--- /dev/null
+(* 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/.
+ *)
+
+(* $Id$ *)
+
+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 (* 5 *) 4;; (* 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.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 result =
+ | ParamodulationFailure
+ | ParamodulationSuccess of Inference.proof option * environment
+;;
+
+type goal = proof * Cic.metasenv * Cic.term;;
+
+type theorem = Cic.term * Cic.term * Cic.metasenv;;
+
+
+let symbols_of_equality ((_, _, (_, left, right, _), _, _) as equality) =
+ 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
+;;
+
+
+module OrderedEquality = struct
+ type t = Inference.equality
+
+ let compare eq1 eq2 =
+ match meta_convertibility_eq eq1 eq2 with
+ | true -> 0
+ | false ->
+ let w1, _, (ty, left, right, _), _, a = eq1
+ and w2, _, (ty', left', right', _), _, a' = eq2 in
+ match Pervasives.compare w1 w2 with
+ | 0 ->
+ let res = (List.length a) - (List.length a') in
+ if res <> 0 then res else (
+ try
+ let res = Pervasives.compare (List.hd a) (List.hd a') in
+ if res <> 0 then res else Pervasives.compare eq1 eq2
+ with Failure "hd" -> Pervasives.compare eq1 eq2
+ )
+ | res -> res
+end
+
+module EqualitySet = Set.Make(OrderedEquality);;
+
+
+(**
+ selects one equality from passive. The selection strategy is a combination
+ of weight, age and goal-similarity
+*)
+let select env goals passive (active, _) =
+ processed_clauses := !processed_clauses + 1;
+ let goal =
+ match (List.rev goals) with (_, goal::_)::_ -> goal | _ -> assert false
+ in
+ let (neg_list, neg_set), (pos_list, pos_set), passive_table = passive in
+ let remove eq l =
+ List.filter (fun e -> e <> eq) 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;
+ match neg_list, pos_list with
+ | hd::tl, pos ->
+ (* Negatives aren't indexed, no need to remove them... *)
+ (Negative, hd),
+ ((tl, EqualitySet.remove hd neg_set), (pos, pos_set), passive_table)
+ | [], (hd:EqualitySet.elt)::tl ->
+ let passive_table =
+ Indexing.remove_index passive_table hd
+ in
+ (Positive, hd),
+ (([], neg_set), (tl, EqualitySet.remove hd pos_set), passive_table)
+ | _, _ -> assert false
+ )
+ | _ when (!symbols_counter > 0) && (EqualitySet.is_empty neg_set) -> (
+ 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
+ (Positive, current),
+ (([], neg_set),
+ (remove current pos_list, EqualitySet.remove current pos_set),
+ passive_table)
+ )
+ | _ ->
+ symbols_counter := !symbols_ratio;
+ let set_selection set = EqualitySet.min_elt set in
+ if EqualitySet.is_empty neg_set then
+ let current = set_selection pos_set in
+ let passive =
+ (neg_list, neg_set),
+ (remove current pos_list, EqualitySet.remove current pos_set),
+ Indexing.remove_index passive_table current
+ in
+ (Positive, current), passive
+ else
+ let current = set_selection neg_set in
+ let passive =
+ (remove current neg_list, EqualitySet.remove current neg_set),
+ (pos_list, pos_set),
+ passive_table
+ in
+ (Negative, current), passive
+;;
+
+
+(* initializes the passive set of equalities *)
+let make_passive neg 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
+ (neg, set_of neg),
+ (pos, set_of pos),
+ table
+;;
+
+
+let make_active () =
+ [], Indexing.empty
+;;
+
+
+(* adds to passive a list of equalities: new_neg is a list of negative
+ equalities, new_pos a list of positive equalities *)
+let add_to_passive passive (new_neg, new_pos) =
+ let (neg_list, neg_set), (pos_list, pos_set), table = passive in
+ let ok set equality = not (EqualitySet.mem equality set) in
+ let neg = List.filter (ok neg_set) new_neg
+ and 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
+ (neg @ neg_list, add neg_set neg),
+ (pos_list @ pos, add pos_set pos),
+ table
+;;
+
+
+let passive_is_empty = function
+ | ([], _), ([], _), _ -> true
+ | _ -> false
+;;
+
+
+let size_of_passive ((_, ns), (_, ps), _) =
+ (EqualitySet.cardinal ns) + (EqualitySet.cardinal ps)
+;;
+
+
+let size_of_active (active_list, _) =
+ List.length active_list
+;;
+
+
+(* removes from passive equalities that are estimated impossible to activate
+ within the current time limit *)
+let prune_passive howmany (active, _) passive =
+ let (nl, ns), (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 symbols, card =
+ match active with
+ | (Negative, e)::_ ->
+ let symbols = symbols_of_equality e in
+ let card = TermMap.fold (fun k v res -> res + v) symbols 0 in
+ Some symbols, card
+ | _ -> None, 0
+ in
+ let counter = ref !symbols_ratio in
+ let rec pickw w ns ps =
+ if w > 0 then
+ if not (EqualitySet.is_empty ns) then
+ let e = EqualitySet.min_elt ns in
+ let ns', ps = pickw (w-1) (EqualitySet.remove e ns) ps in
+ EqualitySet.add e ns', ps
+ else if !counter > 0 then
+ let _ =
+ counter := !counter - 1;
+ if !counter = 0 then counter := !symbols_ratio
+ in
+ match symbols with
+ | None ->
+ let e = EqualitySet.min_elt ps in
+ let ns, ps' = pickw (w-1) ns (EqualitySet.remove e ps) in
+ ns, EqualitySet.add e ps'
+ | Some symbols ->
+ 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 ps in
+ let initial =
+ let common, others =
+ TermMap.fold foldfun (symbols_of_equality e1) (0, 0)
+ in
+ (others + (abs (common - card))), e1
+ in
+ let _, e = EqualitySet.fold f ps initial in
+ let ns, ps' = pickw (w-1) ns (EqualitySet.remove e ps) in
+ ns, EqualitySet.add e ps'
+ else
+ let e = EqualitySet.min_elt ps in
+ let ns, ps' = pickw (w-1) ns (EqualitySet.remove e ps) in
+ ns, EqualitySet.add e ps'
+ else
+ EqualitySet.empty, EqualitySet.empty
+ in
+ let ns, ps = pickw in_weight ns 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 in_age, ns, nl = picka in_age ns nl 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
+ (nl, ns), (pl, ps), tbl
+;;
+
+
+(** inference of new equalities between current and some in active *)
+let infer env sign current (active_list, active_table) =
+ let new_neg, new_pos =
+ match sign with
+ | Negative ->
+ let maxm, res =
+ Indexing.superposition_left !maxmeta env active_table current in
+ maxmeta := maxm;
+ res, []
+ | Positive ->
+ let maxm, res =
+ Indexing.superposition_right !maxmeta env active_table current in
+ maxmeta := maxm;
+ let rec infer_positive table = function
+ | [] -> [], []
+ | (Negative, equality)::tl ->
+ let maxm, res =
+ Indexing.superposition_left !maxmeta env table equality in
+ maxmeta := maxm;
+ let neg, pos = infer_positive table tl in
+ res @ neg, pos
+ | (Positive, equality)::tl ->
+ let maxm, res =
+ Indexing.superposition_right !maxmeta env table equality in
+ maxmeta := maxm;
+ let neg, pos = infer_positive table tl in
+ neg, res @ pos
+ in
+ let curr_table = Indexing.index Indexing.empty current in
+ let neg, pos = infer_positive curr_table active_list in
+ neg, res @ pos
+ in
+ derived_clauses := !derived_clauses + (List.length new_neg) +
+ (List.length new_pos);
+ match !maximal_retained_equality with
+ | None -> new_neg, new_pos
+ | Some eq ->
+ (* 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 *)
+ let symbols, card =
+ match active_list with
+ | (Negative, e)::_ ->
+ let symbols = symbols_of_equality e in
+ let card = TermMap.fold (fun k v res -> res + v) symbols 0 in
+ Some symbols, card
+ | _ -> None, 0
+ in
+ let new_pos =
+ match symbols with
+ | None ->
+ List.filter (fun e -> OrderedEquality.compare e eq <= 0) new_pos
+ | Some symbols ->
+ let filterfun e =
+ if OrderedEquality.compare e eq <= 0 then
+ true
+ else
+ 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 initial =
+ let common, others =
+ TermMap.fold foldfun (symbols_of_equality eq) (0, 0) in
+ others + (abs (common - card))
+ in
+ let common, others =
+ TermMap.fold foldfun (symbols_of_equality e) (0, 0) in
+ let c = others + (abs (common - card)) in
+ if c < initial then true else false
+ in
+ List.filter filterfun new_pos
+ in
+ new_neg, new_pos
+;;
+
+
+let contains_empty env (negative, positive) =
+ let metasenv, context, ugraph = env in
+ try
+ let found =
+ List.find
+ (fun (w, proof, (ty, left, right, ordering), m, a) ->
+ fst (CicReduction.are_convertible context left right ugraph))
+ negative
+ in
+ true, Some found
+ with Not_found ->
+ false, None
+;;
+
+
+(** simplifies current using active and passive *)
+let forward_simplify env (sign, current) ?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 all = if pl = [] then active_list else active_list @ pl in
+
+ let demodulate table current =
+ let newmeta, newcurrent =
+ Indexing.demodulation_equality !maxmeta env table sign current in
+ maxmeta := newmeta;
+ if is_identity env newcurrent then
+ if sign = Negative then Some (sign, newcurrent)
+ else (
+(* 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 (sign, newcurrent)
+ in
+ let res =
+ let res = demodulate active_table current in
+ match res with
+ | None -> None
+ | Some (sign, newcurrent) ->
+ match passive_table with
+ | None -> res
+ | Some passive_table -> demodulate passive_table newcurrent
+ in
+ match res with
+ | None -> None
+ | Some (Negative, c) ->
+ let ok = not (
+ List.exists
+ (fun (s, eq) -> s = Negative && meta_convertibility_eq eq c)
+ all)
+ in
+ if ok then res else None
+ | Some (Positive, c) ->
+ if Indexing.in_index active_table c then
+ None
+ else
+ match passive_table with
+ | None ->
+ if fst (Indexing.subsumption env active_table c) then
+ None
+ else
+ res
+ | Some passive_table ->
+ if Indexing.in_index passive_table c then None
+ else
+ let r1, _ = Indexing.subsumption env active_table c in
+ if r1 then None else
+ let r2, _ = Indexing.subsumption env passive_table c in
+ if r2 then None else res
+;;
+
+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_neg, new_pos) ?passive active =
+ let t1 = Unix.gettimeofday () in
+
+ let active_list, active_table = active in
+ 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 all = active_list @ pl 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
+
+ let new_neg, new_pos =
+ let new_neg = List.map (demodulate Negative active_table) new_neg
+ and new_pos = List.map (demodulate Positive active_table) new_pos in
+ match passive_table with
+ | None -> new_neg, new_pos
+ | Some passive_table ->
+ List.map (demodulate Negative passive_table) new_neg,
+ List.map (demodulate Positive passive_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 (Inference.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 -> not (fst (Indexing.subsumption env active_table e)))
+ | Some passive_table ->
+ (fun e -> not ((fst (Indexing.subsumption env active_table e)) ||
+ (fst (Indexing.subsumption env passive_table e))))
+ 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
+ new_neg, List.filter subs (List.filter is_duplicate new_pos)
+;;
+
+
+(** 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 =
+ List.fold_right
+ (fun (s, equality) (res, newn) ->
+ let ew, _, _, _, _ = equality in
+ if ew < min_weight then
+ (s, equality)::res, newn
+ else
+ match forward_simplify env (s, equality) (new_pos, new_table) with
+ | None -> res, newn
+ | Some (s, e) ->
+ if equality = e then
+ (s, e)::res, newn
+ else
+ res, (s, e)::newn)
+ active_list ([], [])
+ in
+ let find eq1 where =
+ List.exists (fun (s, e) -> meta_convertibility_eq eq1 e) where
+ in
+ let active, newa =
+ List.fold_right
+ (fun (s, eq) (res, tbl) ->
+ if List.mem (s, eq) res then
+ res, tbl
+ else if (is_identity env eq) || (find eq res) then (
+ res, tbl
+ )
+ else
+ (s, eq)::res, if s = Negative then tbl else Indexing.index tbl eq)
+ active_list ([], Indexing.empty),
+ List.fold_right
+ (fun (s, eq) (n, p) ->
+ if (s <> Negative) && (is_identity env eq) then (
+ (n, p)
+ ) else
+ if s = Negative then eq::n, p
+ else n, eq::p)
+ newa ([], [])
+ in
+ match newa with
+ | [], [] -> active, None
+ | _ -> active, Some newa
+;;
+
+
+(** simplifies passive using new *)
+let backward_simplify_passive env new_pos new_table min_weight passive =
+ let (nl, ns), (pl, ps), passive_table = passive in
+ let f sign equality (resl, ress, newn) =
+ let ew, _, _, _, _ = 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 (s, e) ->
+ if equality = e then
+ equality::resl, ress, newn
+ else
+ let ress = EqualitySet.remove equality ress in
+ resl, ress, e::newn
+ in
+ let nl, ns, newn = List.fold_right (f Negative) nl ([], ns, [])
+ and 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 newn, newp with
+ | [], [] -> ((nl, ns), (pl, ps), passive_table), None
+ | _, _ -> ((nl, ns), (pl, ps), passive_table), Some (newn, newp)
+;;
+
+
+let backward_simplify env new' ?passive active =
+ let new_pos, new_table, min_weight =
+ List.fold_left
+ (fun (l, t, w) e ->
+ let ew, _, _, _, _ = e in
+ (Positive, e)::l, Indexing.index t e, min ew w)
+ ([], Indexing.empty, 1000000) (snd new')
+ in
+ let active, newa =
+ backward_simplify_active env new_pos new_table min_weight active in
+ match passive with
+ | None ->
+ active, (make_passive [] []), newa, None
+ | Some passive ->
+ let passive, newp =
+ backward_simplify_passive env new_pos new_table min_weight passive in
+ active, passive, newa, newp
+;;
+
+
+(* 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) =
+ match passive with
+ | goal_conj::tl -> true, (goal_conj::active, tl)
+ | [] -> false, (active, passive)
+;;
+
+
+let activate_theorem (active, passive) =
+ match passive with
+ | theorem::tl -> true, (theorem::active, tl)
+ | [] -> false, (active, passive)
+;;
+
+
+(** simplifies a goal with equalities in active and passive *)
+let simplify_goal env goal ?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 all = if pl = [] then active_list else active_list @ pl in
+
+ let demodulate table goal =
+ let newmeta, newgoal =
+ Indexing.demodulation_goal !maxmeta env table goal in
+ maxmeta := newmeta;
+ goal != newgoal, 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, goal
+;;
+
+
+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
+;;
+
+
+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 all = if pl = [] then active_list else active_list @ pl 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
+;;
+
+
+(* applies equality to goal to see if the goal can be closed *)
+let apply_equality_to_goal env equality goal =
+ let module C = Cic in
+ let module HL = HelmLibraryObjects in
+ let module I = Inference in
+ let metasenv, context, ugraph = env in
+ let _, proof, (ty, left, right, _), metas, args = equality in
+ let eqterm =
+ C.Appl [C.MutInd (LibraryObjects.eq_URI (), 0, []); ty; left; right] in
+ let gproof, gmetas, gterm = goal in
+(* debug_print *)
+(* (lazy *)
+(* (Printf.sprintf "APPLY EQUALITY TO GOAL: %s, %s" *)
+(* (string_of_equality equality) (CicPp.ppterm gterm))); *)
+ try
+ let subst, metasenv', _ =
+ let menv = metasenv @ metas @ gmetas in
+ Inference.unification menv context eqterm gterm ugraph
+ in
+ let newproof =
+ match proof with
+ | I.BasicProof t -> I.BasicProof (CicMetaSubst.apply_subst subst t)
+ | I.ProofBlock (s, uri, nt, t, pe, p) ->
+ I.ProofBlock (subst @ s, uri, nt, t, pe, p)
+ | _ -> assert false
+ in
+ let newgproof =
+ let rec repl = function
+ | I.ProofGoalBlock (_, gp) -> I.ProofGoalBlock (newproof, gp)
+ | I.NoProof -> newproof
+ | I.BasicProof p -> newproof
+ | I.SubProof (t, i, p) -> I.SubProof (t, i, repl p)
+ | _ -> assert false
+ in
+ repl gproof
+ in
+ true, subst, newgproof
+ with CicUnification.UnificationFailure _ ->
+ false, [], I.NoProof
+;;
+
+
+
+let new_meta metasenv =
+ let m = CicMkImplicit.new_meta metasenv [] in
+ incr maxmeta;
+ while !maxmeta <= m do incr maxmeta done;
+ !maxmeta
+;;
+
+
+(* applies a theorem or an equality to goal, returning a list of subgoals or
+ an indication of failure *)
+let apply_to_goal env theorems ?passive active goal =
+ let metasenv, context, ugraph = env in
+ let proof, metas, term = goal in
+ (* debug_print *)
+ (* (lazy *)
+ (* (Printf.sprintf "apply_to_goal with goal: %s" *)
+ (* (\* (string_of_proof proof) *\)(CicPp.ppterm term))); *)
+ let status =
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context in
+ let proof', newmeta =
+ let rec get_meta = function
+ | SubProof (t, i, p) ->
+ let t', i' = get_meta p in
+ if i' = -1 then t, i else t', i'
+ | ProofGoalBlock (_, p) -> get_meta p
+ | _ -> Cic.Implicit None, -1
+ in
+ let p, m = get_meta proof in
+ if m = -1 then
+ let n = new_meta (metasenv @ metas) in
+ Cic.Meta (n, irl), n
+ else
+ p, m
+ in
+ let metasenv = (newmeta, context, term)::metasenv @ metas in
+ let bit = new_meta metasenv, context, term in
+ let metasenv' = bit::metasenv in
+ ((None, metasenv', Cic.Meta (newmeta, irl), term), newmeta)
+ in
+ let rec aux = function
+ | [] -> `No
+ | (theorem, thmty, _)::tl ->
+ try
+ let subst, (newproof, newgoals) =
+ PrimitiveTactics.apply_tac_verbose_with_subst ~term:theorem status
+ in
+ if newgoals = [] then
+ let _, _, p, _ = newproof in
+ let newp =
+ let rec repl = function
+ | Inference.ProofGoalBlock (_, gp) ->
+ Inference.ProofGoalBlock (Inference.BasicProof p, gp)
+ | Inference.NoProof -> Inference.BasicProof p
+ | Inference.BasicProof _ -> Inference.BasicProof p
+ | Inference.SubProof (t, i, p2) ->
+ Inference.SubProof (t, i, repl p2)
+ | _ -> assert false
+ in
+ repl proof
+ in
+ let _, m = status in
+ let subst = List.filter (fun (i, _) -> i = m) subst in
+ `Ok (subst, [newp, metas, term])
+ else
+ let _, menv, p, _ = newproof in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
+ in
+ let goals =
+ List.map
+ (fun i ->
+ let _, _, ty = CicUtil.lookup_meta i menv in
+ let p' =
+ let rec gp = function
+ | SubProof (t, i, p) ->
+ SubProof (t, i, gp p)
+ | ProofGoalBlock (sp1, sp2) ->
+ ProofGoalBlock (sp1, gp sp2)
+ | BasicProof _
+ | NoProof ->
+ SubProof (p, i, BasicProof (Cic.Meta (i, irl)))
+ | ProofSymBlock (s, sp) ->
+ ProofSymBlock (s, gp sp)
+ | ProofBlock (s, u, nt, t, pe, sp) ->
+ ProofBlock (s, u, nt, t, pe, gp sp)
+ in gp proof
+ in
+ (p', menv, ty))
+ newgoals
+ in
+ let goals =
+ let weight t =
+ let w, m = weight_of_term t in
+ w + 2 * (List.length m)
+ in
+ List.sort
+ (fun (_, _, t1) (_, _, t2) ->
+ Pervasives.compare (weight t1) (weight t2))
+ goals
+ in
+ let best = aux tl in
+ match best with
+ | `Ok (_, _) -> best
+ | `No -> `GoOn ([subst, goals])
+ | `GoOn sl -> `GoOn ((subst, goals)::sl)
+ with ProofEngineTypes.Fail msg ->
+ aux tl
+ in
+ let r, s, l =
+ if Inference.term_is_equality term then
+ let rec appleq_a = function
+ | [] -> false, [], []
+ | (Positive, equality)::tl ->
+ let ok, s, newproof = apply_equality_to_goal env equality goal in
+ if ok then true, s, [newproof, metas, term] else appleq_a tl
+ | _::tl -> appleq_a tl
+ in
+ let rec appleq_p = function
+ | [] -> false, [], []
+ | equality::tl ->
+ let ok, s, newproof = apply_equality_to_goal env equality goal in
+ if ok then true, s, [newproof, metas, term] else appleq_p tl
+ in
+ let al, _ = active in
+ match passive with
+ | None -> appleq_a al
+ | Some (_, (pl, _), _) ->
+ let r, s, l = appleq_a al in if r then r, s, l else appleq_p pl
+ else
+ false, [], []
+ in
+ if r = true then `Ok (s, l) else aux theorems
+;;
+
+
+(* sorts a conjunction of goals in order to detect earlier if it is
+ unsatisfiable. Non-predicate goals are placed at the end of the list *)
+let sort_goal_conj (metasenv, context, ugraph) (depth, gl) =
+ let gl =
+ List.stable_sort
+ (fun (_, e1, g1) (_, e2, g2) ->
+ let ty1, _ =
+ CicTypeChecker.type_of_aux' (e1 @ metasenv) context g1 ugraph
+ and ty2, _ =
+ CicTypeChecker.type_of_aux' (e2 @ metasenv) context g2 ugraph
+ in
+ let prop1 =
+ let b, _ =
+ CicReduction.are_convertible context (Cic.Sort Cic.Prop) ty1 ugraph
+ in
+ if b then 0 else 1
+ and prop2 =
+ let b, _ =
+ CicReduction.are_convertible context (Cic.Sort Cic.Prop) ty2 ugraph
+ in
+ if b then 0 else 1
+ in
+ if prop1 = 0 && prop2 = 0 then
+ let e1 = if Inference.term_is_equality g1 then 0 else 1
+ and e2 = if Inference.term_is_equality g2 then 0 else 1 in
+ e1 - e2
+ else
+ prop1 - prop2)
+ gl
+ in
+ (depth, gl)
+;;
+
+
+let is_meta_closed goals =
+ List.for_all (fun (_, _, g) -> CicUtil.is_meta_closed g) goals
+;;
+
+
+(* applies a series of theorems/equalities to a conjunction of goals *)
+let rec apply_to_goal_conj env theorems ?passive active (depth, goals) =
+ let aux (goal, r) tl =
+ let propagate_subst subst (proof, metas, term) =
+ let rec repl = function
+ | NoProof -> NoProof
+ | BasicProof t ->
+ BasicProof (CicMetaSubst.apply_subst subst t)
+ | ProofGoalBlock (p, pb) ->
+ let pb' = repl pb in
+ ProofGoalBlock (p, pb')
+ | SubProof (t, i, p) ->
+ let t' = CicMetaSubst.apply_subst subst t in
+ let p = repl p in
+ SubProof (t', i, p)
+ | ProofSymBlock (ens, p) -> ProofSymBlock (ens, repl p)
+ | ProofBlock (s, u, nty, t, pe, p) ->
+ ProofBlock (subst @ s, u, nty, t, pe, p)
+ in (repl proof, metas, term)
+ in
+ (* let r = apply_to_goal env theorems ?passive active goal in *) (
+ match r with
+ | `No -> `No (depth, goals)
+ | `GoOn sl ->
+ let l =
+ List.map
+ (fun (s, gl) ->
+ let tl = List.map (propagate_subst s) tl in
+ sort_goal_conj env (depth+1, gl @ tl)) sl
+ in
+ `GoOn l
+ | `Ok (subst, gl) ->
+ if tl = [] then
+ `Ok (depth, gl)
+ else
+ let p, _, _ = List.hd gl in
+ let subproof =
+ let rec repl = function
+ | SubProof (_, _, p) -> repl p
+ | ProofGoalBlock (p1, p2) ->
+ ProofGoalBlock (repl p1, repl p2)
+ | p -> p
+ in
+ build_proof_term (repl p)
+ in
+ let i =
+ let rec get_meta = function
+ | SubProof (_, i, p) ->
+ let i' = get_meta p in
+ if i' = -1 then i else i'
+(* max i (get_meta p) *)
+ | ProofGoalBlock (_, p) -> get_meta p
+ | _ -> -1
+ in
+ get_meta p
+ in
+ let subst =
+ let _, (context, _, _) = List.hd subst in
+ [i, (context, subproof, Cic.Implicit None)]
+ in
+ let tl = List.map (propagate_subst subst) tl in
+ let conj = sort_goal_conj env (depth(* +1 *), tl) in
+ `GoOn ([conj])
+ )
+ in
+ if depth > !maxdepth || (List.length goals) > !maxwidth then
+ `No (depth, goals)
+ else
+ let rec search_best res = function
+ | [] -> res
+ | goal::tl ->
+ let r = apply_to_goal env theorems ?passive active goal in
+ match r with
+ | `Ok _ -> (goal, r)
+ | `No -> search_best res tl
+ | `GoOn l ->
+ let newres =
+ match res with
+ | _, `Ok _ -> assert false
+ | _, `No -> goal, r
+ | _, `GoOn l2 ->
+ if (List.length l) < (List.length l2) then goal, r else res
+ in
+ search_best newres tl
+ in
+ let hd = List.hd goals in
+ let res = hd, (apply_to_goal env theorems ?passive active hd) in
+ let best =
+ match res with
+ | _, `Ok _ -> res
+ | _, _ -> search_best res (List.tl goals)
+ in
+ let res = aux best (List.filter (fun g -> g != (fst best)) goals) in
+ match res with
+ | `GoOn ([conj]) when is_meta_closed (snd conj) &&
+ (List.length (snd conj)) < (List.length goals)->
+ apply_to_goal_conj env theorems ?passive active conj
+ | _ -> res
+;;
+
+
+(*
+module OrderedGoals = struct
+ type t = int * (Inference.proof * Cic.metasenv * Cic.term) list
+
+ let compare g1 g2 =
+ let d1, l1 = g1
+ and d2, l2 = g2 in
+ let r = d2 - d1 in
+ if r <> 0 then r
+ else let r = (List.length l1) - (List.length l2) in
+ if r <> 0 then r
+ else
+ let res = ref 0 in
+ let _ =
+ List.exists2
+ (fun (_, _, t1) (_, _, t2) ->
+ let r = Pervasives.compare t1 t2 in
+ if r <> 0 then (
+ res := r;
+ true
+ ) else
+ false) l1 l2
+ in !res
+end
+
+module GoalsSet = Set.Make(OrderedGoals);;
+
+
+exception SearchSpaceOver;;
+*)
+
+
+(*
+let apply_to_goals env is_passive_empty theorems active goals =
+ debug_print (lazy "\n\n\tapply_to_goals\n\n");
+ let add_to set goals =
+ List.fold_left (fun s g -> GoalsSet.add g s) set goals
+ in
+ let rec aux set = function
+ | [] ->
+ debug_print (lazy "HERE!!!");
+ if is_passive_empty then raise SearchSpaceOver else false, set
+ | goals::tl ->
+ let res = apply_to_goal_conj env theorems active goals in
+ match res with
+ | `Ok newgoals ->
+ let _ =
+ let d, p, t =
+ match newgoals with
+ | (d, (p, _, t)::_) -> d, p, t
+ | _ -> assert false
+ in
+ debug_print
+ (lazy
+ (Printf.sprintf "\nOK!!!!\ndepth: %d\nProof: %s\ngoal: %s\n"
+ d (string_of_proof p) (CicPp.ppterm t)))
+ in
+ true, GoalsSet.singleton newgoals
+ | `GoOn newgoals ->
+ let set' = add_to set (goals::tl) in
+ let set' = add_to set' newgoals in
+ false, set'
+ | `No newgoals ->
+ aux set tl
+ in
+ let n = List.length goals in
+ let res, goals = aux (add_to GoalsSet.empty goals) goals in
+ let goals = GoalsSet.elements goals in
+ debug_print (lazy "\n\tapply_to_goals end\n");
+ let m = List.length goals in
+ if m = n && is_passive_empty then
+ raise SearchSpaceOver
+ else
+ res, goals
+;;
+*)
+
+
+(* sorts the list of passive goals to minimize the search for a proof (doesn't
+ work that well yet...) *)
+let sort_passive_goals goals =
+ List.stable_sort
+ (fun (d1, l1) (d2, l2) ->
+ let r1 = d2 - d1
+ and r2 = (List.length l1) - (List.length l2) in
+ let foldfun ht (_, _, t) =
+ let _ = List.map (fun i -> Hashtbl.replace ht i 1) (metas_of_term t)
+ in ht
+ in
+ let m1 = Hashtbl.length (List.fold_left foldfun (Hashtbl.create 3) l1)
+ and m2 = Hashtbl.length (List.fold_left foldfun (Hashtbl.create 3) l2)
+ in let r3 = m1 - m2 in
+ if r3 <> 0 then r3
+ else if r2 <> 0 then r2
+ else r1)
+ (* let _, _, g1 = List.hd l1 *)
+(* and _, _, g2 = List.hd l2 in *)
+(* let e1 = if Inference.term_is_equality g1 then 0 else 1 *)
+(* and e2 = if Inference.term_is_equality g2 then 0 else 1 *)
+(* in let r4 = e1 - e2 in *)
+(* if r4 <> 0 then r3 else r1) *)
+ goals
+;;
+
+
+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))
+;;
+
+
+(* tries to prove the first conjunction in goals with applications of
+ theorems/equalities, returning new sub-goals or an indication of success *)
+let apply_goal_to_theorems dbd env theorems ?passive active goals =
+ let theorems, _ = theorems in
+ let a_goals, p_goals = goals in
+ let goal = List.hd a_goals in
+ let not_in_active gl =
+ not
+ (List.exists
+ (fun (_, gl') ->
+ if (List.length gl) = (List.length gl') then
+ List.for_all2 (fun (_, _, g1) (_, _, g2) -> g1 = g2) gl gl'
+ else
+ false)
+ a_goals)
+ in
+ let aux theorems =
+ let res = apply_to_goal_conj env theorems ?passive active goal in
+ match res with
+ | `Ok newgoals ->
+ true, ([newgoals], [])
+ | `No _ ->
+ false, (a_goals, p_goals)
+ | `GoOn newgoals ->
+ let newgoals =
+ List.filter
+ (fun (d, gl) ->
+ (d <= !maxdepth) && (List.length gl) <= !maxwidth &&
+ not_in_active gl)
+ newgoals in
+ let p_goals = newgoals @ p_goals in
+ let p_goals = sort_passive_goals p_goals in
+ false, (a_goals, p_goals)
+ in
+ aux theorems
+;;
+
+
+let apply_theorem_to_goals env theorems active goals =
+ let a_goals, p_goals = goals in
+ let theorem = List.hd (fst theorems) in
+ let theorems = [theorem] in
+ let rec aux p = function
+ | [] -> false, ([], p)
+ | goal::tl ->
+ let res = apply_to_goal_conj env theorems active goal in
+ match res with
+ | `Ok newgoals -> true, ([newgoals], [])
+ | `No _ -> aux p tl
+ | `GoOn newgoals -> aux (newgoals @ p) tl
+ in
+ let ok, (a, p) = aux p_goals a_goals in
+ if ok then
+ ok, (a, p)
+ else
+ let p_goals =
+ List.stable_sort
+ (fun (d1, l1) (d2, l2) ->
+ let r = d2 - d1 in
+ if r <> 0 then r
+ else let r = (List.length l1) - (List.length l2) in
+ if r <> 0 then r
+ else
+ let res = ref 0 in
+ let _ =
+ List.exists2
+ (fun (_, _, t1) (_, _, t2) ->
+ let r = Pervasives.compare t1 t2 in
+ if r <> 0 then (res := r; true) else false) l1 l2
+ in !res)
+ p
+ in
+ ok, (a_goals, p_goals)
+;;
+
+
+(* given-clause algorithm with lazy reduction strategy *)
+let rec given_clause dbd env goals theorems passive active =
+ let goals = simplify_goals env goals active in
+ let ok, goals = activate_goal goals in
+ (* let theorems = simplify_theorems env theorems active in *)
+ if ok then
+ let ok, goals = apply_goal_to_theorems dbd 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_aux dbd env goals theorems passive active
+ else
+(* let ok', theorems = activate_theorem theorems in *)
+ let ok', theorems = false, 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_aux dbd env goals theorems passive active
+ else
+ if (passive_is_empty passive) then ParamodulationFailure
+ else given_clause_aux dbd env goals theorems passive active
+
+and given_clause_aux dbd env goals theorems passive active =
+ let time1 = Unix.gettimeofday () 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 dbd env goals theorems passive active
+ | false ->
+ let (sign, current), passive = select env (fst goals) passive active in
+ let time1 = Unix.gettimeofday () in
+ let res = forward_simplify env (sign, current) ~passive active in
+ let time2 = Unix.gettimeofday () in
+ forward_simpl_time := !forward_simpl_time +. (time2 -. time1);
+ match res with
+ | None ->
+ given_clause dbd env goals theorems passive active
+ | Some (sign, current) ->
+ if (sign = Negative) && (is_identity env current) then (
+ debug_print
+ (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
+ (string_of_equality ~env current)));
+ let _, proof, _, _, _ = current in
+ ParamodulationSuccess (Some proof, env)
+ ) else (
+ debug_print
+ (lazy "\n================================================");
+ debug_print (lazy (Printf.sprintf "selected: %s %s"
+ (string_of_sign sign)
+ (string_of_equality ~env current)));
+
+ let t1 = Unix.gettimeofday () in
+ let new' = infer env sign current active in
+ let t2 = Unix.gettimeofday () in
+ infer_time := !infer_time +. (t2 -. t1);
+
+ let res, goal' = contains_empty env new' in
+ if res then
+ let proof =
+ match goal' with
+ | Some goal -> let _, proof, _, _, _ = goal in Some proof
+ | None -> None
+ in
+ ParamodulationSuccess (proof, env)
+ else
+ let t1 = Unix.gettimeofday () in
+ let new' = forward_simplify_new env new' active in
+ let t2 = Unix.gettimeofday () in
+ let _ =
+ forward_simpl_new_time :=
+ !forward_simpl_new_time +. (t2 -. t1)
+ in
+ let active =
+ match sign with
+ | Negative -> active
+ | Positive ->
+ let t1 = Unix.gettimeofday () in
+ let active, _, newa, _ =
+ backward_simplify env ([], [current]) active
+ in
+ let t2 = Unix.gettimeofday () in
+ backward_simpl_time :=
+ !backward_simpl_time +. (t2 -. t1);
+ match newa with
+ | None -> active
+ | Some (n, p) ->
+ let al, tbl = active in
+ let nn = List.map (fun e -> Negative, e) n in
+ let pp, tbl =
+ List.fold_right
+ (fun e (l, t) ->
+ (Positive, e)::l,
+ Indexing.index tbl e)
+ p ([], tbl)
+ in
+ nn @ al @ pp, tbl
+ in
+ match contains_empty env new' with
+ | false, _ ->
+ let active =
+ let al, tbl = active in
+ match sign with
+ | Negative -> (sign, current)::al, tbl
+ | Positive ->
+ al @ [(sign, current)], Indexing.index tbl current
+ in
+ let passive = add_to_passive passive new' in
+ let (_, ns), (_, ps), _ = passive in
+ given_clause dbd env goals theorems passive active
+ | true, goal ->
+ let proof =
+ match goal with
+ | Some goal ->
+ let _, proof, _, _, _ = goal in Some proof
+ | None -> None
+ in
+ ParamodulationSuccess (proof, env)
+ )
+;;
+
+
+(** 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 ok, goals = activate_goal goals in
+(* let theorems = simplify_theorems env theorems ~passive active in *)
+ if ok then
+(* 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, goals =
+ apply_goal_to_theorems dbd env theorems ~passive 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 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 =
+ let time1 = Unix.gettimeofday () 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 (sign, current), passive = select env (fst goals) passive active in
+ let time1 = Unix.gettimeofday () in
+ let res = forward_simplify env (sign, current) ~passive active in
+ let time2 = Unix.gettimeofday () in
+ forward_simpl_time := !forward_simpl_time +. (time2 -. time1);
+ match res with
+ | None ->
+ given_clause_fullred dbd env goals theorems passive active
+ | Some (sign, current) ->
+ if (sign = Negative) && (is_identity env current) then (
+ debug_print
+ (lazy (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
+ (string_of_equality ~env current)));
+ let _, proof, _, _, _ = current in
+ ParamodulationSuccess (Some proof, env)
+ ) else (
+ debug_print
+ (lazy "\n================================================");
+ debug_print (lazy (Printf.sprintf "selected: %s %s"
+ (string_of_sign sign)
+ (string_of_equality ~env current)));
+
+ let t1 = Unix.gettimeofday () in
+ let new' = infer env sign current active in
+ let t2 = Unix.gettimeofday () in
+ infer_time := !infer_time +. (t2 -. t1);
+
+ let active =
+ if is_identity env current then active
+ else
+ let al, tbl = active in
+ match sign with
+ | Negative -> (sign, current)::al, tbl
+ | Positive ->
+ al @ [(sign, 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 =
+ backward_simplify env new' ~passive active in
+ let t2 = Unix.gettimeofday () in
+ backward_simpl_time := !backward_simpl_time +. (t2 -. t1);
+ match newa, retained with
+ | None, None -> active, passive, new'
+ | Some (n, p), None
+ | None, Some (n, p) ->
+ let nn, np = new' in
+ simplify (nn @ n, np @ p) active passive
+ | Some (n, p), Some (rn, rp) ->
+ let nn, np = new' in
+ simplify (nn @ n @ rn, np @ p @ rp) active passive
+ in
+ let active, passive, new' = simplify new' active passive in
+
+ 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 (s, e) -> (string_of_sign s) ^ " " ^
+ (string_of_equality ~env e))
+ (fst active))))))
+ in
+ let _ =
+ match new' with
+ | neg, pos ->
+ debug_print
+ (lazy
+ (Printf.sprintf "new':\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
+ match contains_empty env new' with
+ | false, _ ->
+ let passive = add_to_passive passive new' in
+ given_clause_fullred dbd env goals theorems passive active
+ | true, goal ->
+ let proof =
+ match goal with
+ | Some goal -> let _, proof, _, _, _ = goal in Some proof
+ | None -> None
+ in
+ ParamodulationSuccess (proof, env)
+ )
+;;
+
+
+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 (sign, current), passive = select env [1, [goal]] passive active in
+ let res = forward_simplify env (sign, current) ~passive active in
+ match res with
+ | None ->
+ saturate_equations env goal accept_fun passive active
+ | Some (sign, current) ->
+ assert (sign = Positive);
+ debug_print
+ (lazy "\n================================================");
+ debug_print (lazy (Printf.sprintf "selected: %s %s"
+ (string_of_sign sign)
+ (string_of_equality ~env current)));
+ let new' = infer env sign current active in
+ let active =
+ if is_identity env current then active
+ else
+ let al, tbl = active in
+ al @ [(sign, 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 =
+ backward_simplify env new' ~passive active in
+ match newa, retained with
+ | None, None -> active, passive, new'
+ | Some (n, p), None
+ | None, Some (n, p) ->
+ let nn, np = new' in
+ simplify (nn @ n, np @ p) active passive
+ | Some (n, p), Some (rn, rp) ->
+ let nn, np = new' in
+ simplify (nn @ n @ rn, np @ 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 (s, e) -> (string_of_sign s) ^ " " ^
+ (string_of_equality ~env e))
+ (fst active))))))
+ in
+ let _ =
+ match new' with
+ | neg, pos ->
+ debug_print
+ (lazy
+ (Printf.sprintf "new':\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
+ let new' = match new' with _, pos -> [], List.filter accept_fun pos 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 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 = Inference.BasicProof new_meta_goal, [], goal in
+ let equalities =
+ let equalities = equalities @ library_equalities in
+ debug_print
+ (lazy
+ (Printf.sprintf "equalities:\n%s\n"
+ (String.concat "\n"
+ (List.map string_of_equality equalities))));
+ debug_print (lazy "SIMPLYFYING EQUALITIES...");
+ let rec simpl 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 e (active, tbl) in
+ match others with
+ | hd::tl -> (
+ match res with
+ | None -> simpl hd tl others_simpl
+ | Some e -> simpl hd tl (e::others_simpl)
+ )
+ | [] -> (
+ match res with
+ | None -> others_simpl
+ | Some e -> e::others_simpl
+ )
+ in
+ match equalities with
+ | [] -> []
+ | hd::tl ->
+ let others = List.map (fun e -> (Positive, e)) tl in
+ let res =
+ List.rev (List.map snd (simpl (Positive, hd) others []))
+ in
+ debug_print
+ (lazy
+ (Printf.sprintf "equalities AFTER:\n%s\n"
+ (String.concat "\n"
+ (List.map string_of_equality res))));
+ res
+ 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
+ (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)
+ 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 proof, env) ->
+ let proof = Inference.build_proof_term proof in
+ Printf.printf "OK, found a proof!\n";
+ (* 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
+ print_endline (PP.pp proof names);
+ let newmetasenv =
+ List.fold_left
+ (fun m (_, _, _, menv, _) -> 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, env) ->
+ Printf.printf "Success, but no proof?!?\n\n"
+ in
+ Printf.printf ("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.printf "passive_maintainance_time: %.9f\n"
+ !passive_maintainance_time;
+ Printf.printf " successful unification/matching time: %.9f\n"
+ !Indexing.match_unif_time_ok;
+ Printf.printf " failed unification/matching time: %.9f\n"
+ !Indexing.match_unif_time_no;
+ Printf.printf " indexing retrieval time: %.9f\n"
+ !Indexing.indexing_retrieval_time;
+ Printf.printf " demodulate_term.build_newtarget_time: %.9f\n"
+ !Indexing.build_newtarget_time;
+ Printf.printf "derived %d clauses, kept %d clauses.\n"
+ !derived_clauses !kept_clauses;
+ 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;
+;;
+
+let saturate
+ dbd ?(full=false) ?(depth=default_depth) ?(width=default_width) status =
+ let module C = Cic in
+ reset_refs ();
+ Indexing.init_index ();
+ maxdepth := depth;
+ maxwidth := width;
+ 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 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 goal = Inference.BasicProof new_meta_goal, [], 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 =
+ let equalities = equalities @ library_equalities in
+ debug_print
+ (lazy
+ (Printf.sprintf "equalities:\n%s\n"
+ (String.concat "\n"
+ (List.map string_of_equality equalities))));
+ debug_print (lazy "SIMPLYFYING EQUALITIES...");
+ let rec simpl 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 e (active, tbl) in
+ match others with
+ | hd::tl -> (
+ match res with
+ | None -> simpl hd tl others_simpl
+ | Some e -> simpl hd tl (e::others_simpl)
+ )
+ | [] -> (
+ match res with
+ | None -> others_simpl
+ | Some e -> e::others_simpl
+ )
+ in
+ match equalities with
+ | [] -> []
+ | hd::tl ->
+ let others = List.map (fun e -> (Positive, e)) tl in
+ let res =
+ List.rev (List.map snd (simpl (Positive, hd) others []))
+ in
+ debug_print
+ (lazy
+ (Printf.sprintf "equalities AFTER:\n%s\n"
+ (String.concat "\n"
+ (List.map string_of_equality res))));
+ res
+ 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
+ in
+ let finish = Unix.gettimeofday () in
+ (res, finish -. start)
+ in
+ match res with
+ | ParamodulationSuccess (Some proof, env) ->
+ debug_print (lazy "OK, found a proof!");
+ let proof = Inference.build_proof_term proof in
+ let names = names_of_context context in
+ let newmetasenv =
+ let i1 =
+ match new_meta_goal with
+ | C.Meta (i, _) -> i | _ -> assert false
+ in
+ List.filter (fun (i, _, _) -> i <> i1 && i <> goal') metasenv
+ in
+ let newstatus =
+ try
+ let ty, ug =
+ CicTypeChecker.type_of_aux' newmetasenv context proof ugraph
+ in
+ debug_print (lazy (CicPp.pp proof [](* names *)));
+ 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 equality_for_replace i t1 =
+ match t1 with
+ | C.Meta (n, _) -> n = i
+ | _ -> false
+ in
+ let real_proof =
+ ProofEngineReduction.replace
+ ~equality:equality_for_replace
+ ~what:[goal'] ~with_what:[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)));
+ ((uri, newmetasenv, real_proof, term_to_prove), [])
+ with CicTypeChecker.TypeCheckerFailure _ ->
+ debug_print (lazy "THE PROOF DOESN'T TYPECHECK!!!");
+ debug_print (lazy (CicPp.pp proof names));
+ raise (ProofEngineTypes.Fail
+ (lazy "Found a proof, but it doesn't typecheck"))
+ in
+ debug_print (lazy (Printf.sprintf "\nTIME NEEDED: %.9f" time));
+ newstatus
+ | _ ->
+ raise (ProofEngineTypes.Fail (lazy "NO proof found"))
+;;
+
+(* dummy function called within matita to trigger linkage *)
+let init () = ();;
+
+
+(* UGLY SIDE EFFECT... *)
+if connect_to_auto then (
+ AutoTactic.paramodulation_tactic := saturate;
+ AutoTactic.term_is_equality := Inference.term_is_equality;
+);;
+
+
+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 goal = Inference.BasicProof new_meta_goal, [], goal 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 =
+ 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 "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, (snd e))::others_simpl)
+ )
+ | [] -> (
+ match res with
+ | None -> others_simpl
+ | Some e -> (u, (snd e))::others_simpl
+ )
+ in
+ 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)
+ (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
+ let t1 = Unix.gettimeofday () in
+ try
+ let goal = Inference.BasicProof new_meta_goal, [], goal in
+ let equalities =
+ let equalities = equalities @ library_equalities in
+ debug_print
+ (lazy
+ (Printf.sprintf "equalities:\n%s\n"
+ (String.concat "\n"
+ (List.map string_of_equality equalities))));
+ debug_print (lazy "SIMPLYFYING EQUALITIES...");
+ let rec simpl 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 e (active, tbl) in
+ match others with
+ | hd::tl -> (
+ match res with
+ | None -> simpl hd tl others_simpl
+ | Some e -> simpl hd tl (e::others_simpl)
+ )
+ | [] -> (
+ match res with
+ | None -> others_simpl
+ | Some e -> e::others_simpl
+ )
+ in
+ match equalities with
+ | [] -> []
+ | hd::tl ->
+ let others = List.map (fun e -> (Positive, e)) tl in
+ let res =
+ List.rev (List.map snd (simpl (Positive, hd) others []))
+ in
+ debug_print
+ (lazy
+ (Printf.sprintf "equalities AFTER:\n%s\n"
+ (String.concat "\n"
+ (List.map string_of_equality res))));
+ res
+ 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
+ (string_of_equality ~env) equalities));
+ print_endline "--------------------------------------------------";
+ let start = Unix.gettimeofday () in
+ 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 finish = Unix.gettimeofday () 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
+ | (n, _), (p, _), _ ->
+ EqualitySet.elements (List.fold_left addfun EqualitySet.empty p)
+ in
+ let active =
+ let l = List.map snd (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 (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 (term_of_equality e)) passive));
+ print_newline ();
+ with e ->
+ debug_print (lazy ("EXCEPTION: " ^ (Printexc.to_string e)))
+;;
projects / helm.git / blobdiff