(*  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 * real) list

  val nickname_of : thm -> string

  val suggested_facts :

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

  val mesh_facts :

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

  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 option

  val atp_dependencies_of :

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

    -> thm -> string list option

  val mash_CLEAR : Proof.context -> unit

  val mash_ADD :

    Proof.context -> bool

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

  val mash_REPROVE :

    Proof.context -> bool -> (string * string list) list -> unit

  val mash_QUERY :

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

    -> (string * real) list

  val mash_unlearn : Proof.context -> unit

  val mash_could_suggest_facts : unit -> bool

  val mash_can_suggest_facts : Proof.context -> bool

  val mash_suggested_facts :

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

    -> fact list -> (fact * real) list * fact list

  val mash_learn_proof :

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

    -> unit

  val mash_learn :

    Proof.context -> params -> fact_override -> thm list -> 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_model_dir () =

  getenv "ISABELLE_HOME_USER" ^ "/mash"

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

val mash_state_dir = mash_model_dir

fun mash_state_file () = mash_state_dir () ^ "/state"

(*** 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_node line =

  case space_explode ":" line of

    [name, parents] => (unescape_meta name, unescape_metas parents)

  | _ => ("", [])

fun extract_suggestion sugg =

  case space_explode "=" sugg of

    [name, weight] =>

    SOME (unescape_meta name, Real.fromString weight |> the_default 0.0)

  | _ => NONE

fun extract_query line =

  case space_explode ":" line of

    [goal, suggs] =>

    (unescape_meta goal,

     map_filter extract_suggestion (space_explode " " 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 =

  if Thm.has_name_hint th then

    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 suf =>

        parent_of_local_thm th ^ Long_Name.separator ^ Long_Name.separator ^ suf

      | NONE => hint

    end

  else

    backquote_thm th

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

    fun find_sugg (name, weight) =

      Symtab.lookup tab name |> Option.map (rpair weight)

  in map_filter find_sugg suggs end

fun sum_avg [] = 0

  | sum_avg xs =

    Real.ceil (100000000.0 * fold (curry (op +)) xs 0.0) div length xs

fun normalize_scores [] = []

  | normalize_scores ((fact, score) :: tail) =

    (fact, 1.0) :: map (apsnd (curry Real.* (1.0 / score))) tail

fun mesh_facts max_facts [(sels, unks)] =

    map fst (take max_facts sels) @ take (max_facts - length sels) unks

  | mesh_facts max_facts mess =

    let

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

      val fact_eq = Thm.eq_thm o pairself snd

      fun score_at sels = try (nth sels) #> Option.map snd

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

        case find_index (curry fact_eq fact o fst) sels of

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

                   ~1 => score_at sels sel_len

                 | _ => NONE)

        | rank => score_at sels rank

      fun weight_of fact = mess |> map_filter (score_in fact) |> sum_avg

      val facts =

        fold (union fact_eq o map fst o take max_facts o snd o fst) mess []

    in

      facts |> map (`weight_of) |> sort (int_ord o swap o pairself fst)

            |> map snd |> take max_facts

    end

val thy_feature_name_of = prefix "y"

val const_name_of = prefix "c"

val type_name_of = prefix "t"

val class_name_of = prefix "s"

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 (K ())) prover params (K (K (K "")))

                          problem

  end

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

val logical_consts =

  [@{const_name prop}, @{const_name Pure.conjunction}] @ atp_logical_consts

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 =) 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 (x as (s, _)), args) =>

          if is_bad_const x args then ""

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

        | _ => ""

    fun add_pattern depth t =

      case patternify depth t of "" => I | s => insert (op =) s

    fun add_term_patterns ~1 _ = I

      | add_term_patterns depth t =

        add_pattern 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 (_, T) => 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 string_of_status status of "" => I | s => cons s)

(* 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 = 15

val atp_dependency_default_max_fact = 50

(* "type_definition_xxx" facts are characterized by their use of "CollectI". *)

val typedef_sig = [@{thm CollectI} |> nickname_of]

(* "Rep_xxx_inject", "Abs_xxx_inverse", etc., are derived using these facts. *)

val typedef_ths =

  @{thms type_definition.Abs_inverse type_definition.Rep_inverse

         type_definition.Rep type_definition.Rep_inject

         type_definition.Abs_inject type_definition.Rep_cases

         type_definition.Abs_cases type_definition.Rep_induct

         type_definition.Abs_induct type_definition.Rep_range

         type_definition.Abs_image}

  |> map nickname_of

fun trim_dependencies deps =

  if length deps > max_dependencies orelse deps = typedef_sig orelse

     exists (member (op =) typedef_ths) deps then

    NONE

  else

    SOME deps

fun isar_dependencies_of all_names =

  thms_in_proof (SOME all_names) #> trim_dependencies

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

                        auto_level facts all_names th =

  case isar_dependencies_of all_names th of

    SOME [] => NONE

  | 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 |> mepo_suggested_facts ctxt params prover

                     (max_facts |> the_default atp_dependency_default_max_fact)

                     NONE hyp_ts concl_t

              |> fold (add_isar_dep facts) (these isar_deps)

              |> map fix_name

    in

      if verbose andalso auto_level = 0 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 auto_level = 0 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 |> trim_dependencies)

      | _ => NONE

    end

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

(* more friendly than "try o File.rm" for those who keep the files open in their

   text editor *)

fun wipe_out_file file = File.write (Path.explode file) ""

fun write_file heading (xs, f) file =

  let val path = Path.explode file in

    File.write path heading;

    xs |> chunk_list 500

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

  end

fun run_mash_tool ctxt overlord save max_suggs write_cmds read_suggs =

  let

    val (temp_dir, serial) =

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

      else (getenv "ISABELLE_TMP", serial_string ())

    val log_file = if overlord then temp_dir ^ "/mash_log" else "/dev/null"

    val err_file = temp_dir ^ "/mash_err" ^ serial

    val sugg_file = temp_dir ^ "/mash_suggs" ^ serial

    val cmd_file = temp_dir ^ "/mash_commands" ^ serial

    val core =

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

      " --numberOfPredictions " ^ string_of_int max_suggs ^

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

    val command =

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

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

  in

    write_file "" ([], K "") sugg_file;

    write_file "" write_cmds cmd_file;

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

    Isabelle_System.bash command;

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

    |> tap (fn _ => trace_msg ctxt (fn () =>

           case try File.read (Path.explode err_file) of

             NONE => "Done"

           | SOME "" => "Done"

           | SOME s => "Error: " ^ elide_string 1000 s))

    |> not overlord

       ? tap (fn _ => List.app wipe_out_file [err_file, sugg_file, cmd_file])

  end

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

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

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

fun str_of_reprove (name, deps) =

  "p " ^ escape_meta name ^ ": " ^ escape_metas deps ^ "\n"

fun str_of_query (parents, feats) =

  "? " ^ escape_metas parents ^ "; " ^ escape_metas feats ^ "\n"

fun mash_CLEAR ctxt =

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

    trace_msg ctxt (K "MaSh CLEAR");

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

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

                  path NONE;

    ()

  end

fun mash_ADD _ _ [] = ()

  | mash_ADD ctxt overlord adds =

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

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

     run_mash_tool ctxt overlord true 0 (adds, str_of_add) (K ()))

fun mash_REPROVE _ _ [] = ()

  | mash_REPROVE ctxt overlord reps =

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

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

     run_mash_tool ctxt overlord true 0 (reps, str_of_reprove) (K ()))

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

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

   run_mash_tool ctxt overlord false max_suggs

       ([query], str_of_query)

       (fn suggs =>

           case suggs () of

             [] => []

           | 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)

fun graph_info G =

  string_of_int (length (Graph.keys G)) ^ " node(s), " ^

  string_of_int (fold (Integer.add o length o snd) (Graph.dest G) 0) ^

  " edge(s), " ^

  string_of_int (length (Graph.minimals G)) ^ " minimal, " ^

  string_of_int (length (Graph.maximals G)) ^ " maximal"

type mash_state = {fact_G : unit Graph.T}

val empty_state = {fact_G = Graph.empty}

local

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

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

  | load ctxt _ =

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

      (true,

       case try File.read_lines path of

         SOME (version' :: node_lines) =>

         let

           fun add_edge_to name parent =

             Graph.default_node (parent, ()) #> Graph.add_edge (parent, name)

           fun add_node line =

             case extract_node line of

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

             | (name, parents) =>

               Graph.default_node (name, ()) #> fold (add_edge_to name) parents

           val fact_G =

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

                 Graph.empty |> version' = version ? fold add_node node_lines)

         in

           trace_msg ctxt (fn () =>

               "Loaded fact graph (" ^ graph_info fact_G ^ ")");

           {fact_G = fact_G}

         end

       | _ => empty_state)

    end

fun save ctxt {fact_G} =

  let

    fun str_of_entry (name, parents) =

      escape_meta name ^ ": " ^ escape_metas parents ^ "\n"

    fun append_entry (name, ((), (parents, _))) =

      cons (name, Graph.Keys.dest parents)

    val entries = [] |> Graph.fold append_entry fact_G

  in

    write_file (version ^ "\n") (entries, str_of_entry) (mash_state_file ());

    trace_msg ctxt (fn () => "Saved fact graph (" ^ graph_info fact_G ^ ")")

  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 ctxt)))

fun mash_peek ctxt f =

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

fun mash_get ctxt =

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

fun mash_unlearn ctxt =

  Synchronized.change global_state (fn _ =>

      (mash_CLEAR ctxt;

       wipe_out_file (mash_state_file ());

       (true, empty_state)))

end

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

fun mash_can_suggest_facts ctxt = not (Graph.is_empty (#fact_G (mash_get ctxt)))

fun num_keys keys = Graph.Keys.fold (K (Integer.add 1)) keys 0

fun maximal_in_graph fact_G facts =

  let

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

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

    fun insert_new seen name =

      not (Symtab.defined seen name) ? insert (op =) name

    fun find_maxes _ (maxs, []) = map snd maxs

      | find_maxes seen (maxs, new :: news) =

        find_maxes

            (seen |> num_keys (Graph.imm_succs fact_G new) > 1

                     ? Symtab.default (new, ()))

            (if Symtab.defined tab new then

               let

                 val newp = Graph.all_preds fact_G [new]

                 fun is_ancestor x yp = member (op =) yp x

                 val maxs =

                   maxs |> filter (fn (_, max) => not (is_ancestor max newp))

               in

                 if exists (is_ancestor new o fst) maxs then

                   (maxs, news)

                 else

                   ((newp, new)

                    :: filter_out (fn (_, max) => is_ancestor max newp) maxs,

                    news)

               end

             else

               (maxs, Graph.Keys.fold (insert_new seen)

                                      (Graph.imm_preds fact_G new) news))

  in find_maxes Symtab.empty ([], Graph.maximals fact_G) 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 (50, max_facts)

fun is_fact_in_graph fact_G (_, th) =

  can (Graph.get_node fact_G) (nickname_of th)

fun interleave [] ys = ys

  | interleave xs [] = xs

  | interleave (x :: xs) (y :: ys) = x :: y :: interleave xs ys

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

                         concl_t facts =

  let

    val thy = Proof_Context.theory_of ctxt

    val (fact_G, suggs) =

      mash_peek ctxt (fn {fact_G} =>

          if Graph.is_empty fact_G then

            (fact_G, [])

          else

            let

              val parents = maximal_in_graph fact_G facts

              val feats =

                features_of ctxt prover thy (Local, General) (concl_t :: hyp_ts)

            in

              (fact_G, mash_QUERY ctxt overlord (max_suggs_of max_facts)

                                  (parents, feats))

            end)

    val sels =

      facts |> suggested_facts suggs

            (* The weights currently returned by "mash.py" are too extreme to

               make any sense. *)

            |> map fst

    val (unk_global, unk_local) =

      facts |> filter_out (is_fact_in_graph fact_G)

            |> List.partition (fn ((_, (loc, _)), _) => loc = Global)

  in (interleave unk_local sels |> weight_mepo_facts, unk_global) end

fun add_to_fact_graph ctxt (name, parents, feats, deps) (adds, 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) |> fold maybe_add_from deps

  in ((name, parents, feats, deps) :: adds, 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 freshish_name () =

  Date.fmt ".%Y_%m_%d_%H_%M_%S__" (Date.fromTimeLocal (Time.now ())) ^

  serial_string ()

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 = freshish_name ()

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

          val deps = used_ths |> map nickname_of

        in

          mash_peek ctxt (fn {fact_G} =>

              let val parents = maximal_in_graph fact_G facts in

                mash_ADD ctxt overlord [(name, parents, feats, deps)]

              end);

          (true, "")

        end)

fun sendback sub =

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

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, ...}) prover

                     auto_level atp learn_timeout facts =

  let

    val timer = Timer.startRealTimer ()

    fun next_commit_time () =

      Time.+ (Timer.checkRealTimer timer, commit_timeout)

    val {fact_G} = mash_get ctxt

    val (old_facts, new_facts) =

      facts |> List.partition (is_fact_in_graph fact_G)

            ||> sort (thm_ord o pairself snd)

  in

    if null new_facts andalso (not atp orelse null old_facts) then

      if auto_level < 2 then

        "No new " ^ (if atp then "ATP" else "Isar") ^ " proofs to learn." ^

        (if auto_level = 0 andalso not atp then

           "\n\nHint: Try " ^ sendback learn_atpN ^ " to learn from ATP proofs."

         else

           "")

      else

        ""

    else

      let

        val all_names =

          facts |> map snd |> map (rpair () o nickname_of) |> Symtab.make

        val deps_of =

          if atp then

            atp_dependencies_of ctxt params prover auto_level facts all_names

          else

            isar_dependencies_of all_names

        fun do_commit [] [] state = state

          | do_commit adds reps {fact_G} =

            let

              val (adds, fact_G) =

                ([], fact_G) |> fold (add_to_fact_graph ctxt) adds

            in

              mash_ADD ctxt overlord (rev adds);

              mash_REPROVE ctxt overlord reps;

              {fact_G = fact_G}

            end

        fun commit last adds reps =

          (if debug andalso auto_level = 0 then

             Output.urgent_message "Committing..."

           else

             ();

           mash_map ctxt (do_commit (rev adds) reps);

           if not last andalso auto_level = 0 then

             let val num_proofs = length adds + length reps in

               "Learned " ^ string_of_int num_proofs ^ " " ^

               (if atp then "ATP" else "Isar") ^ " proof" ^

               plural_s num_proofs ^ " in the last " ^

               string_from_time commit_timeout ^ "."

               |> Output.urgent_message

             end

           else

             ())

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

          | learn_new_fact ((_, stature), th)

                           (adds, (parents, n, next_commit, _)) =

            let

              val name = nickname_of th

              val feats =

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

              val deps = deps_of th |> these

              val n = n |> not (null deps) ? Integer.add 1

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

              val (adds, next_commit) =

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

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

                else

                  (adds, next_commit)

              val timed_out = Time.> (Timer.checkRealTimer timer, learn_timeout)

            in (adds, ([name], n, next_commit, timed_out)) end

        val n =

          if null new_facts then

            0

          else

            let

              val last_th = new_facts |> List.last |> snd

              (* crude approximation *)

              val ancestors =

                old_facts

                |> filter (fn (_, th) => thm_ord (th, last_th) <> GREATER)

              val parents = maximal_in_graph fact_G ancestors

              val (adds, (_, n, _, _)) =

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

                |> fold learn_new_fact new_facts

            in commit true adds []; n end

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

          | relearn_old_fact (_, th) (reps, (n, next_commit, _)) =

            let

              val name = nickname_of th

              val (n, reps) =

                case deps_of th of

                  SOME deps => (n + 1, (name, deps) :: reps)

                | NONE => (n, reps)

              val (reps, next_commit) =

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

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

                else

                  (reps, next_commit)

              val timed_out = Time.> (Timer.checkRealTimer timer, learn_timeout)

            in (reps, (n, next_commit, timed_out)) end

        val n =

          if not atp orelse null old_facts then

            n

          else

            let

              fun priority_of (_, th) =

                random_range 0 (1000 * max_dependencies)

                - 500 * (th |> isar_dependencies_of all_names

                            |> Option.map length

                            |> the_default max_dependencies)

              val old_facts =

                old_facts |> map (`priority_of)

                          |> sort (int_ord o pairself fst)

                          |> map snd

              val (reps, (n, _, _)) =

                ([], (n, next_commit_time (), false))

                |> fold relearn_old_fact old_facts

            in commit true [] reps; n end

      in

        if verbose orelse auto_level < 2 then

          "Learned " ^ string_of_int n ^ " nontrivial " ^

          (if atp then "ATP" else "Isar") ^ " 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, timeout, ...}) fact_override chained

               atp =

  let

    val css = Sledgehammer_Fact.clasimpset_rule_table_of ctxt

    val ctxt = ctxt |> Config.put instantiate_inducts false

    val facts =

      nearly_all_facts ctxt false fact_override Symtab.empty css chained []

                       @{prop True}

    val num_facts = length facts

    val prover = hd provers

    fun learn auto_level atp =

      mash_learn_facts ctxt params prover auto_level atp infinite_timeout facts

      |> Output.urgent_message

  in

    (if atp then

       ("MaShing through " ^ string_of_int num_facts ^ " fact" ^

        plural_s num_facts ^ " for ATP proofs (" ^ quote prover ^ " timeout: " ^

        string_from_time timeout ^ ").\n\nCollecting Isar proofs first..."

        |> Output.urgent_message;

        learn 1 false;

        "Now collecting ATP proofs. This may take several hours. You can \

        \safely stop the learning process at any point."

        |> Output.urgent_message;

        learn 0 true)

     else

       ("MaShing through " ^ string_of_int num_facts ^ " fact" ^

        plural_s num_facts ^ " for Isar proofs..."

        |> Output.urgent_message;

        learn 0 false))

  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 2 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_could_suggest_facts () then

            (maybe_learn ();

             if mash_can_suggest_facts ctxt then meshN else 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 mepo () =

        facts |> mepo_suggested_facts ctxt params prover max_facts NONE hyp_ts

                                      concl_t

              |> weight_mepo_facts

      fun mash () =

        mash_suggested_facts ctxt params prover max_facts hyp_ts concl_t facts

      val mess =

        [] |> (if fact_filter <> mashN then cons (mepo (), []) 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;