(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_provers.ML

    Author:     Fabian Immler, TU Muenchen

    Author:     Makarius

    Author:     Jasmin Blanchette, TU Muenchen

Generic prover abstraction for Sledgehammer.

*)

signature SLEDGEHAMMER_PROVERS =

sig

  type failure = ATP_Proof.failure

  type stature = ATP_Problem_Generate.stature

  type type_enc = ATP_Problem_Generate.type_enc

  type reconstructor = ATP_Proof_Reconstruct.reconstructor

  type play = ATP_Proof_Reconstruct.play

  type minimize_command = ATP_Proof_Reconstruct.minimize_command

  type relevance_fudge = Sledgehammer_Filter_Iter.relevance_fudge

  datatype mode = Auto_Try | Try | Normal | Auto_Minimize | Minimize

  type params =

    {debug: bool,

     verbose: bool,

     overlord: bool,

     blocking: bool,

     provers: string list,

     type_enc: string option,

     strict: bool,

     lam_trans: string option,

     uncurried_aliases: bool option,

     relevance_thresholds: real * real,

     max_relevant: int option,

     max_mono_iters: int option,

     max_new_mono_instances: int option,

     isar_proof: bool,

     isar_shrink_factor: int,

     slice: bool,

     minimize: bool option,

     timeout: Time.time,

     preplay_timeout: Time.time,

     expect: string}

  datatype prover_fact =

    Untranslated_Fact of (string * stature) * thm |

    SMT_Weighted_Fact of (string * stature) * (int option * thm)

  type prover_problem =

    {state: Proof.state,

     goal: thm,

     subgoal: int,

     subgoal_count: int,

     facts: prover_fact list}

  type prover_result =

    {outcome: failure option,

     used_facts: (string * stature) list,

     run_time: Time.time,

     preplay: unit -> play,

     message: play -> string,

     message_tail: string}

  type prover =

    params -> ((string * string list) list -> string -> minimize_command)

    -> prover_problem -> prover_result

  val dest_dir : string Config.T

  val problem_prefix : string Config.T

  val completish : bool Config.T

  val atp_full_names : bool Config.T

  val smt_triggers : bool Config.T

  val smt_weights : bool Config.T

  val smt_weight_min_facts : int Config.T

  val smt_min_weight : int Config.T

  val smt_max_weight : int Config.T

  val smt_max_weight_index : int Config.T

  val smt_weight_curve : (int -> int) Unsynchronized.ref

  val smt_max_slices : int Config.T

  val smt_slice_fact_frac : real Config.T

  val smt_slice_time_frac : real Config.T

  val smt_slice_min_secs : int Config.T

  val das_tool : string

  val plain_metis : reconstructor

  val select_smt_solver : string -> Proof.context -> Proof.context

  val extract_reconstructor :

    params -> reconstructor -> string * (string * string list) list

  val is_reconstructor : string -> bool

  val is_atp : theory -> string -> bool

  val is_smt_prover : Proof.context -> string -> bool

  val is_ho_atp: Proof.context -> string -> bool

  val is_unit_equational_atp : Proof.context -> string -> bool

  val is_prover_supported : Proof.context -> string -> bool

  val is_prover_installed : Proof.context -> string -> bool

  val default_max_relevant_for_prover : Proof.context -> bool -> string -> int

  val is_unit_equality : term -> bool

  val is_appropriate_prop_for_prover : Proof.context -> string -> term -> bool

  val is_built_in_const_for_prover :

    Proof.context -> string -> string * typ -> term list -> bool * term list

  val atp_relevance_fudge : relevance_fudge

  val smt_relevance_fudge : relevance_fudge

  val relevance_fudge_for_prover : Proof.context -> string -> relevance_fudge

  val weight_smt_fact :

    Proof.context -> int -> ((string * stature) * thm) * int

    -> (string * stature) * (int option * thm)

  val untranslated_fact : prover_fact -> (string * stature) * thm

  val smt_weighted_fact :

    Proof.context -> int -> prover_fact * int

    -> (string * stature) * (int option * thm)

  val supported_provers : Proof.context -> unit

  val kill_provers : unit -> unit

  val running_provers : unit -> unit

  val messages : int option -> unit

  val filter_used_facts : ''a list -> (''a * 'b) list -> (''a * 'b) list

  val get_prover : Proof.context -> mode -> string -> prover

end;

structure Sledgehammer_Provers : SLEDGEHAMMER_PROVERS =

struct

open ATP_Util

open ATP_Problem

open ATP_Proof

open ATP_Systems

open ATP_Problem_Generate

open ATP_Proof_Reconstruct

open Metis_Tactic

open Sledgehammer_Util

open Sledgehammer_Filter_Iter

(** The Sledgehammer **)

datatype mode = Auto_Try | Try | Normal | Auto_Minimize | Minimize

(* Identifier that distinguishes Sledgehammer from other tools that could use

   "Async_Manager". *)

val das_tool = "Sledgehammer"

val reconstructor_names = [metisN, smtN]

val plain_metis = Metis (hd partial_type_encs, combsN)

val is_reconstructor = member (op =) reconstructor_names

val is_atp = member (op =) o supported_atps

val select_smt_solver = Context.proof_map o SMT_Config.select_solver

fun is_smt_prover ctxt = member (op =) (SMT_Solver.available_solvers_of ctxt)

fun is_atp_for_format is_format ctxt name =

  let val thy = Proof_Context.theory_of ctxt in

    case try (get_atp thy) name of

      SOME config =>

      exists (fn (_, (_, ((_, format, _, _, _), _))) => is_format format)

             (#best_slices (config ()) ctxt)

    | NONE => false

  end

val is_unit_equational_atp = is_atp_for_format (curry (op =) CNF_UEQ)

val is_ho_atp = is_atp_for_format is_format_higher_order

fun is_prover_supported ctxt =

  let val thy = Proof_Context.theory_of ctxt in

    is_reconstructor orf is_atp thy orf is_smt_prover ctxt

  end

fun is_prover_installed ctxt =

  is_reconstructor orf is_smt_prover ctxt orf

  is_atp_installed (Proof_Context.theory_of ctxt)

fun get_slices slice slices =

  (0 upto length slices - 1) ~~ slices |> not slice ? (List.last #> single)

val reconstructor_default_max_relevant = 20

fun default_max_relevant_for_prover ctxt slice name =

  let val thy = Proof_Context.theory_of ctxt in

    if is_reconstructor name then

      reconstructor_default_max_relevant

    else if is_atp thy name then

      fold (Integer.max o #1 o fst o snd o snd o snd)

           (get_slices slice (#best_slices (get_atp thy name ()) ctxt)) 0

    else (* is_smt_prover ctxt name *)

      SMT_Solver.default_max_relevant ctxt name

  end

fun is_if (@{const_name If}, _) = true

  | is_if _ = false

(* Beware of "if and only if" (which is translated as such) and "If" (which is

   translated to conditional equations). *)

fun is_good_unit_equality T t u =

  T <> @{typ bool} andalso not (exists (exists_Const is_if) [t, u])

fun is_unit_equality (@{const Trueprop} $ t) = is_unit_equality t

  | is_unit_equality (Const (@{const_name all}, _) $ Abs (_, _, t)) =

    is_unit_equality t

  | is_unit_equality (Const (@{const_name All}, _) $ Abs (_, _, t)) =

    is_unit_equality t

  | is_unit_equality (Const (@{const_name "=="}, Type (_, [T, _])) $ t $ u) =

    is_good_unit_equality T t u

  | is_unit_equality (Const (@{const_name HOL.eq}, Type (_ , [T, _])) $ t $ u) =

    is_good_unit_equality T t u

  | is_unit_equality _ = false

fun is_appropriate_prop_for_prover ctxt name =

  if is_unit_equational_atp ctxt name then is_unit_equality else K true

fun is_built_in_const_for_prover ctxt name =

  if is_smt_prover ctxt name then

    let val ctxt = ctxt |> select_smt_solver name in

      fn x => fn ts =>

         if SMT_Builtin.is_builtin_num_ext ctxt (list_comb (Const x, ts)) then

           (true, [])

         else if SMT_Builtin.is_builtin_fun_ext ctxt x ts then

           (true, ts)

         else

           (false, ts)

    end

  else

    fn (s, _) => fn ts => (member (op =) atp_irrelevant_consts s, ts)

(* FUDGE *)

val atp_relevance_fudge =

  {local_const_multiplier = 1.5,

   worse_irrel_freq = 100.0,

   higher_order_irrel_weight = 1.05,

   abs_rel_weight = 0.5,

   abs_irrel_weight = 2.0,

   skolem_irrel_weight = 0.05,

   theory_const_rel_weight = 0.5,

   theory_const_irrel_weight = 0.25,

   chained_const_irrel_weight = 0.25,

   intro_bonus = 0.15,

   elim_bonus = 0.15,

   simp_bonus = 0.15,

   local_bonus = 0.55,

   assum_bonus = 1.05,

   chained_bonus = 1.5,

   max_imperfect = 11.5,

   max_imperfect_exp = 1.0,

   threshold_divisor = 2.0,

   ridiculous_threshold = 0.01}

(* FUDGE (FIXME) *)

val smt_relevance_fudge =

  {local_const_multiplier = #local_const_multiplier atp_relevance_fudge,

   worse_irrel_freq = #worse_irrel_freq atp_relevance_fudge,

   higher_order_irrel_weight = #higher_order_irrel_weight atp_relevance_fudge,

   abs_rel_weight = #abs_rel_weight atp_relevance_fudge,

   abs_irrel_weight = #abs_irrel_weight atp_relevance_fudge,

   skolem_irrel_weight = #skolem_irrel_weight atp_relevance_fudge,

   theory_const_rel_weight = #theory_const_rel_weight atp_relevance_fudge,

   theory_const_irrel_weight = #theory_const_irrel_weight atp_relevance_fudge,

   chained_const_irrel_weight = #chained_const_irrel_weight atp_relevance_fudge,

   intro_bonus = #intro_bonus atp_relevance_fudge,

   elim_bonus = #elim_bonus atp_relevance_fudge,

   simp_bonus = #simp_bonus atp_relevance_fudge,

   local_bonus = #local_bonus atp_relevance_fudge,

   assum_bonus = #assum_bonus atp_relevance_fudge,

   chained_bonus = #chained_bonus atp_relevance_fudge,

   max_imperfect = #max_imperfect atp_relevance_fudge,

   max_imperfect_exp = #max_imperfect_exp atp_relevance_fudge,

   threshold_divisor = #threshold_divisor atp_relevance_fudge,

   ridiculous_threshold = #ridiculous_threshold atp_relevance_fudge}

fun relevance_fudge_for_prover ctxt name =

  if is_smt_prover ctxt name then smt_relevance_fudge else atp_relevance_fudge

fun supported_provers ctxt =

  let

    val thy = Proof_Context.theory_of ctxt

    val (remote_provers, local_provers) =

      reconstructor_names @

      sort_strings (supported_atps thy) @

      sort_strings (SMT_Solver.available_solvers_of ctxt)

      |> List.partition (String.isPrefix remote_prefix)

  in

    Output.urgent_message ("Supported provers: " ^

                           commas (local_provers @ remote_provers) ^ ".")

  end

fun kill_provers () = Async_Manager.kill_threads das_tool "prover"

fun running_provers () = Async_Manager.running_threads das_tool "prover"

val messages = Async_Manager.thread_messages das_tool "prover"

(** problems, results, ATPs, etc. **)

type params =

  {debug: bool,

   verbose: bool,

   overlord: bool,

   blocking: bool,

   provers: string list,

   type_enc: string option,

   strict: bool,

   lam_trans: string option,

   uncurried_aliases: bool option,

   relevance_thresholds: real * real,

   max_relevant: int option,

   max_mono_iters: int option,

   max_new_mono_instances: int option,

   isar_proof: bool,

   isar_shrink_factor: int,

   slice: bool,

   minimize: bool option,

   timeout: Time.time,

   preplay_timeout: Time.time,

   expect: string}

datatype prover_fact =

  Untranslated_Fact of (string * stature) * thm |

  SMT_Weighted_Fact of (string * stature) * (int option * thm)

type prover_problem =

  {state: Proof.state,

   goal: thm,

   subgoal: int,

   subgoal_count: int,

   facts: prover_fact list}

type prover_result =

  {outcome: failure option,

   used_facts: (string * stature) list,

   run_time: Time.time,

   preplay: unit -> play,

   message: play -> string,

   message_tail: string}

type prover =

  params -> ((string * string list) list -> string -> minimize_command)

  -> prover_problem -> prover_result

(* configuration attributes *)

(* Empty string means create files in Isabelle's temporary files directory. *)

val dest_dir =

  Attrib.setup_config_string @{binding sledgehammer_dest_dir} (K "")

val problem_prefix =

  Attrib.setup_config_string @{binding sledgehammer_problem_prefix} (K "prob")

val completish =

  Attrib.setup_config_bool @{binding sledgehammer_completish} (K false)

(* In addition to being easier to read, readable names are often much shorter,

   especially if types are mangled in names. This makes a difference for some

   provers (e.g., E). For these reason, short names are enabled by default. *)

val atp_full_names =

  Attrib.setup_config_bool @{binding sledgehammer_atp_full_names} (K false)

val smt_triggers =

  Attrib.setup_config_bool @{binding sledgehammer_smt_triggers} (K true)

val smt_weights =

  Attrib.setup_config_bool @{binding sledgehammer_smt_weights} (K true)

val smt_weight_min_facts =

  Attrib.setup_config_int @{binding sledgehammer_smt_weight_min_facts} (K 20)

(* FUDGE *)

val smt_min_weight =

  Attrib.setup_config_int @{binding sledgehammer_smt_min_weight} (K 0)

val smt_max_weight =

  Attrib.setup_config_int @{binding sledgehammer_smt_max_weight} (K 10)

val smt_max_weight_index =

  Attrib.setup_config_int @{binding sledgehammer_smt_max_weight_index} (K 200)

val smt_weight_curve = Unsynchronized.ref (fn x : int => x * x)

fun smt_fact_weight ctxt j num_facts =

  if Config.get ctxt smt_weights andalso

     num_facts >= Config.get ctxt smt_weight_min_facts then

    let

      val min = Config.get ctxt smt_min_weight

      val max = Config.get ctxt smt_max_weight

      val max_index = Config.get ctxt smt_max_weight_index

      val curve = !smt_weight_curve

    in

      SOME (max - (max - min + 1) * curve (Int.max (0, max_index - j - 1))

            div curve max_index)

    end

  else

    NONE

fun weight_smt_fact ctxt num_facts ((info, th), j) =

  let val thy = Proof_Context.theory_of ctxt in

    (info, (smt_fact_weight ctxt j num_facts, th |> Thm.transfer thy))

  end

fun untranslated_fact (Untranslated_Fact p) = p

  | untranslated_fact (SMT_Weighted_Fact (info, (_, th))) = (info, th)

fun smt_weighted_fact _ _ (SMT_Weighted_Fact p, _) = p

  | smt_weighted_fact ctxt num_facts (fact, j) =

    (untranslated_fact fact, j) |> weight_smt_fact ctxt num_facts

fun overlord_file_location_for_prover prover =

  (getenv "ISABELLE_HOME_USER", "prob_" ^ prover)

fun with_path cleanup after f path =

  Exn.capture f path

  |> tap (fn _ => cleanup path)

  |> Exn.release

  |> tap (after path)

fun proof_banner mode name =

  case mode of

    Auto_Try => "Auto Sledgehammer (" ^ quote name ^ ") found a proof"

  | Try => "Sledgehammer (" ^ quote name ^ ") found a proof"

  | _ => "Try this"

fun bunch_of_reconstructors needs_full_types lam_trans =

  [(false, Metis (partial_type_enc, lam_trans false)),

   (true, Metis (full_type_enc, lam_trans false)),

   (false, Metis (no_typesN, lam_trans true)),

   (true, Metis (really_full_type_enc, lam_trans true)),

   (true, SMT)]

  |> map_filter (fn (full_types, reconstr) =>

                    if needs_full_types andalso not full_types then NONE

                    else SOME reconstr)

fun extract_reconstructor ({type_enc, lam_trans, ...} : params)

                          (Metis (type_enc', lam_trans')) =

    let

      val override_params =

        (if is_none type_enc andalso type_enc' = hd partial_type_encs then

           []

         else

           [("type_enc", [hd (unalias_type_enc type_enc')])]) @

        (if is_none lam_trans andalso lam_trans' = metis_default_lam_trans then

           []

         else

           [("lam_trans", [lam_trans'])])

    in (metisN, override_params) end

  | extract_reconstructor _ SMT = (smtN, [])

(* based on "Mirabelle.can_apply" and generalized *)

fun timed_apply timeout tac state i =

  let

    val {context = ctxt, facts, goal} = Proof.goal state

    val full_tac = Method.insert_tac facts i THEN tac ctxt i

  in TimeLimit.timeLimit timeout (try (Seq.pull o full_tac)) goal end

fun tac_for_reconstructor (Metis (type_enc, lam_trans)) =

    metis_tac [type_enc] lam_trans

  | tac_for_reconstructor SMT = SMT_Solver.smt_tac

fun timed_reconstructor reconstr debug timeout ths =

  (Config.put Metis_Tactic.verbose debug

   #> Config.put SMT_Config.verbose debug

   #> (fn ctxt => tac_for_reconstructor reconstr ctxt ths))

  |> timed_apply timeout

fun filter_used_facts used = filter (member (op =) used o fst)

fun play_one_line_proof mode debug verbose timeout pairs state i preferred

                        reconstrs =

  let

    val _ =

      if mode = Minimize andalso Time.> (timeout, Time.zeroTime) then

        Output.urgent_message "Preplaying proof..."

      else

        ()

    val ths = pairs |> sort_wrt (fst o fst) |> map snd

    fun get_preferred reconstrs =

      if member (op =) reconstrs preferred then preferred

      else List.last reconstrs

    fun play [] [] = Failed_to_Play (get_preferred reconstrs)

      | play timed_outs [] =

        Trust_Playable (get_preferred timed_outs, SOME timeout)

      | play timed_out (reconstr :: reconstrs) =

        let

          val _ =

            if verbose then

              "Trying \"" ^ string_for_reconstructor reconstr ^ "\" for " ^

              string_from_time timeout ^ "..."

              |> Output.urgent_message

            else

              ()

          val timer = Timer.startRealTimer ()

        in

          case timed_reconstructor reconstr debug timeout ths state i of

            SOME (SOME _) => Played (reconstr, Timer.checkRealTimer timer)

          | _ => play timed_out reconstrs

        end

        handle TimeLimit.TimeOut => play (reconstr :: timed_out) reconstrs

  in

    if timeout = Time.zeroTime then

      Trust_Playable (get_preferred reconstrs, NONE)

    else

      play [] reconstrs

  end

(* generic TPTP-based ATPs *)

(* Too general means, positive equality literal with a variable X as one

   operand, when X does not occur properly in the other operand. This rules out

   clearly inconsistent facts such as X = a | X = b, though it by no means

   guarantees soundness. *)

(* Unwanted equalities are those between a (bound or schematic) variable that

   does not properly occur in the second operand. *)

val is_exhaustive_finite =

  let

    fun is_bad_equal (Var z) t =

        not (exists_subterm (fn Var z' => z = z' | _ => false) t)

      | is_bad_equal (Bound j) t = not (loose_bvar1 (t, j))

      | is_bad_equal _ _ = false

    fun do_equals t1 t2 = is_bad_equal t1 t2 orelse is_bad_equal t2 t1

    fun do_formula pos t =

      case (pos, t) of

        (_, @{const Trueprop} $ t1) => do_formula pos t1

      | (true, Const (@{const_name all}, _) $ Abs (_, _, t')) =>

        do_formula pos t'

      | (true, Const (@{const_name All}, _) $ Abs (_, _, t')) =>

        do_formula pos t'

      | (false, Const (@{const_name Ex}, _) $ Abs (_, _, t')) =>

        do_formula pos t'

      | (_, @{const "==>"} $ t1 $ t2) =>

        do_formula (not pos) t1 andalso

        (t2 = @{prop False} orelse do_formula pos t2)

      | (_, @{const HOL.implies} $ t1 $ t2) =>

        do_formula (not pos) t1 andalso

        (t2 = @{const False} orelse do_formula pos t2)

      | (_, @{const Not} $ t1) => do_formula (not pos) t1

      | (true, @{const HOL.disj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]

      | (false, @{const HOL.conj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]

      | (true, Const (@{const_name HOL.eq}, _) $ t1 $ t2) => do_equals t1 t2

      | (true, Const (@{const_name "=="}, _) $ t1 $ t2) => do_equals t1 t2

      | _ => false

  in do_formula true end

fun has_bound_or_var_of_type pred =

  exists_subterm (fn Var (_, T as Type _) => pred T

                   | Abs (_, T as Type _, _) => pred T

                   | _ => false)

(* Facts are forbidden to contain variables of these types. The typical reason

   is that they lead to unsoundness. Note that "unit" satisfies numerous

   equations like "?x = ()". The resulting clauses will have no type constraint,

   yielding false proofs. Even "bool" leads to many unsound proofs, though only

   for higher-order problems. *)

(* Facts containing variables of type "unit" or "bool" or of the form

   "ALL x. x = A | x = B | x = C" are likely to lead to unsound proofs if types

   are omitted. *)

fun is_dangerous_prop ctxt =

  transform_elim_prop

  #> (has_bound_or_var_of_type (is_type_surely_finite ctxt) orf

      is_exhaustive_finite)

(* Important messages are important but not so important that users want to see

   them each time. *)

val atp_important_message_keep_quotient = 25

fun choose_type_enc soundness best_type_enc format =

  the_default best_type_enc

  #> type_enc_from_string soundness

  #> adjust_type_enc format

val metis_minimize_max_time = seconds 2.0

fun choose_minimize_command params minimize_command name preplay =

  let

    val (name, override_params) =

      case preplay of

        Played (reconstr, time) =>

        if Time.<= (time, metis_minimize_max_time) then

          extract_reconstructor params reconstr

        else

          (name, [])

      | _ => (name, [])

  in minimize_command override_params name end

fun repair_monomorph_context max_iters best_max_iters max_new_instances

                             best_max_new_instances =

  Config.put Monomorph.max_rounds (max_iters |> the_default best_max_iters)

  #> Config.put Monomorph.max_new_instances

         (max_new_instances |> the_default best_max_new_instances)

  #> Config.put Monomorph.keep_partial_instances false

fun suffix_for_mode Auto_Try = "_auto_try"

  | suffix_for_mode Try = "_try"

  | suffix_for_mode Normal = ""

  | suffix_for_mode Auto_Minimize = "_auto_min"

  | suffix_for_mode Minimize = "_min"

(* Give the ATPs some slack before interrupting them the hard way. "z3_tptp" on

   Linux appears to be the only ATP that does not honor its time limit. *)

val atp_timeout_slack = seconds 1.0

fun run_atp mode name

        ({exec, required_vars, arguments, proof_delims, known_failures,

          prem_role, best_slices, best_max_mono_iters,

          best_max_new_mono_instances, ...} : atp_config)

        (params as {debug, verbose, overlord, type_enc, strict, lam_trans,

                    uncurried_aliases, max_relevant, max_mono_iters,

                    max_new_mono_instances, isar_proof, isar_shrink_factor,

                    slice, timeout, preplay_timeout, ...})

        minimize_command

        ({state, goal, subgoal, subgoal_count, facts, ...} : prover_problem) =

  let

    val thy = Proof.theory_of state

    val ctxt = Proof.context_of state

    val atp_mode =

      if Config.get ctxt completish then Sledgehammer_Completish

      else Sledgehammer

    val (_, hyp_ts, concl_t) = strip_subgoal ctxt goal subgoal

    val (dest_dir, problem_prefix) =

      if overlord then overlord_file_location_for_prover name

      else (Config.get ctxt dest_dir, Config.get ctxt problem_prefix)

    val problem_file_name =

      Path.basic (problem_prefix ^ (if overlord then "" else serial_string ()) ^

                  suffix_for_mode mode ^ "_" ^ string_of_int subgoal)

    val problem_path_name =

      if dest_dir = "" then

        File.tmp_path problem_file_name

      else if File.exists (Path.explode dest_dir) then

        Path.append (Path.explode dest_dir) problem_file_name

      else

        error ("No such directory: " ^ quote dest_dir ^ ".")

    val command =

      case find_first (fn var => getenv var <> "") (fst exec) of

        SOME var => Path.explode (getenv var ^ "/" ^ snd exec)

      | NONE => error ("The environment variable " ^ quote (hd (fst exec)) ^

                       " is not set.")

    fun split_time s =

      let

        val split = String.tokens (fn c => str c = "\n")

        val (output, t) =

          s |> split |> (try split_last #> the_default ([], "0"))

            |>> cat_lines

        fun as_num f = f >> (fst o read_int)

        val num = as_num (Scan.many1 Symbol.is_ascii_digit)

        val digit = Scan.one Symbol.is_ascii_digit

        val num3 = as_num (digit ::: digit ::: (digit >> single))

        val time = num --| Scan.$$ "." -- num3 >> (fn (a, b) => a * 1000 + b)

        val as_time =

          raw_explode #> Scan.read Symbol.stopper time #> the_default 0

      in (output, as_time t |> Time.fromMilliseconds) end

    fun run_on prob_file =

      case find_first (forall (fn var => getenv var = ""))

                      (fst exec :: required_vars) of

        SOME home_vars =>

        error ("The environment variable " ^ quote (hd home_vars) ^

               " is not set.")

      | NONE =>

        if File.exists command then

          let

            (* If slicing is disabled, we expand the last slice to fill the

               entire time available. *)

            val actual_slices = get_slices slice (best_slices ctxt)

            val num_actual_slices = length actual_slices

            fun monomorphize_facts facts =

              let

                val ctxt =

                  ctxt

                  |> repair_monomorph_context max_mono_iters best_max_mono_iters

                          max_new_mono_instances best_max_new_mono_instances

                (* pseudo-theorem involving the same constants as the subgoal *)

                val subgoal_th =

                  Logic.list_implies (hyp_ts, concl_t)

                  |> Skip_Proof.make_thm thy

                val rths =

                  facts |> chop (length facts div 4)

                        |>> map (pair 1 o snd)

                        ||> map (pair 2 o snd)

                        |> op @

                        |> cons (0, subgoal_th)

              in

                Monomorph.monomorph atp_schematic_consts_of rths ctxt

                |> fst |> tl

                |> curry ListPair.zip (map fst facts)

                |> maps (fn (name, rths) =>

                            map (pair name o zero_var_indexes o snd) rths)

              end

            fun run_slice time_left (cache_key, cache_value)

                    (slice, (time_frac, (complete,

                        (key as (best_max_relevant, format, best_type_enc,

                                 best_lam_trans, best_uncurried_aliases),

                                 extra)))) =

              let

                val num_facts =

                  length facts |> is_none max_relevant

                                  ? Integer.min best_max_relevant

                val soundness = if strict then Strict else Non_Strict

                val type_enc =

                  type_enc |> choose_type_enc soundness best_type_enc format

                val sound = is_type_enc_sound type_enc

                val real_ms = Real.fromInt o Time.toMilliseconds

                val slice_timeout =

                  ((real_ms time_left

                    |> (if slice < num_actual_slices - 1 then

                          curry Real.min (time_frac * real_ms timeout)

                        else

                          I))

                   * 0.001) |> seconds

                val generous_slice_timeout =

                  Time.+ (slice_timeout, atp_timeout_slack)

                val _ =

                  if debug then

                    quote name ^ " slice #" ^ string_of_int (slice + 1) ^

                    " with " ^ string_of_int num_facts ^ " fact" ^

                    plural_s num_facts ^ " for " ^

                    string_from_time slice_timeout ^ "..."

                    |> Output.urgent_message

                  else

                    ()

                val readable_names = not (Config.get ctxt atp_full_names)

                val lam_trans =

                  case lam_trans of

                    SOME s => s

                  | NONE => best_lam_trans

                val uncurried_aliases =

                  case uncurried_aliases of

                    SOME b => b

                  | NONE => best_uncurried_aliases

                val value as (atp_problem, _, fact_names, _, _) =

                  if cache_key = SOME key then

                    cache_value

                  else

                    facts

                    |> map untranslated_fact

                    |> not sound

                       ? filter_out (is_dangerous_prop ctxt o prop_of o snd)

                    |> take num_facts

                    |> not (is_type_enc_polymorphic type_enc)

                       ? monomorphize_facts

                    |> map (apsnd prop_of)

                    |> prepare_atp_problem ctxt format prem_role type_enc

                                           atp_mode lam_trans uncurried_aliases

                                           readable_names true hyp_ts concl_t

                fun sel_weights () = atp_problem_selection_weights atp_problem

                fun ord_info () = atp_problem_term_order_info atp_problem

                val ord = effective_term_order ctxt name

                val full_proof = debug orelse isar_proof

                val args = arguments ctxt full_proof extra slice_timeout

                                     (ord, ord_info, sel_weights)

                val command =

                  File.shell_path command ^ " " ^ args ^ " " ^

                  File.shell_path prob_file

                  |> enclose "TIMEFORMAT='%3R'; { time " " ; } 2>&1"

                val _ =

                  atp_problem

                  |> lines_for_atp_problem format ord ord_info

                  |> cons ("% " ^ command ^ "\n")

                  |> File.write_list prob_file

                val ((output, run_time), (atp_proof, outcome)) =

                  TimeLimit.timeLimit generous_slice_timeout

                                      Isabelle_System.bash_output command

                  |>> (if overlord then

                         prefix ("% " ^ command ^ "\n% " ^ timestamp () ^ "\n")

                       else

                         I)

                  |> fst |> split_time

                  |> (fn accum as (output, _) =>

                         (accum,

                          extract_tstplike_proof_and_outcome verbose complete

                              proof_delims known_failures output

                          |>> atp_proof_from_tstplike_proof atp_problem

                          handle UNRECOGNIZED_ATP_PROOF () =>

                                 ([], SOME ProofIncomplete)))

                  handle TimeLimit.TimeOut =>

                         (("", slice_timeout), ([], SOME TimedOut))

                val outcome =

                  case outcome of

                    NONE =>

                    (case used_facts_in_unsound_atp_proof ctxt fact_names

                                                          atp_proof

                          |> Option.map (sort string_ord) of

                       SOME facts =>

                       let

                         val failure =

                           UnsoundProof (is_type_enc_sound type_enc, facts)

                       in

                         if debug then

                           (warning (string_for_failure failure); NONE)

                         else

                           SOME failure

                       end

                     | NONE => NONE)

                  | _ => outcome

              in ((SOME key, value), (output, run_time, atp_proof, outcome)) end

            val timer = Timer.startRealTimer ()

            fun maybe_run_slice slice

                    (result as (cache, (_, run_time0, _, SOME _))) =

                let

                  val time_left = Time.- (timeout, Timer.checkRealTimer timer)

                in

                  if Time.<= (time_left, Time.zeroTime) then

                    result

                  else

                    run_slice time_left cache slice

                    |> (fn (cache, (output, run_time, atp_proof, outcome)) =>

                           (cache, (output, Time.+ (run_time0, run_time),

                                    atp_proof, outcome)))

                end

              | maybe_run_slice _ result = result

          in

            ((NONE, ([], Symtab.empty, Vector.fromList [], [], Symtab.empty)),

             ("", Time.zeroTime, [], SOME InternalError))

            |> fold maybe_run_slice actual_slices

          end

        else

          error ("Bad executable: " ^ Path.print command)

    (* If the problem file has not been exported, remove it; otherwise, export

       the proof file too. *)

    fun cleanup prob_file =

      if dest_dir = "" then try File.rm prob_file else NONE

    fun export prob_file (_, (output, _, _, _)) =

      if dest_dir = "" then

        ()

      else

        File.write (Path.explode (Path.implode prob_file ^ "_proof")) output

    val ((_, (_, pool, fact_names, _, sym_tab)),

         (output, run_time, atp_proof, outcome)) =

      with_path cleanup export run_on problem_path_name

    val important_message =

      if mode = Normal andalso

         random_range 0 (atp_important_message_keep_quotient - 1) = 0 then

        extract_important_message output

      else

        ""

    val (used_facts, preplay, message, message_tail) =

      case outcome of

        NONE =>

        let

          val used_facts = used_facts_in_atp_proof ctxt fact_names atp_proof

          val needs_full_types = is_typed_helper_used_in_atp_proof atp_proof

          val reconstrs =

            bunch_of_reconstructors needs_full_types

                (lam_trans_from_atp_proof atp_proof

                 o (fn desperate => if desperate then hide_lamsN

                                    else metis_default_lam_trans))

        in

          (used_facts,

           fn () =>

              let

                val used_pairs =

                  facts |> map untranslated_fact |> filter_used_facts used_facts

              in

                play_one_line_proof mode debug verbose preplay_timeout

                    used_pairs state subgoal (hd reconstrs) reconstrs

              end,

           fn preplay =>

              let

                val isar_params =

                  (debug, isar_shrink_factor, pool, fact_names, sym_tab,

                   atp_proof, goal)

                val one_line_params =

                  (preplay, proof_banner mode name, used_facts,

                   choose_minimize_command params minimize_command name preplay,

                   subgoal, subgoal_count)

              in proof_text ctxt isar_proof isar_params one_line_params end,

           (if verbose then

              "\nATP real CPU time: " ^ string_from_time run_time ^ "."

            else

              "") ^

           (if important_message <> "" then

              "\n\nImportant message from Dr. Geoff Sutcliffe:\n" ^

              important_message

            else

              ""))

        end

      | SOME failure =>

        ([], K (Failed_to_Play plain_metis),

         fn _ => string_for_failure failure, "")

  in

    {outcome = outcome, used_facts = used_facts, run_time = run_time,

     preplay = preplay, message = message, message_tail = message_tail}

  end

(* "SMT_Failure.Abnormal_Termination" carries the solver's return code. Until

   these are sorted out properly in the SMT module, we have to interpret these

   ourselves. *)

val remote_smt_failures =

  [(2, NoLibwwwPerl),

   (22, CantConnect)]

val z3_failures =

  [(101, OutOfResources),

   (103, MalformedInput),

   (110, MalformedInput)]

val unix_failures =

  [(139, Crashed)]

val smt_failures = remote_smt_failures @ z3_failures @ unix_failures

fun failure_from_smt_failure (SMT_Failure.Counterexample {is_real_cex, ...}) =

    if is_real_cex then Unprovable else GaveUp

  | failure_from_smt_failure SMT_Failure.Time_Out = TimedOut

  | failure_from_smt_failure (SMT_Failure.Abnormal_Termination code) =

    (case AList.lookup (op =) smt_failures code of

       SOME failure => failure

     | NONE => UnknownError ("Abnormal termination with exit code " ^

                             string_of_int code ^ "."))

  | failure_from_smt_failure SMT_Failure.Out_Of_Memory = OutOfResources

  | failure_from_smt_failure (SMT_Failure.Other_Failure msg) =

    UnknownError msg

(* FUDGE *)

val smt_max_slices =

  Attrib.setup_config_int @{binding sledgehammer_smt_max_slices} (K 8)

val smt_slice_fact_frac =

  Attrib.setup_config_real @{binding sledgehammer_smt_slice_fact_frac} (K 0.5)

val smt_slice_time_frac =

  Attrib.setup_config_real @{binding sledgehammer_smt_slice_time_frac} (K 0.5)

val smt_slice_min_secs =

  Attrib.setup_config_int @{binding sledgehammer_smt_slice_min_secs} (K 5)

fun smt_filter_loop ctxt name

                    ({debug, verbose, overlord, max_mono_iters,

                      max_new_mono_instances, timeout, slice, ...} : params)

                    state i =

  let

    val max_slices = if slice then Config.get ctxt smt_max_slices else 1

    val repair_context =

      select_smt_solver name

      #> Config.put SMT_Config.verbose debug

      #> (if overlord then

            Config.put SMT_Config.debug_files

                       (overlord_file_location_for_prover name

                        |> (fn (path, name) => path ^ "/" ^ name))

          else

            I)

      #> Config.put SMT_Config.infer_triggers (Config.get ctxt smt_triggers)

    val state = state |> Proof.map_context repair_context

    fun do_slice timeout slice outcome0 time_so_far facts =

      let

        val timer = Timer.startRealTimer ()

        val state =

          state |> Proof.map_context

                       (repair_monomorph_context max_mono_iters

                            default_max_mono_iters max_new_mono_instances

                            default_max_new_mono_instances)

        val ms = timeout |> Time.toMilliseconds

        val slice_timeout =

          if slice < max_slices then

            Int.min (ms,

                Int.max (1000 * Config.get ctxt smt_slice_min_secs,

                    Real.ceil (Config.get ctxt smt_slice_time_frac

                               * Real.fromInt ms)))

            |> Time.fromMilliseconds

          else

            timeout

        val num_facts = length facts

        val _ =

          if debug then

            quote name ^ " slice " ^ string_of_int slice ^ " with " ^

            string_of_int num_facts ^ " fact" ^ plural_s num_facts ^ " for " ^

            string_from_time slice_timeout ^ "..."

            |> Output.urgent_message

          else

            ()

        val birth = Timer.checkRealTimer timer

        val _ =

          if debug then Output.urgent_message "Invoking SMT solver..." else ()

        val (outcome, used_facts) =

          SMT_Solver.smt_filter_preprocess state facts i

          |> SMT_Solver.smt_filter_apply slice_timeout

          |> (fn {outcome, used_facts} => (outcome, used_facts))

          handle exn => if Exn.is_interrupt exn then

                          reraise exn

                        else

                          (ML_Compiler.exn_message exn

                           |> SMT_Failure.Other_Failure |> SOME, [])

        val death = Timer.checkRealTimer timer

        val outcome0 = if is_none outcome0 then SOME outcome else outcome0

        val time_so_far = Time.+ (time_so_far, Time.- (death, birth))

        val too_many_facts_perhaps =

          case outcome of

            NONE => false

          | SOME (SMT_Failure.Counterexample _) => false

          | SOME SMT_Failure.Time_Out => slice_timeout <> timeout

          | SOME (SMT_Failure.Abnormal_Termination _) => true (* kind of *)

          | SOME SMT_Failure.Out_Of_Memory => true

          | SOME (SMT_Failure.Other_Failure _) => true

        val timeout = Time.- (timeout, Timer.checkRealTimer timer)

      in

        if too_many_facts_perhaps andalso slice < max_slices andalso

           num_facts > 0 andalso Time.> (timeout, Time.zeroTime) then

          let

            val new_num_facts =

              Real.ceil (Config.get ctxt smt_slice_fact_frac

                         * Real.fromInt num_facts)

            val _ =

              if verbose andalso is_some outcome then

                quote name ^ " invoked with " ^ string_of_int num_facts ^

                " fact" ^ plural_s num_facts ^ ": " ^

                string_for_failure (failure_from_smt_failure (the outcome)) ^

                " Retrying with " ^ string_of_int new_num_facts ^ " fact" ^

                plural_s new_num_facts ^ "..."

                |> Output.urgent_message

              else

                ()

          in

            facts |> take new_num_facts

                  |> do_slice timeout (slice + 1) outcome0 time_so_far

          end

        else

          {outcome = if is_none outcome then NONE else the outcome0,