(*  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

   datatype mode = Auto_Try | Try | Normal | MaSh | 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,

      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_proof : bool,

      isar_shrink_factor : int,

      slice : bool,

      minimize : bool option,

      timeout : Time.time,

      preplay_timeout : Time.time,

      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,

      skolem_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}

   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 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 default_max_facts_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

 (** The Sledgehammer **)

 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_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_facts = 20

 fun default_max_facts_for_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 #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 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,

    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_proof : bool,

    isar_shrink_factor : int,

    slice : bool,

    minimize : bool option,

    timeout : Time.time,

    preplay_timeout : Time.time,

    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,

    skolem_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}

 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 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 MaSh = "_mash"

   | 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

 val mono_max_privileged_facts = 10

 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, max_facts, 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 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 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 (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 () =

       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 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 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_facts, format, best_type_enc,

                               best_lam_trans, best_uncurried_aliases),

                       extra)))) =

           let

             val num_facts =

               length facts |> is_none max_facts ? Integer.min best_max_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 =

               ((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 =

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

               File.shell_path prob_path ^ ")"

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

             val _ =

               atp_problem

               |> lines_for_atp_problem format ord ord_info

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

               |> File.write_list prob_path

             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

     (* 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, _, sym_tab)),

          (output, run_time, 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_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,

            used_facts = used_facts, run_time = time_so_far}

       end

   in do_slice timeout 1 NONE Time.zeroTime end

 fun run_smt_solver mode name (params as {debug, verbose, preplay_timeout, ...})

         minimize_command

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

   let

     val ctxt = Proof.context_of state

     val num_facts = length facts

     val facts = facts ~~ (0 upto num_facts - 1)

                 |> map (smt_weighted_fact ctxt num_facts)

     val {outcome, used_facts = used_pairs, run_time} =

       smt_filter_loop ctxt name params state subgoal facts

     val used_facts = used_pairs |> map fst

     val outcome = outcome |> Option.map failure_from_smt_failure

     val (preplay, message, message_tail) =

       case outcome of

         NONE =>

         (fn () =>

             play_one_line_proof mode debug verbose preplay_timeout used_pairs

                 state subgoal SMT

                 (bunch_of_reconstructors false

                      (fn plain =>

                          if plain then metis_default_lam_trans else liftingN)),

          fn preplay =>

             let

               val one_line_params =

                 (preplay, proof_banner mode name, used_facts,

                  choose_minimize_command params minimize_command name preplay,

                  subgoal, subgoal_count)

             in one_line_proof_text one_line_params end,

          if verbose then

            "\nSMT solver real CPU time: " ^ string_from_time run_time ^ "."

          else

            "")

       | 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

 fun run_reconstructor mode name

         (params as {debug, verbose, timeout, type_enc, lam_trans, ...})

         minimize_command

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

   let

     val reconstr =

       if name = metisN then

         Metis (type_enc |> the_default (hd partial_type_encs),

                lam_trans |> the_default metis_default_lam_trans)

       else if name = smtN then

         SMT

       else

         raise Fail ("unknown reconstructor: " ^ quote name)

     val used_pairs = facts |> map untranslated_fact

     val used_facts = used_pairs |> map fst

   in

     case play_one_line_proof (if mode = Minimize then Normal else mode) debug

                              verbose timeout used_pairs state subgoal reconstr

                              [reconstr] of

       play as Played (_, time) =>

       {outcome = NONE, used_facts = used_facts, run_time = time,

        preplay = K play,

        message =

          fn play =>

             let

               val (_, override_params) = extract_reconstructor params reconstr

               val one_line_params =

                 (play, proof_banner mode name, used_facts,

                  minimize_command override_params name, subgoal,

                  subgoal_count)

             in one_line_proof_text one_line_params end,

        message_tail = ""}

     | play =>

       let

         val failure = case play of Failed_to_Play _ => GaveUp | _ => TimedOut

       in

         {outcome = SOME failure, used_facts = [], run_time = Time.zeroTime,

          preplay = K play, message = fn _ => string_for_failure failure,

          message_tail = ""}

       end

   end

 fun get_prover ctxt mode name =

   let val thy = Proof_Context.theory_of ctxt in

     if is_reconstructor name then run_reconstructor mode name

     else if is_atp thy name then run_atp mode name (get_atp thy name ())

     else if is_smt_prover ctxt name then run_smt_solver mode name

     else error ("No such prover: " ^ name ^ ".")

   end

 end;