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

    Author:     Jasmin Blanchette, TU Muenchen

Sledgehammer's machine-learning-based relevance filter (MaSh).

*)

signature SLEDGEHAMMER_FILTER_MASH =

sig

  type status = ATP_Problem_Generate.status

  type stature = ATP_Problem_Generate.stature

  type fact = Sledgehammer_Fact.fact

  type fact_override = Sledgehammer_Fact.fact_override

  type params = Sledgehammer_Provers.params

  type relevance_fudge = Sledgehammer_Provers.relevance_fudge

  type prover_result = Sledgehammer_Provers.prover_result

  val trace : bool Config.T

  val MaShN : string

  val meshN : string

  val iterN : string

  val mashN : string

  val fact_filters : string list

  val escape_meta : string -> string

  val escape_metas : string list -> string

  val unescape_meta : string -> string

  val unescape_metas : string -> string list

  val extract_query : string -> string * string list

  val suggested_facts : string list -> ('a * thm) list -> ('a * thm) list

  val mesh_facts :

    int -> (('a * thm) list * ('a * thm) list) list -> ('a * thm) list

  val is_likely_tautology : Proof.context -> string -> thm -> bool

  val is_too_meta : thm -> bool

  val theory_ord : theory * theory -> order

  val thm_ord : thm * thm -> order

  val features_of :

    Proof.context -> string -> theory -> status -> term list -> string list

  val isabelle_dependencies_of : unit Symtab.table -> thm -> string list

  val goal_of_thm : theory -> thm -> thm

  val run_prover_for_mash :

    Proof.context -> params -> string -> fact list -> thm -> prover_result

  val mash_RESET : Proof.context -> unit

  val mash_INIT :

    Proof.context -> bool

    -> (string * string list * string list * string list) list -> unit

  val mash_ADD :

    Proof.context -> bool

    -> (string * string list * string list * string list) list -> unit

  val mash_QUERY :

    Proof.context -> bool -> int -> string list * string list -> string list

  val mash_reset : Proof.context -> unit

  val mash_could_suggest_facts : unit -> bool

  val mash_can_suggest_facts : Proof.context -> bool

  val mash_suggest_facts :

    Proof.context -> params -> string -> int -> term list -> term

    -> ('a * thm) list -> ('a * thm) list * ('a * thm) list

  val mash_learn_thy :

    Proof.context -> params -> theory -> Time.time -> fact list -> string

  val mash_learn_proof :

    Proof.context -> params -> term -> ('a * thm) list -> thm list -> unit

  val relevant_facts :

    Proof.context -> params -> string -> int -> fact_override -> term list

    -> term -> fact list -> fact list

  val kill_learners : unit -> unit

  val running_learners : unit -> unit

end;

structure Sledgehammer_Filter_MaSh : SLEDGEHAMMER_FILTER_MASH =

struct

open ATP_Util

open ATP_Problem_Generate

open Sledgehammer_Util

open Sledgehammer_Fact

open Sledgehammer_Filter_Iter

open Sledgehammer_Provers

open Sledgehammer_Minimize

val trace =

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

fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()

val MaShN = "MaSh"

val meshN = "mesh"

val iterN = "iter"

val mashN = "mash"

val fact_filters = [meshN, iterN, mashN]

fun mash_home () = getenv "MASH_HOME"

fun mash_state_dir () =

  getenv "ISABELLE_HOME_USER" ^ "/mash"

  |> tap (Isabelle_System.mkdir o Path.explode)

fun mash_state_path () = mash_state_dir () ^ "/state" |> Path.explode

(*** Isabelle helpers ***)

fun meta_char c =

  if Char.isAlphaNum c orelse c = #"_" orelse c = #"." orelse c = #"(" orelse

     c = #")" orelse c = #"," then

    String.str c

  else

    (* fixed width, in case more digits follow *)

    "\\" ^ stringN_of_int 3 (Char.ord c)

fun unmeta_chars accum [] = String.implode (rev accum)

  | unmeta_chars accum (#"\\" :: d1 :: d2 :: d3 :: cs) =

    (case Int.fromString (String.implode [d1, d2, d3]) of

       SOME n => unmeta_chars (Char.chr n :: accum) cs

     | NONE => "" (* error *))

  | unmeta_chars _ (#"\\" :: _) = "" (* error *)

  | unmeta_chars accum (c :: cs) = unmeta_chars (c :: accum) cs

val escape_meta = String.translate meta_char

val escape_metas = map escape_meta #> space_implode " "

val unescape_meta = String.explode #> unmeta_chars []

val unescape_metas =

  space_explode " " #> filter_out (curry (op =) "") #> map unescape_meta

fun extract_query line =

  case space_explode ":" line of

    [goal_name, suggs] => (unescape_meta goal_name, unescape_metas suggs)

  | _ => ("", [])

fun find_suggested facts sugg =

  find_first (fn (_, th) => Thm.get_name_hint th = sugg) facts

fun suggested_facts suggs facts = map_filter (find_suggested facts) suggs

fun sum_avg _ [] = 1000000000 (* big number *)

  | sum_avg n xs = fold (Integer.add o Integer.mult n) xs 0 div (length xs)

fun mesh_facts max_facts [(selected, unknown)] =

    take max_facts selected @ take (max_facts - length selected) unknown

  | mesh_facts max_facts mess =

    let

      val mess = mess |> map (apfst (`length))

      val n = length mess

      val fact_eq = Thm.eq_thm o pairself snd

      fun score_in fact ((sel_len, sels), unks) =

        case find_index (curry fact_eq fact) sels of

          ~1 => (case find_index (curry fact_eq fact) unks of

                   ~1 => SOME sel_len

                 | _ => NONE)

        | j => SOME j

      fun score_of fact = mess |> map_filter (score_in fact) |> sum_avg n

      val facts = fold (union fact_eq o take max_facts o snd o fst) mess []

    in

      facts |> map (`score_of) |> sort (int_ord o pairself fst) |> map snd

            |> take max_facts

    end

val thy_feature_prefix = "y_"

val thy_feature_name_of = prefix thy_feature_prefix

val const_name_of = prefix const_prefix

val type_name_of = prefix type_const_prefix

val class_name_of = prefix class_prefix

local

fun has_bool @{typ bool} = true

  | has_bool (Type (_, Ts)) = exists has_bool Ts

  | has_bool _ = false

fun has_fun (Type (@{type_name fun}, _)) = true

  | has_fun (Type (_, Ts)) = exists has_fun Ts

  | has_fun _ = false

val is_conn = member (op =)

  [@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},

   @{const_name HOL.implies}, @{const_name Not},

   @{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex},

   @{const_name HOL.eq}]

val has_bool_arg_const =

  exists_Const (fn (c, T) =>

                   not (is_conn c) andalso exists has_bool (binder_types T))

fun higher_inst_const thy (s, T) =

  case binder_types T of

    [] => false

  | Ts => length (binder_types (Sign.the_const_type thy s)) <> length Ts

  handle TYPE _ => false

val binders = [@{const_name All}, @{const_name Ex}]

in

fun is_fo_term thy t =

  let

    val t =

      t |> Envir.beta_eta_contract

        |> transform_elim_prop

        |> Object_Logic.atomize_term thy

  in

    Term.is_first_order binders t andalso

    not (exists_subterm (fn Var (_, T) => has_bool T orelse has_fun T

                          | _ => false) t orelse

         has_bool_arg_const t orelse exists_Const (higher_inst_const thy) t)

  end

end

fun interesting_terms_types_and_classes ctxt prover term_max_depth

                                        type_max_depth ts =

  let

    val bad_types = [@{type_name prop}, @{type_name bool}, @{type_name fun}]

    fun is_bad_const (x as (s, _)) args =

      member (op =) atp_logical_consts s orelse

      fst (is_built_in_const_for_prover ctxt prover x args)

    fun add_classes @{sort type} = I

      | add_classes S = union (op =) (map class_name_of S)

    fun do_add_type (Type (s, Ts)) =

        (not (member (op =) bad_types s) ? insert (op =) (type_name_of s))

        #> fold do_add_type Ts

      | do_add_type (TFree (_, S)) = add_classes S

      | do_add_type (TVar (_, S)) = add_classes S

    fun add_type T = type_max_depth >= 0 ? do_add_type T

    fun mk_app s args =

      if member (op <>) args "" then s ^ "(" ^ space_implode "," args ^ ")"

      else s

    fun patternify ~1 _ = ""

      | patternify depth t =

        case strip_comb t of

          (Const (s, _), args) =>

          mk_app (const_name_of s) (map (patternify (depth - 1)) args)

        | _ => ""

    fun add_term_patterns ~1 _ = I

      | add_term_patterns depth t =

        insert (op =) (patternify depth t)

        #> add_term_patterns (depth - 1) t

    val add_term = add_term_patterns term_max_depth

    fun add_patterns t =

      let val (head, args) = strip_comb t in

        (case head of

           Const (x as (_, T)) =>

           not (is_bad_const x args) ? (add_term t #> add_type T)

         | Free (_, T) => add_type T

         | Var (_, T) => add_type T

         | Abs (_, T, body) => add_type T #> add_patterns body

         | _ => I)

        #> fold add_patterns args

      end

  in [] |> fold add_patterns ts |> sort string_ord end

fun is_likely_tautology ctxt prover th =

  null (interesting_terms_types_and_classes ctxt prover 0 ~1 [prop_of th])

  andalso not (Thm.eq_thm_prop (@{thm ext}, th))

(* ### FIXME: optimize *)

fun is_too_meta th =

  fastype_of (Object_Logic.atomize_term (theory_of_thm th) (prop_of th))

  <> @{typ bool}

fun theory_ord p =

  if Theory.eq_thy p then

    EQUAL

  else if Theory.subthy p then

    LESS

  else if Theory.subthy (swap p) then

    GREATER

  else case int_ord (pairself (length o Theory.ancestors_of) p) of

    EQUAL => string_ord (pairself Context.theory_name p)

  | order => order

val thm_ord = theory_ord o pairself theory_of_thm

fun is_exists (s, _) = (s = @{const_name Ex} orelse s = @{const_name Ex1})

val term_max_depth = 1

val type_max_depth = 1

(* TODO: Generate type classes for types? *)

fun features_of ctxt prover thy status ts =

  thy_feature_name_of (Context.theory_name thy) ::

  interesting_terms_types_and_classes ctxt prover term_max_depth type_max_depth

                                      ts

  |> exists (not o is_lambda_free) ts ? cons "lambdas"

  |> exists (exists_Const is_exists) ts ? cons "skolems"

  |> exists (not o is_fo_term thy) ts ? cons "ho"

  |> (case status of

        General => I

      | Induction => cons "induction"

      | Intro => cons "intro"

      | Inductive => cons "inductive"

      | Elim => cons "elim"

      | Simp => cons "simp"

      | Def => cons "def")

fun isabelle_dependencies_of all_facts =

  thms_in_proof (SOME all_facts) #> sort string_ord

val freezeT = Type.legacy_freeze_type

fun freeze (t $ u) = freeze t $ freeze u

  | freeze (Abs (s, T, t)) = Abs (s, freezeT T, freeze t)

  | freeze (Var ((s, _), T)) = Free (s, freezeT T)

  | freeze (Const (s, T)) = Const (s, freezeT T)

  | freeze (Free (s, T)) = Free (s, freezeT T)

  | freeze t = t

fun goal_of_thm thy = prop_of #> freeze #> cterm_of thy #> Goal.init

fun run_prover_for_mash ctxt params prover facts goal =

  let

    val problem =

      {state = Proof.init ctxt, goal = goal, subgoal = 1, subgoal_count = 1,

       facts = facts |> map (apfst (apfst (fn name => name ())))

                     |> map Untranslated_Fact}

    val prover = get_minimizing_prover ctxt Normal (K ()) prover

  in prover params (K (K (K ""))) problem end

(*** Low-level communication with MaSh ***)

fun write_file (xs, f) file =

  let val path = Path.explode file in

    File.write path "";

    xs |> chunk_list 500

       |> List.app (File.append path o space_implode "" o map f)

  end

fun mash_info overlord =

  if overlord then (getenv "ISABELLE_HOME_USER", "")

  else (getenv "ISABELLE_TMP", serial_string ())

fun run_mash ctxt (temp_dir, serial) core =

  let

    val log_file = temp_dir ^ "/mash_log" ^ serial

    val err_file = temp_dir ^ "/mash_err" ^ serial

    val command =

      mash_home () ^ "/mash.py --quiet --outputDir " ^ mash_state_dir () ^

      " --log " ^ log_file ^ " " ^ core ^ " 2>&1 > " ^ err_file

  in

    trace_msg ctxt (fn () => "Running " ^ command);

    write_file ([], K "") log_file;

    write_file ([], K "") err_file;

    Isabelle_System.bash command; ()

  end

fun run_mash_init ctxt overlord write_access write_feats write_deps =

  let

    val info as (temp_dir, serial) = mash_info overlord

    val in_dir = temp_dir ^ "/mash_init" ^ serial

                 |> tap (Isabelle_System.mkdir o Path.explode)

  in

    write_file write_access (in_dir ^ "/mash_accessibility");

    write_file write_feats (in_dir ^ "/mash_features");

    write_file write_deps (in_dir ^ "/mash_dependencies");

    run_mash ctxt info ("--init --inputDir " ^ in_dir)

  end

fun run_mash_commands ctxt overlord save max_suggs write_cmds read_suggs =

  let

    val info as (temp_dir, serial) = mash_info overlord

    val sugg_file = temp_dir ^ "/mash_suggs" ^ serial

    val cmd_file = temp_dir ^ "/mash_commands" ^ serial

  in

    write_file ([], K "") sugg_file;

    write_file write_cmds cmd_file;

    run_mash ctxt info

             ("--inputFile " ^ cmd_file ^ " --predictions " ^ sugg_file ^

              " --numberOfPredictions " ^ string_of_int max_suggs ^

              (if save then " --saveModel" else ""));

    read_suggs (fn () => File.read_lines (Path.explode sugg_file))

  end

fun str_of_update (name, parents, feats, deps) =

  "! " ^ escape_meta name ^ ": " ^ escape_metas parents ^ "; " ^

  escape_metas feats ^ "; " ^ escape_metas deps ^ "\n"

fun str_of_query (parents, feats) =

  "? " ^ escape_metas parents ^ "; " ^ escape_metas feats

fun init_str_of_update get (upd as (name, _, _, _)) =

  escape_meta name ^ ": " ^ escape_metas (get upd) ^ "\n"

fun mash_RESET ctxt =

  let val path = mash_state_dir () |> Path.explode in

    trace_msg ctxt (K "MaSh RESET");

    File.fold_dir (fn file => fn () =>

                      File.rm (Path.append path (Path.basic file)))

                  path ()

  end

fun mash_INIT ctxt _ [] = mash_RESET ctxt

  | mash_INIT ctxt overlord upds =

    (trace_msg ctxt (fn () => "MaSh INIT " ^

         elide_string 1000 (space_implode " " (map #1 upds)));

     run_mash_init ctxt overlord (upds, init_str_of_update #2)

                   (upds, init_str_of_update #3) (upds, init_str_of_update #4))

fun mash_ADD _ _ [] = ()

  | mash_ADD ctxt overlord upds =

    (trace_msg ctxt (fn () => "MaSh ADD " ^

         elide_string 1000 (space_implode " " (map #1 upds)));

     run_mash_commands ctxt overlord true 0 (upds, str_of_update) (K ()))

fun mash_QUERY ctxt overlord max_suggs (query as (_, feats)) =

  (trace_msg ctxt (fn () => "MaSh QUERY " ^ space_implode " " feats);

   run_mash_commands ctxt overlord false max_suggs

       ([query], str_of_query)

       (fn suggs => snd (extract_query (List.last (suggs ()))))

   handle List.Empty => [])

(*** High-level communication with MaSh ***)

fun try_graph ctxt when def f =

  f ()

  handle Graph.CYCLES (cycle :: _) =>

         (trace_msg ctxt (fn () =>

              "Cycle involving " ^ commas cycle ^ " when " ^ when); def)

       | Graph.UNDEF name =>

         (trace_msg ctxt (fn () =>

              "Unknown fact " ^ quote name ^ " when " ^ when); def)

type mash_state =

  {thys : bool Symtab.table,

   fact_graph : unit Graph.T}

val empty_state = {thys = Symtab.empty, fact_graph = Graph.empty}

local

fun mash_load _ (state as (true, _)) = state

  | mash_load ctxt _ =

    let val path = mash_state_path () in

      (true,

       case try File.read_lines path of

         SOME (comp_thys :: incomp_thys :: fact_lines) =>

         let

           fun add_thy comp thy = Symtab.update (thy, comp)

           fun add_edge_to name parent =

             Graph.default_node (parent, ())

             #> Graph.add_edge (parent, name)

           fun add_fact_line line =

             case extract_query line of

               ("", _) => I (* shouldn't happen *)

             | (name, parents) =>

               Graph.default_node (name, ())

               #> fold (add_edge_to name) parents

           val thys =

             Symtab.empty |> fold (add_thy true) (unescape_metas comp_thys)

                          |> fold (add_thy false) (unescape_metas incomp_thys)

           val fact_graph =

             try_graph ctxt "loading state" Graph.empty (fn () =>

                 Graph.empty |> fold add_fact_line fact_lines)

         in {thys = thys, fact_graph = fact_graph} end

       | _ => empty_state)

    end

fun mash_save ({thys, fact_graph, ...} : mash_state) =

  let

    val path = mash_state_path ()

    val thys = Symtab.dest thys

    val line_for_thys = escape_metas o AList.find (op =) thys

    fun fact_line_for name parents =

      escape_meta name ^ ": " ^ escape_metas parents

    val append_fact = File.append path o suffix "\n" oo fact_line_for

  in

    File.write path (line_for_thys true ^ "\n" ^ line_for_thys false ^ "\n");

    Graph.fold (fn (name, ((), (parents, _))) => fn () =>

                   append_fact name (Graph.Keys.dest parents))

        fact_graph ()

  end

val global_state =

  Synchronized.var "Sledgehammer_Filter_MaSh.global_state" (false, empty_state)

in

fun mash_map ctxt f =

  Synchronized.change global_state (mash_load ctxt ##> (f #> tap mash_save))

fun mash_get ctxt =

  Synchronized.change_result global_state (mash_load ctxt #> `snd)

fun mash_reset ctxt =

  Synchronized.change global_state (fn _ =>

      (mash_RESET ctxt; File.write (mash_state_path ()) "";

       (true, empty_state)))

end

fun mash_could_suggest_facts () = mash_home () <> ""

fun mash_can_suggest_facts ctxt =

  not (Graph.is_empty (#fact_graph (mash_get ctxt)))

fun parents_wrt_facts ctxt facts fact_graph =

  let

    val graph_facts = Symtab.make (map (rpair ()) (Graph.keys fact_graph))

    val facts =

      try_graph ctxt "when computing ancestor facts" [] (fn () =>

          [] |> fold (cons o Thm.get_name_hint o snd) facts

             |> filter (Symtab.defined graph_facts)

             |> Graph.all_preds fact_graph)

    val facts = Symtab.empty |> fold (fn name => Symtab.update (name, ())) facts

  in

    try_graph ctxt "when computing parent facts" [] (fn () =>

        fact_graph |> Graph.restrict (Symtab.defined facts) |> Graph.maximals)

  end

(* Generate more suggestions than requested, because some might be thrown out

   later for various reasons and "meshing" gives better results with some

   slack. *)

fun max_suggs_of max_facts = max_facts + Int.min (200, max_facts)

fun is_fact_in_graph fact_graph (_, th) =

  can (Graph.get_node fact_graph) (Thm.get_name_hint th)

fun mash_suggest_facts ctxt ({overlord, ...} : params) prover max_facts hyp_ts

                       concl_t facts =

  let

    val thy = Proof_Context.theory_of ctxt

    val fact_graph = #fact_graph (mash_get ctxt)

    val parents = parents_wrt_facts ctxt facts fact_graph

    val feats = features_of ctxt prover thy General (concl_t :: hyp_ts)

    val suggs =

      if Graph.is_empty fact_graph then []

      else mash_QUERY ctxt overlord (max_suggs_of max_facts) (parents, feats)

    val selected = facts |> suggested_facts suggs

    val unknown = facts |> filter_out (is_fact_in_graph fact_graph)

  in (selected, unknown) end

fun add_thys_for thy =

  let fun add comp thy = Symtab.update (Context.theory_name thy, comp) in

    add false thy #> fold (add true) (Theory.ancestors_of thy)

  end

fun update_fact_graph ctxt (name, parents, feats, deps) (upds, graph) =

  let

    fun maybe_add_from from (accum as (parents, graph)) =

      try_graph ctxt "updating graph" accum (fn () =>

          (from :: parents, Graph.add_edge_acyclic (from, name) graph))

    val graph = graph |> Graph.default_node (name, ())

    val (parents, graph) = ([], graph) |> fold maybe_add_from parents

    val (deps, graph) = ([], graph) |> fold maybe_add_from deps

  in ((name, parents, feats, deps) :: upds, graph) end

val pass1_learn_timeout_factor = 0.5

(* The timeout is understood in a very slack fashion. *)

fun mash_learn_thy ctxt ({provers, verbose, overlord, ...} : params) thy timeout

                   facts =

  let

    val timer = Timer.startRealTimer ()

    val prover = hd provers

    fun timed_out frac =

      Time.> (Timer.checkRealTimer timer, time_mult frac timeout)

    val {fact_graph, ...} = mash_get ctxt

    val new_facts =

      facts |> filter_out (is_fact_in_graph fact_graph)

            |> sort (thm_ord o pairself snd)

  in

    if null new_facts then

      ""

    else

      let

        val ths = facts |> map snd

        val all_names =

          ths |> filter_out (is_likely_tautology ctxt prover orf is_too_meta)

              |> map (rpair () o Thm.get_name_hint)

              |> Symtab.make

        fun do_fact _ (accum as (_, true)) = accum

          | do_fact ((_, (_, status)), th) ((parents, upds), false) =

            let

              val name = Thm.get_name_hint th

              val feats = features_of ctxt prover thy status [prop_of th]

              val deps = isabelle_dependencies_of all_names th

              val upd = (name, parents, feats, deps)

            in (([name], upd :: upds), timed_out pass1_learn_timeout_factor) end

        val parents = parents_wrt_facts ctxt facts fact_graph

        val ((_, upds), _) =

          ((parents, []), false) |> fold do_fact new_facts |>> apsnd rev

        val n = length upds

        fun trans {thys, fact_graph} =

          let

            val mash_INIT_or_ADD =

              if Graph.is_empty fact_graph then mash_INIT else mash_ADD

            val (upds, fact_graph) =

              ([], fact_graph) |> fold (update_fact_graph ctxt) upds

          in

            (mash_INIT_or_ADD ctxt overlord (rev upds);

             {thys = thys |> add_thys_for thy,

              fact_graph = fact_graph})

          end

      in

        mash_map ctxt trans;

        if verbose then

          "Processed " ^ string_of_int n ^ " proof" ^ plural_s n ^

          (if verbose then

             " in " ^ string_from_time (Timer.checkRealTimer timer)

           else

             "") ^ "."

        else

          ""

      end

  end

fun mash_learn_proof ctxt ({provers, overlord, ...} : params) t facts used_ths =

  let

    val thy = Proof_Context.theory_of ctxt

    val prover = hd provers

    val name = ATP_Util.timestamp () ^ serial_string () (* fresh enough *)

    val feats = features_of ctxt prover thy General [t]

    val deps = used_ths |> map Thm.get_name_hint

  in

    mash_map ctxt (fn {thys, fact_graph} =>

        let

          val parents = parents_wrt_facts ctxt facts fact_graph

          val upds = [(name, parents, feats, deps)]

          val (upds, fact_graph) =

            ([], fact_graph) |> fold (update_fact_graph ctxt) upds

        in

          mash_ADD ctxt overlord upds;

          {thys = thys, fact_graph = fact_graph}

        end)

  end

(* The threshold should be large enough so that MaSh doesn't kick in for Auto

   Sledgehammer and Try. *)

val min_secs_for_learning = 15

val short_learn_timeout_factor = 0.2

val long_learn_timeout_factor = 4.0

fun relevant_facts ctxt (params as {learn, fact_filter, timeout, ...}) prover

        max_facts ({add, only, ...} : fact_override) hyp_ts concl_t facts =

  if not (subset (op =) (the_list fact_filter, fact_filters)) then

    error ("Unknown fact filter: " ^ quote (the fact_filter) ^ ".")

  else if only then

    facts

  else if max_facts <= 0 orelse null facts then

    []

  else

    let

      val thy = Proof_Context.theory_of ctxt

      fun maybe_learn can_suggest =

        if not learn orelse Async_Manager.has_running_threads MaShN then

          ()

        else if Time.toSeconds timeout >= min_secs_for_learning then

          let

            val factor =

              if can_suggest then short_learn_timeout_factor

              else long_learn_timeout_factor

            val soft_timeout = time_mult factor timeout

            val hard_timeout = time_mult 2.0 soft_timeout

            val birth_time = Time.now ()

            val death_time = Time.+ (birth_time, hard_timeout)

            val desc = ("machine learner for Sledgehammer", "")

          in

            Async_Manager.launch MaShN birth_time death_time desc

                (fn () =>

                    (true, mash_learn_thy ctxt params thy soft_timeout facts))

          end

        else

          ()

      val fact_filter =

        case fact_filter of

          SOME ff =>

          (if ff <> iterN then maybe_learn (mash_can_suggest_facts ctxt)

           else (); ff)

        | NONE =>

          if mash_can_suggest_facts ctxt then (maybe_learn true; meshN)

          else if mash_could_suggest_facts () then (maybe_learn false; iterN)

          else iterN

      val add_ths = Attrib.eval_thms ctxt add

      fun prepend_facts ths accepts =

        ((facts |> filter (member Thm.eq_thm_prop ths o snd)) @

         (accepts |> filter_out (member Thm.eq_thm_prop ths o snd)))

        |> take max_facts

      fun iter () =

        iterative_relevant_facts ctxt params prover max_facts NONE hyp_ts

                                 concl_t facts

      fun mash () =

        mash_suggest_facts ctxt params prover max_facts hyp_ts concl_t facts

      val mess =

        [] |> (if fact_filter <> mashN then cons (iter (), []) else I)

           |> (if fact_filter <> iterN then cons (mash ()) else I)

    in

      mesh_facts max_facts mess

      |> not (null add_ths) ? prepend_facts add_ths

    end

fun kill_learners () = Async_Manager.kill_threads MaShN "learner"

fun running_learners () = Async_Manager.running_threads MaShN "learner"

end;