2 ||M|| This file is part of HELM, an Hypertextual, Electronic
3 ||A|| Library of Mathematics, developed at the Computer Science
4 ||T|| Department, University of Bologna, Italy.
6 ||T|| HELM is free software; you can redistribute it and/or
7 ||A|| modify it under the terms of the GNU General Public License
8 \ / version 2 or (at your option) any later version.
9 \ / This software is distributed as is, NO WARRANTY.
10 V_______________________________________________________________ *)
12 (* $Id: nCic.ml 9058 2008-10-13 17:42:30Z tassi $ *)
17 let debug_print s = if debug then prerr_endline (Lazy.force s) else ()
19 open Continuationals.Stack
21 module Ast = CicNotationPt
23 let id_tac status = status ;;
24 let print_tac print_status message status =
25 if print_status then pp_status status;
26 prerr_endline message;
32 match status#stack with
34 | ([], _, [], _) :: _ as stack ->
35 (* backward compatibility: do-nothing-dot *)
37 | (g, t, k, tag) :: s ->
38 match filter_open g, k with
40 (([ loc ], t, loc_tl @+ k, tag) :: s)
43 (([ loc ], t, k, tag) :: s)
44 | _ -> fail (lazy "can't use \".\" here")
46 status#set_stack gstatus
49 let branch_tac status =
51 match status#stack with
53 | (g, t, k, tag) :: s ->
54 match init_pos g with (* TODO *)
55 | [] | [ _ ] -> fail (lazy "too few goals to branch");
57 ([ loc ], [], [], `BranchTag) :: (loc_tl, t, k, tag) :: s
59 status#set_stack gstatus
62 let shift_tac status =
64 match status#stack with
65 | (g, t, k, `BranchTag) :: (g', t', k', tag) :: s ->
67 | [] -> fail (lazy "no more goals to shift")
69 (([ loc ], t @+ filter_open g @+ k, [],`BranchTag)
70 :: (loc_tl, t', k', tag) :: s))
71 | _ -> fail (lazy "can't shift goals here")
73 status#set_stack gstatus
76 let pos_tac i_s status =
78 match status#stack with
80 | ([ loc ], t, [],`BranchTag) :: (g', t', k', tag) :: s
82 let l_js = List.filter (fun (i, _) -> List.mem i i_s) ([loc] @+ g') in
83 ((l_js, t , [],`BranchTag)
84 :: (([ loc ] @+ g') @- l_js, t', k', tag) :: s)
85 | _ -> fail (lazy "can't use relative positioning here")
87 status#set_stack gstatus
90 let wildcard_tac status =
92 match status#stack with
94 | ([ loc ] , t, [], `BranchTag) :: (g', t', k', tag) :: s
96 (([loc] @+ g', t, [], `BranchTag) :: ([], t', k', tag) :: s)
97 | _ -> fail (lazy "can't use wildcard here")
99 status#set_stack gstatus
102 let merge_tac status =
104 match status#stack with
106 | (g, t, k,`BranchTag) :: (g', t', k', tag) :: s ->
107 ((t @+ filter_open g @+ g' @+ k, t', k', tag) :: s)
108 | _ -> fail (lazy "can't merge goals here")
110 status#set_stack gstatus
113 let focus_tac gs status =
115 match status#stack with
117 | s -> assert(gs <> []);
119 let add_l acc _ _ l = if is_open l then l :: acc else acc in
120 fold ~env:add_l ~cont:add_l ~todo:add_l [] s
124 if not (List.exists (fun l -> goal_of_loc l = g) stack_locs) then
125 fail (lazy (sprintf "goal %d not found (or closed)" g)))
127 (zero_pos gs, [], [], `FocusTag) :: deep_close gs s
129 status#set_stack gstatus
132 let unfocus_tac status =
134 match status#stack with
136 | ([], [], [], `FocusTag) :: s -> s
137 | _ -> fail (lazy "can't unfocus, some goals are still open")
139 status#set_stack gstatus
142 let skip_tac status =
144 match status#stack with
146 | (gl, t, k, tag) :: s ->
147 let gl = List.map switch_of_loc gl in
148 if List.exists (function Open _ -> true | Closed _ -> false) gl then
149 fail (lazy "cannot skip an open goal")
153 status#set_stack gstatus
156 let block_tac l status =
157 List.fold_left (fun status tac -> tac status) status l
161 let compare_statuses ~past ~present =
162 let _,_,past,_,_ = past#obj in
163 let _,_,present,_,_ = present#obj in
164 List.map fst (List.filter (fun (i,_) -> not(List.mem_assoc i past)) present),
165 List.map fst (List.filter (fun (i,_) -> not (List.mem_assoc i present)) past)
170 (* Exec and distribute_tac form a retraction pair:
171 1) exec (distribute_tac low_tac) (s,i) = low_tac (s,i)
172 2) tac [s]::G = G1::...::Gn::G' && G' is G with some goals closed =>
173 distribute_tac (exec tac) [s]::G = (G1@...Gn)::G'
174 3) tac G = distribute_tac (exec tac) G if
175 tac = distribute_tac lowtac
176 4) atomic_tac t === distribute_tac (exec t)
178 Note that executing an high tactic on a set of goals may be stronger
179 than executing the same tactic on those goals, but once at a time
180 (e.g. the tactic could perform a global analysis of the set of goals)
183 let exec tac (low_status : #lowtac_status) g =
184 let stack = [ [0,Open g], [], [], `NoTag ] in
186 (new NTacStatus.status low_status#obj stack)#set_estatus low_status
188 let status = tac status in
189 (low_status#set_estatus status)#set_obj status#obj
192 let distribute_tac tac (status : #tac_status) =
193 match status#stack with
195 | (g, t, k, tag) :: s ->
196 debug_print (lazy ("context length " ^string_of_int (List.length g)));
197 let rec aux s go gc =
200 debug_print (lazy "no selected goals");
203 debug_print (lazy "inner eval tactical");
205 if List.exists ((=) (goal_of_loc loc)) gc then
208 match switch_of_loc loc with
209 | Closed _ -> fail (lazy "cannot apply to a Closed goal")
212 let go', gc' = compare_statuses ~past:s ~present:sn in
213 sn, ((go @+ [n]) @- gc') @+ go', gc @+ gc'
218 (new NTacStatus.status status#obj ())#set_estatus
219 (status :> NEstatus.status) in
220 let s0, go0, gc0 = s0, [], [] in
221 let sn, gon, gcn = aux s0 go0 gc0 g in
222 debug_print (lazy ("opened: "
223 ^ String.concat " " (List.map string_of_int gon)));
224 debug_print (lazy ("closed: "
225 ^ String.concat " " (List.map string_of_int gcn)));
227 (zero_pos gon, t @~- gcn, k @~- gcn, tag) :: deep_close gcn s
229 ((status#set_stack stack)#set_obj(sn:>lowtac_status)#obj)#set_estatus sn
232 let atomic_tac htac : #tac_status as 'a -> 'a = distribute_tac (exec htac) ;;
235 let rec repeat t (status : #tac_status as 'a) : 'a =
236 try repeat t (t status)
237 with NTacStatus.Error _ -> status
239 atomic_tac (repeat t) s
243 let try_tac tac status =
246 with NTacStatus.Error _ ->
250 let first_tac tacl status =
253 (fun tac _ -> try Some (tac status) with NTacStatus.Error _ -> None) tacl
256 | None -> fail (lazy "No tactics left")
260 let exact_tac t : 's tactic = distribute_tac (fun status goal ->
261 let goalty = get_goalty status goal in
262 let status, t = disambiguate status t (Some goalty) (ctx_of goalty) in
263 instantiate status goal t)
266 let assumption_tac status = distribute_tac (fun status goal ->
267 let gty = get_goalty status goal in
268 let context = ctx_of gty in
271 (List.map (fun (name,_) -> exact_tac ("",0,(Ast.Ident (name,None))))
274 exec htac status goal) status
277 let find_in_context name context =
278 let rec aux acc = function
279 | [] -> raise Not_found
280 | (hd,_) :: tl when hd = name -> acc
281 | _ :: tl -> aux (acc + 1) tl
286 let clear_tac names =
287 if names = [] then id_tac
289 distribute_tac (fun status goal ->
290 let goalty = get_goalty status goal in
294 try find_in_context name (ctx_of goalty)
296 fail (lazy ("hypothesis '" ^ name ^ "' not found")))
299 let n,h,metasenv,subst,o = status#obj in
300 let metasenv,subst,_ = NCicMetaSubst.restrict metasenv subst goal js in
301 status#set_obj (n,h,metasenv,subst,o))
304 let generalize0_tac args =
305 if args = [] then id_tac
306 else exact_tac ("",0,Ast.Appl (Ast.Implicit `JustOne :: args))
309 let select0_tac ~where:(wanted,hyps,where) ~job =
310 let found, postprocess =
312 | `Substexpand argsno -> mk_in_scope, mk_out_scope argsno
313 | `Collect l -> (fun s t -> l := t::!l; mk_in_scope s t), mk_out_scope 1
314 | `ChangeWith f -> f,(fun s t -> s, t)
316 distribute_tac (fun status goal ->
317 let goalty = get_goalty status goal in
319 match where with None -> NCic.Implicit `Term | Some where -> where
321 let status, newgoalctx =
323 (fun (name,d as entry) (status,ctx) ->
325 let path = List.assoc name hyps in
329 select_term status ~found ~postprocess (mk_cic_term ctx ty)
331 let status,ty = term_of_cic_term status ty ctx in
332 status,(name,NCic.Decl ty)::ctx
333 | NCic.Def (bo,ty) ->
335 select_term status ~found ~postprocess (mk_cic_term ctx bo)
337 let status,bo = term_of_cic_term status bo ctx in
338 status,(name,NCic.Def (bo,ty))::ctx
340 Not_found -> status, entry::ctx
341 ) (ctx_of goalty) (status,[])
343 let status, newgoalty =
344 select_term status ~found ~postprocess goalty (wanted,path) in
345 (* WARNING: the next two lines simply change the context of newgoalty
346 from the old to the new one. Otherwise mk_meta will do that herself,
347 calling relocate that calls delift. However, newgoalty is now
348 ?[out_scope] and thus the delift would trigger the special unification
349 case, which is wrong now :-( *)
350 let status,newgoalty = term_of_cic_term status newgoalty (ctx_of goalty) in
351 let newgoalty = mk_cic_term newgoalctx newgoalty in
353 let status, instance =
354 mk_meta status newgoalctx (`Decl newgoalty)
356 instantiate status goal instance)
359 let select_tac ~where ~job move_down_hyps =
360 let (wanted,hyps,where) = GrafiteDisambiguate.disambiguate_npattern where in
362 match where with None -> NCic.Implicit `Term | Some where -> where in
363 if not move_down_hyps then
364 select0_tac ~where:(wanted,hyps,Some path) ~job
368 (fun path (name,path_name) -> NCic.Prod ("_",path_name,path))
372 generalize0_tac (List.map (fun (name,_) -> Ast.Ident (name,None)) hyps);
373 select0_tac ~where:(wanted,[],Some path) ~job;
374 clear_tac (List.map fst hyps) ]
377 let generalize_tac ~where =
380 select_tac ~where ~job:(`Collect l) true;
381 print_tac true "ha selezionato?";
382 (fun s -> distribute_tac (fun status goal ->
383 let goalty = get_goalty status goal in
384 let status,canon,rest =
388 _,_,(None,_,_) -> fail (lazy "No term to generalize")
389 | txt,txtlen,(Some what,_,_) ->
391 disambiguate status (txt,txtlen,what) None (ctx_of goalty)
395 | he::tl -> status,he,tl in
398 (fun s t -> unify s (ctx_of goalty) canon t) status rest in
399 let status, canon = term_of_cic_term status canon (ctx_of goalty) in
400 instantiate status goal
401 (mk_cic_term (ctx_of goalty) (NCic.Appl [NCic.Implicit `Term ; canon ]))
407 exact_tac ("",0, Ast.Appl [Ast.Implicit `JustOne; Ast.Implicit `JustOne]);
409 pos_tac [2]; exact_tac t;
410 shift_tac; pos_tac [1]; skip_tac;
414 let lapply_tac (s,n,t) =
415 exact_tac (s,n, Ast.Appl [Ast.Implicit `JustOne; t])
418 let reduce_tac ~reduction ~where =
419 let change status t =
421 | `Normalize perform_delta ->
423 ?delta:(if perform_delta then None else Some max_int) (ctx_of t) t
424 | `Whd perform_delta ->
426 ?delta:(if perform_delta then None else Some max_int) (ctx_of t) t
428 let where = GrafiteDisambiguate.disambiguate_npattern where in
429 select0_tac ~where ~job:(`ChangeWith change)
432 let change_tac ~where ~with_what =
433 let change status t =
434 let status, ww = disambiguate status with_what None (ctx_of t) in
435 let status = unify status (ctx_of t) t ww in
438 let where = GrafiteDisambiguate.disambiguate_npattern where in
439 select0_tac ~where ~job:(`ChangeWith change)
442 let letin_tac ~where ~what:(_,_,w) name =
444 select_tac ~where ~job:(`Substexpand 1) true;
446 ("",0,Ast.LetIn((Ast.Ident (name,None),None),w,Ast.Implicit `JustOne));
450 let apply_tac (s,n,t) =
451 let t = Ast.Appl [t; Ast.Implicit `Vector] in
459 lefts: NCic.term list;
460 rights: NCic.term list;
461 reference: NReference.reference;
465 let analyze_indty_tac ~what indtyref =
466 distribute_tac (fun status goal ->
467 let goalty = get_goalty status goal in
468 let status, what = disambiguate status what None (ctx_of goalty) in
469 let status, ty_what = typeof status (ctx_of what) what in
470 let status, (r,consno,lefts,rights) = analyse_indty status ty_what in
471 let leftno = List.length lefts in
472 let rightno = List.length rights in
474 rightno = rightno; leftno = leftno; consno = consno;
475 lefts = lefts; rights = rights; reference = r;
477 exec id_tac status goal)
480 let sort_of_goal_tac sortref = distribute_tac (fun status goal ->
481 let goalty = get_goalty status goal in
482 let status,sort = typeof status (ctx_of goalty) goalty in
483 let sort = fix_sorts sort in
484 let status, sort = term_of_cic_term status sort (ctx_of goalty) in
489 let elim_tac ~what:(txt,len,what) ~where =
490 let what = txt, len, Ast.Appl [what; Ast.Implicit `Vector] in
491 let indtyinfo = ref None in
492 let sort = ref (NCic.Rel 1) in
493 atomic_tac (block_tac [
494 analyze_indty_tac ~what indtyinfo;
496 ~where ~job:(`Substexpand ((HExtlib.unopt !indtyinfo).rightno+1)) true s);
497 sort_of_goal_tac sort;
499 let ity = HExtlib.unopt !indtyinfo in
500 let NReference.Ref (uri, _) = ity.reference in
502 NUri.name_of_uri uri ^ "_" ^
503 snd (NCicElim.ast_of_sort
504 (match !sort with NCic.Sort x -> x | _ -> assert false))
508 Ast.Appl [ Ast.Ident (name,None) ; Ast.Implicit `Vector ; w ]
510 exact_tac ("",0,eliminator) status) ])
513 let rewrite_tac ~dir ~what:(_,_,what) ~where status =
514 let sortref = ref (NCic.Rel 1) in
515 let status = sort_of_goal_tac sortref status in
516 let suffix = "_" ^ snd (NCicElim.ast_of_sort
517 (match !sortref with NCic.Sort x -> x | _ -> assert false))
521 `LeftToRight -> "eq" ^ suffix ^ "_r"
522 | `RightToLeft -> "eq" ^ suffix
525 [ select_tac ~where ~job:(`Substexpand 1) true;
528 Ast.Appl(Ast.Ident(name,None)::HExtlib.mk_list (Ast.Implicit `JustOne) 5@
535 ("",0,(Ast.Binder (`Lambda,
536 (Ast.Ident (name,None),None),Ast.Implicit `JustOne)));
537 if name = "_" then clear_tac [name] else id_tac ]
540 let cases ~what status goal =
541 let gty = get_goalty status goal in
542 let status, what = disambiguate status what None (ctx_of gty) in
543 let status, ty = typeof status (ctx_of what) what in
544 let status, (ref, consno, _, _) = analyse_indty status ty in
545 let status, what = term_of_cic_term status what (ctx_of gty) in
547 NCic.Match (ref,NCic.Implicit `Term, what,
548 HExtlib.mk_list (NCic.Implicit `Term) consno)
550 let ctx = ctx_of gty in
551 let status,t,ty = refine status ctx (mk_cic_term ctx t) (Some gty) in
552 instantiate status goal t
555 let cases_tac ~what:(txt,len,what) ~where =
556 let what = txt, len, Ast.Appl [what; Ast.Implicit `Vector] in
557 let indtyinfo = ref None in
560 analyze_indty_tac ~what indtyinfo;
562 ~where ~job:(`Substexpand ((HExtlib.unopt !indtyinfo).rightno+1))true s);
563 distribute_tac (cases ~what) ])
567 let name = if name = "_" then "_clearme" else name in
568 block_tac [ intro_tac name;
570 ~where:("",0,(None,[],None))
571 ~what:("",0,Ast.Ident (name,None));
572 if name = "_clearme" then clear_tac ["_clearme"] else id_tac ]
575 let constructor ?(num=1) ~args status goal =
576 if num < 1 then fail (lazy "constructor numbers begin with 1");
577 let gty = get_goalty status goal in
578 let status, (r,_,_,_) = analyse_indty status gty in
579 let ref = NReference.mk_constructor num r in
581 if args = [] then Ast.NRef ref else
582 Ast.Appl (HExtlib.list_concat ~sep:[Ast.Implicit `Vector]
583 ([Ast.NRef ref] :: List.map (fun _,_,x -> [x]) args))
585 exec (apply_tac ("",0,t)) status goal
588 let constructor_tac ?num ~args = distribute_tac (constructor ?num ~args);;
590 let assert0_tac (hyps,concl) = distribute_tac (fun status goal ->
591 let gty = get_goalty status goal in
592 let eq status ctx t1 t2 =
593 let status,t1 = disambiguate status t1 None ctx in
594 let status,t1 = apply_subst status ctx t1 in
595 let status,t1 = term_of_cic_term status t1 ctx in
596 let t2 = mk_cic_term ctx t2 in
597 let status,t2 = apply_subst status ctx t2 in
598 let status,t2 = term_of_cic_term status t2 ctx in
599 prerr_endline ("COMPARING: " ^ NCicPp.ppterm ~subst:[] ~metasenv:[] ~context:ctx t1 ^ " vs " ^ NCicPp.ppterm ~subst:[] ~metasenv:[] ~context:ctx t2);
603 let status,gty' = term_of_cic_term status gty (ctx_of gty) in
604 let status = eq status (ctx_of gty) concl gty' in
607 (fun (id1,e1) ((id2,e2) as item) (status,ctx) ->
608 assert (id1=id2 || (prerr_endline (id1 ^ " vs " ^ id2); false));
610 `Decl t1, NCic.Decl t2 ->
611 let status = eq status ctx t1 t2 in
613 | `Def (b1,t1), NCic.Def (b2,t2) ->
614 let status = eq status ctx t1 t2 in
615 let status = eq status ctx b1 b2 in
618 ) hyps (ctx_of gty) (status,[])
620 exec id_tac status goal)
623 let assert_tac seqs status =
624 match status#stack with
627 assert (List.length g = List.length seqs);
630 | [seq] -> assert0_tac seq
634 HExtlib.list_concat ~sep:[shift_tac]
635 (List.map (fun seq -> [assert0_tac seq]) seqs)@
640 let auto ~params:(l,_) status goal =
641 let gty = get_goalty status goal in
642 let n,h,metasenv,subst,o = status#obj in
643 let status,t = term_of_cic_term status gty (ctx_of gty) in
646 (fun (status, l) t ->
647 let status, t = disambiguate status t None (ctx_of gty) in
648 let status, ty = typeof status (ctx_of t) t in
649 let status, t = term_of_cic_term status t (ctx_of gty) in
650 let status, ty = term_of_cic_term status ty (ctx_of ty) in
651 (status, (t,ty) :: l))
655 NCicParamod.nparamod status metasenv subst (ctx_of gty) (NCic.Rel ~-1,t) l
657 | [] -> raise (NTacStatus.Error (lazy "no proof found",None))
658 | (pt, metasenv, subst)::_ ->
659 let status = status#set_obj (n,h,metasenv,subst,o) in
660 instantiate status goal (NTacStatus.mk_cic_term (ctx_of gty) pt)
663 let auto_tac ~params status =
664 distribute_tac (auto ~params) status