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

     Author:     Jasmin Blanchette, TU Muenchen

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

 *)

 signature SLEDGEHAMMER_MASH =

 sig

   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 mepoN : string

   val mashN : string

   val meshN : string

   val unlearnN : string

   val learn_isarN : string

   val learn_atpN : string

   val relearn_isarN : string

   val relearn_atpN : 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 nickname_of : thm -> string

   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_or_too_meta : thm -> bool

   val theory_ord : theory * theory -> order

   val thm_ord : thm * thm -> order

   val goal_of_thm : theory -> thm -> thm

   val run_prover_for_mash :

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

   val features_of :

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

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

   val atp_dependencies_of :

     Proof.context -> params -> string -> bool -> fact list -> unit Symtab.table

     -> thm -> string list

   val mash_CLEAR : Proof.context -> 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_unlearn : 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_proof :

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

     -> unit

   val mash_learn_facts :

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

     -> string

   val mash_learn : Proof.context -> params -> bool -> 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_MaSh : SLEDGEHAMMER_MASH =

 struct

 open ATP_Util

 open ATP_Problem_Generate

 open Sledgehammer_Util

 open Sledgehammer_Fact

 open Sledgehammer_Provers

 open Sledgehammer_Minimize

 open Sledgehammer_MePo

 val trace =

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

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

 val MaShN = "MaSh"

 val mepoN = "mepo"

 val mashN = "mash"

 val meshN = "mesh"

 val fact_filters = [meshN, mepoN, mashN]

 val unlearnN = "unlearn"

 val learn_isarN = "learn_isar"

 val learn_atpN = "learn_atp"

 val relearn_isarN = "relearn_isar"

 val relearn_atpN = "relearn_atp"

 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 parent_of_local_thm th =

   let

     val thy = th |> Thm.theory_of_thm

     val facts = thy |> Global_Theory.facts_of

     val space = facts |> Facts.space_of

     fun id_of s = #id (Name_Space.the_entry space s)

     fun max_id (s', _) (s, id) =

       let val id' = id_of s' in if id > id' then (s, id) else (s', id') end

   in ("", ~1) |> Facts.fold_static max_id facts |> fst end

 val local_prefix = "local" ^ Long_Name.separator

 fun nickname_of th =

   let val hint = Thm.get_name_hint th in

     (* FIXME: There must be a better way to detect local facts. *)

     case try (unprefix local_prefix) hint of

       SOME suff =>

       parent_of_local_thm th ^ Long_Name.separator ^ Long_Name.separator ^ suff

     | NONE => hint

   end

 fun suggested_facts suggs facts =

   let

     fun add_fact (fact as (_, th)) = Symtab.default (nickname_of th, fact)

     val tab = Symtab.empty |> fold add_fact facts

   in map_filter (Symtab.lookup tab) suggs end

 (* Ad hoc score function roughly based on Blanchette's Ringberg 2011 data. *)

 fun score x = Math.pow (1.5, 15.5 - 0.05 * Real.fromInt x) + 15.0

 fun sum_sq_avg [] = 0

   | sum_sq_avg xs =

     Real.ceil (100000.0 * fold (curry (op +) o score) xs 0.0) 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 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_sq_avg

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

     in

       facts |> map (`score_of) |> sort (int_ord o swap 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

 fun is_likely_tautology_or_too_meta th =

   let

     val is_boring_const = member (op =) atp_widely_irrelevant_consts

     fun is_boring_bool t =

       not (exists_Const (not o is_boring_const o fst) t) orelse

       exists_type (exists_subtype (curry (op =) @{typ prop})) t

     fun is_boring_prop (@{const Trueprop} $ t) = is_boring_bool t

       | is_boring_prop (@{const "==>"} $ t $ u) =

         is_boring_prop t andalso is_boring_prop u

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

         is_boring_prop t andalso is_boring_prop u

       | is_boring_prop (Const (@{const_name "=="}, _) $ t $ u) =

         is_boring_bool t andalso is_boring_bool u

       | is_boring_prop _ = true

   in

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

   end

 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

 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}

   in

     get_minimizing_prover ctxt MaSh (K ()) prover params (K (K (K "")))

                           problem

   end

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

 fun interesting_terms_types_and_classes ctxt prover term_max_depth

                                         type_max_depth ts =

   let

     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 end

 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 (scope, status) ts =

   thy_feature_name_of (Context.theory_name thy) ::

   interesting_terms_types_and_classes ctxt prover term_max_depth type_max_depth

                                       ts

   |> forall is_lambda_free ts ? cons "no_lams"

   |> forall (not o exists_Const is_exists) ts ? cons "no_skos"

   |> scope <> Global ? cons "local"

   |> (case status of

         General => I

       | Induction => cons "induction"

       | Intro => cons "intro"

       | Inductive => cons "inductive"

       | Elim => cons "elim"

       | Simp => cons "simp"

       | Def => cons "def")

 fun isar_dependencies_of all_facts = thms_in_proof (SOME all_facts)

 val atp_dep_default_max_fact = 50

 fun atp_dependencies_of ctxt (params as {verbose, max_facts, ...}) prover auto

                         facts all_names th =

   case isar_dependencies_of all_names th of

     [] => []

   | isar_deps =>

     let

       val thy = Proof_Context.theory_of ctxt

       val goal = goal_of_thm thy th

       val (_, hyp_ts, concl_t) = ATP_Util.strip_subgoal ctxt goal 1

       val facts = facts |> filter (fn (_, th') => thm_ord (th', th) = LESS)

       fun fix_name ((_, stature), th) = ((fn () => nickname_of th, stature), th)

       fun is_dep dep (_, th) = nickname_of th = dep

       fun add_isar_dep facts dep accum =

         if exists (is_dep dep) accum then

           accum

         else case find_first (is_dep dep) facts of

           SOME ((name, status), th) => accum @ [((name, status), th)]

         | NONE => accum (* shouldn't happen *)

       val facts =

         facts |> iterative_relevant_facts ctxt params prover

                      (max_facts |> the_default atp_dep_default_max_fact) NONE

                      hyp_ts concl_t

               |> fold (add_isar_dep facts) isar_deps

               |> map fix_name

     in

       if verbose andalso not auto then

         let val num_facts = length facts in

           "MaSh: " ^ quote prover ^ " on " ^ quote (nickname_of th) ^

           " with " ^ string_of_int num_facts ^ " fact" ^ plural_s num_facts ^

           "."

           |> Output.urgent_message

         end

       else

         ();

       case run_prover_for_mash ctxt params prover facts goal of

         {outcome = NONE, used_facts, ...} =>

         (if verbose andalso not auto then

            let val num_facts = length used_facts in

              "Found proof with " ^ string_of_int num_facts ^ " fact" ^

              plural_s num_facts ^ "."

              |> Output.urgent_message

            end

          else

            ();

          used_facts |> map fst)

       | _ => isar_deps

     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 and_rm_files overlord flags files =

   if overlord then

     ""

   else

     " && rm -f" ^ flags ^ " -- " ^

     space_implode " " (map File.shell_quote files)

 fun run_mash ctxt overlord (temp_dir, serial) async core =

   let

     val log_file = temp_dir ^ "/mash_log" ^ serial

     val err_file = temp_dir ^ "/mash_err" ^ serial

     val command =

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

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

       and_rm_files overlord "" [log_file, err_file] ^

       (if async then " &" else "")

   in

     trace_msg ctxt (fn () =>

         (if async then "Launching " else "Running ") ^ command);

     write_file ([], K "") log_file;

     write_file ([], K "") err_file;

     Isabelle_System.bash command;

     if not async then trace_msg ctxt (K "Done") else ()

   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 overlord info false

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

               " --numberOfPredictions " ^ string_of_int max_suggs ^

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

               (and_rm_files overlord "" [sugg_file, cmd_file]));

     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 mash_CLEAR ctxt =

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

     trace_msg ctxt (K "MaSh CLEAR");

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

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

                   path ()

   end

 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.DUP name =>

          (trace_msg ctxt (fn () =>

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

        | Graph.UNDEF name =>

          (trace_msg ctxt (fn () =>

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

        | exn =>

          if Exn.is_interrupt exn then

            reraise exn

          else

            (trace_msg ctxt (fn () =>

                 "Internal error when " ^ when ^ ":\n" ^

                 ML_Compiler.exn_message exn); def)

 type mash_state = {fact_graph : unit Graph.T}

 val empty_state = {fact_graph = Graph.empty}

 local

 val version = "*** MaSh 0.0 ***"

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

   | load ctxt _ =

     let val path = mash_state_path () in

       (true,

        case try File.read_lines path of

          SOME (version' :: fact_lines) =>

          let

            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 fact_graph =

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

                  Graph.empty |> version' = version

                                 ? fold add_fact_line fact_lines)

          in {fact_graph = fact_graph} end

        | _ => empty_state)

     end

 fun save {fact_graph} =

   let

     val path = mash_state_path ()

     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 (version ^ "\n");

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

                    append_fact name (Graph.Keys.dest parents))

         fact_graph ()

   end

 val global_state =

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

 in

 fun mash_map ctxt f =

   Synchronized.change global_state (load ctxt ##> (f #> tap save))

 fun mash_get ctxt =

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

 fun mash_unlearn ctxt =

   Synchronized.change global_state (fn _ =>

       (mash_CLEAR 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 facts fact_graph =

   let

     val facts = [] |> fold (cons o nickname_of o snd) facts

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

     fun insert_not_seen seen name =

       not (member (op =) seen name) ? insert (op =) name

     fun parents_of _ parents [] = parents

       | parents_of seen parents (name :: names) =

         if Symtab.defined tab name then

           parents_of (name :: seen) (name :: parents) names

         else

           parents_of (name :: seen) parents

                      (Graph.Keys.fold (insert_not_seen seen)

                                       (Graph.imm_preds fact_graph name) names)

   in parents_of [] [] (Graph.maximals fact_graph) 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) (nickname_of 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 facts fact_graph

     val feats = features_of ctxt prover thy (Local, 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 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 learn_timeout_slack = 2.0

 fun launch_thread timeout task =

   let

     val hard_timeout = time_mult learn_timeout_slack 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 task end

 fun mash_learn_proof ctxt ({overlord, timeout, ...} : params) prover t facts

                      used_ths =

   if is_smt_prover ctxt prover then

     ()

   else

     launch_thread timeout

         (fn () =>

             let

               val thy = Proof_Context.theory_of ctxt

               val name = timestamp () ^ " " ^ serial_string () (* freshish *)

               val feats = features_of ctxt prover thy (Local, General) [t]

               val deps = used_ths |> map nickname_of

             in

               mash_map ctxt (fn {fact_graph} =>

                   let

                     val parents = parents_wrt_facts 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; {fact_graph = fact_graph}

                   end);

               (true, "")

             end)

 fun sendback sub =

   Markup.markup Isabelle_Markup.sendback (sledgehammerN ^ " " ^ sub)

 (* Too many dependencies is a sign that a decision procedure is at work. There

    isn't much too learn from such proofs. *)

 val max_dependencies = 10

 val commit_timeout = seconds 30.0

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

 fun mash_learn_facts ctxt (params as {debug, verbose, overlord, timeout, ...})

                      prover auto atp learn_timeout facts =

   let

     val timer = Timer.startRealTimer ()

     fun next_commit_time () =

       Time.+ (Timer.checkRealTimer timer, commit_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)

     val num_new_facts = length new_facts

   in

     "MaShing" ^

     (if not auto then

        " " ^ string_of_int num_new_facts ^ " fact" ^

        plural_s num_new_facts ^

        (if atp then " (ATP timeout: " ^ string_from_time timeout ^ ")" else "")

      else

        "") ^ "..."

     |> Output.urgent_message;

     if null new_facts then

       if verbose orelse not auto then

         "Nothing to learn.\n\nHint: Try " ^ sendback relearn_isarN ^ " or " ^

         sendback relearn_atpN ^ "  to learn from scratch."

       else

         ""

     else

       let

         val ths = facts |> map snd

         val all_names =

           ths |> filter_out is_likely_tautology_or_too_meta

               |> map (rpair () o nickname_of)

               |> Symtab.make

         fun do_commit [] state = state

           | do_commit upds {fact_graph} =

             let

               val (upds, fact_graph) =

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

             in mash_ADD ctxt overlord (rev upds); {fact_graph = fact_graph} end

         fun trim_deps deps = if length deps > max_dependencies then [] else deps

         fun commit last upds =

           (if debug andalso not auto then Output.urgent_message "Committing..."

            else ();

            mash_map ctxt (do_commit (rev upds));

            if not last andalso not auto then

              let val num_upds = length upds in

                "Processed " ^ string_of_int num_upds ^ " fact" ^

                plural_s num_upds ^ " in the last " ^

                string_from_time commit_timeout ^ "."

                |> Output.urgent_message

              end

            else

              ())

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

           | do_fact ((_, stature), th)

                     (upds, (parents, n, next_commit, false)) =

             let

               val name = nickname_of th

               val feats =

                 features_of ctxt prover (theory_of_thm th) stature [prop_of th]

               val deps =

                 (if atp then atp_dependencies_of ctxt params prover auto facts

                  else isar_dependencies_of) all_names th

                 |> trim_deps

               val upds = (name, parents, feats, deps) :: upds

               val (upds, next_commit) =

                 if Time.> (Timer.checkRealTimer timer, next_commit) then

                   (commit false upds; ([], next_commit_time ()))

                 else

                   (upds, next_commit)

               val timed_out =

                 Time.> (Timer.checkRealTimer timer, learn_timeout)

             in (upds, ([name], n + 1, next_commit, timed_out)) end

         val parents = parents_wrt_facts facts fact_graph

         val (upds, (_, n, _, _)) =

           ([], (parents, 0, next_commit_time (), false))

           |> fold do_fact new_facts

       in

         commit true upds;

         if verbose orelse not auto then

           "Learned " ^ 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 ctxt (params as {provers, ...}) atp =

   let

     val thy = Proof_Context.theory_of ctxt

     val css_table = Sledgehammer_Fact.clasimpset_rule_table_of ctxt

     val facts = all_facts_of thy css_table

   in

      mash_learn_facts ctxt params (hd provers) false atp infinite_timeout facts

      |> Output.urgent_message

   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

 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

       fun maybe_learn () =

         if learn andalso not (Async_Manager.has_running_threads MaShN) andalso

            Time.toSeconds timeout >= min_secs_for_learning then

           let val timeout = time_mult learn_timeout_slack timeout in

             launch_thread timeout

                 (fn () => (true, mash_learn_facts ctxt params prover true false

                                                   timeout facts))

           end

         else

           ()

       val fact_filter =

         case fact_filter of

           SOME ff => (() |> ff <> mepoN ? maybe_learn; ff)

         | NONE =>

           if is_smt_prover ctxt prover then mepoN

           else if mash_can_suggest_facts ctxt then (maybe_learn (); meshN)

           else if mash_could_suggest_facts () then (maybe_learn (); mepoN)

           else mepoN

       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 <> mepoN 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;