(* Copyright (C) 2005, HELM Team. * * This file is part of HELM, an Hypertextual, Electronic * Library of Mathematics, developed at the Computer Science * Department, University of Bologna, Italy. * * HELM is free software; you can redistribute it and/or * modify it under the terms of the GNU General Public License * as published by the Free Software Foundation; either version 2 * of the License, or (at your option) any later version. * * HELM is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with HELM; if not, write to the Free Software * Foundation, Inc., 59 Temple Place - Suite 330, Boston, * MA 02111-1307, USA. * * For details, see the HELM World-Wide-Web page, * http://cs.unibo.it/helm/. *) (* $Id$ *) (* <:profiler<"saturation">> *) open Inference;; open Utils;; (* set to false to disable paramodulation inside auto_tac *) let connect_to_auto = true;; (* profiling statistics... *) let infer_time = ref 0.;; let forward_simpl_time = ref 0.;; let forward_simpl_new_time = ref 0.;; let backward_simpl_time = ref 0.;; let passive_maintainance_time = ref 0.;; (* limited-resource-strategy related globals *) let processed_clauses = ref 0;; (* number of equalities selected so far... *) let time_limit = ref 0.;; (* in seconds, settable by the user... *) let start_time = ref 0.;; (* time at which the execution started *) let elapsed_time = ref 0.;; (* let maximal_weight = ref None;; *) let maximal_retained_equality = ref None;; (* equality-selection related globals *) let use_fullred = ref true;; let weight_age_ratio = ref 6 (* 5 *);; (* settable by the user *) let weight_age_counter = ref !weight_age_ratio ;; let symbols_ratio = ref 0 (* 3 *);; let symbols_counter = ref 0;; (* non-recursive Knuth-Bendix term ordering by default *) (* Utils.compare_terms := Utils.rpo;; *) (* Utils.compare_terms := Utils.nonrec_kbo;; *) (* Utils.compare_terms := Utils.ao;; *) (* statistics... *) let derived_clauses = ref 0;; let kept_clauses = ref 0;; (* index of the greatest Cic.Meta created - TODO: find a better way! *) let maxmeta = ref 0;; (* varbiables controlling the search-space *) let maxdepth = ref 3;; let maxwidth = ref 3;; type new_proof = Equality.goal_proof * Equality.proof * Subst.substitution * Cic.metasenv type result = | ParamodulationFailure of string | ParamodulationSuccess of new_proof ;; type goal = Equality.goal_proof * Cic.metasenv * Cic.term;; type theorem = Cic.term * Cic.term * Cic.metasenv;; let symbols_of_equality equality = let (_, _, (_, left, right, _), _,_) = Equality.open_equality equality in let m1 = symbols_of_term left in let m = TermMap.fold (fun k v res -> try let c = TermMap.find k res in TermMap.add k (c+v) res with Not_found -> TermMap.add k v res) (symbols_of_term right) m1 in m ;; (* griggio *) module OrderedEquality = struct type t = Equality.equality let compare eq1 eq2 = match Equality.meta_convertibility_eq eq1 eq2 with | true -> 0 | false -> let w1, _, (ty,left, right, _), m1,_ = Equality.open_equality eq1 in let w2, _, (ty',left', right', _), m2,_ = Equality.open_equality eq2 in match Pervasives.compare w1 w2 with | 0 -> let res = (List.length m1) - (List.length m2) in if res <> 0 then res else Equality.compare eq1 eq2 | res -> res end module EqualitySet = Set.Make(OrderedEquality);; exception Empty_list;; let passive_is_empty = function | ([], _), _ -> true | _ -> false ;; let size_of_passive ((passive_list, ps), _) = List.length passive_list (* EqualitySet.cardinal ps *) ;; let size_of_active (active_list, _) = List.length active_list ;; let age_factor = 0.01;; (** selects one equality from passive. The selection strategy is a combination of weight, age and goal-similarity *) let rec select env goals passive = processed_clauses := !processed_clauses + 1; let goal = match (List.rev goals) with (_, goal::_)::_ -> goal | _ -> assert false in let (pos_list, pos_set), passive_table = passive in let remove eq l = List.filter (fun e -> Equality.compare e eq <> 0) l in if !weight_age_ratio > 0 then weight_age_counter := !weight_age_counter - 1; match !weight_age_counter with | 0 -> ( weight_age_counter := !weight_age_ratio; let rec skip_giant pos_list pos_set passive_table = match pos_list with | (hd:EqualitySet.elt)::tl -> let w,_,_,_,_ = Equality.open_equality hd in let passive_table = Indexing.remove_index passive_table hd in let pos_set = EqualitySet.remove hd pos_set in if w < 500 then hd, ((tl, pos_set), passive_table) else (prerr_endline ("\n\n\nGIANT SKIPPED: "^string_of_int w^"\n\n\n"); skip_giant tl pos_set passive_table) | _ -> assert false in skip_giant pos_list pos_set passive_table) | _ when (!symbols_counter > 0) -> (symbols_counter := !symbols_counter - 1; let cardinality map = TermMap.fold (fun k v res -> res + v) map 0 in let symbols = let _, _, term = goal in symbols_of_term term in let card = cardinality symbols in let foldfun k v (r1, r2) = if TermMap.mem k symbols then let c = TermMap.find k symbols in let c1 = abs (c - v) in let c2 = v - c1 in r1 + c2, r2 + c1 else r1, r2 + v in let f equality (i, e) = let common, others = TermMap.fold foldfun (symbols_of_equality equality) (0, 0) in let c = others + (abs (common - card)) in if c < i then (c, equality) else (i, e) in let e1 = EqualitySet.min_elt pos_set in let initial = let common, others = TermMap.fold foldfun (symbols_of_equality e1) (0, 0) in (others + (abs (common - card))), e1 in let _, current = EqualitySet.fold f pos_set initial in let passive_table = Indexing.remove_index passive_table current in current, ((remove current pos_list, EqualitySet.remove current pos_set), passive_table)) | _ -> symbols_counter := !symbols_ratio; let current = EqualitySet.min_elt pos_set in let passive_table = Indexing.remove_index passive_table current in current, ((remove current pos_list, EqualitySet.remove current pos_set), passive_table) ;; let filter_dependent passive id = prerr_endline ("+++++++++++++++passives "^ ( string_of_int (size_of_passive passive))); let (pos_list, pos_set), passive_table = passive in let passive = List.fold_right (fun eq ((list,set),table) -> if Equality.depend eq id then (let _,_,_,_,id_eq = Equality.open_equality eq in if id_eq = 9228 then prerr_endline ("\n\n--------filtering "^(string_of_int id_eq)); ((list, EqualitySet.remove eq set), Indexing.remove_index table eq)) else ((eq::list, set),table)) pos_list (([],pos_set),passive_table) in prerr_endline ("+++++++++++++++passives "^ ( string_of_int (size_of_passive passive))); passive ;; (* initializes the passive set of equalities *) let make_passive pos = let set_of equalities = List.fold_left (fun s e -> EqualitySet.add e s) EqualitySet.empty equalities in let table = List.fold_left (fun tbl e -> Indexing.index tbl e) Indexing.empty pos in (pos, set_of pos), table ;; let make_active () = [], Indexing.empty ;; (* adds to passive a list of equalities new_pos *) let add_to_passive passive new_pos = let (pos_list, pos_set), table = passive in let ok set equality = not (EqualitySet.mem equality set) in let pos = List.filter (ok pos_set) new_pos in let table = List.fold_left (fun tbl e -> Indexing.index tbl e) table pos in let add set equalities = List.fold_left (fun s e -> EqualitySet.add e s) set equalities in (pos_list @ pos, add pos_set pos), table ;; (* TODO *) (* removes from passive equalities that are estimated impossible to activate within the current time limit *) let prune_passive howmany (active, _) passive = let (pl, ps), tbl = passive in let howmany = float_of_int howmany and ratio = float_of_int !weight_age_ratio in let round v = let t = ceil v in int_of_float (if t -. v < 0.5 then t else v) in let in_weight = round (howmany *. ratio /. (ratio +. 1.)) and in_age = round (howmany /. (ratio +. 1.)) in debug_print (lazy (Printf.sprintf "in_weight: %d, in_age: %d\n" in_weight in_age)); let counter = ref !symbols_ratio in let rec pickw w ps = if w > 0 then if !counter > 0 then let _ = counter := !counter - 1; if !counter = 0 then counter := !symbols_ratio in let e = EqualitySet.min_elt ps in let ps' = pickw (w-1) (EqualitySet.remove e ps) in EqualitySet.add e ps' else let e = EqualitySet.min_elt ps in let ps' = pickw (w-1) (EqualitySet.remove e ps) in EqualitySet.add e ps' else EqualitySet.empty in let ps = pickw in_weight ps in let rec picka w s l = if w > 0 then match l with | [] -> w, s, [] | hd::tl when not (EqualitySet.mem hd s) -> let w, s, l = picka (w-1) s tl in w, EqualitySet.add hd s, hd::l | hd::tl -> let w, s, l = picka w s tl in w, s, hd::l else 0, s, l in let _, ps, pl = picka in_age ps pl in if not (EqualitySet.is_empty ps) then maximal_retained_equality := Some (EqualitySet.max_elt ps); let tbl = EqualitySet.fold (fun e tbl -> Indexing.index tbl e) ps Indexing.empty in (pl, ps), tbl ;; (** inference of new equalities between current and some in active *) let infer env current (active_list, active_table) = let (_,c,_) = env in if Utils.debug_metas then (ignore(Indexing.check_target c current "infer1"); ignore(List.map (function current -> Indexing.check_target c current "infer2") active_list)); let new_pos = let maxm, res = Indexing.superposition_right !maxmeta env active_table current in if Utils.debug_metas then ignore(List.map (function current -> Indexing.check_target c current "sup0") res); maxmeta := maxm; let rec infer_positive table = function | [] -> [] | equality::tl -> let maxm, res = Indexing.superposition_right !maxmeta env table equality in maxmeta := maxm; if Utils.debug_metas then ignore (List.map (function current -> Indexing.check_target c current "sup2") res); let pos = infer_positive table tl in res @ pos in let maxm, copy_of_current = Equality.fix_metas !maxmeta current in maxmeta := maxm; let curr_table = Indexing.index Indexing.empty current in let pos = infer_positive curr_table (copy_of_current::active_list) in if Utils.debug_metas then ignore(List.map (function current -> Indexing.check_target c current "sup3") pos); res @ pos in derived_clauses := !derived_clauses + (List.length new_pos); match !maximal_retained_equality with | None -> new_pos | Some eq -> ignore(assert false); (* if we have a maximal_retained_equality, we can discard all equalities "greater" than it, as they will never be reached... An equality is greater than maximal_retained_equality if it is bigger wrt. OrderedEquality.compare and it is less similar than maximal_retained_equality to the current goal *) List.filter (fun e -> OrderedEquality.compare e eq <= 0) new_pos ;; let check_for_deep_subsumption env active_table eq = let _,_,(eq_ty, left, right, order),metas,id = Equality.open_equality eq in if id = 14242 then assert false; let check_subsumed deep l r = let eqtmp = Equality.mk_tmp_equality(0,(eq_ty,l,r,Utils.Incomparable),metas)in match Indexing.subsumption env active_table eqtmp with | None -> false | Some (s,eq') -> (* prerr_endline ("\n\n " ^ Equality.string_of_equality ~env eq ^ "\nis"^(if deep then " CONTEXTUALLY " else " ")^"subsumed by \n " ^ Equality.string_of_equality ~env eq' ^ "\n\n"); *) true in let rec aux b (ok_so_far, subsumption_used) t1 t2 = match t1,t2 with | t1, t2 when not ok_so_far -> ok_so_far, subsumption_used | t1, t2 when subsumption_used -> t1 = t2, subsumption_used (* VERSIONE ERRATA | Cic.Appl (h1::l),Cic.Appl (h2::l') when h1 = h2 -> let rc = check_subsumed b t1 t1 in if rc then true, true else if h1 = h2 then (try List.fold_left2 (fun (ok_so_far, subsumption_used) t t' -> aux true (ok_so_far, subsumption_used) t t') (ok_so_far, subsumption_used) l l' with Invalid_argument _ -> false,subsumption_used) else false, subsumption_used | _ -> false, subsumption_used *) | Cic.Appl (h1::l),Cic.Appl (h2::l') -> let rc = check_subsumed b t1 t2 in if rc then true, true else if h1 = h2 then (try List.fold_left2 (fun (ok_so_far, subsumption_used) t t' -> aux true (ok_so_far, subsumption_used) t t') (ok_so_far, subsumption_used) l l' with Invalid_argument _ -> false,subsumption_used) else false, subsumption_used | _ -> false, subsumption_used in fst (aux false (true,false) left right) ;; (* let check_for_deep env active_table eq = match Indexing.subsumption env active_table eq with | None -> false | Some _ -> true ;; *) let profiler = HExtlib.profile "check_for_deep";; let check_for_deep_subsumption env active_table eq = profiler.HExtlib.profile (check_for_deep_subsumption env active_table) eq ;; (* buttare via sign *) (** simplifies current using active and passive *) let forward_simplify env (sign,current) ?passive (active_list, active_table) = let _, context, _ = env in let passive_table = match passive with | None -> None | Some ((_, _), pt) -> Some pt in let demodulate table current = let newmeta, newcurrent = Indexing.demodulation_equality !maxmeta env table sign current in maxmeta := newmeta; if Equality.is_identity env newcurrent then (* debug_print *) (* (lazy *) (* (Printf.sprintf "\ncurrent was: %s\nnewcurrent is: %s\n" *) (* (string_of_equality current) *) (* (string_of_equality newcurrent))); *) (* debug_print *) (* (lazy *) (* (Printf.sprintf "active is: %s" *) (* (String.concat "\n" *) (* (List.map (fun (_, e) -> (string_of_equality e)) active_list)))); *) None else Some newcurrent in let rec demod current = if Utils.debug_metas then ignore (Indexing.check_target context current "demod0"); let res = demodulate active_table current in if Utils.debug_metas then ignore ((function None -> () | Some x -> ignore (Indexing.check_target context x "demod1");()) res); match res with | None -> None | Some newcurrent -> match passive_table with | None -> res | Some passive_table -> match demodulate passive_table newcurrent with | None -> None | Some newnewcurrent -> if Equality.compare newcurrent newnewcurrent <> 0 then demod newnewcurrent else Some newnewcurrent in let res = demod current in match res with | None -> None | Some c -> if Indexing.in_index active_table c then None else match passive_table with | None -> if check_for_deep_subsumption env active_table c then None else res (* if Indexing.subsumption env active_table c = None then res else None *) | Some passive_table -> if Indexing.in_index passive_table c then None else if check_for_deep_subsumption env active_table c then None else (* if Indexing.subsumption env active_table c = None then*) (match Indexing.subsumption env passive_table c with | None -> res | Some (_,c') -> None (*prerr_endline "\n\nPESCO DALLE PASSIVE LA PIU' GENERALE\n\n"; Some c'*)) (* else None *) ;; type fs_time_info_t = { mutable build_all: float; mutable demodulate: float; mutable subsumption: float; };; let fs_time_info = { build_all = 0.; demodulate = 0.; subsumption = 0. };; (** simplifies new using active and passive *) let forward_simplify_new env new_pos ?passive active = if Utils.debug_metas then begin let m,c,u = env in ignore(List.map (fun current -> Indexing.check_target c current "forward new pos") new_pos;) end; let t1 = Unix.gettimeofday () in let active_list, active_table = active in let passive_table = match passive with | None -> None | Some ((_, _), pt) -> Some pt in let t2 = Unix.gettimeofday () in fs_time_info.build_all <- fs_time_info.build_all +. (t2 -. t1); let demodulate sign table target = let newmeta, newtarget = Indexing.demodulation_equality !maxmeta env table sign target in maxmeta := newmeta; newtarget in let t1 = Unix.gettimeofday () in (* we could also demodulate using passive. Currently we don't *) let new_pos = List.map (demodulate Positive active_table) new_pos in let t2 = Unix.gettimeofday () in fs_time_info.demodulate <- fs_time_info.demodulate +. (t2 -. t1); let new_pos_set = List.fold_left (fun s e -> if not (Equality.is_identity env e) then if EqualitySet.mem e s then s else EqualitySet.add e s else s) EqualitySet.empty new_pos in let new_pos = EqualitySet.elements new_pos_set in let subs = match passive_table with | None -> (fun e -> (Indexing.subsumption env active_table e = None)) | Some passive_table -> (fun e -> ((Indexing.subsumption env active_table e = None) && (Indexing.subsumption env passive_table e = None))) in (* let t1 = Unix.gettimeofday () in *) (* let t2 = Unix.gettimeofday () in *) (* fs_time_info.subsumption <- fs_time_info.subsumption +. (t2 -. t1); *) let is_duplicate = match passive_table with | None -> (fun e -> not (Indexing.in_index active_table e)) | Some passive_table -> (fun e -> not ((Indexing.in_index active_table e) || (Indexing.in_index passive_table e))) in List.filter subs (List.filter is_duplicate new_pos) ;; (** simplifies a goal with equalities in active and passive *) let rec simplify_goal env goal ?passive (active_list, active_table) = let passive_table = match passive with | None -> None | Some ((_, _), pt) -> Some pt in let demodulate table goal = let changed, newmeta, newgoal = Indexing.demodulation_goal !maxmeta env table goal in maxmeta := newmeta; changed, newgoal in let changed, goal = match passive_table with | None -> demodulate active_table goal | Some passive_table -> let changed, goal = demodulate active_table goal in (* let changed', goal = demodulate passive_table goal in*) (changed (*|| changed'*)), goal in changed, if not changed then goal else snd (simplify_goal env goal ?passive (active_list, active_table)) ;; let simplify_goals env goals ?passive active = let a_goals, p_goals = goals in let p_goals = List.map (fun (d, gl) -> let gl = List.map (fun g -> snd (simplify_goal env g ?passive active)) gl in d, gl) p_goals in let goals = List.fold_left (fun (a, p) (d, gl) -> let changed = ref false in let gl = List.map (fun g -> let c, g = simplify_goal env g ?passive active in changed := !changed || c; g) gl in if !changed then (a, (d, gl)::p) else ((d, gl)::a, p)) ([], p_goals) a_goals in goals ;; (** simplifies active usign new *) let backward_simplify_active env new_pos new_table min_weight active = let active_list, active_table = active in let active_list, newa, pruned = List.fold_right (fun equality (res, newn,pruned) -> let ew, _, _, _,id = Equality.open_equality equality in if ew < min_weight then equality::res, newn,pruned else match forward_simplify env (Utils.Positive, equality) (new_pos, new_table) with | None -> res, newn, id::pruned | Some e -> if Equality.compare equality e = 0 then e::res, newn, pruned else res, e::newn, pruned) active_list ([], [],[]) in let find eq1 where = List.exists (Equality.meta_convertibility_eq eq1) where in let id_of_eq eq = let _, _, _, _,id = Equality.open_equality eq in id in let ((active1,pruned),tbl), newa = List.fold_right (fun eq ((res,pruned), tbl) -> if List.mem eq res then (res, (id_of_eq eq)::pruned),tbl else if (Equality.is_identity env eq) || (find eq res) then ( (res, (id_of_eq eq)::pruned),tbl ) else (eq::res,pruned), Indexing.index tbl eq) active_list (([],pruned), Indexing.empty), List.fold_right (fun eq p -> if (Equality.is_identity env eq) then p else eq::p) newa [] in if List.length active1 <> List.length (fst active) then prerr_endline "\n\n\nMANCAVANO DELLE PRUNED!!!!\n\n\n"; match newa with | [] -> (active1,tbl), None, pruned | _ -> (active1,tbl), Some newa, pruned ;; (** simplifies passive using new *) let backward_simplify_passive env new_pos new_table min_weight passive = let (pl, ps), passive_table = passive in let f sign equality (resl, ress, newn) = let ew, _, _, _ , _ = Equality.open_equality equality in if ew < min_weight then equality::resl, ress, newn else match forward_simplify env (sign, equality) (new_pos, new_table) with | None -> resl, EqualitySet.remove equality ress, newn | Some e -> if equality = e then equality::resl, ress, newn else let ress = EqualitySet.remove equality ress in resl, ress, e::newn in let pl, ps, newp = List.fold_right (f Positive) pl ([], ps, []) in let passive_table = List.fold_left (fun tbl e -> Indexing.index tbl e) Indexing.empty pl in match newp with | [] -> ((pl, ps), passive_table), None | _ -> ((pl, ps), passive_table), Some (newp) ;; let build_table equations = List.fold_left (fun (l, t, w) e -> let ew, _, _, _ , _ = Equality.open_equality e in e::l, Indexing.index t e, min ew w) ([], Indexing.empty, 1000000) equations ;; let backward_simplify env new' ?passive active = let new_pos, new_table, min_weight = build_table new' in (* List.fold_left (fun (l, t, w) e -> let ew, _, _, _ , _ = Equality.open_equality e in e::l, Indexing.index t e, min ew w) ([], Indexing.empty, 1000000) new' in *) let active, newa, pruned = backward_simplify_active env new_pos new_table min_weight active in match passive with | None -> active, (make_passive []), newa, None, pruned | Some passive -> active, passive, newa, None, pruned (* prova let passive, newp = backward_simplify_passive env new_pos new_table min_weight passive in active, passive, newa, newp *) ;; let close env new' given = let new_pos, new_table, min_weight = List.fold_left (fun (l, t, w) e -> let ew, _, _, _ , _ = Equality.open_equality e in e::l, Indexing.index t e, min ew w) ([], Indexing.empty, 1000000) (snd new') in List.fold_left (fun p c -> let pos = infer env c (new_pos,new_table) in pos@p) [] given ;; let is_commutative_law eq = let w, proof, (eq_ty, left, right, order), metas , _ = Equality.open_equality eq in match left,right with Cic.Appl[f1;Cic.Meta _ as a1;Cic.Meta _ as b1], Cic.Appl[f2;Cic.Meta _ as a2;Cic.Meta _ as b2] -> f1 = f2 && a1 = b2 && a2 = b1 | _ -> false ;; let prova env new' active = let given = List.filter is_commutative_law (fst active) in let _ = debug_print (lazy (Printf.sprintf "symmetric:\n%s\n" (String.concat "\n" (List.map (fun e -> Equality.string_of_equality ~env e) given)))) in close env new' given ;; (* returns an estimation of how many equalities in passive can be activated within the current time limit *) let get_selection_estimate () = elapsed_time := (Unix.gettimeofday ()) -. !start_time; (* !processed_clauses * (int_of_float (!time_limit /. !elapsed_time)) *) int_of_float ( ceil ((float_of_int !processed_clauses) *. ((!time_limit (* *. 2. *)) /. !elapsed_time -. 1.))) ;; (** initializes the set of goals *) let make_goals goal = let active = [] and passive = [0, [goal]] in active, passive ;; (** initializes the set of theorems *) let make_theorems theorems = theorems, [] ;; let activate_goal (active, passive) = if active = [] then match passive with | goal_conj::tl -> true, (goal_conj::active, tl) | [] -> false, (active, passive) else true, (active,passive) ;; let activate_theorem (active, passive) = match passive with | theorem::tl -> true, (theorem::active, tl) | [] -> false, (active, passive) ;; let simplify_theorems env theorems ?passive (active_list, active_table) = let pl, passive_table = match passive with | None -> [], None | Some ((pn, _), (pp, _), pt) -> let pn = List.map (fun e -> (Negative, e)) pn and pp = List.map (fun e -> (Positive, e)) pp in pn @ pp, Some pt in let a_theorems, p_theorems = theorems in let demodulate table theorem = let newmeta, newthm = Indexing.demodulation_theorem !maxmeta env table theorem in maxmeta := newmeta; theorem != newthm, newthm in let foldfun table (a, p) theorem = let changed, theorem = demodulate table theorem in if changed then (a, theorem::p) else (theorem::a, p) in let mapfun table theorem = snd (demodulate table theorem) in match passive_table with | None -> let p_theorems = List.map (mapfun active_table) p_theorems in List.fold_left (foldfun active_table) ([], p_theorems) a_theorems | Some passive_table -> let p_theorems = List.map (mapfun active_table) p_theorems in let p_theorems, a_theorems = List.fold_left (foldfun active_table) ([], p_theorems) a_theorems in let p_theorems = List.map (mapfun passive_table) p_theorems in List.fold_left (foldfun passive_table) ([], p_theorems) a_theorems ;; let rec simpl env e others others_simpl = let active = others @ others_simpl in let tbl = List.fold_left (fun t e -> Indexing.index t e) Indexing.empty active in let res = forward_simplify env (Positive,e) (active, tbl) in match others with | hd::tl -> ( match res with | None -> simpl env hd tl others_simpl | Some e -> simpl env hd tl (e::others_simpl) ) | [] -> ( match res with | None -> others_simpl | Some e -> e::others_simpl ) ;; let simplify_equalities env equalities = debug_print (lazy (Printf.sprintf "equalities:\n%s\n" (String.concat "\n" (List.map Equality.string_of_equality equalities)))); debug_print (lazy "SIMPLYFYING EQUALITIES..."); match equalities with | [] -> [] | hd::tl -> let res = List.rev (simpl env hd tl []) in debug_print (lazy (Printf.sprintf "equalities AFTER:\n%s\n" (String.concat "\n" (List.map Equality.string_of_equality res)))); res ;; let print_goals goals = (String.concat "\n" (List.map (fun (d, gl) -> let gl' = List.map (fun (p, _, t) -> (* (string_of_proof p) ^ ", " ^ *) (CicPp.ppterm t)) gl in Printf.sprintf "%d: %s" d (String.concat "; " gl')) goals)) ;; let check_if_goal_is_subsumed ((_,ctx,_) as env) table (goalproof,menv,ty) = let names = names_of_context ctx in Printf.eprintf "check_goal_subsumed: %s\n" (CicPp.pp ty names); match ty with | Cic.Appl[Cic.MutInd(uri,_,_);eq_ty;left;right] when UriManager.eq uri (LibraryObjects.eq_URI ()) -> (let goal_equation = Equality.mk_equality (0,Equality.Exact (Cic.Implicit None),(eq_ty,left,right,Eq),menv) in match Indexing.subsumption env table goal_equation with (* match Indexing.unification env table goal_equation with *) | Some (subst, equality ) -> let (_,p,(ty,l,r,_),m,id) = Equality.open_equality equality in let cicmenv = Subst.apply_subst_metasenv subst (m @ menv) in Some (goalproof, p, subst, cicmenv) | None -> None) | _ -> None ;; let counter = ref 0 (** given-clause algorithm with full reduction strategy *) let rec given_clause_fullred dbd env goals theorems ~passive active = let goals = simplify_goals env goals ~passive active in let _,context,_ = env in let ok, goals = activate_goal goals in (* let theorems = simplify_theorems env theorems ~passive active in *) if ok then let names = List.map (HExtlib.map_option (fun (name,_) -> name)) context in let _, _, t = List.hd (snd (List.hd (fst goals))) in let _ = prerr_endline ("goal activated = " ^ (CicPp.pp t names)) in (* let _ = *) (* debug_print *) (* (lazy *) (* (Printf.sprintf "\ngoals = \nactive\n%s\npassive\n%s\n" *) (* (print_goals (fst goals)) (print_goals (snd goals)))); *) (* let current = List.hd (fst goals) in *) (* let p, _, t = List.hd (snd current) in *) (* debug_print *) (* (lazy *) (* (Printf.sprintf "goal activated:\n%s\n%s\n" *) (* (CicPp.ppterm t) (string_of_proof p))); *) (* in *) let ok, proof = (* apply_goal_to_theorems dbd env theorems ~passive active goals in *) let iseq uri = UriManager.eq uri (LibraryObjects.eq_URI ()) in match (fst goals) with | (_,[goalproof,m,Cic.Appl[Cic.MutInd(uri,_,ens);eq_ty;left;right]])::_ when left = right && iseq uri -> let reflproof = Equality.Exact (Equality.refl_proof eq_ty left) in true, Some (goalproof, reflproof, Subst.empty_subst,m) | (_, [goal])::_ -> (match check_if_goal_is_subsumed env (snd active) goal with | None -> false,None | Some p -> prerr_endline "Proof found by subsumption!"; true, Some p) | _ -> false, None in if ok then ( prerr_endline "esco qui"; (* let s = Printf.sprintf "actives:\n%s\n" (String.concat "\n" ((List.map (fun (s, e) -> (string_of_sign s) ^ " " ^ (string_of_equality ~env e)) (fst active)))) in let sp = Printf.sprintf "passives:\n%s\n" (String.concat "\n" (List.map (string_of_equality ~env) (let x,y,_ = passive in (fst x)@(fst y)))) in prerr_endline s; prerr_endline sp; *) match proof with | None -> assert false | Some p -> ParamodulationSuccess p) else given_clause_fullred_aux dbd env goals theorems passive active else (* let ok', theorems = activate_theorem theorems in *) (* if ok' then *) (* let ok, goals = apply_theorem_to_goals env theorems active goals in *) (* if ok then *) (* let proof = *) (* match (fst goals) with *) (* | (_, [proof, _, _])::_ -> Some proof *) (* | _ -> assert false *) (* in *) (* ParamodulationSuccess (proof, env) *) (* else *) (* given_clause_fullred_aux env goals theorems passive active *) (* else *) if (passive_is_empty passive) then ParamodulationFailure "" else given_clause_fullred_aux dbd env goals theorems passive active and given_clause_fullred_aux dbd env goals theorems passive active = prerr_endline (string_of_int !counter ^ " MAXMETA: " ^ string_of_int !maxmeta ^ " #ACTIVES: " ^ string_of_int (size_of_active active) ^ " #PASSIVES: " ^ string_of_int (size_of_passive passive)); incr counter; (* if !counter mod 10 = 0 then begin let size = HExtlib.estimate_size (passive,active) in let sizep = HExtlib.estimate_size (passive) in let sizea = HExtlib.estimate_size (active) in let (l1,s1),(l2,s2), t = passive in let sizetbl = HExtlib.estimate_size t in let sizel = HExtlib.estimate_size (l1,l2) in let sizes = HExtlib.estimate_size (s1,s2) in prerr_endline ("SIZE: " ^ string_of_int size); prerr_endline ("SIZE P: " ^ string_of_int sizep); prerr_endline ("SIZE A: " ^ string_of_int sizea); prerr_endline ("SIZE TBL: " ^ string_of_int sizetbl ^ " SIZE L: " ^ string_of_int sizel ^ " SIZE S:" ^ string_of_int sizes); end;*) (* if (size_of_active active) mod 50 = 0 then (let s = Printf.sprintf "actives:\n%s\n" (String.concat "\n" ((List.map (fun (s, e) -> (string_of_sign s) ^ " " ^ (string_of_equality ~env e)) (fst active)))) in let sp = Printf.sprintf "passives:\n%s\n" (String.concat "\n" (List.map (string_of_equality ~env) (let x,y,_ = passive in (fst x)@(fst y)))) in prerr_endline s; prerr_endline sp); *) let time1 = Unix.gettimeofday () in let (_,context,_) = env in let selection_estimate = get_selection_estimate () in let kept = size_of_passive passive in let passive = if !time_limit = 0. || !processed_clauses = 0 then passive else if !elapsed_time > !time_limit then ( debug_print (lazy (Printf.sprintf "Time limit (%.2f) reached: %.2f\n" !time_limit !elapsed_time)); make_passive [] ) else if kept > selection_estimate then ( debug_print (lazy (Printf.sprintf ("Too many passive equalities: pruning..." ^^ "(kept: %d, selection_estimate: %d)\n") kept selection_estimate)); prune_passive selection_estimate active passive ) else passive in let time2 = Unix.gettimeofday () in passive_maintainance_time := !passive_maintainance_time +. (time2 -. time1); kept_clauses := (size_of_passive passive) + (size_of_active active); match passive_is_empty passive with | true -> ParamodulationFailure "" (* given_clause_fullred dbd env goals theorems passive active *) | false -> let current, passive = select env (fst goals) passive in prerr_endline ("Selected = " ^ Equality.string_of_equality ~env current); (* ^ (let w,p,(t,l,r,o),m = current in " size w: " ^ string_of_int (HExtlib.estimate_size w)^ " size p: " ^ string_of_int (HExtlib.estimate_size p)^ " size t: " ^ string_of_int (HExtlib.estimate_size t)^ " size l: " ^ string_of_int (HExtlib.estimate_size l)^ " size r: " ^ string_of_int (HExtlib.estimate_size r)^ " size o: " ^ string_of_int (HExtlib.estimate_size o)^ " size m: " ^ string_of_int (HExtlib.estimate_size m)^ " size m-c: " ^ string_of_int (HExtlib.estimate_size (List.map (fun (x,_,_) -> x) m)))) *) let time1 = Unix.gettimeofday () in let res = forward_simplify env (Positive, current) ~passive active in let time2 = Unix.gettimeofday () in forward_simpl_time := !forward_simpl_time +. (time2 -. time1); match res with | None -> (* weight_age_counter := !weight_age_counter + 1; *) given_clause_fullred dbd env goals theorems passive active | Some current -> (* prerr_endline (Printf.sprintf "selected simpl: %s" (Equality.string_of_equality ~env current));*) let t1 = Unix.gettimeofday () in let new' = infer env current active in let _ = debug_print (lazy (Printf.sprintf "new' (senza semplificare):\n%s\n" (String.concat "\n" (List.map (fun e -> "Positive " ^ (Equality.string_of_equality ~env e)) new')))) in let t2 = Unix.gettimeofday () in infer_time := !infer_time +. (t2 -. t1); let active = if Equality.is_identity env current then active else let al, tbl = active in al @ [current], Indexing.index tbl current in let rec simplify new' active passive = let t1 = Unix.gettimeofday () in let new' = forward_simplify_new env new'~passive active in let t2 = Unix.gettimeofday () in forward_simpl_new_time := !forward_simpl_new_time +. (t2 -. t1); let t1 = Unix.gettimeofday () in let active, passive, newa, retained, pruned = backward_simplify env new' ~passive active in let passive = List.fold_left filter_dependent passive pruned in let t2 = Unix.gettimeofday () in backward_simpl_time := !backward_simpl_time +. (t2 -. t1); match newa, retained with | None, None -> active, passive, new' | Some p, None | None, Some p -> if Utils.debug_metas then begin List.iter (fun x->Indexing.check_target context x "simplify1") p; end; simplify (new' @ p) active passive | Some p, Some rp -> simplify (new' @ p @ rp) active passive in let active, passive, new' = simplify new' active passive in let goals = let a,b,_ = build_table new' in simplify_goals env goals ~passive (a,b) in (* pessima prova let new1 = prova env new' active in let new' = (fst new') @ (fst new1), (snd new') @ (snd new1) in let _ = match new1 with | neg, pos -> debug_print (lazy (Printf.sprintf "new1:\n%s\n" (String.concat "\n" ((List.map (fun e -> "Negative " ^ (string_of_equality ~env e)) neg) @ (List.map (fun e -> "Positive " ^ (string_of_equality ~env e)) pos))))) in end prova *) let k = size_of_passive passive in if k < (kept - 1) then processed_clauses := !processed_clauses + (kept - 1 - k); let _ = debug_print (lazy (Printf.sprintf "active:\n%s\n" (String.concat "\n" ((List.map (fun e -> (Equality.string_of_equality ~env e)) (fst active)))))) in let _ = debug_print (lazy (Printf.sprintf "new':\n%s\n" (String.concat "\n" ((List.map (fun e -> "Negative " ^ (Equality.string_of_equality ~env e)) new'))))) in let passive = add_to_passive passive new' in given_clause_fullred dbd env goals theorems passive active ;; (* let profiler0 = HExtlib.profile "P/Saturation.given_clause_fullred" let given_clause_fullred dbd env goals theorems passive active = profiler0.HExtlib.profile (given_clause_fullred dbd env goals theorems passive) active *) let iseq uri = UriManager.eq uri (LibraryObjects.eq_URI ());; let check_if_goal_is_identity env = function | (goalproof,m,Cic.Appl[Cic.MutInd(uri,_,ens);eq_ty;left;right]) when left = right && iseq uri -> let reflproof = Equality.Exact (Equality.refl_proof eq_ty left) in Some (goalproof, reflproof,Subst.empty_subst,m) | _ -> None ;; let rec check goal = function | [] -> None | f::tl -> match f goal with | None -> check goal tl | (Some p) as ok -> ok ;; let simplify_goal_set env goals passive active = (* let supl_goals = (List.flatten (List.map (Indexing.superposition_left env (snd active)) goals)) in *) let simplified = HExtlib.filter_map (fun g -> match simplify_goal env g ~passive active with | true, g -> Some g | false, g -> Some g) goals in HExtlib.list_uniq ~eq:(fun (_,_,t1) (_,_,t2) -> t1 = t2) (List.sort (fun (_,_,t1) (_,_,t2) -> compare t1 t1) ((*goals @*) simplified)) ;; let check_if_goals_set_is_solved env active goals = List.fold_left (fun proof goal -> match proof with | Some p -> proof | None -> check goal [ check_if_goal_is_identity env; check_if_goal_is_subsumed env (snd active)]) None goals ;; let size_of_goal_set = List.length;; (** given-clause algorithm with full reduction strategy: NEW implementation *) (* here goals is a set of goals in OR *) let given_clause ((_,context,_) as env) goals theorems passive active max_iterations max_time = let initial_time = Unix.gettimeofday () in let iterations_left iterno = let now = Unix.gettimeofday () in let time_left = max_time -. now in let time_spent_until_now = now -. initial_time in let iteration_medium_cost = time_spent_until_now /. (float_of_int iterno) in let iterations_left = time_left /. iteration_medium_cost in int_of_float iterations_left in let rec step goals theorems passive active iterno = if iterno > max_iterations then (ParamodulationFailure "No more iterations to spend") else if Unix.gettimeofday () > max_time then (ParamodulationFailure "No more time to spend") else let goals = simplify_goal_set env goals passive active in match check_if_goals_set_is_solved env active goals with | Some p -> Printf.eprintf "Found a proof in: %f\n" (Unix.gettimeofday() -. initial_time); ParamodulationSuccess p | None -> prerr_endline (Printf.sprintf "%d #ACTIVES: %d #PASSIVES: %d #GOALSET: %d\n" iterno (size_of_active active) (size_of_passive passive) (size_of_goal_set goals)); (* PRUNING OF PASSIVE THAT WILL NEVER BE PROCESSED *) let passive = let selection_estimate = iterations_left iterno in let kept = size_of_passive passive in if kept > selection_estimate then begin (*Printf.eprintf "Too many passive equalities: pruning..."; prune_passive selection_estimate active*) passive end else passive in kept_clauses := (size_of_passive passive) + (size_of_active active); (* SELECTION *) if passive_is_empty passive then ParamodulationFailure "No more passive" (* maybe this is a success! *) else begin let current, passive = select env [1,goals] passive in Printf.eprintf "Selected = %s\n" (Equality.string_of_equality ~env current); (* SIMPLIFICATION OF CURRENT *) let res = forward_simplify env (Positive, current) ~passive active in match res with | None -> step goals theorems passive active (iterno+1) | Some current -> (* GENERATION OF NEW EQUATIONS *) let new' = infer env current active in let active = if Equality.is_identity env current then assert false (* nonsense code, check to se if it can be removed *) else let al, tbl = active in al @ [current], Indexing.index tbl current in (* FORWARD AND BACKWARD SIMPLIFICATION *) let rec simplify new' active passive = let new' = forward_simplify_new env new' ~passive active in let active, passive, newa, retained, pruned = backward_simplify env new' ~passive active in let passive = List.fold_left filter_dependent passive pruned in match newa, retained with | None, None -> active, passive, new' | Some p, None | None, Some p -> simplify (new' @ p) active passive | Some p, Some rp -> simplify (new' @ p @ rp) active passive in let active, passive, new' = simplify new' active passive in let goals = let a,b,_ = build_table new' in simplify_goal_set env goals passive (a,b) in let passive = add_to_passive passive new' in step goals theorems passive active (iterno+1) end in step goals theorems passive active 1 ;; let rec saturate_equations env goal accept_fun passive active = elapsed_time := Unix.gettimeofday () -. !start_time; if !elapsed_time > !time_limit then (active, passive) else let current, passive = select env [1, [goal]] passive in let res = forward_simplify env (Positive, current) ~passive active in match res with | None -> saturate_equations env goal accept_fun passive active | Some current -> debug_print (lazy (Printf.sprintf "selected: %s" (Equality.string_of_equality ~env current))); let new' = infer env current active in let active = if Equality.is_identity env current then active else let al, tbl = active in al @ [current], Indexing.index tbl current in let rec simplify new' active passive = let new' = forward_simplify_new env new' ~passive active in let active, passive, newa, retained, pruned = backward_simplify env new' ~passive active in let passive = List.fold_left filter_dependent passive pruned in match newa, retained with | None, None -> active, passive, new' | Some p, None | None, Some p -> simplify (new' @ p) active passive | Some p, Some rp -> simplify (new' @ p @ rp) active passive in let active, passive, new' = simplify new' active passive in let _ = debug_print (lazy (Printf.sprintf "active:\n%s\n" (String.concat "\n" (List.map (fun e -> Equality.string_of_equality ~env e) (fst active))))) in let _ = debug_print (lazy (Printf.sprintf "new':\n%s\n" (String.concat "\n" (List.map (fun e -> "Negative " ^ (Equality.string_of_equality ~env e)) new')))) in let new' = List.filter accept_fun new' in let passive = add_to_passive passive new' in saturate_equations env goal accept_fun passive active ;; let main dbd full term metasenv ugraph = () (* let main dbd full term metasenv ugraph = let module C = Cic in let module T = CicTypeChecker in let module PET = ProofEngineTypes in let module PP = CicPp in let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in let proof, goals = status in let goal' = List.nth goals 0 in let _, metasenv, meta_proof, _ = proof in let _, context, goal = CicUtil.lookup_meta goal' metasenv in let eq_indexes, equalities, maxm = find_equalities context proof in let lib_eq_uris, library_equalities, maxm = find_library_equalities dbd context (proof, goal') (maxm+2) in let library_equalities = List.map snd library_equalities in maxmeta := maxm+2; (* TODO ugly!! *) let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in let new_meta_goal, metasenv, type_of_goal = let _, context, ty = CicUtil.lookup_meta goal' metasenv in debug_print (lazy (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n\n" (CicPp.ppterm ty))); Cic.Meta (maxm+1, irl), (maxm+1, context, ty)::metasenv, ty in let env = (metasenv, context, ugraph) in let t1 = Unix.gettimeofday () in let theorems = if full then let theorems = find_library_theorems dbd env (proof, goal') lib_eq_uris in let context_hyp = find_context_hypotheses env eq_indexes in context_hyp @ theorems, [] else let refl_equal = let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in UriManager.uri_of_string (us ^ "#xpointer(1/1/1)") in let t = CicUtil.term_of_uri refl_equal in let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in [(t, ty, [])], [] in let t2 = Unix.gettimeofday () in debug_print (lazy (Printf.sprintf "Time to retrieve theorems: %.9f\n" (t2 -. t1))); let _ = debug_print (lazy (Printf.sprintf "Theorems:\n-------------------------------------\n%s\n" (String.concat "\n" (List.map (fun (t, ty, _) -> Printf.sprintf "Term: %s, type: %s" (CicPp.ppterm t) (CicPp.ppterm ty)) (fst theorems))))) in (*try*) let goal = ([],Equality.BasicProof (Equality.empty_subst ,new_meta_goal)), [], goal in let equalities = simplify_equalities env (equalities@library_equalities) in let active = make_active () in let passive = make_passive equalities in Printf.printf "\ncurrent goal: %s\n" (let _, _, g = goal in CicPp.ppterm g); Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context); Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv); Printf.printf "\nequalities:\n%s\n" (String.concat "\n" (List.map (Equality.string_of_equality ~env) equalities)); (* (equalities @ library_equalities))); *) print_endline "--------------------------------------------------"; let start = Unix.gettimeofday () in print_endline "GO!"; start_time := Unix.gettimeofday (); let res = let goals = make_goals goal in (if !use_fullred then given_clause_fullred else given_clause_fullred) dbd env goals theorems passive active in let finish = Unix.gettimeofday () in let _ = match res with | ParamodulationFailure -> Printf.printf "NO proof found! :-(\n\n" | ParamodulationSuccess (Some ((cicproof,cicmenv),(proof, env))) -> Printf.printf "OK, found a proof!\n"; let oldproof = Equation.build_proof_term proof in let newproof,_,newenv,_ = CicRefine.type_of_aux' cicmenv context cicproof CicUniv.empty_ugraph in (* REMEMBER: we have to instantiate meta_proof, we should use apply the "apply" tactic to proof and status *) let names = names_of_context context in prerr_endline "OLD PROOF"; print_endline (PP.pp proof names); prerr_endline "NEW PROOF"; print_endline (PP.pp newproof names); let newmetasenv = List.fold_left (fun m eq -> let (_, _, _, menv,_) = Equality.open_equality eq in m @ menv) metasenv equalities in let _ = (*try*) let ty, ug = CicTypeChecker.type_of_aux' newmetasenv context proof ugraph in print_endline (string_of_float (finish -. start)); Printf.printf "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n\n" (CicPp.pp type_of_goal names) (CicPp.pp ty names) (string_of_bool (fst (CicReduction.are_convertible context type_of_goal ty ug))); (*with e -> Printf.printf "\nEXCEPTION!!! %s\n" (Printexc.to_string e); Printf.printf "MAXMETA USED: %d\n" !maxmeta; print_endline (string_of_float (finish -. start));*) in () | ParamodulationSuccess None -> Printf.printf "Success, but no proof?!?\n\n" in if Utils.time then begin prerr_endline ((Printf.sprintf ("infer_time: %.9f\nforward_simpl_time: %.9f\n" ^^ "forward_simpl_new_time: %.9f\n" ^^ "backward_simpl_time: %.9f\n") !infer_time !forward_simpl_time !forward_simpl_new_time !backward_simpl_time) ^ (Printf.sprintf "passive_maintainance_time: %.9f\n" !passive_maintainance_time) ^ (Printf.sprintf " successful unification/matching time: %.9f\n" !Indexing.match_unif_time_ok) ^ (Printf.sprintf " failed unification/matching time: %.9f\n" !Indexing.match_unif_time_no) ^ (Printf.sprintf " indexing retrieval time: %.9f\n" !Indexing.indexing_retrieval_time) ^ (Printf.sprintf " demodulate_term.build_newtarget_time: %.9f\n" !Indexing.build_newtarget_time) ^ (Printf.sprintf "derived %d clauses, kept %d clauses.\n" !derived_clauses !kept_clauses)) end (* with exc -> print_endline ("EXCEPTION: " ^ (Printexc.to_string exc)); raise exc *) ;; *) let default_depth = !maxdepth and default_width = !maxwidth;; let reset_refs () = maxmeta := 0; symbols_counter := 0; weight_age_counter := !weight_age_ratio; processed_clauses := 0; start_time := 0.; elapsed_time := 0.; maximal_retained_equality := None; infer_time := 0.; forward_simpl_time := 0.; forward_simpl_new_time := 0.; backward_simpl_time := 0.; passive_maintainance_time := 0.; derived_clauses := 0; kept_clauses := 0; Equality.reset (); ;; let saturate dbd ?(full=false) ?(depth=default_depth) ?(width=default_width) status = let module C = Cic in reset_refs (); Indexing.init_index (); counter := 0; maxdepth := depth; maxwidth := width; (* CicUnification.unif_ty := false;*) let proof, goal = status in let goal' = goal in let uri, metasenv, meta_proof, term_to_prove = proof in let _, context, goal = CicUtil.lookup_meta goal' metasenv in let names = names_of_context context in let eq_indexes, equalities, maxm = find_equalities context proof in let new_meta_goal, metasenv, type_of_goal = let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in let _, context, ty = CicUtil.lookup_meta goal' metasenv in debug_print (lazy (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n" (CicPp.ppterm ty))); Cic.Meta (maxm+1, irl), (maxm+1, context, ty)::metasenv, ty in let ugraph = CicUniv.empty_ugraph in let env = (metasenv, context, ugraph) in prerr_endline ("METASENV DEL GOAL: " ^ CicMetaSubst.ppmetasenv [] metasenv ); let goal = [], metasenv, goal in let res, time = let t1 = Unix.gettimeofday () in let lib_eq_uris, library_equalities, maxm = find_library_equalities dbd context (proof, goal') (maxm+2) in let library_equalities = List.map snd library_equalities in let t2 = Unix.gettimeofday () in maxmeta := maxm+2; let equalities = simplify_equalities env (equalities@library_equalities) in debug_print (lazy (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1))); let t1 = Unix.gettimeofday () in let theorems = if full then let thms = find_library_theorems dbd env (proof, goal') lib_eq_uris in let context_hyp = find_context_hypotheses env eq_indexes in context_hyp @ thms, [] else let refl_equal = let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in UriManager.uri_of_string (us ^ "#xpointer(1/1/1)") in let t = CicUtil.term_of_uri refl_equal in let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in [(t, ty, [])], [] in let t2 = Unix.gettimeofday () in let _ = debug_print (lazy (Printf.sprintf "Theorems:\n-------------------------------------\n%s\n" (String.concat "\n" (List.map (fun (t, ty, _) -> Printf.sprintf "Term: %s, type: %s" (CicPp.ppterm t) (CicPp.ppterm ty)) (fst theorems))))); debug_print (lazy (Printf.sprintf "Time to retrieve theorems: %.9f\n" (t2 -. t1))); in let active = make_active () in let passive = make_passive equalities in let start = Unix.gettimeofday () in let res = (* let goals = make_goals goal in given_clause_fullred dbd env goals theorems passive active *) let goals = [goal] in let max_iterations = 1000 in let max_time = Unix.gettimeofday () +. 600. (* minutes *) in given_clause env goals theorems passive active max_iterations max_time in let finish = Unix.gettimeofday () in (res, finish -. start) in match res with | ParamodulationFailure s -> raise (ProofEngineTypes.Fail (lazy ("NO proof found: " ^ s))) | ParamodulationSuccess (goalproof,newproof,subsumption_subst, proof_menv) -> prerr_endline "OK, found a proof!"; prerr_endline "NEWPROOF"; (* prerr_endline (Equality.string_of_proof_new ~names newproof * goalproof);*) prerr_endline (Equality.pp_proof names goalproof newproof); (* assert false; *) (* generation of the proof *) let cic_proof_new = Equality.build_goal_proof goalproof (Equality.build_proof_term newproof) type_of_goal in let cic_proof_new = Subst.apply_subst subsumption_subst cic_proof_new in (* replacing fake mets with real ones *) let equality_for_replace i t1 = match t1 with | C.Meta (n, _) -> n = i | _ -> false in let mkirl = CicMkImplicit.identity_relocation_list_for_metavariable in prerr_endline "replacing metas (new)"; let newproof_menv, what, with_what,_ = let irl = mkirl context in List.fold_left (fun (acc1,acc2,acc3,uniq) (i,_,ty) -> match uniq with | Some m -> acc1, (Cic.Meta(i,[]))::acc2, m::acc3, uniq | None -> [i,context,ty], (Cic.Meta(i,[]))::acc2, (Cic.Meta(i,irl)) ::acc3,Some (Cic.Meta(i,irl))) ([],[],[],None) proof_menv in let cic_proof_new = ProofEngineReduction.replace_lifting ~equality:(=) ~what ~with_what ~where:cic_proof_new in (* pp new/old proof *) (* prerr_endline "NEWPROOFCIC";*) (* prerr_endline (CicPp.pp cic_proof_new names); *) (* generation of proof metasenv *) let newmetasenv_new = metasenv@newproof_menv in let newmetasenv_new = let i1 = match new_meta_goal with | C.Meta (i, _) -> i | _ -> assert false in List.filter (fun (i, _, _) -> i <> i1 && i <> goal') newmetasenv_new in (* check/refine/... build the new proof *) let newstatus = let cic_proof,newmetasenv,proof_menv,ty, ug = let cic_proof_new,new_ty,newmetasenv_new,newug = try (* prerr_endline "refining ... (new) "; CicRefine.type_of_aux' newmetasenv_new context cic_proof_new ugraph *) let ty,ug = prerr_endline "typechecking ... (new) "; CicTypeChecker.type_of_aux' newmetasenv_new context cic_proof_new ugraph in cic_proof_new, ty, newmetasenv_new, ug with | CicTypeChecker.TypeCheckerFailure s -> prerr_endline "THE PROOF DOESN'T TYPECHECK!!!"; prerr_endline (Lazy.force s); assert false | CicRefine.RefineFailure s | CicRefine.Uncertain s | CicRefine.AssertFailure s -> prerr_endline "FAILURE IN REFINE"; prerr_endline (Lazy.force s); assert false in if List.length newmetasenv_new <> 0 then prerr_endline ("Some METAS are still open: "(* ^ CicMetaSubst.ppmetasenv [] newmetasenv_new*)); cic_proof_new, newmetasenv_new, newmetasenv_new,new_ty, newug (* THE OLD PROOF: cic_proof,newmetasenv,proof_menv,oldty,oldug *) in prerr_endline "FINAL PROOF"; prerr_endline (CicPp.pp cic_proof names); prerr_endline "ENDOFPROOFS"; (* debug_print (lazy (Printf.sprintf "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n" (CicPp.pp type_of_goal names) (CicPp.pp ty names) (string_of_bool (fst (CicReduction.are_convertible context type_of_goal ty ug))))); *) let real_proof = ProofEngineReduction.replace ~equality:equality_for_replace ~what:[goal'] ~with_what:[cic_proof] ~where:meta_proof in (* debug_print (lazy (Printf.sprintf "status:\n%s\n%s\n%s\n%s\n" (match uri with Some uri -> UriManager.string_of_uri uri | None -> "") (print_metasenv newmetasenv) (CicPp.pp real_proof [](* names *)) (CicPp.pp term_to_prove names))); *) let open_goals = List.map (fun (i,_,_) -> i) proof_menv in (uri, newmetasenv, real_proof, term_to_prove), open_goals in if Utils.time then begin let tall = fs_time_info.build_all in let tdemodulate = fs_time_info.demodulate in let tsubsumption = fs_time_info.subsumption in prerr_endline ( (Printf.sprintf "\nTIME NEEDED: %.9f" time) ^ (Printf.sprintf "\ntall: %.9f" tall) ^ (Printf.sprintf "\ntdemod: %.9f" tdemodulate) ^ (Printf.sprintf "\ntsubsumption: %.9f" tsubsumption) ^ (Printf.sprintf "\ninfer_time: %.9f" !infer_time) ^ (Printf.sprintf "\nforward_simpl_times: %.9f" !forward_simpl_time) ^ (Printf.sprintf "\nforward_simpl_new_times: %.9f" !forward_simpl_new_time) ^ (Printf.sprintf "\nbackward_simpl_times: %.9f" !backward_simpl_time) ^ (Printf.sprintf "\npassive_maintainance_time: %.9f" !passive_maintainance_time)) end; newstatus ;; let retrieve_and_print dbd term metasenv ugraph = let module C = Cic in let module T = CicTypeChecker in let module PET = ProofEngineTypes in let module PP = CicPp in let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in let proof, goals = status in let goal' = List.nth goals 0 in let uri, metasenv, meta_proof, term_to_prove = proof in let _, context, goal = CicUtil.lookup_meta goal' metasenv in let eq_indexes, equalities, maxm = find_equalities context proof in let new_meta_goal, metasenv, type_of_goal = let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in let _, context, ty = CicUtil.lookup_meta goal' metasenv in debug_print (lazy (Printf.sprintf "\n\nTIPO DEL GOAL: %s\n" (CicPp.ppterm ty))); Cic.Meta (maxm+1, irl), (maxm+1, context, ty)::metasenv, ty in let ugraph = CicUniv.empty_ugraph in let env = (metasenv, context, ugraph) in let t1 = Unix.gettimeofday () in let lib_eq_uris, library_equalities, maxm = find_library_equalities dbd context (proof, goal') (maxm+2) in let t2 = Unix.gettimeofday () in maxmeta := maxm+2; let equalities = (* equalities @ *) library_equalities in debug_print (lazy (Printf.sprintf "\n\nequalities:\n%s\n" (String.concat "\n" (List.map (fun (u, e) -> (* Printf.sprintf "%s: %s" *) (UriManager.string_of_uri u) (* (string_of_equality e) *) ) equalities)))); debug_print (lazy "RETR: SIMPLYFYING EQUALITIES..."); let rec simpl e others others_simpl = let (u, e) = e in let active = List.map (fun (u, e) -> (Positive, e)) (others @ others_simpl) in let tbl = List.fold_left (fun t (_, e) -> Indexing.index t e) Indexing.empty active in let res = forward_simplify env (Positive, e) (active, tbl) in match others with | hd::tl -> ( match res with | None -> simpl hd tl others_simpl | Some e -> simpl hd tl ((u, e)::others_simpl) ) | [] -> ( match res with | None -> others_simpl | Some e -> (u, e)::others_simpl ) in let _equalities = match equalities with | [] -> [] | hd::tl -> let others = tl in (* List.map (fun e -> (Positive, e)) tl in *) let res = List.rev (simpl (*(Positive,*) hd others []) in debug_print (lazy (Printf.sprintf "\nequalities AFTER:\n%s\n" (String.concat "\n" (List.map (fun (u, e) -> Printf.sprintf "%s: %s" (UriManager.string_of_uri u) (Equality.string_of_equality e) ) res)))); res in debug_print (lazy (Printf.sprintf "Time to retrieve equalities: %.9f\n" (t2 -. t1))) ;; let main_demod_equalities dbd term metasenv ugraph = let module C = Cic in let module T = CicTypeChecker in let module PET = ProofEngineTypes in let module PP = CicPp in let proof = None, (1, [], term)::metasenv, C.Meta (1, []), term in let status = PET.apply_tactic (PrimitiveTactics.intros_tac ()) (proof, 1) in let proof, goals = status in let goal' = List.nth goals 0 in let _, metasenv, meta_proof, _ = proof in let _, context, goal = CicUtil.lookup_meta goal' metasenv in let eq_indexes, equalities, maxm = find_equalities context proof in let lib_eq_uris, library_equalities, maxm = find_library_equalities dbd context (proof, goal') (maxm+2) in let library_equalities = List.map snd library_equalities in maxmeta := maxm+2; (* TODO ugly!! *) let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in let new_meta_goal, metasenv, type_of_goal = let _, context, ty = CicUtil.lookup_meta goal' metasenv in debug_print (lazy (Printf.sprintf "\n\nTRYING TO INFER EQUALITIES MATCHING: %s\n\n" (CicPp.ppterm ty))); Cic.Meta (maxm+1, irl), (maxm+1, context, ty)::metasenv, ty in let env = (metasenv, context, ugraph) in (*try*) let goal = [], [], goal in let equalities = simplify_equalities env (equalities@library_equalities) in let active = make_active () in let passive = make_passive equalities in Printf.printf "\ncontext:\n%s\n" (PP.ppcontext context); Printf.printf "\nmetasenv:\n%s\n" (print_metasenv metasenv); Printf.printf "\nequalities:\n%s\n" (String.concat "\n" (List.map (Equality.string_of_equality ~env) equalities)); print_endline "--------------------------------------------------"; print_endline "GO!"; start_time := Unix.gettimeofday (); if !time_limit < 1. then time_limit := 60.; let ra, rp = saturate_equations env goal (fun e -> true) passive active in let initial = List.fold_left (fun s e -> EqualitySet.add e s) EqualitySet.empty equalities in let addfun s e = if not (EqualitySet.mem e initial) then EqualitySet.add e s else s in let passive = match rp with | (p, _), _ -> EqualitySet.elements (List.fold_left addfun EqualitySet.empty p) in let active = let l = fst ra in EqualitySet.elements (List.fold_left addfun EqualitySet.empty l) in Printf.printf "\n\nRESULTS:\nActive:\n%s\n\nPassive:\n%s\n" (String.concat "\n" (List.map (Equality.string_of_equality ~env) active)) (* (String.concat "\n" (List.map (fun e -> CicPp.ppterm (term_of_equality e)) active)) *) (* (String.concat "\n" (List.map (string_of_equality ~env) passive)); *) (String.concat "\n" (List.map (fun e -> CicPp.ppterm (Equality.term_of_equality e)) passive)); print_newline (); (* with e -> debug_print (lazy ("EXCEPTION: " ^ (Printexc.to_string e))) *) ;; let demodulate_tac ~dbd ~pattern ((proof,goal) as initialstatus) = let module I = Inference in let curi,metasenv,pbo,pty = proof in let metano,context,ty = CicUtil.lookup_meta goal metasenv in let eq_indexes, equalities, maxm = I.find_equalities context proof in let lib_eq_uris, library_equalities, maxm = I.find_library_equalities dbd context (proof, goal) (maxm+2) in if library_equalities = [] then prerr_endline "VUOTA!!!"; let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in let library_equalities = List.map snd library_equalities in let initgoal = [], [], ty in let env = (metasenv, context, CicUniv.empty_ugraph) in let equalities = simplify_equalities env (equalities@library_equalities) in let table = List.fold_left (fun tbl eq -> Indexing.index tbl eq) Indexing.empty equalities in let _, newmeta,(newproof,newmetasenv, newty) = Indexing.demodulation_goal maxm (metasenv,context,CicUniv.empty_ugraph) table initgoal in if newmeta != maxm then begin let opengoal = Cic.Meta(maxm,irl) in let proofterm = Equality.build_goal_proof newproof opengoal ty in let extended_metasenv = (maxm,context,newty)::metasenv in let extended_status = (curi,extended_metasenv,pbo,pty),goal in let (status,newgoals) = ProofEngineTypes.apply_tactic (PrimitiveTactics.apply_tac ~term:proofterm) extended_status in (status,maxm::newgoals) end else if newty = ty then raise (ProofEngineTypes.Fail (lazy "no progress")) else ProofEngineTypes.apply_tactic (ReductionTactics.simpl_tac ~pattern) initialstatus ;; let demodulate_tac ~dbd ~pattern = ProofEngineTypes.mk_tactic (demodulate_tac ~dbd ~pattern) ;;