6 | Success of Cic.term option * environment
11 let symbols_of_equality (_, (_, left, right), _, _) =
12 TermSet.union (symbols_of_term left) (symbols_of_term right)
16 let symbols_of_equality ((_, (_, left, right, _), _, _) as equality) =
17 let m1 = symbols_of_term left in
22 let c = TermMap.find k res in
23 TermMap.add k (c+v) res
26 (symbols_of_term right) m1
28 (* Printf.printf "symbols_of_equality %s:\n" *)
29 (* (string_of_equality equality); *)
30 (* TermMap.iter (fun k v -> Printf.printf "%s: %d\n" (CicPp.ppterm k) v) m; *)
31 (* print_newline (); *)
36 module OrderedEquality =
38 type t = Inference.equality
41 match meta_convertibility_eq eq1 eq2 with
44 let _, (ty, left, right, _), _, _ = eq1
45 and _, (ty', left', right', _), _, _ = eq2 in
46 let weight_of t = fst (weight_of_term ~consider_metas:false t) in
47 let w1 = (weight_of ty) + (weight_of left) + (weight_of right)
48 and w2 = (weight_of ty') + (weight_of left') + (weight_of right') in
49 match Pervasives.compare w1 w2 with
50 | 0 -> Pervasives.compare eq1 eq2
54 module EqualitySet = Set.Make(OrderedEquality);;
57 let weight_age_ratio = ref 0;; (* settable by the user from the command line *)
58 let weight_age_counter = ref !weight_age_ratio;;
60 let symbols_ratio = ref 0;;
61 let symbols_counter = ref 0;;
64 let select env passive (active, _) =
65 let (neg_list, neg_set), (pos_list, pos_set), passive_table = passive in
67 List.filter (fun e -> e <> eq) l
69 if !weight_age_ratio > 0 then
70 weight_age_counter := !weight_age_counter - 1;
71 match !weight_age_counter with
73 weight_age_counter := !weight_age_ratio;
74 match neg_list, pos_list with
76 (* Negatives aren't indexed, no need to remove them... *)
78 ((tl, EqualitySet.remove hd neg_set), (pos, pos_set), passive_table)
80 let passive_table = Indexing.remove_index passive_table hd in
82 (([], neg_set), (tl, EqualitySet.remove hd pos_set), passive_table)
83 | _, _ -> assert false
85 | _ when (!symbols_counter > 0) && (EqualitySet.is_empty neg_set) -> (
86 symbols_counter := !symbols_counter - 1;
88 TermMap.fold (fun k v res -> res + v) map 0
92 let symbols = symbols_of_equality e in
93 let card = cardinality symbols in
94 let f equality (i, e) =
98 if TermMap.mem k symbols then
99 let c = TermMap.find k symbols in
100 let c1 = abs (c - v) in
105 (symbols_of_equality equality) (0, 0)
107 (* Printf.printf "equality: %s, common: %d, others: %d\n" *)
108 (* (string_of_equality ~env equality) common others; *)
109 let c = others + (abs (common - card)) in
110 if c < i then (c, equality)
113 let e1 = EqualitySet.min_elt pos_set in
118 if TermMap.mem k symbols then
119 let c = TermMap.find k symbols in
120 let c1 = abs (c - v) in
121 let c2 = v - (abs (c - v)) in
125 (symbols_of_equality e1) (0, 0)
127 (others + (abs (common - card))), e1
129 let _, current = EqualitySet.fold f pos_set initial in
130 (* Printf.printf "\nsymbols-based selection: %s\n\n" *)
131 (* (string_of_equality ~env current); *)
132 let passive_table = Indexing.remove_index passive_table current in
135 (remove current pos_list, EqualitySet.remove current pos_set),
138 let current = EqualitySet.min_elt pos_set in
141 (remove current pos_list, EqualitySet.remove current pos_set),
142 Indexing.remove_index passive_table current
144 (Positive, current), passive
147 symbols_counter := !symbols_ratio;
148 let set_selection set = EqualitySet.min_elt set in
149 if EqualitySet.is_empty neg_set then
150 let current = set_selection pos_set in
153 (remove current pos_list, EqualitySet.remove current pos_set),
154 Indexing.remove_index passive_table current
156 (Positive, current), passive
158 let current = set_selection neg_set in
160 (remove current neg_list, EqualitySet.remove current neg_set),
164 (Negative, current), passive
168 let make_passive neg pos =
169 let set_of equalities =
170 List.fold_left (fun s e -> EqualitySet.add e s) EqualitySet.empty equalities
172 let table = Hashtbl.create (List.length pos) in
175 List.fold_left (fun tbl e -> Indexing.index tbl e) table pos
184 let add_to_passive passive (new_neg, new_pos) =
185 let (neg_list, neg_set), (pos_list, pos_set), table = passive in
186 let ok set equality = not (EqualitySet.mem equality set) in
187 let neg = List.filter (ok neg_set) new_neg
188 and pos = List.filter (ok pos_set) new_pos in
189 let add set equalities =
190 List.fold_left (fun s e -> EqualitySet.add e s) set equalities
192 (neg @ neg_list, add neg_set neg),
193 (pos_list @ pos, add pos_set pos),
194 List.fold_left (fun tbl e -> Indexing.index tbl e) table pos
198 let passive_is_empty = function
199 | ([], _), ([], _), _ -> true
204 (* TODO: find a better way! *)
205 let maxmeta = ref 0;;
207 let infer env sign current (active_list, active_table) =
210 Indexing.superposition_left env active_table current, []
213 Indexing.superposition_right !maxmeta env active_table current in
215 let rec infer_positive table = function
217 | (Negative, equality)::tl ->
218 let res = Indexing.superposition_left env table equality in
219 let neg, pos = infer_positive table tl in
221 | (Positive, equality)::tl ->
223 Indexing.superposition_right !maxmeta env table equality in
225 let neg, pos = infer_positive table tl in
228 let curr_table = Indexing.index (Hashtbl.create 1) current in
229 let neg, pos = infer_positive curr_table active_list in
234 let contains_empty env (negative, positive) =
235 let metasenv, context, ugraph = env in
237 let (proof, _, _, _) =
239 (fun (proof, (ty, left, right, ordering), m, a) ->
240 fst (CicReduction.are_convertible context left right ugraph))
249 let forward_simplify env (sign, current) ?passive (active_list, active_table) =
250 let pl, passive_table =
253 | Some ((pn, _), (pp, _), pt) ->
254 let pn = List.map (fun e -> (Negative, e)) pn
255 and pp = List.map (fun e -> (Positive, e)) pp in
258 let all = active_list @ pl in
259 let rec find_duplicate sign current = function
261 | (s, eq)::tl when s = sign ->
262 if meta_convertibility_eq current eq then true
263 else find_duplicate sign current tl
264 | _::tl -> find_duplicate sign current tl
266 let demodulate table current =
267 let newmeta, newcurrent =
268 Indexing.demodulation !maxmeta env table current in
270 if is_identity env newcurrent then
271 if sign = Negative then Some (sign, newcurrent) else None
273 Some (sign, newcurrent)
276 let res = demodulate active_table current in
279 | Some (sign, newcurrent) ->
280 match passive_table with
282 | Some passive_table -> demodulate passive_table newcurrent
287 if find_duplicate s c all then
290 let pred (sign, eq) =
291 if sign <> s then false
292 else subsumption env c eq
294 if List.exists pred all then None
299 let forward_simplify_new env (new_neg, new_pos) ?passive active =
300 let active_list, active_table = active in
301 let pl, passive_table =
304 | Some ((pn, _), (pp, _), pt) ->
305 let pn = List.map (fun e -> (Negative, e)) pn
306 and pp = List.map (fun e -> (Positive, e)) pp in
309 let all = active_list @ pl in
310 let demodulate table target =
311 let newmeta, newtarget = Indexing.demodulation !maxmeta env table target in
315 let new_neg, new_pos =
316 let new_neg = List.map (demodulate active_table) new_neg
317 and new_pos = List.map (demodulate active_table) new_pos in
318 match passive_table with
319 | None -> new_neg, new_pos
320 | Some passive_table ->
321 List.map (demodulate passive_table) new_neg,
322 List.map (demodulate passive_table) new_pos
327 if not (Inference.is_identity env e) then EqualitySet.add e s else s)
328 EqualitySet.empty new_pos
330 let new_pos = EqualitySet.elements new_pos_set in
331 let f sign' target (sign, eq) =
332 if sign <> sign' then false
333 else subsumption env target eq
335 (List.filter (fun e -> not (List.exists (f Negative e) all)) new_neg,
336 List.filter (fun e -> not (List.exists (f Positive e) all)) new_pos)
340 let backward_simplify_active env (new_neg, new_pos) active =
341 let active_list, active_table = active in
342 let new_pos, new_table =
344 (fun (l, t) e -> (Positive, e)::l, Indexing.index t e)
345 ([], Hashtbl.create (List.length new_pos)) new_pos
347 let active_list, newa =
349 (fun (s, equality) (res, newn) ->
350 match forward_simplify env (s, equality) (new_pos, new_table) with
360 List.exists (fun (s, e) -> meta_convertibility_eq eq1 e) where
364 (fun (s, eq) (res, tbl) ->
365 if (is_identity env eq) || (find eq res) then
368 (s, eq)::res, if s = Negative then tbl else Indexing.index tbl eq)
369 active_list ([], Hashtbl.create (List.length active_list)),
371 (fun (s, eq) (n, p) ->
372 if (s <> Negative) && (is_identity env eq) then
375 if s = Negative then eq::n, p
380 | [], [] -> active, None
381 | _ -> active, Some newa
385 let backward_simplify_passive env (new_neg, new_pos) passive =
386 let new_pos, new_table =
388 (fun (l, t) e -> (Positive, e)::l, Indexing.index t e)
389 ([], Hashtbl.create (List.length new_pos)) new_pos
391 let (nl, ns), (pl, ps), passive_table = passive in
392 let f sign equality (resl, ress, newn) =
393 match forward_simplify env (sign, equality) (new_pos, new_table) with
394 | None -> resl, EqualitySet.remove equality ress, newn
397 equality::resl, ress, newn
399 let ress = EqualitySet.remove equality ress in
402 let nl, ns, newn = List.fold_right (f Negative) nl ([], ns, [])
403 and pl, ps, newp = List.fold_right (f Positive) pl ([], ps, []) in
406 (fun tbl e -> Indexing.index tbl e) (Hashtbl.create (List.length pl)) pl
408 match newn, newp with
409 | [], [] -> ((nl, ns), (pl, ps), passive_table), None
410 | _, _ -> ((nl, ns), (pl, ps), passive_table), Some (newn, newp)
414 let backward_simplify env new' ?passive active =
415 let active, newa = backward_simplify_active env new' active in
418 active, (make_passive [] []), newa, None
421 backward_simplify_passive env new' passive in
422 active, passive, newa, newp
426 let rec given_clause env passive active =
427 match passive_is_empty passive with
430 let (sign, current), passive = select env passive active in
431 match forward_simplify env (sign, current) ~passive active with
433 given_clause env passive active
434 | Some (sign, current) ->
435 if (sign = Negative) && (is_identity env current) then (
436 Printf.printf "OK!!! %s %s" (string_of_sign sign)
437 (string_of_equality ~env current);
439 let proof, _, _, _ = current in
440 Success (Some proof, env)
442 print_endline "\n================================================";
443 Printf.printf "selected: %s %s"
444 (string_of_sign sign) (string_of_equality ~env current);
447 let new' = infer env sign current active in
448 let res, proof = contains_empty env new' in
452 let new' = forward_simplify_new env new' active in
457 let active, _, newa, _ =
458 backward_simplify env ([], [current]) active
463 let al, tbl = active in
464 let nn = List.map (fun e -> Negative, e) n in
469 Indexing.index tbl e)
475 Printf.printf "active:\n%s\n"
478 (fun (s, e) -> (string_of_sign s) ^ " " ^
479 (string_of_equality ~env e)) (fst active))));
485 Printf.printf "new':\n%s\n"
488 (fun e -> "Negative " ^
489 (string_of_equality ~env e)) neg) @
491 (fun e -> "Positive " ^
492 (string_of_equality ~env e)) pos)));
495 match contains_empty env new' with
498 let al, tbl = active in
500 | Negative -> (sign, current)::al, tbl
502 al @ [(sign, current)], Indexing.index tbl current
504 let passive = add_to_passive passive new' in
505 let (_, ns), (_, ps), _ = passive in
506 Printf.printf "passive:\n%s\n"
508 ((List.map (fun e -> "Negative " ^
509 (string_of_equality ~env e))
510 (EqualitySet.elements ns)) @
511 (List.map (fun e -> "Positive " ^
512 (string_of_equality ~env e))
513 (EqualitySet.elements ps))));
515 given_clause env passive active
522 let rec given_clause_fullred env passive active =
523 match passive_is_empty passive with
526 let (sign, current), passive = select env passive active in
527 match forward_simplify env (sign, current) ~passive active with
529 given_clause_fullred env passive active
530 | Some (sign, current) ->
531 if (sign = Negative) && (is_identity env current) then (
532 Printf.printf "OK!!! %s %s" (string_of_sign sign)
533 (string_of_equality ~env current);
535 let proof, _, _, _ = current in
536 Success (Some proof, env)
538 print_endline "\n================================================";
539 Printf.printf "selected: %s %s"
540 (string_of_sign sign) (string_of_equality ~env current);
543 let new' = infer env sign current active in
546 if is_identity env current then active
548 let al, tbl = active in
550 | Negative -> (sign, current)::al, tbl
551 | Positive -> al @ [(sign, current)], Indexing.index tbl current
553 let rec simplify new' active passive =
554 let new' = forward_simplify_new env new' ~passive active in
555 let active, passive, newa, retained =
556 backward_simplify env new' ~passive active
558 match newa, retained with
559 | None, None -> active, passive, new'
561 | None, Some (n, p) ->
563 simplify (nn @ n, np @ p) active passive
564 | Some (n, p), Some (rn, rp) ->
566 simplify (nn @ n @ rn, np @ p @ rp) active passive
568 let active, passive, new' = simplify new' active passive in
570 Printf.printf "active:\n%s\n"
573 (fun (s, e) -> (string_of_sign s) ^ " " ^
574 (string_of_equality ~env e)) (fst active))));
580 Printf.printf "new':\n%s\n"
583 (fun e -> "Negative " ^
584 (string_of_equality ~env e)) neg) @
586 (fun e -> "Positive " ^
587 (string_of_equality ~env e)) pos)));
590 match contains_empty env new' with
592 let passive = add_to_passive passive new' in
593 given_clause_fullred env passive active
600 let get_from_user () =
601 let dbd = Mysql.quick_connect
602 ~host:"localhost" ~user:"helm" ~database:"mowgli" () in
604 match read_line () with
608 let term_string = String.concat "\n" (get ()) in
609 let env, metasenv, term, ugraph =
610 List.nth (Disambiguate.Trivial.disambiguate_string dbd term_string) 0
612 term, metasenv, ugraph
616 let given_clause_ref = ref given_clause;;
620 let module C = Cic in
621 let module T = CicTypeChecker in
622 let module PET = ProofEngineTypes in
623 let module PP = CicPp in
624 let term, metasenv, ugraph = get_from_user () in
625 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
627 PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
628 let goal = List.nth goals 0 in
629 let _, metasenv, meta_proof, _ = proof in
630 let _, context, goal = CicUtil.lookup_meta goal metasenv in
631 let equalities, maxm = find_equalities context proof in
632 maxmeta := maxm; (* TODO ugly!! *)
633 let env = (metasenv, context, ugraph) in
635 let term_equality = equality_of_term meta_proof goal in
636 let meta_proof, (eq_ty, left, right, ordering), _, _ = term_equality in
637 let active = make_active () in
638 let passive = make_passive [term_equality] equalities in
639 Printf.printf "\ncurrent goal: %s\n"
640 (string_of_equality ~env term_equality);
641 Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context);
642 Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv);
643 Printf.printf "\nequalities:\n%s\n"
646 (string_of_equality ~env)
648 print_endline "--------------------------------------------------";
649 let start = Unix.gettimeofday () in
651 let res = !given_clause_ref env passive active in
652 let finish = Unix.gettimeofday () in
655 Printf.printf "NO proof found! :-(\n\n"
656 | Success (Some proof, env) ->
657 Printf.printf "OK, found a proof!:\n%s\n%.9f\n"
658 (PP.pp proof (names_of_context context))
660 | Success (None, env) ->
661 Printf.printf "Success, but no proof?!?\n\n"
663 print_endline ("EXCEPTION: " ^ (Printexc.to_string exc));
667 let configuration_file = ref "../../gTopLevel/gTopLevel.conf.xml";;
670 let set_ratio v = weight_age_ratio := (v+1); weight_age_counter := (v+1)
671 and set_sel v = symbols_ratio := v; symbols_counter := v;
672 and set_conf f = configuration_file := f
673 and set_lpo () = Utils.compare_terms := lpo
674 and set_kbo () = Utils.compare_terms := nonrec_kbo
675 and set_fullred () = given_clause_ref := given_clause_fullred
678 "-f", Arg.Unit set_fullred, "Use full-reduction strategy";
680 "-r", Arg.Int set_ratio, "Weight-Age equality selection ratio (default: 0)";
682 "-s", Arg.Int set_sel,
683 "symbols-based selection ratio (relative to the weight ratio)";
685 "-c", Arg.String set_conf, "Configuration file (for the db connection)";
687 "-lpo", Arg.Unit set_lpo, "Use lpo term ordering";
689 "-kbo", Arg.Unit set_kbo, "Use (non-recursive) kbo term ordering (default)";
690 ] (fun a -> ()) "Usage:"
692 Helm_registry.load_from !configuration_file;