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;; 

(* 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;;


type result =
  | ParamodulationFailure
  | ParamodulationSuccess of Inference.equality option * environment
;;


(*
let symbols_of_equality (_, (_, left, right), _, _) =
  TermSet.union (symbols_of_term left) (symbols_of_term right)
;;
*)

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
(*   Printf.printf "symbols_of_equality %s:\n" *)
(*     (string_of_equality equality); *)
(*   TermMap.iter (fun k v -> Printf.printf "%s: %d\n" (CicPp.ppterm k) v) m; *)
(*   print_newline (); *)
  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
(*         let weight_of t = fst (weight_of_term ~consider_metas:false t) in *)
(*         let w1 = (weight_of ty) + (weight_of left) + (weight_of right) *)
(*         and w2 = (weight_of ty') + (weight_of left') + (weight_of right') 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
(*               match a, a' with *)
(*               | (Cic.Meta (i, _)::_), (Cic.Meta (j, _)::_) -> *)
(*                   let res = Pervasives.compare i j in *)
(*                   if res <> 0 then res else Pervasives.compare eq1 eq2 *)
(*               | _, _ -> Pervasives.compare eq1 eq2 *)
            )
        | res -> res
end

module EqualitySet = Set.Make(OrderedEquality);;


let select env passive (active, _) =
  processed_clauses := !processed_clauses + 1;
  
  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::tl ->
          let passive_table =
            Indexing.remove_index passive_table hd
(*             if !use_fullred then Indexing.remove_index passive_table hd *)
(*             else passive_table *)
          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
      match active with
      | (Negative, e)::_ ->
          let symbols = symbols_of_equality e 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 if c = i then *)
(*               match OrderedEquality.compare equality e with *)
(*               | -1 -> (c, equality) *)
(*               | res -> (i, e) *)
            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
(*           Printf.printf "\nsymbols-based selection: %s\n\n" *)
(*             (string_of_equality ~env current); *)
          let passive_table =
            Indexing.remove_index passive_table current
(*             if !use_fullred then Indexing.remove_index passive_table current *)
(*             else passive_table *)
          in
          (Positive, current),
          (([], neg_set),
           (remove current pos_list, EqualitySet.remove current pos_set),
           passive_table)
      | _ ->
          let current = EqualitySet.min_elt pos_set in
          let passive_table =
            Indexing.remove_index passive_table current
(*             if !use_fullred then Indexing.remove_index passive_table current *)
(*             else passive_table *)
          in
          let passive =
            (neg_list, neg_set),
            (remove current pos_list, EqualitySet.remove current pos_set),
            passive_table
          in
          (Positive, current), passive
    )
  | _ ->
      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
(*           if !use_fullred then Indexing.remove_index passive_table current *)
(*           else passive_table *)
        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
;;


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_table ()) pos
(*     if !use_fullred then *)
(*       List.fold_left (fun tbl e -> Indexing.index tbl e) *)
(*         (Indexing.empty_table ()) pos *)
(*     else *)
(*       Indexing.empty_table () *)
  in
  (neg, set_of neg),
  (pos, set_of pos),
  table
;;


let make_active () =
  [], Indexing.empty_table () 
;;


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
(*     if !use_fullred then *)
(*       List.fold_left (fun tbl e -> Indexing.index tbl e) table pos *)
(*     else *)
(*       table *)
  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
;;


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 (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 in_weight, ns = pickw in_weight ns in *)
(*   let _, ps = pickw in_weight ps 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_weight := Some (weight_of_equality (EqualitySet.max_elt ps)); *)
    maximal_retained_equality := Some (EqualitySet.max_elt ps); 
  let tbl =
    EqualitySet.fold
      (fun e tbl -> Indexing.index tbl e) ps (Indexing.empty_table ())
(*     if !use_fullred then *)
(*       EqualitySet.fold *)
(*         (fun e tbl -> Indexing.index tbl e) ps (Indexing.empty_table ()) *)
(*     else *)
(*       tbl *)
  in
  (nl, ns), (pl, ps), tbl  
;;


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_table ()) 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
;;


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 rec find_duplicate sign current = function *)
(*     | [] -> false *)
(*     | (s, eq)::tl when s = sign -> *)
(*         if meta_convertibility_eq current eq then true *)
(*         else find_duplicate sign current tl *)
(*     | _::tl -> find_duplicate sign current tl *)
(*   in *)

(*   let res =  *)
(*     if sign = Positive then *)
(*       Indexing.subsumption env active_table current *)
(*     else *)
(*       false *)
(*   in *)
(*   if res then *)
(*     None *)
(*   else *)
  
  let demodulate table current = 
    let newmeta, newcurrent =
      Indexing.demodulation !maxmeta env table sign current in
    maxmeta := newmeta;
    if is_identity env newcurrent then
      if sign = Negative then Some (sign, newcurrent)
      else 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 -> res
        | Some passive_table ->
            if Indexing.in_index passive_table c then None
            else res

(*   | Some (s, c) -> if find_duplicate s c all then None else res *)

(*         if s = Utils.Negative then *)
(*           res *)
(*         else *)
(*           if Indexing.subsumption env active_table c then *)
(*             None *)
(*           else ( *)
(*             match passive_table with *)
(*             | None -> res *)
(*             | Some passive_table -> *)
(*                 if Indexing.subsumption env passive_table c then *)
(*                   None *)
(*                 else *)
(*                   res *)
(*           ) *)

(*         let pred (sign, eq) = *)
(*           if sign <> s then false *)
(*           else subsumption env c eq *)
(*         in *)
(*         if List.exists pred all 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. };;


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 !maxmeta env table sign target in
    maxmeta := newmeta;
    newtarget
  in
(*   let f sign' target (sign, eq) = *)
(*     if sign <> sign' then false *)
(*     else subsumption env target eq  *)
(*   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 (Indexing.subsumption env active_table e))
    | Some passive_table ->
        (fun e -> not ((Indexing.subsumption env active_table e) ||
                         (Indexing.subsumption env passive_table e)))
  in

  let t1 = Unix.gettimeofday () in

(*   let new_neg, new_pos = *)
(*     List.filter subs new_neg, *)
(*     List.filter subs new_pos *)
(*   in *)

(*   let new_neg, new_pos =  *)
(*     (List.filter (fun e -> not (List.exists (f Negative e) all)) new_neg, *)
(*      List.filter (fun e -> not (List.exists (f Positive e) all)) new_pos) *)
(*   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 is_duplicate new_pos

(*   new_neg, new_pos *)

(*   let res = *)
(*     (List.filter (fun e -> not (List.exists (f Negative e) all)) new_neg, *)
(*      List.filter (fun e -> not (List.exists (f Positive e) all)) new_pos) *)
(*   in *)
(*   res *)
;;


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 if (find eq res) then *)
(*            res, tbl *)
         else
           (s, eq)::res, if s = Negative then tbl else Indexing.index tbl eq)
      active_list ([], Indexing.empty_table ()),
    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
;;


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
(*       let _ = debug_print (Printf.sprintf "OK: %d %d" ew min_weight) in *)
      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_table ()) 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_table (), 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
;;


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.)))
;;

  
let rec given_clause env 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 (Printf.sprintf "Time limit (%.2f) reached: %.2f\n"
                     !time_limit !elapsed_time);
      make_passive [] []
    ) else if kept > selection_estimate then (
      debug_print (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
  | false ->
      let (sign, current), passive = select env 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 env passive active
      | Some (sign, current) ->
          if (sign = Negative) && (is_identity env current) then (
            debug_print (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
                           (string_of_equality ~env current));
            ParamodulationSuccess (Some current, env)
          ) else (            
            debug_print "\n================================================";
            debug_print (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
              ParamodulationSuccess (goal, env)
            else 
              let t1 = Unix.gettimeofday () in
              let new' = forward_simplify_new env new' (* ~passive *) 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
(*               let _ = *)
(*                 Printf.printf "active:\n%s\n" *)
(*                   (String.concat "\n" *)
(*                      ((List.map *)
(*                          (fun (s, e) -> (string_of_sign s) ^ " " ^ *)
(*                             (string_of_equality ~env e)) (fst active)))); *)
(*                 print_newline (); *)
(*               in *)
(*               let _ = *)
(*                 match new' with *)
(*                 | neg, pos -> *)
(*                     Printf.printf "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))); *)
(*                     print_newline (); *)
(*               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
(*                   Printf.printf "passive:\n%s\n" *)
(*                     (String.concat "\n" *)
(*                        ((List.map (fun e -> "Negative " ^ *)
(*                                      (string_of_equality ~env e)) *)
(*                            (EqualitySet.elements ns)) @ *)
(*                           (List.map (fun e -> "Positive " ^ *)
(*                                        (string_of_equality ~env e)) *)
(*                              (EqualitySet.elements ps)))); *)
(*                   print_newline (); *)
                  given_clause env passive active
              | true, goal ->
                  ParamodulationSuccess (goal, env)
          )
;;


let rec given_clause_fullred env 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 (Printf.sprintf "Time limit (%.2f) reached: %.2f\n"
                     !time_limit !elapsed_time);
      make_passive [] []
    ) else if kept > selection_estimate then (
      debug_print (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
  | false ->
      let (sign, current), passive = select env 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 env passive active
      | Some (sign, current) ->
          if (sign = Negative) && (is_identity env current) then (
            debug_print (Printf.sprintf "OK!!! %s %s" (string_of_sign sign)
                           (string_of_equality ~env current));
            ParamodulationSuccess (Some current, env)
          ) else (
            debug_print "\n================================================";
            debug_print (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 (
                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 (
                    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
(*                 let (_, ns), (_, ps), _ = passive in *)
(*                 Printf.printf "passive:\n%s\n" *)
(*                   (String.concat "\n" *)
(*                      ((List.map (fun e -> "Negative " ^ *)
(*                                    (string_of_equality ~env e)) *)
(*                          (EqualitySet.elements ns)) @ *)
(*                         (List.map (fun e -> "Positive " ^ *)
(*                                      (string_of_equality ~env e)) *)
(*                            (EqualitySet.elements ps)))); *)
(*                 print_newline (); *)
                given_clause_fullred env passive active
            | true, goal ->
                ParamodulationSuccess (goal, env)
          )
;;


let given_clause_ref = ref given_clause;;


let main 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 equalities, maxm = find_equalities context proof in
  let library_equalities, maxm =
    find_library_equalities ~dbd context (proof, goal') (maxm+2)
  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
    Printf.printf "\n\nTIPO DEL GOAL: %s\n" (CicPp.ppterm ty);
    print_newline ();
    Cic.Meta (maxm+1, irl),
    (maxm+1, context, ty)::metasenv,
    ty
  in
(*   let new_meta_goal = Cic.Meta (goal', irl) in *)
  let env = (metasenv, context, ugraph) in
  try
    let term_equality = equality_of_term new_meta_goal goal in
    let _, meta_proof, (eq_ty, left, right, ordering), _, _ = term_equality in
    if is_identity env term_equality then
      let proof =
        Cic.Appl [Cic.MutConstruct (* reflexivity *)
                    (HelmLibraryObjects.Logic.eq_URI, 0, 1, []);
                  eq_ty; left]
      in
      let _ = 
        Printf.printf "OK, found a proof!\n";
        let names = names_of_context context in
        print_endline (PP.pp proof names)
      in
      ()
    else
      let equalities =
        let equalities = equalities @ library_equalities in
        debug_print (
          Printf.sprintf "equalities:\n%s\n"
            (String.concat "\n"
               (List.map string_of_equality equalities)));
        debug_print "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_table ()) 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 (
              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 [term_equality] equalities in
      Printf.printf "\ncurrent goal: %s\n"
        (string_of_equality ~env term_equality);
      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 @ library_equalities)));
      print_endline "--------------------------------------------------";
      let start = Unix.gettimeofday () in
      print_endline "GO!";
      start_time := Unix.gettimeofday ();
      let res =
        (if !use_fullred then given_clause_fullred else given_clause)
          env passive active
      in
      let finish = Unix.gettimeofday () in
      let _ =
        match res with
        | ParamodulationFailure ->
            Printf.printf "NO proof found! :-(\n\n"
        | ParamodulationSuccess (Some goal, env) ->
            let proof = Inference.build_proof_term goal in         
            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
                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);
                (*           print_endline (PP.ppterm proof); *)
                
                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 saturate dbd (proof, goal) =
  let module C = Cic in
  maxmeta := 0;
  let goal' = goal in
  let uri, metasenv, meta_proof, term_to_prove = proof in
  let _, context, goal = CicUtil.lookup_meta goal' metasenv in
  let 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 (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
(*   try *)
  let term_equality = equality_of_term new_meta_goal goal in
  let res, time = 
    if is_identity env term_equality then
      let w, _, (eq_ty, left, right, o), m, a = term_equality in
      let proof =
        Cic.Appl [Cic.MutConstruct (* reflexivity *)
                    (HelmLibraryObjects.Logic.eq_URI, 0, 1, []);
                  eq_ty; left]
      in
      (ParamodulationSuccess
         (Some (0, Inference.BasicProof proof,
                (eq_ty, left, right, o), m, a), env), 0.)
    else
      let library_equalities, maxm =
        find_library_equalities ~dbd context (proof, goal') (maxm+2)
      in
      maxmeta := maxm+2;
      let equalities =
        let equalities = equalities @ library_equalities in
        debug_print (
          Printf.sprintf "equalities:\n%s\n"
            (String.concat "\n"
               (List.map string_of_equality equalities)));
        debug_print "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_table ()) 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 (
              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 [term_equality] equalities in
      let start = Unix.gettimeofday () in
      let res = given_clause_fullred env passive active in
      let finish = Unix.gettimeofday () in
      (res, finish -. start)
  in
  match res with
  | ParamodulationSuccess (Some goal, env) ->
      debug_print "OK, found a proof!";
      let proof = Inference.build_proof_term goal in         
      let names = names_of_context context in
      let newmetasenv =
        let i1 =
          match new_meta_goal with
          | C.Meta (i, _) -> i | _ -> assert false
        in
(*           let i2 = *)
(*             match meta_proof with *)
(*             | C.Meta (i, _) -> i *)
(*             | t -> *)
(*                 Printf.printf "\nHMMM!!! meta_proof: %s\ngoal': %s" *)
(*                   (CicPp.pp meta_proof names) (string_of_int goal'); *)
(*                 print_newline (); *)
(*                 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 (CicPp.pp proof [](* names *));
          debug_print
            (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 (
            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 "THE PROOF DOESN'T TYPECHECK!!!";
          debug_print (CicPp.pp proof names);
          raise (ProofEngineTypes.Fail
                   "Found a proof, but it doesn't typecheck")
      in
      debug_print (Printf.sprintf "\nTIME NEEDED: %.9f" time);
      newstatus          
  | _ ->
      raise (ProofEngineTypes.Fail "NO proof found")
(*   with e -> *)
(*     raise (Failure "saturation failed") *)
;;


(* 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;
);;