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 in
67 List.filter (fun e -> not (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 (Negative, hd), ((tl, EqualitySet.remove hd neg_set), (pos, pos_set))
78 (Positive, hd), (([], neg_set), (tl, EqualitySet.remove hd pos_set))
79 | _, _ -> assert false
81 | _ when (!symbols_counter > 0) && (EqualitySet.is_empty neg_set) -> (
82 symbols_counter := !symbols_counter - 1;
84 TermMap.fold (fun k v res -> res + v) map 0
88 let symbols = symbols_of_equality e in
89 let card = cardinality symbols in
90 let f equality (i, e) =
94 if TermMap.mem k symbols then
95 let c = TermMap.find k symbols in
96 let c1 = abs (c - v) in
101 (symbols_of_equality equality) (0, 0)
103 (* Printf.printf "equality: %s, common: %d, others: %d\n" *)
104 (* (string_of_equality ~env equality) common others; *)
105 let c = others + (abs (common - card)) in
106 if c < i then (c, equality)
109 let e1 = EqualitySet.min_elt pos_set in
114 if TermMap.mem k symbols then
115 let c = TermMap.find k symbols in
116 let c1 = abs (c - v) in
117 let c2 = v - (abs (c - v)) in
121 (symbols_of_equality e1) (0, 0)
123 (others + (abs (common - card))), e1
125 let _, current = EqualitySet.fold f pos_set initial in
126 (* Printf.printf "\nsymbols-based selection: %s\n\n" *)
127 (* (string_of_equality ~env current); *)
130 (remove current pos_list, EqualitySet.remove current pos_set))
132 let current = EqualitySet.min_elt pos_set in
135 (remove current pos_list, EqualitySet.remove current pos_set)
137 (Positive, current), passive
140 symbols_counter := !symbols_ratio;
141 let set_selection set = EqualitySet.min_elt set in
142 if EqualitySet.is_empty neg_set then
143 let current = set_selection pos_set in
146 (remove current pos_list, EqualitySet.remove current pos_set)
148 (Positive, current), passive
150 let current = set_selection neg_set in
152 (remove current neg_list, EqualitySet.remove current neg_set),
155 (Negative, current), passive
159 let make_passive neg pos =
160 let set_of equalities =
161 List.fold_left (fun s e -> EqualitySet.add e s) EqualitySet.empty equalities
163 (neg, set_of neg), (pos, set_of pos)
167 let add_to_passive passive (new_neg, new_pos) =
168 let (neg_list, neg_set), (pos_list, pos_set) = passive in
169 let ok set equality = not (EqualitySet.mem equality set) in
170 let neg = List.filter (ok neg_set) new_neg
171 and pos = List.filter (ok pos_set) new_pos in
172 let add set equalities =
173 List.fold_left (fun s e -> EqualitySet.add e s) set equalities
175 (neg @ neg_list, add neg_set neg), (pos_list @ pos, add pos_set pos)
179 let passive_is_empty = function
180 | ([], _), ([], _) -> true
185 (* TODO: find a better way! *)
186 let maxmeta = ref 0;;
188 let infer env sign current active =
189 let rec infer_negative current = function
191 | (Negative, _)::tl -> infer_negative current tl
192 | (Positive, equality)::tl ->
193 let res = superposition_left env current equality in
194 let neg, pos = infer_negative current tl in
197 and infer_positive current = function
199 | (Negative, equality)::tl ->
200 let res = superposition_left env equality current in
201 let neg, pos = infer_positive current tl in
203 | (Positive, equality)::tl ->
204 let maxm, res = superposition_right !maxmeta env current equality in
205 let maxm, res' = superposition_right maxm env equality current in
207 let neg, pos = infer_positive current tl in
209 (* Printf.printf "risultato di superposition_right: %s %s\n%s\n\n" *)
210 (* (string_of_equality ~env current) (string_of_equality ~env equality) *)
211 (* (String.concat "\n" (List.map (string_of_equality ~env) res)); *)
212 (* Printf.printf "risultato di superposition_right: %s %s\n%s\n\n" *)
213 (* (string_of_equality ~env equality) (string_of_equality ~env current) *)
214 (* (String.concat "\n" (List.map (string_of_equality ~env) res')); *)
216 neg, res @ res' @ pos
219 | Negative -> infer_negative current active
220 | Positive -> infer_positive current active
224 let contains_empty env (negative, positive) =
225 let metasenv, context, ugraph = env in
227 let (proof, _, _, _) =
229 (fun (proof, (ty, left, right, ordering), m, a) ->
230 fst (CicReduction.are_convertible context left right ugraph))
239 let forward_simplify env (sign, current) ?passive active =
243 | Some ((pn, _), (pp, _)) ->
244 (List.map (fun e -> Negative, e) pn),
245 (List.map (fun e -> Positive, e) pp)
247 let all = active @ pn @ pp in
248 let rec find_duplicate sign current = function
250 | (s, eq)::tl when s = sign ->
251 if meta_convertibility_eq current eq then true
252 else find_duplicate sign current tl
253 | _::tl -> find_duplicate sign current tl
255 (* let duplicate = find_duplicate sign current all in *)
256 (* if duplicate then *)
259 let rec aux env (sign, current) = function
260 | [] -> Some (sign, current)
261 | (Negative, _)::tl -> aux env (sign, current) tl
262 | (Positive, equality)::tl ->
263 let newmeta, newcurrent =
264 demodulation !maxmeta env current equality in
266 if is_identity env newcurrent then
267 if sign = Negative then
271 else if newcurrent <> current then
272 aux env (sign, newcurrent) active
274 aux env (sign, newcurrent) tl
276 let res = aux env (sign, current) all in
280 if find_duplicate s c all then
283 let pred (sign, eq) =
284 if sign <> s then false
285 else subsumption env c eq
287 if List.exists pred all then None
292 let forward_simplify_new env (new_neg, new_pos) ?passive active =
296 | Some ((pn, _), (pp, _)) ->
297 (List.map (fun e -> Negative, e) pn),
298 (List.map (fun e -> Positive, e) pp)
300 let all = active @ pn @ pp in
301 let remove_identities equalities =
302 let ok eq = not (is_identity env eq) in
303 List.filter ok equalities
305 let rec simpl all' target =
308 | (Negative, _)::tl -> simpl tl target
309 | (Positive, source)::tl ->
310 let newmeta, newtarget = demodulation !maxmeta env target source in
312 if is_identity env newtarget then newtarget
313 else if newtarget <> target then (
314 (* Printf.printf "OK:\n%s\n%s\n" *)
315 (* (string_of_equality ~env target) *)
316 (* (string_of_equality ~env newtarget); *)
317 (* print_newline (); *)
320 else simpl tl newtarget
322 let new_neg = List.map (simpl all) new_neg
323 and new_pos = remove_identities (List.map (simpl all) new_pos) in
325 List.fold_left (fun s e -> EqualitySet.add e s) EqualitySet.empty new_pos
327 let new_pos = EqualitySet.elements new_pos_set in
328 let f sign' target (sign, eq) =
329 (* Printf.printf "f %s <%s> (%s, <%s>)\n" *)
330 (* (string_of_sign sign') (string_of_equality ~env target) *)
331 (* (string_of_sign sign) (string_of_equality ~env eq); *)
332 if sign <> sign' then false
333 else subsumption env target eq
335 (* new_neg, new_pos *)
336 (List.filter (fun e -> not (List.exists (f Negative e) all)) new_neg,
337 List.filter (fun e -> not (List.exists (f Positive e) all)) new_pos)
341 let backward_simplify_active env (new_neg, new_pos) active =
342 let new_pos = List.map (fun e -> Positive, e) new_pos in
345 (fun (s, equality) (res, newn) ->
346 match forward_simplify env (s, equality) new_pos with
347 | None when s = Negative ->
348 Printf.printf "\nECCO QUI: %s\n"
349 (string_of_equality ~env equality);
361 List.exists (fun (s, e) -> meta_convertibility_eq eq1 e) where
365 if (is_identity env eq) || (find eq res) then res else (s, eq)::res
369 if (is_identity env eq) || (find eq res) then res else (s, eq)::res)
372 (fun (s, eq) (n, p) ->
373 if (s <> Negative) && (is_identity env eq) then
376 if s = Negative then eq::n, p
381 | [], [] -> active, None
382 | _ -> active, Some newa
386 let backward_simplify_passive env (new_neg, new_pos) passive =
387 let new_pos = List.map (fun e -> Positive, e) new_pos in
388 let (nl, ns), (pl, ps) = passive in
389 let f sign equality (resl, ress, newn) =
390 match forward_simplify env (sign, equality) new_pos with
391 | None -> resl, EqualitySet.remove equality ress, newn
394 equality::resl, ress, newn
396 let ress = EqualitySet.remove equality ress in
399 let nl, ns, newn = List.fold_right (f Negative) nl ([], ns, [])
400 and pl, ps, newp = List.fold_right (f Positive) pl ([], ps, []) in
401 match newn, newp with
402 | [], [] -> ((nl, ns), (pl, ps)), None
403 | _, _ -> ((nl, ns), (pl, ps)), Some (newn, newp)
407 let backward_simplify env new' ?passive active =
408 let active, newa = backward_simplify_active env new' active in
411 active, (([], EqualitySet.empty), ([], EqualitySet.empty)), newa, None
414 backward_simplify_passive env new' passive in
415 active, passive, newa, newp
420 let rec given_clause env passive active =
421 match passive_is_empty passive with
424 (* Printf.printf "before select\n"; *)
425 let (sign, current), passive = select env passive active in
426 (* Printf.printf "before simplification: sign: %s\ncurrent: %s\n\n" *)
427 (* (string_of_sign sign) (string_of_equality ~env current); *)
428 match forward_simplify env (sign, current) ~passive active with
429 (* | None when sign = Negative -> *)
430 (* Printf.printf "OK!!! %s %s" (string_of_sign sign) *)
431 (* (string_of_equality ~env current); *)
432 (* print_newline (); *)
433 (* let proof, _, _, _ = current in *)
434 (* Success (Some proof, env) *)
436 (* Printf.printf "avanti... %s %s" (string_of_sign sign) *)
437 (* (string_of_equality ~env current); *)
438 (* print_newline (); *)
439 given_clause env passive active
440 | Some (sign, current) ->
441 if (sign = Negative) && (is_identity env current) then (
442 Printf.printf "OK!!! %s %s" (string_of_sign sign)
443 (string_of_equality ~env current);
445 let proof, _, _, _ = current in
446 Success (Some proof, env)
448 print_endline "\n================================================";
449 Printf.printf "selected: %s %s"
450 (string_of_sign sign) (string_of_equality ~env current);
453 let new' = infer env sign current active in
454 let res, proof = contains_empty env new' in
458 let new' = forward_simplify_new env new' active in
463 let active, _, newa, _ =
464 backward_simplify env ([], [current]) active
469 let nn = List.map (fun e -> Negative, e) n
470 and pp = List.map (fun e -> Positive, e) p in
474 Printf.printf "active:\n%s\n"
477 (fun (s, e) -> (string_of_sign s) ^ " " ^
478 (string_of_equality ~env e)) active)));
484 Printf.printf "new':\n%s\n"
487 (fun e -> "Negative " ^
488 (string_of_equality ~env e)) neg) @
490 (fun e -> "Positive " ^
491 (string_of_equality ~env e)) pos)));
494 match contains_empty env new' with
498 | Negative -> (sign, current)::active
499 | Positive -> active @ [(sign, current)]
501 let passive = add_to_passive passive new' in
502 let (_, ns), (_, ps) = passive in
503 Printf.printf "passive:\n%s\n"
505 ((List.map (fun e -> "Negative " ^
506 (string_of_equality ~env e))
507 (EqualitySet.elements ns)) @
508 (List.map (fun e -> "Positive " ^
509 (string_of_equality ~env e))
510 (EqualitySet.elements ps))));
512 given_clause env passive active
519 let rec given_clause_fullred env passive active =
520 match passive_is_empty passive with
523 (* Printf.printf "before select\n"; *)
524 let (sign, current), passive = select env passive active in
525 (* Printf.printf "before simplification: sign: %s\ncurrent: %s\n\n" *)
526 (* (string_of_sign sign) (string_of_equality ~env current); *)
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
549 | Negative -> (sign, current)::active
550 | Positive -> active @ [(sign, current)]
553 (* match new' with *)
555 (* Printf.printf "new' before simpl:\n%s\n" *)
556 (* (String.concat "\n" *)
558 (* (fun e -> "Negative " ^ *)
559 (* (string_of_equality ~env e)) neg) @ *)
561 (* (fun e -> "Positive " ^ *)
562 (* (string_of_equality ~env e)) pos))); *)
563 (* print_newline (); *)
565 let rec simplify new' active passive =
566 let new' = forward_simplify_new env new' ~passive active in
567 let active, passive, newa, retained =
568 backward_simplify env new' ~passive active
570 match newa, retained with
571 | None, None -> active, passive, new'
573 | None, Some (n, p) ->
575 simplify (nn @ n, np @ p) active passive
576 | Some (n, p), Some (rn, rp) ->
578 simplify (nn @ n @ rn, np @ p @ rp) active passive
580 let active, passive, new' = simplify new' active passive in
582 Printf.printf "active:\n%s\n"
585 (fun (s, e) -> (string_of_sign s) ^ " " ^
586 (string_of_equality ~env e)) active)));
592 Printf.printf "new':\n%s\n"
595 (fun e -> "Negative " ^
596 (string_of_equality ~env e)) neg) @
598 (fun e -> "Positive " ^
599 (string_of_equality ~env e)) pos)));
602 match contains_empty env new' with
604 let passive = add_to_passive passive new' in
605 (* let (_, ns), (_, ps) = passive in *)
606 (* Printf.printf "passive:\n%s\n" *)
607 (* (String.concat "\n" *)
608 (* ((List.map (fun e -> "Negative " ^ *)
609 (* (string_of_equality ~env e)) *)
610 (* (EqualitySet.elements ns)) @ *)
611 (* (List.map (fun e -> "Positive " ^ *)
612 (* (string_of_equality ~env e)) *)
613 (* (EqualitySet.elements ps)))); *)
614 (* print_newline (); *)
615 given_clause_fullred env passive active
622 let get_from_user () =
623 let dbd = Mysql.quick_connect
624 ~host:"localhost" ~user:"helm" ~database:"mowgli" () in
626 match read_line () with
630 let term_string = String.concat "\n" (get ()) in
631 let env, metasenv, term, ugraph =
632 List.nth (Disambiguate.Trivial.disambiguate_string dbd term_string) 0
634 term, metasenv, ugraph
638 let given_clause_ref = ref given_clause;;
642 let module C = Cic in
643 let module T = CicTypeChecker in
644 let module PET = ProofEngineTypes in
645 let module PP = CicPp in
646 let term, metasenv, ugraph = get_from_user () in
647 let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in
649 PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in
650 let goal = List.nth goals 0 in
651 let _, metasenv, meta_proof, _ = proof in
652 let _, context, goal = CicUtil.lookup_meta goal metasenv in
653 let equalities, maxm = find_equalities context proof in
654 maxmeta := maxm; (* TODO ugly!! *)
655 let env = (metasenv, context, ugraph) in
657 let term_equality = equality_of_term meta_proof goal in
658 let meta_proof, (eq_ty, left, right, ordering), _, _ = term_equality in
660 let passive = make_passive [term_equality] equalities in
661 Printf.printf "\ncurrent goal: %s\n"
662 (string_of_equality ~env term_equality);
663 Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context);
664 Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv);
665 Printf.printf "\nequalities:\n%s\n"
668 (string_of_equality ~env)
670 print_endline "--------------------------------------------------";
671 let start = Unix.gettimeofday () in
673 let res = !given_clause_ref env passive active in
674 let finish = Unix.gettimeofday () in
677 Printf.printf "NO proof found! :-(\n\n"
678 | Success (Some proof, env) ->
679 Printf.printf "OK, found a proof!:\n%s\n%.9f\n" (PP.ppterm proof)
681 | Success (None, env) ->
682 Printf.printf "Success, but no proof?!?\n\n"
684 print_endline ("EXCEPTION: " ^ (Printexc.to_string exc));
688 let configuration_file = ref "../../gTopLevel/gTopLevel.conf.xml";;
691 let set_ratio v = weight_age_ratio := (v+1); weight_age_counter := (v+1)
692 and set_sel v = symbols_ratio := v; symbols_counter := v;
693 and set_conf f = configuration_file := f
694 and set_lpo () = Utils.compare_terms := lpo
695 and set_kbo () = Utils.compare_terms := nonrec_kbo
696 and set_fullred () = given_clause_ref := given_clause_fullred
699 "-f", Arg.Unit set_fullred, "Use full-reduction strategy";
701 "-r", Arg.Int set_ratio, "Weight-Age equality selection ratio (default: 0)";
703 "-s", Arg.Int set_sel,
704 "symbols-based selection ratio (relative to the weight ratio)";
706 "-c", Arg.String set_conf, "Configuration file (for the db connection)";
708 "-lpo", Arg.Unit set_lpo, "Use lpo term ordering";
710 "-kbo", Arg.Unit set_kbo, "Use (non-recursive) kbo term ordering (default)";
711 ] (fun a -> ()) "Usage:"
713 Helm_registry.load_from !configuration_file;