.length ctx - i), kind
493 with Failure _ | Invalid_argument _ -> status, None, `Blob
497 let rec destruct_tac0 nprods acc status goal =
498 let ctx = get_ctx status goal in
499 let subst = get_subst status in
500 let get_newgoal os ns ogoal =
501 let go, gc = NTactics.compare_statuses ~past:os ~present:ns in
502 let go' = ([ogoal] @- gc) @+ go in
503 match go' with [] -> assert false | g::_ -> g
505 let status, selection, kind = select_eq ctx acc status goal in
506 pp (lazy ("destruct: acc is " ^ String.concat "," acc ));
507 match selection, kind with
509 pp (lazy (Printf.sprintf "destruct: nprods is %d, no selection, context is %s" nprods (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
511 let status' = NTactics.exec (NTactics.intro_tac (mk_fresh_name ctx 'e' 0)) status goal in
512 destruct_tac0 (nprods-1) acc status' (get_newgoal status status' goal)
515 | Some cur_eq, `Discriminate (newprods,conflict) ->
516 pp (lazy (Printf.sprintf "destruct: discriminate - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
517 let status' = NTactics.exec (discriminate_tac ~context:ctx cur_eq) status goal in
518 if conflict then status'
519 else destruct_tac0 (nprods+newprods)
520 (name_of_rel ~context:ctx cur_eq::acc) status' (get_newgoal status status' goal)
521 | Some cur_eq, `Subst dir ->
522 pp (lazy (Printf.sprintf "destruct: subst - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
523 let status' = NTactics.exec (subst_tac ~context:ctx ~dir cur_eq) status goal in
524 pp (lazy (Printf.sprintf " ctx after subst = %s" (NCicPp.ppcontext ~metasenv:[] ~subst (get_ctx status' (get_newgoal status status' goal)))));
525 let eq_name,_ = List.nth ctx (cur_eq-1) in
526 destruct_tac0 nprods (List.filter (fun x -> x <> eq_name) acc) status' (get_newgoal status status' goal)
527 | Some cur_eq, `Identity ->
528 pp (lazy (Printf.sprintf "destruct: identity - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
529 let eq_name,_ = List.nth ctx (cur_eq-1) in
530 let status' = NTactics.exec (clearid_tac ~context:ctx cur_eq) status goal in
531 destruct_tac0 nprods (List.filter (fun x -> x <> eq_name) acc) status' (get_newgoal status status' goal)
532 | Some cur_eq, `Cycle -> (* TODO, should never happen *)
533 pp (lazy (Printf.sprintf "destruct: cycle - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
535 | Some cur_eq, `Blob ->
536 pp (lazy (Printf.sprintf "destruct: blob - nprods is %d, selection is %d, context is %s" nprods cur_eq (NCicPp.ppcontext ~metasenv:[] ~subst ctx)));
541 let destruct_tac s = NTactics.distribute_tac (destruct_tac0 0 []) s;;