(*
MSAT is free software, using the Apache license, see file LICENSE
Copyright 2014 Guillaume Bury
Copyright 2014 Simon Cruanes
*)

module Make
    (St : Solver_types.S)
    (Plugin : Plugin_intf.S with type term = St.term
                             and type formula = St.formula
                             and type proof = St.proof)
    (Dummy: sig end)
= struct

  module Proof = Res.Make(St)

  open St

  exception Sat
  exception Unsat
  exception UndecidedLit
  exception Restart
  exception Conflict of clause

  (* a push/pop state *)
  type user_level = {
    (* User levels always refer to decision_level 0 *)
    ul_elt_lvl : int;     (* Number of atoms in trail at decision level 0 *)
    ul_th_lvl : int;      (* Number of atoms known by the theory at decision level 0 *)
    ul_th_env : Plugin.level; (* Theory state at level 0 *)
    ul_clauses : int;     (* number of clauses *)
    ul_learnt : int;      (* number of learnt clauses *)
  }

  (* Singleton type containing the current state *)
  type env = {

    (* Clauses are simplified for eficiency purposes. In the following
       vectors, the comments actually refer to the original non-simplified
       clause. *)

    clauses_hyps : clause Vec.t;
    (* clauses assumed (subject to user levels) *)
    clauses_learnt : clause Vec.t;
    (* learnt clauses (tautologies true at any time, whatever the user level) *)

    clauses_to_add : clause Stack.t;
    (* Clauses either assumed or pushed by the theory, waiting to be added. *)


    mutable unsat_conflict : clause option;
    (* conflict clause at decision level 0, if any *)
    mutable next_decision : atom option;
    (* When the last conflict was a semantic one, this stores the next decision to make *)

    elt_queue : t Vec.t;
    (* decision stack + propagated elements (atoms or assignments).
       Also called "trail" in some solvers. *)

    elt_levels : int Vec.t;
    (* decision levels in [trail]  *)
    th_levels : Plugin.level Vec.t;
    (* theory states corresponding to elt_levels *)
    user_levels : user_level Vec.t;
    (* user-defined levels, for {!push} and {!pop} *)

    mutable th_head : int;
    (* Start offset in the queue {!elt_queue} of
       unit facts not yet seen by the theory. *)
    mutable elt_head : int;
    (* Start offset in the queue {!elt_queue} of
       unit facts to propagate, within the trail *)

    (* invariant:
       - during propagation, th_head <= elt_head
       - then, once elt_head reaches length elt_queue, Th.assume is
         called so that th_head can catch up with elt_head
       - this is repeated until a fixpoint is reached;
       - before a decision (and after the fixpoint),
         th_head = elt_head = length elt_queue
      *)


    mutable simpDB_props : int;
    (* remaining number of propagations before the next call to [simplify ()] *)
    mutable simpDB_assigns : int;
    (* number of toplevel assignments since last call to [simplify ()] *)


    order : Iheap.t;
    (* Heap ordered by variable activity *)

    var_decay : float;
    (* inverse of the activity factor for variables. Default 1/0.999 *)
    clause_decay : float;
    (* inverse of the activity factor for clauses. Default 1/0.95 *)

    mutable var_incr : float;
    (* increment for variables' activity *)
    mutable clause_incr : float;
    (* increment for clauses' activity *)

    remove_satisfied : bool;
    (* Wether to remove satisfied learnt clauses when simplifying *)


    restart_inc : float;
    (* multiplicative factor for restart limit, default 1.5 *)
    mutable restart_first : int;
    (* intial restart limit, default 100 *)


    learntsize_inc : float;
    (* multiplicative factor for [learntsize_factor] at each restart, default 1.1 *)
    mutable learntsize_factor : float;
    (* initial limit for the number of learnt clauses, 1/3 of initial
        number of clauses by default *)

    mutable starts : int;
    mutable decisions : int;
    mutable propagations : int;
    mutable conflicts : int;
    mutable clauses_literals : int;
    mutable learnts_literals : int;
    mutable nb_init_clauses : int;
  }

  (* Starting environment. *)
  let env = {
    unsat_conflict = None;
    next_decision = None;

    clauses_hyps = Vec.make 0 dummy_clause;
    clauses_learnt = Vec.make 0 dummy_clause;
    clauses_to_add = Stack.create ();

    th_head = 0;
    elt_head = 0;

    elt_queue = Vec.make 601 (of_atom dummy_atom);
    elt_levels = Vec.make 601 (-1);
    th_levels = Vec.make 100 Plugin.dummy;

    user_levels = Vec.make 20 {
        ul_elt_lvl = 0;
        ul_th_lvl = 0;
        ul_learnt = 0;
        ul_clauses = 0;
        ul_th_env = Plugin.dummy;
      };

    order = Iheap.init 0;

    var_incr = 1.;
    clause_incr = 1.;
    var_decay = 1. /. 0.95;
    clause_decay = 1. /. 0.999;

    simpDB_assigns = -1;
    simpDB_props = 0;

    remove_satisfied = false;

    restart_inc = 1.5;
    restart_first = 100;

    learntsize_factor = 1. /. 3. ;
    learntsize_inc = 1.1;

    starts = 0;
    decisions = 0;
    propagations = 0;
    conflicts = 0;
    clauses_literals = 0;
    learnts_literals = 0;
    nb_init_clauses = 0;
  }

  (* Misc functions *)
  let to_float i = float_of_int i
  let to_int f = int_of_float f

  let nb_clauses () = Vec.size env.clauses_hyps
  let nb_vars    () = St.nb_elt ()
  let decision_level () = Vec.size env.elt_levels

  let f_weight i j =
    get_elt_weight (St.get_elt j) < get_elt_weight (St.get_elt i)

  (* Are the assumptions currently unsat ? *)
  let is_unsat () =
    match env.unsat_conflict with
    | Some _ -> true
    | None -> false

  (* Level for push/pop operations *)
  type level = int

  (* Push/Pop *)
  let current_level () = Vec.size env.user_levels

  let push () : level =
    if is_unsat () then
      (* When unsat, pushing does nothing, since adding more assumptions
         can not make the proof disappear. *)
      current_level ()
    else begin
      (* The assumptions are sat, or at least not yet detected unsat,
         we need to save enough to be able to restore the current decision
         level 0. *)
      let res = current_level () in
      (* To restore decision level 0, we need the solver queue, and theory state. *)
      let ul_elt_lvl, ul_th_lvl =
        if Vec.is_empty env.elt_levels then
          env.elt_head, env.th_head
        else (
          let l = Vec.get env.elt_levels 0 in
          l, l
        )
      and ul_th_env =
        if Vec.is_empty env.th_levels
        then Plugin.current_level ()
        else Vec.get env.th_levels 0
      in
      (* Keep in mind what are the current assumptions. *)
      let ul_clauses = Vec.size env.clauses_hyps in
      let ul_learnt = Vec.size env.clauses_learnt in
      Vec.push env.user_levels {ul_elt_lvl; ul_th_lvl; ul_th_env; ul_clauses; ul_learnt;};
      res
    end

  (* To store info for level 0, it is easier to push at module
     initialisation, when there are no assumptions. *)
  let base_level =
    let l = push () in
    assert (l = 0);
    l

  (* Iteration over subterms.
     When incrementing activity, we want to be able to iterate over
     all subterms of a formula. However, the function provided by the theory
     may be costly (if it walks a tree-like structure, and does some processing
     to ignore some subterms for instance), so we want to 'cache' to list
     of subterms of each formula. To do so we use a hashtable from variable id to
     list of subterms. *)
  let iter_map = Hashtbl.create 1003

  let iter_sub f v =
    List.iter f (Hashtbl.find iter_map v.vid)

  (* When we have a new literal,
     we need to first create the list of its subterms. *)
  let atom (f:St.formula) : atom =
    let res = add_atom f in
    if not (Hashtbl.mem iter_map res.var.vid) then begin
      let l = ref [] in
      Plugin.iter_assignable (fun t -> l := add_term t :: !l) res.var.pa.lit;
      Hashtbl.add iter_map res.var.vid !l
    end;
    res

  (* Variable and literal activity.
     Activity is used to decide on which variable to decide when propagation
     is done. Uses a heap (implemented in Iheap), to keep track of variable activity.
     To be more general, the heap only stores the variable/literal id (i.e an int).
     When we add a variable (which wraps a formula), we also need to add all
     its subterms.
  *)
  let rec insert_var_order = function
    | E_lit l -> Iheap.insert f_weight env.order l.lid
    | E_var v ->
      Iheap.insert f_weight env.order v.vid;
      iter_sub (fun t -> insert_var_order (E_lit t)) v

  (* Rather than iterate over all the heap when we want to decrease all the
     variables/literals activity, we instead increase the value by which
     we increase the activity of 'interesting' var/lits. *)
  let var_decay_activity () =
    env.var_incr <- env.var_incr *. env.var_decay

  let clause_decay_activity () =
    env.clause_incr <- env.clause_incr *. env.clause_decay

  (* increase activity of [v] *)
  let var_bump_activity_aux v =
    v.v_weight <- v.v_weight +. env.var_incr;
    if v.v_weight > 1e100 then begin
      for i = 0 to (St.nb_elt ()) - 1 do
        set_elt_weight (St.get_elt i) ((get_elt_weight (St.get_elt i)) *. 1e-100)
      done;
      env.var_incr <- env.var_incr *. 1e-100;
    end;
    if Iheap.in_heap env.order v.vid then
      Iheap.decrease f_weight env.order v.vid

  (* increase activity of literal [l] *)
  let lit_bump_activity_aux (l:lit): unit =
    l.l_weight <- l.l_weight +. env.var_incr;
    if l.l_weight > 1e100 then begin
      for i = 0 to (St.nb_elt ()) - 1 do
        set_elt_weight (St.get_elt i) ((get_elt_weight (St.get_elt i)) *. 1e-100)
      done;
      env.var_incr <- env.var_incr *. 1e-100;
    end;
    if Iheap.in_heap env.order l.lid then
      Iheap.decrease f_weight env.order l.lid

  (* increase activity of var [v] *)
  let var_bump_activity (v:var): unit =
    var_bump_activity_aux v;
    iter_sub lit_bump_activity_aux v

  (* increase activity of clause [c] *)
  let clause_bump_activity (c:clause) : unit =
    c.activity <- c.activity +. env.clause_incr;
    if c.activity > 1e20 then begin
      for i = 0 to (Vec.size env.clauses_learnt) - 1 do
        (Vec.get env.clauses_learnt i).activity <-
          (Vec.get env.clauses_learnt i).activity *. 1e-20;
      done;
      env.clause_incr <- env.clause_incr *. 1e-20
    end

  (* Simplification of clauses.
     When adding new clauses, it is desirable to 'simplify' them, i.e:
     - remove variables that are false at level 0, since it is a fact
       that they cannot be true, and therefore can not help to satisfy the clause
     - return the list of undecided atoms, and the list of clauses that
       justify why the other atoms are false (and will remain so).

     Motivation: Simplification of clauses greatly reduces the search space
     for new watched literals during propagation.

     Aditionally, since we can do push/pop on the assumptions, we need to
     keep track of what assumptions were used to simplify a given clause.
  *)
  exception Trivial

  let simplify_zero atoms : atom list * clause list=
    (* Eliminates dead literals from clauses when at decision level 0 (see above) *)
    assert (decision_level () = 0);
    let aux (atoms, history) a =
      if a.is_true then raise Trivial;
      (* If a variable is true at level 0, then the clause is always satisfied *)
      if a.neg.is_true then begin
        (* If a variable is false, we need to see why it is false. *)
        match a.var.reason with
        | None | Some Decision -> assert false
        (* The var must have a reason, and it cannot be a decision, since we are
           at level 0. *)
        | Some (Bcp cl) -> atoms, cl :: history
        (* The variable has been set to false because of another clause,
           we then need to keep track of the assumption level used. *)
        | Some (Semantic 0) -> atoms, history
        (* Semantic propagations at level 0 are, well not easy to deal with,
           this shouldn't really happen actually (because semantic propagations
           at level 0 should come with a proof). *)
        | Some (Semantic _) ->
          Log.debugf 0 "Unexpected semantic propagation at level 0: %a"
            (fun k->k St.pp_atom a);
          assert false
      end else
        a::atoms, history
        (* General case, we do not know the truth value of a, just let it be. *)
    in
    let atoms, init = Array.fold_left aux ([], []) atoms in
    (* TODO: Why do we sort the atoms here ? *)
    List.fast_sort (fun a b -> a.var.vid - b.var.vid) atoms, init

  (* [arr_to_list a i] converts [a.(i), ... a.(length a-1)] into a list *)
  let arr_to_list arr i : _ list =
    if i >= Array.length arr then []
    else Array.to_list (Array.sub arr i (Array.length arr - i))

  (* Partition literals for new clauses, into:
     - true literals (maybe makes the clause trivial if the lit is proved true)
     - false literals (-> removed, also return the list of reasons those are false)
     - unassigned literals, yet to be decided

     Motivation: it is better to watch true literals, and then unassigned literals.
  *)
  let partition atoms : atom list * clause list =
    let rec partition_aux trues unassigned falses history i =
      if i >= Array.length atoms then
        trues @ unassigned @ falses, history
      else begin
        let a = atoms.(i) in
        if a.is_true then
          if a.var.v_level = 0 then
            raise Trivial
            (* A var true at level 0 gives a trivially true clause *)
          else
            (a :: trues) @ unassigned @ falses @
            (arr_to_list atoms (i + 1)), history
          (* A var true at level > 0 does not change anything, but is unlikely
             to be watched, so we put prefer to put them at the end. *)
        else if a.neg.is_true then
          if a.var.v_level = 0 then begin
            match a.var.reason with
            | Some (Bcp cl) ->
              partition_aux trues unassigned falses (cl :: history) (i + 1)
            (* Same as before, a var false at level 0 can be eliminated from the clause,
               but we need to kepp in mind that we used another clause to simplify it. *)
            | Some (Semantic 0) ->
              partition_aux trues unassigned falses history (i + 1)
            | _ -> assert false
          end else
            partition_aux trues unassigned (a::falses) history (i + 1)
        else
          partition_aux trues (a::unassigned) falses history (i + 1)
      end
    in
    if decision_level () = 0 then
      simplify_zero atoms
    else
      partition_aux [] [] [] [] 0


  (* Making a decision.
     Before actually creatig a new decision level, we check that
     all propagations have been done and propagated to the theory,
     i.e that the theoriy state indeed takes into account the whole
     stack of literals
     i.e we have indeed reached a propagation fixpoint before making
     a new decision *)
  let new_decision_level() =
    assert (env.th_head = Vec.size env.elt_queue);
    assert (env.elt_head = Vec.size env.elt_queue);
    Vec.push env.elt_levels (Vec.size env.elt_queue);
    Vec.push env.th_levels (Plugin.current_level ()); (* save the current theory state *)
    ()

  (* Attach/Detach a clause.

     A clause is attached (to its watching lits) when it is first added,
     either because it is assumed or learnt.

     A clause is detached once it dies (because of pop())
  *)
  let attach_clause c =
    if not c.attached then begin
      Log.debugf 60 "Attaching %a" (fun k -> k St.pp_clause c);
      c.attached <- true;
      Vec.push c.atoms.(0).neg.watched c;
      Vec.push c.atoms.(1).neg.watched c;
    end

  let detach_clause c =
    if c.attached then begin
      c.attached <- false;
      Log.debugf 10 "Removing clause @[%a@]" (fun k->k St.pp_clause c);
      Vec.remove c.atoms.(0).neg.watched c;
      Vec.remove c.atoms.(1).neg.watched c;
    end

  (* Is a clause satisfied ? *)
  let satisfied c = Array_util.exists (fun atom -> atom.is_true) c.atoms

  (* Backtracking.
     Used to backtrack, i.e cancel down to [lvl] excluded,
     i.e we want to go back to the state the solver was in
         when decision level [lvl] was created. *)
  let cancel_until lvl =
    (* Nothing to do if we try to backtrack to a non-existent level. *)
    if decision_level () > lvl then begin
      Log.debugf 5 "Backtracking to lvl %d" (fun k -> k lvl);
      (* We set the head of the solver and theory queue to what it was. *)
      env.elt_head <- Vec.get env.elt_levels lvl;
      env.th_head <- env.elt_head;
      (* Now we need to cleanup the vars that are not valid anymore
         (i.e to the right of elt_head in the queue. *)
      for c = env.elt_head to Vec.size env.elt_queue - 1 do
        match (Vec.get env.elt_queue c) with
        (* A literal is unassigned, we nedd to add it back to
           the heap of potentially assignable literals. *)
        | Lit l ->
          l.assigned <- None;
          l.l_level <- -1;
          insert_var_order (elt_of_lit l)
        (* A variable is not true/false anymore, one of two things can happen: *)
        | Atom a ->
          if a.var.v_level <= lvl then begin
            (* It is a semantic propagation, which can be late, and has a level
               lower than where we backtrack, so we just move it to the head
               of the queue, to be propagated again. *)
            Vec.set env.elt_queue env.elt_head (of_atom a);
            env.elt_head <- env.elt_head + 1
          end else begin
            (* it is a result of bolean propagation, or a semantic propagation
               with a level higher than the level to which we backtrack,
               in that case, we simply unset its value and reinsert it into the heap. *)
            a.is_true <- false;
            a.neg.is_true <- false;
            a.var.v_level <- -1;
            a.var.reason <- None;
            insert_var_order (elt_of_var a.var)
          end
      done;
      (* Recover the right theory state. *)
      Plugin.backtrack (Vec.get env.th_levels lvl);
      (* Resize the vectors according to their new size. *)
      Vec.shrink env.elt_queue ((Vec.size env.elt_queue) - env.elt_head);
      Vec.shrink env.elt_levels ((Vec.size env.elt_levels) - lvl);
      Vec.shrink env.th_levels ((Vec.size env.th_levels) - lvl);
    end;
    assert (Vec.size env.elt_levels = Vec.size env.th_levels);
    ()

  (* Unsatisfiability is signaled through an exception, since it can happen
     in multiple places (adding new clauses, or solving for instance). *)
  let report_unsat ({atoms=atoms} as confl) : _ =
    Log.debugf 5 "@[Unsat conflict: %a@]" (fun k -> k St.pp_clause confl);
    env.unsat_conflict <- Some confl;
    raise Unsat

  (* Simplification of boolean propagation reasons.
     When doing boolean propagation *at level 0*, it can happen
     that the clause cl, which propagates a formula, also contains
     other formulas, but has been simplified. in which case, we
     need to rebuild a clause with correct history, in order to
     be able to build a correct proof at the end of proof search. *)
  let simpl_reason : reason -> reason = function
    | (Bcp cl) as r ->
      let l, history = partition cl.atoms in
      begin match l with
        | [ a ] ->
          if history = [] then r
          (* no simplification has been done, so [cl] is actually a clause with only
             [a], so it is a valid reason for propagating [a]. *)
          else
            (* Clauses in [history] have been used to simplify [cl] into a clause [tmp_cl]
               with only one formula (which is [a]). So we explicitly create that clause
               and set it as the cause for the propagation of [a], that way we can
               rebuild the whole resolution tree when we want to prove [a]. *)
            Bcp (make_clause (fresh_tname ()) l (History (cl :: history)))
        | _ -> assert false
      end
    | r -> r

  (* Boolean propagation.
     Wrapper function for adding a new propagated formula. *)
  let enqueue_bool a ~level:lvl reason : unit =
    if a.neg.is_true then begin
      Log.debugf 0 "Trying to enqueue a false literal: %a" (fun k->k St.pp_atom a);
      assert false
    end;
    if not a.is_true then begin
      assert (a.var.v_level < 0 && a.var.reason = None && lvl >= 0);
      let reason =
        if lvl > 0 then reason
        else simpl_reason reason
      in
      a.is_true <- true;
      a.var.v_level <- lvl;
      a.var.reason <- Some reason;
      Vec.push env.elt_queue (of_atom a);
      Log.debugf 20 "Enqueue (%d): %a"
        (fun k->k (Vec.size env.elt_queue) pp_atom a)
    end

  (* MCsat semantic assignment *)
  let enqueue_assign l value lvl =
    match l.assigned with
    | Some _ ->
      Log.debugf 0 "Trying to assign an already assigned literal: %a"
        (fun k -> k St.pp_lit l);
      assert false
    | None ->
      assert (l.l_level < 0);
      l.assigned <- Some value;
      l.l_level <- lvl;
      Vec.push env.elt_queue (of_lit l);
      ()

  (* evaluate an atom for MCsat, if it's not assigned
     by boolean propagation/decision *)
  let th_eval a : bool option =
    if a.is_true || a.neg.is_true then None
    else match Plugin.eval a.lit with
      | Plugin_intf.Unknown -> None
      | Plugin_intf.Valued (b, lvl) ->
        let atom = if b then a else a.neg in
        enqueue_bool atom ~level:lvl (Semantic lvl);
        Some b

  (* conflict analysis: find the list of atoms of [l] that have the
     maximal level *)
  let max_lvl_atoms (l:atom list) : int * atom list =
    List.fold_left
      (fun (max_lvl, acc) a ->
        if a.var.v_level = max_lvl then (max_lvl, a :: acc)
        else if a.var.v_level > max_lvl then (a.var.v_level, [a])
        else (max_lvl, acc))
      (0, []) l

  (* find which level to backtrack to, given a conflict clause
     and a boolean stating whether it is
     a UIP ("Unique Implication Point")
     precond: the atom list is sorted by decreasing decision level *)
  let backtrack_lvl ~is_uip : atom list -> int = function
    | [] -> 0
    | [a] ->
      assert is_uip;
      0
    | a :: b :: r ->
      if is_uip then (
        (* backtrack below [a], so we can propagate [not a] *)
        assert(a.var.v_level > b.var.v_level);
        b.var.v_level
      ) else (
        assert (a.var.v_level = b.var.v_level);
        max (a.var.v_level - 1) 0
      )

  (* result of conflict analysis, containing the learnt clause and some
     additional info.

     invariant: cr_history's order matters, as its head is later used
     during pop operations to determine the origin of a clause/conflict
     (boolean conflict i.e hypothesis, or theory lemma) *)
  type conflict_res = {
    cr_backtrack_lvl : int; (* level to backtrack to *)
    cr_learnt: atom list; (* lemma learnt from conflict *)
    cr_history: clause list; (* justification *)
    cr_is_uip: bool; (* conflict is UIP? *)
  }

  (* conflict analysis for MCsat
     The idea is to walk the trail/elt_queue starting from the most recent
     atom, and perform resolution steps with each propagation reason, until
     the First UIP clause is found, or we get semantic propagations
     at the highest level (see mcsat paper for more explications).
  *)
  let analyze_mcsat c_clause : conflict_res =
    let tr_ind  = ref (Vec.size env.elt_queue) in
    let is_uip  = ref false in
    let c       = ref (Proof.to_list c_clause) in
    let history = ref [c_clause] in
    clause_bump_activity c_clause;
    let is_semantic a = match a.var.reason with
      | Some Semantic _ -> true
      | _ -> false
    in
    try
      while true do
        let lvl, atoms = max_lvl_atoms !c in
        if lvl = 0 then raise Exit;
        match atoms with
        | [] | [_] ->
          is_uip := true;
          raise Exit
        | _ when List.for_all is_semantic atoms ->
          raise Exit
        | _ ->
          decr tr_ind;
          Log.debugf 20 "Looking at trail element %d" (fun k->k !tr_ind);
          match Vec.get env.elt_queue !tr_ind with
          | Lit _ -> ()
          | Atom a ->
            begin match a.var.reason with
              | Some (Bcp d) ->
                (* resolution step *)
                let tmp, res = Proof.resolve (Proof.merge !c (Proof.to_list d)) in
                begin match tmp with
                  | [] -> ()
                  | [b] when b == a.var.pa ->
                    clause_bump_activity d;
                    var_bump_activity a.var;
                    history := d :: !history;
                    c := res
                  | _ -> assert false
                end
              | None | Some Decision | Some Semantic _ -> ()
            end
      done; assert false
    with Exit ->
      let learnt =
        List.fast_sort
          (fun a b -> Pervasives.compare b.var.v_level a.var.v_level) !c
      in
      let blevel = backtrack_lvl !is_uip learnt in
      { cr_backtrack_lvl = blevel;
        cr_learnt= learnt;
        cr_history = List.rev !history;
        cr_is_uip = !is_uip;
      }

  let get_atom i =
    match Vec.get env.elt_queue i with
    | Lit _ -> assert false | Atom x -> x

  (* conflict analysis for SAT
     Same idea as the mcsat analyze function (without semantic propagations),
     except we look the the Last UIP (TODO: check ?), and do it in an imperative
     and eficient manner. *)
  let analyze_sat c_clause : conflict_res =
    let pathC  = ref 0 in
    let learnt = ref [] in
    let cond   = ref true in
    let blevel = ref 0 in
    let seen   = ref [] in
    let c      = ref c_clause in
    let tr_ind = ref (Vec.size env.elt_queue - 1) in
    let size   = ref 1 in
    let history = ref [] in
    assert (decision_level () > 0);
    while !cond do
      begin match !c.cpremise with
        | History _ -> clause_bump_activity !c
        | Hyp _ | Lemma _ -> ()
      end;
      history := !c :: !history;
      (* visit the current predecessors *)
      for j = 0 to Array.length !c.atoms - 1 do
        let q = !c.atoms.(j) in
        assert (q.is_true || q.neg.is_true && q.var.v_level >= 0); (* unsure? *)
        if q.var.v_level = 0 then begin
          assert (q.neg.is_true);
          match q.var.reason with
          | Some Bcp cl -> history := cl :: !history
          | _ -> assert false
        end;
        if not q.var.seen then begin
          q.var.seen <- true;
          seen := q :: !seen;
          if q.var.v_level > 0 then begin
            var_bump_activity q.var;
            if q.var.v_level >= decision_level () then begin
              incr pathC
            end else begin
              learnt := q :: !learnt;
              incr size;
              blevel := max !blevel q.var.v_level
            end
          end
        end
      done;

      (* look for the next node to expand *)
      while not (get_atom !tr_ind).var.seen do decr tr_ind done;
      decr pathC;
      let p = get_atom !tr_ind in
      decr tr_ind;
      match !pathC, p.var.reason with
      | 0, _ ->
        cond := false;
        learnt := p.neg :: (List.rev !learnt)
      | n, Some Bcp cl ->
        c := cl
      | n, _ -> assert false
    done;
    List.iter (fun q -> q.var.seen <- false) !seen;
    { cr_backtrack_lvl= !blevel;
      cr_learnt= !learnt;
      cr_history= List.rev !history;
      cr_is_uip = true;
    }

  let analyze c_clause : conflict_res =
    if St.mcsat
    then analyze_mcsat c_clause
    else analyze_sat c_clause

  (* add the learnt clause to the clause database, propagate, etc. *)
  let record_learnt_clause (confl:clause) (cr:conflict_res): unit =
    begin match cr.cr_learnt with
      | [] -> assert false
      | [fuip] ->
        assert (cr.cr_backtrack_lvl = 0);
        if fuip.neg.is_true then
          report_unsat confl
        else begin
          let name = fresh_lname () in
          let uclause = make_clause name cr.cr_learnt (History cr.cr_history) in
          Vec.push env.clauses_learnt uclause;
          (* no need to attach [uclause], it is true at level 0 *)
          enqueue_bool fuip ~level:0 (Bcp uclause)
        end
      | fuip :: _ ->
        let name = fresh_lname () in
        let lclause = make_clause name cr.cr_learnt (History cr.cr_history) in
        Vec.push env.clauses_learnt lclause;
        attach_clause lclause;
        clause_bump_activity lclause;
        if cr.cr_is_uip then
          enqueue_bool fuip ~level:cr.cr_backtrack_lvl (Bcp lclause)
        else begin
          env.next_decision <- Some fuip.neg
        end
    end;
    var_decay_activity ();
    clause_decay_activity ()

  (* process a conflict:
     - learn clause
     - backtrack
     - report unsat if conflict at level 0
  *)
  let add_boolean_conflict (confl:clause): unit =
    env.next_decision <- None;
    env.conflicts <- env.conflicts + 1;
    if decision_level() = 0 || Array_util.for_all (fun a -> a.var.v_level = 0) confl.atoms then
      report_unsat confl; (* Top-level conflict *)
    let cr = analyze confl in
    cancel_until cr.cr_backtrack_lvl;
    record_learnt_clause confl cr

  (* Add a new clause, simplifying, propagating, and backtracking if
     the clause is false in the current trail *)
  let add_clause ?(force=false) (init:clause) : unit =
    Log.debugf 90 "Adding clause:@[<hov>%a@]" (fun k -> k St.pp_clause init);
    assert (init.c_level <= current_level ());
    let vec = match init.cpremise with
      | Hyp _ -> env.clauses_hyps
      | Lemma _ -> env.clauses_learnt
      | History _ -> assert false
    in
    try
      let atoms, history = partition init.atoms in
      let clause =
        if history = [] then init
        else make_clause ?tag:init.tag (fresh_name ()) atoms (History (init :: history))
      in
      Log.debugf 4 "New clause:@ @[%a@]" (fun k->k St.pp_clause clause);
      Vec.push vec clause;
      match atoms with
      | [] ->
        report_unsat clause
      | a::b::_ ->
        if a.neg.is_true then begin
          (* Atoms need to be sorted in decreasing order of decision level,
             or we might watch the wrong literals. *)
          Array.sort
            (fun a b -> compare b.var.v_level a.var.v_level)
            clause.atoms;
          attach_clause clause;
          add_boolean_conflict init
        end else begin
          attach_clause clause;
          if b.neg.is_true && not a.is_true && not a.neg.is_true then begin
            let lvl = List.fold_left (fun m a -> max m a.var.v_level) 0 atoms in
            cancel_until lvl;
            enqueue_bool a lvl (Bcp clause)
          end
        end
      | [a]   ->
        Log.debugf 5 "New unit clause, propagating : %a" (fun k->k St.pp_atom a);
        cancel_until 0;
        enqueue_bool a 0 (Bcp clause)
    with Trivial ->
      Vec.push vec init;
      Log.debugf 5 "Trivial clause ignored : @[%a@]" (fun k->k St.pp_clause init)

  let flush_clauses () =
    if not (Stack.is_empty env.clauses_to_add) then begin
      let nbv = St.nb_elt () in
      let nbc = env.nb_init_clauses + Stack.length env.clauses_to_add in
      Iheap.grow_to_by_double env.order nbv;
      St.iter_elt insert_var_order;
      Vec.grow_to_by_double env.clauses_hyps nbc;
      Vec.grow_to_by_double env.clauses_learnt nbc;
      env.nb_init_clauses <- nbc;
      while not (Stack.is_empty env.clauses_to_add) do
        let c = Stack.pop env.clauses_to_add in
        if c.c_level <= current_level () then
          add_clause c
      done
    end

  type watch_res =
    | Watch_kept
    | Watch_removed

  (* boolean propagation.
     [a] is the false atom, one of [c]'s two watch literals
     [i] is the index of [c] in [a.watched]
     @return whether [c] was removed from [a.watched]
  *)
  let propagate_in_clause (a:atom) (c:clause) (i:int): watch_res =
    let atoms = c.atoms in
    let first = atoms.(0) in
    if first == a.neg then (
      (* false lit must be at index 1 *)
      atoms.(0) <- atoms.(1);
      atoms.(1) <- first
    ) else assert (a.neg == atoms.(1));
    let first = atoms.(0) in
    if first.is_true
    then Watch_kept (* true clause, keep it in watched *)
    else (
      try (* look for another watch lit *)
        for k = 2 to Array.length atoms - 1 do
          let ak = atoms.(k) in
          if not (ak.neg.is_true) then begin
            (* watch lit found: update and exit *)
            atoms.(1) <- ak;
            atoms.(k) <- a.neg;
            (* remove [c] from [a.watched], add it to [ak.neg.watched] *)
            Vec.push ak.neg.watched c;
            assert (Vec.get a.watched i == c);
            Vec.fast_remove a.watched i;
            raise Exit
          end
        done;
        (* no watch lit found *)
        if first.neg.is_true || (th_eval first = Some false) then begin
          (* clause is false *)
          env.elt_head <- Vec.size env.elt_queue;
          raise (Conflict c)
        end else begin
          (* clause is unit, keep the same watches, but propagate *)
          enqueue_bool first (decision_level ()) (Bcp c)
        end;
        Watch_kept
      with Exit ->
        Watch_removed
    )

  (* propagate atom [a], which was just decided. This checks every
     clause watching [a] to see if the clause is false, unit, or has
     other possible watches
     @param res the optional conflict clause that the propagation might trigger *)
  let propagate_atom a (res:clause option ref) : unit =
    let watched = a.watched in
    begin
      try
        let rec aux i =
          if i >= Vec.size watched then ()
          else (
            let c = Vec.get watched i in
            assert c.attached;
            let j = match propagate_in_clause a c i with
              | Watch_kept -> i+1
              | Watch_removed -> i (* clause at this index changed *)
            in
            aux j
          )
        in
        aux 0
      with Conflict c ->
        assert (!res = None);
        res := Some c
    end;
    ()

  (* Propagation (boolean and theory) *)
  let new_atom f =
    let a = atom f in
    ignore (th_eval a);
    a

  let slice_get i =
    match Vec.get env.elt_queue i with
    | Atom a ->
      Plugin_intf.Lit a.lit
    | Lit {l_level; term; assigned = Some v} ->
      Plugin_intf.Assign (term, v, l_level)
    | Lit _ -> assert false

  let slice_push (l:formula list) (lemma:proof): unit =
    let atoms = List.rev_map (fun x -> new_atom x) l in
    let c = make_clause (fresh_tname ()) atoms (Lemma lemma) in
    Log.debugf 10 "Pushing clause %a" (fun k->k St.pp_clause c);
    (* do not add the clause yet, wait for the theory propagation to
       be done *)
    Stack.push c env.clauses_to_add

  let slice_propagate f lvl =
    let a = atom f in
    Iheap.grow_to_by_double env.order (St.nb_elt ());
    enqueue_bool a lvl (Semantic lvl)

  let current_slice (): (_,_,_) Plugin_intf.slice = {
    Plugin_intf.start = env.th_head;
    length = (Vec.size env.elt_queue) - env.th_head;
    get = slice_get;
    push = slice_push;
    propagate = slice_propagate;
  }

  (* full slice, for [if_sat] final check *)
  let full_slice () : (_,_,_) Plugin_intf.slice = {
    Plugin_intf.start = 0;
    length = Vec.size env.elt_queue;
    get = slice_get;
    push = slice_push;
    propagate = (fun _ -> assert false);
  }

  (* some boolean literals were decided/propagated within Msat. Now we
     need to inform the theory of those assumptions, so it can do its job.
     @return the conflict clause, if the theory detects unsatisfiability *)
  let rec theory_propagate (): clause option =
    assert (env.elt_head = Vec.size env.elt_queue);
    assert (env.th_head <= env.elt_head);
    if env.th_head = env.elt_head then
      None (* fixpoint/no propagation *)
    else begin
      let slice = current_slice () in
      env.th_head <- env.elt_head; (* catch up *)
      match Plugin.assume slice with
      | Plugin_intf.Sat ->
        propagate ()
      | Plugin_intf.Unsat (l, p) ->
        (* conflict *)
        let l = List.rev_map new_atom l in
        Iheap.grow_to_by_double env.order (St.nb_elt ());
        List.iter (fun a -> insert_var_order (elt_of_var a.var)) l;
        let c = St.make_clause (St.fresh_tname ()) l (Lemma p) in
        Some c
    end

  (* fixpoint between boolean propagation and theory propagation
     @return a conflict clause, if any *)
  and propagate (): clause option =
    (* First, treat the stack of lemmas added by the theory, if any *)
    flush_clauses ();
    (* Now, check that the situation is sane *)
    assert (env.elt_head <= Vec.size env.elt_queue);
    if env.elt_head = Vec.size env.elt_queue then
      theory_propagate ()
    else begin
      let num_props = ref 0 in
      let res = ref None in
      while env.elt_head < Vec.size env.elt_queue do
        begin match Vec.get env.elt_queue env.elt_head with
          | Lit _ -> ()
          | Atom a ->
            incr num_props;
            propagate_atom a res
        end;
        env.elt_head <- env.elt_head + 1;
      done;
      env.propagations <- env.propagations + !num_props;
      env.simpDB_props <- env.simpDB_props - !num_props;
      match !res with
      | None -> theory_propagate ()
      | _ -> !res
    end

  (* remove some learnt clauses
     NOTE: so far we do not forget learnt clauses. We could, as long as
     lemmas from the theory itself are kept. *)
  let reduce_db () = ()

  (* Decide on a new literal, and enqueue it into the trail *)
  let rec pick_branch_aux atom: unit =
    let v = atom.var in
    if v.v_level >= 0 then begin
      assert (v.pa.is_true || v.na.is_true);
      pick_branch_lit ()
    end else match Plugin.eval atom.lit with
      | Plugin_intf.Unknown ->
        env.decisions <- env.decisions + 1;
        new_decision_level();
        let current_level = decision_level () in
        enqueue_bool atom current_level Decision
      | Plugin_intf.Valued (b, lvl) ->
        let a = if b then atom else atom.neg in
        enqueue_bool a lvl (Semantic lvl)

  and pick_branch_lit () =
    match env.next_decision with
    | Some atom ->
      env.next_decision <- None;
      pick_branch_aux atom
    | None ->
      begin try
          begin match St.get_elt (Iheap.remove_min f_weight env.order) with
            | E_lit l ->
              if l.l_level >= 0 then
                pick_branch_lit ()
              else begin
                let value = Plugin.assign l.term in
                env.decisions <- env.decisions + 1;
                new_decision_level();
                let current_level = decision_level () in
                enqueue_assign l value current_level
              end
            | E_var v ->
              pick_branch_aux v.pa
          end
        with Not_found -> raise Sat
      end

  (* do some amount of search, until the number of conflicts or clause learnt
     reaches the given parameters *)
  let search n_of_conflicts n_of_learnts: unit =
    let conflictC = ref 0 in
    env.starts <- env.starts + 1;
    while true do
      match propagate () with
      | Some confl -> (* Conflict *)
        incr conflictC;
        add_boolean_conflict confl

      | None -> (* No Conflict *)
        assert (env.elt_head = Vec.size env.elt_queue);
        assert (env.elt_head = env.th_head);
        if Vec.size env.elt_queue = St.nb_elt ()
        then raise Sat;
        if n_of_conflicts > 0 && !conflictC >= n_of_conflicts then begin
          cancel_until 0;
          raise Restart
        end;
        (* if decision_level() = 0 then simplify (); *)

        if n_of_learnts >= 0 &&
           Vec.size env.clauses_learnt - Vec.size env.elt_queue >= n_of_learnts
        then reduce_db();

        pick_branch_lit ()
    done

  (* check that clause is true *)
  let check_clause (c:clause): unit =
    let ok = Array_util.exists (fun a -> a.is_true) c.atoms in
    assert ok

  let check_vec vec = Vec.iter check_clause vec

  (* fixpoint of propagation and decisions until a model is found, or a
     conflict is reached *)
  let solve (): unit =
    if is_unsat () then raise Unsat;
    let n_of_conflicts = ref (to_float env.restart_first) in
    let n_of_learnts = ref ((to_float (nb_clauses())) *. env.learntsize_factor) in
    try
      while true do
        begin try
            search (to_int !n_of_conflicts) (to_int !n_of_learnts)
          with
          | Restart ->
            n_of_conflicts := !n_of_conflicts *. env.restart_inc;
            n_of_learnts   := !n_of_learnts *. env.learntsize_inc
          | Sat ->
            assert (env.elt_head = Vec.size env.elt_queue);
            Plugin.if_sat (full_slice ());
            flush_clauses();
            if is_unsat () then raise Unsat
            else if env.elt_head = Vec.size env.elt_queue (* sanity check *)
                 && env.elt_head = St.nb_elt ()
                 (* this is the important test to know if the search is finished *)
            then raise Sat
        end
      done
    with
    | Sat -> ()

  let assume ?tag cnf =
    List.iter (fun l ->
        let atoms = List.rev_map atom l in
        let c = make_clause ?tag (fresh_hname ()) atoms (Hyp (current_level ())) in
        Stack.push c env.clauses_to_add
      ) cnf

  let eval_level lit =
    let var, negated = make_boolean_var lit in
    if not var.pa.is_true && not var.na.is_true
    then raise UndecidedLit
    else assert (var.v_level >= 0);
    let truth = var.pa.is_true in
    let value = match negated with
      | Formula_intf.Negated -> not truth
      | Formula_intf.Same_sign -> truth
    in
    value, var.v_level

  let eval lit = fst (eval_level lit)

  let hyps () = env.clauses_hyps

  let history () = env.clauses_learnt

  let unsat_conflict () = env.unsat_conflict

  let model () : (term * term) list =
    let opt = function Some a -> a | None -> assert false in
    Vec.fold
      (fun acc e -> match e with
         | Lit v -> (v.term, opt v.assigned)  :: acc
         | Atom _ -> acc)
      [] env.elt_queue

  (* Backtrack to decision_level 0, with trail_lim && theory env specified *)
  let reset_until push_lvl (ul: user_level) =
    Log.debug 1 "Resetting to decision level 0 (pop/forced)";
    env.th_head <- ul.ul_th_lvl ;
    env.elt_head <- ul.ul_elt_lvl;
    for c = env.elt_head to Vec.size env.elt_queue - 1 do
      match Vec.get env.elt_queue c with
      | Lit l ->
        l.assigned <- None;
        l.l_level <- -1;
        insert_var_order (elt_of_lit l)
      | Atom a ->
        begin match a.var.reason with
          | Some Bcp { c_level } when c_level > push_lvl ->
            a.is_true <- false;
            a.neg.is_true <- false;
            a.var.v_level <- -1;
            a.var.reason <- None;
            insert_var_order (elt_of_var a.var)
          | _ ->
            if a.var.v_level = 0 then begin
              (* [a] is still true, so we move it to the current top position
                 of the trail, as if it was propagated again *)
              Vec.set env.elt_queue env.elt_head (of_atom a);
              env.elt_head <- env.elt_head + 1
            end else begin
              a.is_true <- false;
              a.neg.is_true <- false;
              a.var.v_level <- -1;
              a.var.reason <- None;
              insert_var_order (elt_of_var a.var)
            end
        end
    done;
    Plugin.backtrack ul.ul_th_env; (* recover the right theory env *)
    Vec.shrink env.elt_queue ((Vec.size env.elt_queue) - env.elt_head);
    Vec.clear env.elt_levels;
    Vec.clear env.th_levels;
    assert (Vec.size env.elt_levels = Vec.size env.th_levels);
    assert (env.elt_head = Vec.size env.elt_queue);
    ()

  let pop l: unit =
    (* Check sanity of pop *)
    if l > current_level () then invalid_arg "cannot pop to level, it is too high"
    else if l < current_level () then begin

      let ul = Vec.get env.user_levels l in
      Vec.shrink env.user_levels (max 0 (Vec.size env.user_levels - l - 1));

      (* It is quite hard to check wether unsat status can be kept, so in doubt, we remove it *)
      env.unsat_conflict <- None;

      (* Backtrack to the level 0 with appropriate settings *)
      reset_until l ul;

      (* Log current assumptions for debugging purposes *)
      Log.debugf 99 "@[<v2>Current trail:@ %a@]"
        (fun k->
           let pp out () =
             for i = 0 to Vec.size env.elt_queue - 1 do
               Format.fprintf out "%s%s%d -- %a@,"
                 (if i = ul.ul_elt_lvl then "*" else " ")
                 (if i = ul.ul_th_lvl then "*" else " ")
                 i (fun fmt e ->
                     match e with
                     | Lit l -> St.pp_lit fmt l
                     | Atom a -> St.pp_atom fmt a)
                 (Vec.get env.elt_queue i)
             done
           in
           k pp ());

      (* Clear hypothesis not valid anymore *)
      for i = ul.ul_clauses to Vec.size env.clauses_hyps - 1 do
        let c = Vec.get env.clauses_hyps i in
        assert (c.c_level > l);
        detach_clause c
      done;
      Vec.shrink env.clauses_hyps (Vec.size env.clauses_hyps - ul.ul_clauses);

      (* Refresh the known tautologies simplified because of clauses that have been removed *)
      let s = Stack.create () in
      let new_sz = ref ul.ul_learnt in
      for i = ul.ul_learnt to Vec.size env.clauses_learnt - 1 do
        let c = Vec.get env.clauses_learnt i in
        if c.c_level > l then begin
          detach_clause c;
          match c.cpremise with
          | Lemma _ -> Stack.push c s
          | History ({ cpremise = Lemma _ } as c' :: _ ) -> Stack.push c' s
          | _ -> () (* Only simplified clauses can have a level > 0 *)
        end else begin
          Log.debugf 15 "Keeping intact clause %a" (fun k->k St.pp_clause c);
          Vec.set env.clauses_learnt !new_sz c;
          incr new_sz
        end
      done;
      Vec.shrink env.clauses_learnt (Vec.size env.clauses_learnt - !new_sz);
      Stack.iter (add_clause ~force:true) s
    end

  let reset () = pop base_level

end