(*  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_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_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 status of

         General => I

       | Induction => cons "induction"

       | Intro => cons "intro"

       | Inductive => cons "inductive"

       | Elim => cons "elim"

       | Simp => cons "simp"

       | Def => cons "def")

 (* 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 atp_dependency_default_max_fact = 50

 fun trim_dependencies deps =

   if length deps <= max_dependencies then SOME deps else NONE

 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.write file ""

 fun write_file (xs, f) file =

   let val path = Path.explode file in

     wipe_out path;

     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 o Path.explode)

                                [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_path () 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

     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

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

       append_fact name (Graph.Keys.dest parents)

   in

     File.write path (version ^ "\n");

     Graph.fold append_entry fact_G ();

     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 (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_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

                 |> filter_out is_likely_tautology_or_too_meta

                 |> 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;