(*  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 atp_failure = ATP_Proof.atp_failure

  type stature = ATP_Problem_Generate.stature

  type type_enc = ATP_Problem_Generate.type_enc

  type fact = Sledgehammer_Fact.fact

  type reconstructor = Sledgehammer_Reconstructor.reconstructor

  type play = Sledgehammer_Reconstructor.play

  type minimize_command = Sledgehammer_Reconstructor.minimize_command

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

  type params =

    {debug : bool,

     verbose : bool,

     overlord : bool,

     spy : bool,

     blocking : bool,

     provers : string list,

     type_enc : string option,

     strict : bool,

     lam_trans : string option,

     uncurried_aliases : bool option,

     learn : bool,

     fact_filter : string option,

     max_facts : int option,

     fact_thresholds : real * real,

     max_mono_iters : int option,

     max_new_mono_instances : int option,

     isar_proofs : bool option,

     isar_compress : real,

     isar_try0 : bool,

     slice : bool,

     minimize : bool option,

     timeout : Time.time option,

     preplay_timeout : Time.time option,

     expect : string}

  type relevance_fudge =

    {local_const_multiplier : real,

     worse_irrel_freq : real,

     higher_order_irrel_weight : real,

     abs_rel_weight : real,

     abs_irrel_weight : real,

     theory_const_rel_weight : real,

     theory_const_irrel_weight : real,

     chained_const_irrel_weight : real,

     intro_bonus : real,

     elim_bonus : real,

     simp_bonus : real,

     local_bonus : real,

     assum_bonus : real,

     chained_bonus : real,

     max_imperfect : real,

     max_imperfect_exp : real,

     threshold_divisor : real,

     ridiculous_threshold : real}

  type prover_problem =

    {state : Proof.state,

     goal : thm,

     subgoal : int,

     subgoal_count : int,

     factss : (string * fact list) list}

  type prover_result =

    {outcome : atp_failure option,

     used_facts : (string * stature) list,

     used_from : fact list,

     run_time : Time.time,

     preplay : play Lazy.lazy,

     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_builtin_facts : bool Config.T

  val smt_builtin_trans : 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 SledgehammerN : 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 remotify_prover_if_supported_and_not_already_remote :

    Proof.context -> string -> string option

  val remotify_prover_if_not_installed :

    Proof.context -> string -> string option

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

  val is_unit_equality : term -> bool

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

  val is_built_in_const_of_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_of_prover : Proof.context -> string -> relevance_fudge

  val weight_smt_fact :

    Proof.context -> int -> ((string * stature) * thm) * 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 is_fact_chained : (('a * stature) * 'b) -> bool

  val filter_used_facts :

    bool -> (''a * stature) list -> ((''a * stature) * 'b) list ->

    ((''a * stature) * 'b) list

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

  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_Fact

open Sledgehammer_Reconstructor

open Sledgehammer_Print

open Sledgehammer_Reconstruct

(** The Sledgehammer **)

(* 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_builtin_facts =

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

val smt_builtin_trans =

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

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)

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

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

   "Async_Manager". *)

val SledgehammerN = "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_of_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_of_format (curry (op =) CNF_UEQ)

val is_ho_atp = is_atp_of_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 remotify_prover_if_supported_and_not_already_remote ctxt name =

  if String.isPrefix remote_prefix name then

    SOME name

  else

    let val remote_name = remote_prefix ^ name in

      if is_prover_supported ctxt remote_name then SOME remote_name else NONE

    end

fun remotify_prover_if_not_installed ctxt name =

  if is_prover_supported ctxt name andalso is_prover_installed ctxt name then

    SOME name

  else

    remotify_prover_if_supported_and_not_already_remote ctxt name

fun get_slices slice slices =

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

val reconstructor_default_max_facts = 20

fun slice_max_facts (_, (_, ( ((max_facts, _), _, _, _, _), _))) = max_facts

fun default_max_facts_of_prover ctxt slice name =

  let val thy = Proof_Context.theory_of ctxt in

    if is_reconstructor name then

      reconstructor_default_max_facts

    else if is_atp thy name then

      fold (Integer.max o slice_max_facts)

           (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_of_prover ctxt name =

  if is_unit_equational_atp ctxt name then is_unit_equality else K true

val atp_irrelevant_const_tab =

  Symtab.make (map (rpair ()) atp_irrelevant_consts)

fun is_built_in_const_of_prover ctxt name =

  if is_smt_prover ctxt name andalso Config.get ctxt smt_builtin_facts 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 => (Symtab.defined atp_irrelevant_const_tab 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,

   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,

   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_of_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 SledgehammerN "prover"

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

val messages = Async_Manager.thread_messages SledgehammerN "prover"

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

type params =

  {debug : bool,

   verbose : bool,

   overlord : bool,

   spy : bool,

   blocking : bool,

   provers : string list,

   type_enc : string option,

   strict : bool,

   lam_trans : string option,

   uncurried_aliases : bool option,

   learn : bool,

   fact_filter : string option,

   max_facts : int option,

   fact_thresholds : real * real,

   max_mono_iters : int option,

   max_new_mono_instances : int option,

   isar_proofs : bool option,

   isar_compress : real,

   isar_try0 : bool,

   slice : bool,

   minimize : bool option,

   timeout : Time.time option,

   preplay_timeout : Time.time option,

   expect : string}

type relevance_fudge =

  {local_const_multiplier : real,

   worse_irrel_freq : real,

   higher_order_irrel_weight : real,

   abs_rel_weight : real,

   abs_irrel_weight : real,

   theory_const_rel_weight : real,

   theory_const_irrel_weight : real,

   chained_const_irrel_weight : real,

   intro_bonus : real,

   elim_bonus : real,

   simp_bonus : real,

   local_bonus : real,

   assum_bonus : real,

   chained_bonus : real,

   max_imperfect : real,

   max_imperfect_exp : real,

   threshold_divisor : real,

   ridiculous_threshold : real}

type prover_problem =

  {state : Proof.state,

   goal : thm,

   subgoal : int,

   subgoal_count : int,

   factss : (string * fact list) list}

type prover_result =

  {outcome : atp_failure option,

   used_facts : (string * stature) list,

   used_from : fact list,

   run_time : Time.time,

   preplay : play Lazy.lazy,

   message : play -> string,

   message_tail : string}

type prover =

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

  -> prover_problem -> prover_result

(* 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 overlord_file_location_of_prover prover =

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

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 =

  if needs_full_types then

    [Metis (full_type_enc, lam_trans false),

     Metis (really_full_type_enc, lam_trans false),

     Metis (full_type_enc, lam_trans true),

     Metis (really_full_type_enc, lam_trans true),

     SMT]

  else

    [Metis (partial_type_enc, lam_trans false),

     Metis (full_type_enc, lam_trans false),

     Metis (no_typesN, lam_trans true),

     Metis (really_full_type_enc, lam_trans true),

     SMT]

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 time_limit timeout (try (Seq.pull o full_tac)) goal end

fun tac_of_reconstructor (Metis (type_enc, lam_trans)) =

    metis_tac [type_enc] lam_trans

  | tac_of_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_of_reconstructor reconstr ctxt ths))

  |> timed_apply timeout

fun is_fact_chained ((_, (sc, _)), _) = sc = Chained

fun filter_used_facts keep_chained used =

  filter ((member (op =) used o fst) orf

          (if keep_chained then is_fact_chained else K false))

fun play_one_line_proof mode debug verbose timeout pairs state i preferred

                        reconstrs =

  let

    fun get_preferred reconstrs =

      if member (op =) reconstrs preferred then preferred

      else List.last reconstrs

  in

    if timeout = SOME Time.zeroTime then

      Trust_Playable (get_preferred reconstrs, NONE)

    else

      let

        val _ =

          if mode = Minimize then Output.urgent_message "Preplaying proof..."

          else ()

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

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

          | play timed_outs [] =

            Trust_Playable (get_preferred timed_outs, timeout)

          | play timed_out (reconstr :: reconstrs) =

            let

              val _ =

                if verbose then

                  "Trying \"" ^ string_of_reconstructor reconstr ^ "\"" ^

                  (case timeout of

                     SOME timeout => " for " ^ string_of_time timeout

                   | NONE => "") ^ "..."

                  |> 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 play [] reconstrs end

  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. *)

fun get_facts_of_filter _ [(_, facts)] = facts

  | get_facts_of_filter fact_filter factss =

    case AList.lookup (op =) factss fact_filter of

      SOME facts => facts

    | NONE => snd (hd factss)

(* 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_of_string soundness

  #> adjust_type_enc format

fun isar_proof_reconstructor ctxt name =

  let val thy = Proof_Context.theory_of ctxt in

    if is_atp thy name then name

    else remotify_prover_if_not_installed ctxt eN |> the_default name

  end

(* See the analogous logic in the function "maybe_minimize" in

  "sledgehammer_minimize.ML". *)

fun choose_minimize_command ctxt (params as {isar_proofs, ...}) minimize_command

                            name preplay =

  let

    val maybe_isar_name =

      name |> isar_proofs = SOME true ? isar_proof_reconstructor ctxt

    val (min_name, override_params) =

      case preplay of

        Played (reconstr, _) =>

        if isar_proofs = SOME true then (maybe_isar_name, [])

        else extract_reconstructor params reconstr

      | _ => (maybe_isar_name, [])

  in minimize_command override_params min_name end

val max_fact_instances = 10 (* FUDGE *)

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.max_thm_instances max_fact_instances

fun suffix_of_mode Auto_Try = "_try"

  | suffix_of_mode Try = "_try"

  | suffix_of_mode Normal = ""

  | suffix_of_mode MaSh = ""

  | suffix_of_mode Auto_Minimize = "_min"

  | suffix_of_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

val mono_max_privileged_facts = 10

(* For low values of "max_facts", this fudge value ensures that most slices are

   invoked with a nontrivial amount of facts. *)

val max_fact_factor_fudge = 5

fun run_atp mode name

        ({exec, 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, fact_filter, max_facts, max_mono_iters,

                    max_new_mono_instances, isar_proofs, isar_compress,

                    isar_try0, slice, timeout, preplay_timeout, ...})

        minimize_command

        ({state, goal, subgoal, subgoal_count, factss, ...} : 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 goal subgoal ctxt

    val (dest_dir, problem_prefix) =

      if overlord then overlord_file_location_of_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_of_mode mode ^ "_" ^ string_of_int subgoal)

    val prob_path =

      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 exec = exec ()

    val command0 =

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

        SOME var =>

        let

          val pref = getenv var ^ "/"

          val paths = map (Path.explode o prefix pref) (snd exec)

        in

          case find_first File.exists paths of

            SOME path => path

          | NONE => error ("Bad executable: " ^ Path.print (hd paths) ^ ".")

        end

      | NONE => error ("The environment variable " ^ quote (List.last (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 () =

      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

        val max_fact_factor =

          case max_facts of

            NONE => 1.0

          | SOME max =>

            Real.fromInt max

            / Real.fromInt (fold (Integer.max o slice_max_facts)

                                 actual_slices 0)

        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 mono_max_privileged_facts

                    |>> map (pair 1 o snd)

                    ||> map (pair 2 o snd)

                    |> op @

                    |> cons (0, subgoal_th)

          in

            Monomorph.monomorph atp_schematic_consts_of ctxt rths

            |> 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,

                     (key as ((best_max_facts, best_fact_filter), format,

                              best_type_enc, best_lam_trans,

                              best_uncurried_aliases),

                      extra))) =

          let

            val effective_fact_filter =

              fact_filter |> the_default best_fact_filter

            val facts = get_facts_of_filter effective_fact_filter factss

            val num_facts =

              Real.ceil (max_fact_factor * Real.fromInt best_max_facts) +

              max_fact_factor_fudge

              |> Integer.min (length facts)

            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 =

              case time_left of

                SOME time_left =>

                ((real_ms time_left

                  |> (if slice < num_actual_slices - 1 then

                        curry Real.min (time_frac * real_ms (the timeout))

                      else

                        I))

                 * 0.001)

                |> seconds |> SOME

              | NONE => NONE

            val generous_slice_timeout =

              if mode = MaSh then NONE

              else Option.map (curry Time.+ atp_timeout_slack) slice_timeout

            val _ =

              if debug then

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

                " with " ^ string_of_int num_facts ^ " fact" ^

                plural_s num_facts ^

                (case slice_timeout of

                   SOME timeout => " for " ^ string_of_time timeout

                 | NONE => "") ^ "..."

                |> 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

                |> 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 = isar_proofs |> the_default (mode = Minimize)

            val args =

              arguments ctxt full_proof extra

                        (slice_timeout |> the_default one_day)

                        (File.shell_path prob_path) (ord, ord_info, sel_weights)

            val command =

              "(exec 2>&1; " ^ File.shell_path command0 ^ " " ^ args ^ " " ^ ")"

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

            val _ =

              atp_problem

              |> lines_of_atp_problem format ord ord_info

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

              |> File.write_list prob_path

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

              time_limit 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 proof_delims

                                                         known_failures output

                      |>> atp_proof_of_tstplike_proof atp_problem

                      handle UNRECOGNIZED_ATP_PROOF () =>

                             ([], SOME ProofIncomplete)))

              handle TimeLimit.TimeOut =>

                     (("", the 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_of_atp_failure failure); NONE)

                     else

                       SOME failure

                   end

                 | NONE => NONE)

              | _ => outcome

          in

            ((SOME key, value), (output, run_time, facts, atp_proof, outcome))

          end

        val timer = Timer.startRealTimer ()

        fun maybe_run_slice slice

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

            let

              val time_left =

                Option.map

                    (fn timeout => Time.- (timeout, Timer.checkRealTimer timer))

                    timeout

            in

              if time_left <> NONE andalso

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

                result

              else

                run_slice time_left cache slice

                |> (fn (cache, (output, run_time, used_from, atp_proof,

                                outcome)) =>

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

                                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

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

       the proof file too. *)

    fun clean_up () =

      if dest_dir = "" then (try File.rm prob_path; ()) else ()

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

      if dest_dir = "" then ()

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

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

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

      with_cleanup clean_up run () |> tap export

    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_of_atp_proof atp_proof

                 o (fn desperate => if desperate then hide_lamsN

                                    else metis_default_lam_trans))

        in

          (used_facts,

           Lazy.lazy (fn () =>

             let

               val used_pairs =

                 used_from |> filter_used_facts false used_facts

             in

               play_one_line_proof mode debug verbose preplay_timeout

                   used_pairs state subgoal (hd reconstrs) reconstrs

             end),

           fn preplay =>

              let

                val _ =

                  if verbose then

                    Output.urgent_message "Generating proof text..."

                  else

                    ()

                val isar_params =

                  (debug, verbose, preplay_timeout, isar_compress, isar_try0,

                   pool, fact_names, lifted, sym_tab, atp_proof, goal)

                val one_line_params =

                  (preplay, proof_banner mode name, used_facts,

                   choose_minimize_command ctxt params minimize_command name

                                           preplay,

                   subgoal, subgoal_count)

                val num_chained = length (#facts (Proof.goal state))

              in

                proof_text ctxt isar_proofs isar_params

                           num_chained one_line_params

              end,

           (if verbose then

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

            else

              "") ^

           (if important_message <> "" then

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

              important_message

            else

              ""))

        end

      | SOME failure =>

        ([], Lazy.value (Failed_to_Play plain_metis),

         fn _ => string_of_atp_failure failure, "")

  in

    {outcome = outcome, used_facts = used_facts, used_from = used_from,

     run_time = run_time, preplay = preplay, message = message,

     message_tail = message_tail}

  end

fun rotate_one (x :: xs) = xs @ [x]

(* "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),