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

     Author:     Jasmin Blanchette, TU Muenchen

     Author:     Cezary Kaliszyk, University of Innsbruck

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

 *)

 signature SLEDGEHAMMER_MASH =

 sig

   type stature = ATP_Problem_Generate.stature

   type raw_fact = Sledgehammer_Fact.raw_fact

   type fact = Sledgehammer_Fact.fact

   type fact_override = Sledgehammer_Fact.fact_override

   type params = Sledgehammer_Prover.params

   type prover_result = Sledgehammer_Prover.prover_result

   val trace : bool Config.T

   val duplicates : bool Config.T

   val MePoN : string

   val MaShN : string

   val MeShN : string

   val mepoN : string

   val mashN : string

   val meshN : string

   val unlearnN : string

   val learn_isarN : string

   val learn_proverN : string

   val relearn_isarN : string

   val relearn_proverN : string

   val fact_filters : string list

   val encode_str : string -> string

   val encode_strs : string list -> string

   val decode_str : string -> string

   val decode_strs : string -> string list

   datatype mash_algorithm =

     MaSh_NB

   | MaSh_kNN

   | MaSh_NB_kNN

   | MaSh_NB_Ext

   | MaSh_kNN_Ext

   val is_mash_enabled : unit -> bool

   val the_mash_algorithm : unit -> mash_algorithm

   val str_of_mash_algorithm : mash_algorithm -> string

   val mesh_facts : ('a list -> 'a list) -> ('a * 'a -> bool) -> int ->

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

   val nickname_of_thm : thm -> string

   val find_suggested_facts : Proof.context -> ('b * thm) list -> string list -> ('b * thm) list

   val crude_thm_ord : Proof.context -> thm ord

   val thm_less : thm * thm -> bool

   val goal_of_thm : theory -> thm -> thm

   val run_prover_for_mash : Proof.context -> params -> string -> string -> fact list -> thm ->

     prover_result

   val features_of : Proof.context -> string -> stature -> term list -> string list

   val trim_dependencies : string list -> string list option

   val isar_dependencies_of : string Symtab.table * string Symtab.table -> thm -> string list option

   val prover_dependencies_of : Proof.context -> params -> string -> int -> raw_fact list ->

     string Symtab.table * string Symtab.table -> thm -> bool * string list

   val attach_parents_to_facts : ('a * thm) list -> ('a * thm) list ->

     (string list * ('a * thm)) list

   val num_extra_feature_facts : int

   val extra_feature_factor : real

   val weight_facts_smoothly : 'a list -> ('a * real) list

   val weight_facts_steeply : 'a list -> ('a * real) list

   val find_mash_suggestions : Proof.context -> int -> string list -> ('a * thm) list ->

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

   val mash_suggested_facts : Proof.context -> string -> params -> int -> term list -> term ->

     raw_fact list -> fact list * fact list

   val mash_unlearn : Proof.context -> unit

   val mash_learn_proof : Proof.context -> params -> term -> thm list -> unit

   val mash_learn_facts : Proof.context -> params -> string -> int -> bool -> Time.time ->

     raw_fact list -> string

   val mash_learn : Proof.context -> params -> fact_override -> thm list -> bool -> unit

   val mash_can_suggest_facts : Proof.context -> bool

   val mash_can_suggest_facts_fast : Proof.context -> bool

   val generous_max_suggestions : int -> int

   val mepo_weight : real

   val mash_weight : real

   val relevant_facts : Proof.context -> params -> string -> int -> fact_override -> term list ->

     term -> raw_fact list -> (string * fact list) list

 end;

 structure Sledgehammer_MaSh : SLEDGEHAMMER_MASH =

 struct

 open ATP_Util

 open ATP_Problem_Generate

 open Sledgehammer_Util

 open Sledgehammer_Fact

 open Sledgehammer_Prover

 open Sledgehammer_Prover_Minimize

 open Sledgehammer_MePo

 val anonymous_proof_prefix = "."

 val trace = Attrib.setup_config_bool \<^binding>\<open>sledgehammer_mash_trace\<close> (K false)

 val duplicates = Attrib.setup_config_bool \<^binding>\<open>sledgehammer_fact_duplicates\<close> (K false)

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

 fun gen_eq_thm ctxt = if Config.get ctxt duplicates then Thm.eq_thm_strict else Thm.eq_thm_prop

 val MePoN = "MePo"

 val MaShN = "MaSh"

 val MeShN = "MeSh"

 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_proverN = "learn_prover"

 val relearn_isarN = "relearn_isar"

 val relearn_proverN = "relearn_prover"

 fun map_array_at ary f i = Array.update (ary, i, f (Array.sub (ary, i)))

 type xtab = int * int Symtab.table

 val empty_xtab = (0, Symtab.empty)

 fun add_to_xtab key (next, tab) = (next + 1, Symtab.update_new (key, next) tab)

 fun maybe_add_to_xtab key = perhaps (try (add_to_xtab key))

 fun state_file () = Path.expand (Path.explode "$ISABELLE_HOME_USER/mash_state")

 val remove_state_file = try File.rm o state_file

 datatype mash_algorithm =

   MaSh_NB

 | MaSh_kNN

 | MaSh_NB_kNN

 | MaSh_NB_Ext

 | MaSh_kNN_Ext

 fun mash_algorithm () =

   (case Options.default_string \<^system_option>\<open>MaSh\<close> of

     "yes" => SOME MaSh_NB_kNN

   | "sml" => SOME MaSh_NB_kNN

   | "nb" => SOME MaSh_NB

   | "knn" => SOME MaSh_kNN

   | "nb_knn" => SOME MaSh_NB_kNN

   | "nb_ext" => SOME MaSh_NB_Ext

   | "knn_ext" => SOME MaSh_kNN_Ext

   | "none" => NONE

   | "" => NONE

   | algorithm => (warning ("Unknown MaSh algorithm: " ^ quote algorithm); NONE))

 val is_mash_enabled = is_some o mash_algorithm

 val the_mash_algorithm = the_default MaSh_NB_kNN o mash_algorithm

 fun str_of_mash_algorithm MaSh_NB = "nb"

   | str_of_mash_algorithm MaSh_kNN = "knn"

   | str_of_mash_algorithm MaSh_NB_kNN = "nb_knn"

   | str_of_mash_algorithm MaSh_NB_Ext = "nb_ext"

   | str_of_mash_algorithm MaSh_kNN_Ext = "knn_ext"

 fun scaled_avg [] = 0

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

 fun avg [] = 0.0

   | avg xs = fold (curry (op +)) xs 0.0 / Real.fromInt (length xs)

 fun normalize_scores _ [] = []

   | normalize_scores max_facts xs =

     map (apsnd (curry (op *) (1.0 / avg (map snd (take max_facts xs))))) xs

 fun mesh_facts maybe_distinct _ max_facts [(_, (sels, unks))] =

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

     |> maybe_distinct

   | mesh_facts _ fact_eq max_facts mess =

     let

       val mess = mess |> map (apsnd (apfst (normalize_scores max_facts)))

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

         let val score_at = try (nth sels) #> Option.map (fn (_, score) => global_weight * score) in

           (case find_index (curry fact_eq fact o fst) sels of

             ~1 => if member fact_eq unks fact then NONE else SOME 0.0

           | rank => score_at rank)

         end

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

     in

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

       |> map (`weight_of) |> sort (int_ord o apply2 fst o swap)

       |> map snd |> take max_facts

     end

 fun smooth_weight_of_fact rank = Math.pow (1.3, 15.5 - 0.2 * Real.fromInt rank) + 15.0 (* FUDGE *)

 fun steep_weight_of_fact rank = Math.pow (0.62, log2 (Real.fromInt (rank + 1))) (* FUDGE *)

 fun weight_facts_smoothly facts = facts ~~ map smooth_weight_of_fact (0 upto length facts - 1)

 fun weight_facts_steeply facts = facts ~~ map steep_weight_of_fact (0 upto length facts - 1)

 fun sort_array_suffix cmp needed a =

   let

     exception BOTTOM of int

     val al = Array.length a

     fun maxson l i =

       let val i31 = i + i + i + 1 in

         if i31 + 2 < l then

           let val x = Unsynchronized.ref i31 in

             if is_less (cmp (Array.sub (a, i31), Array.sub (a, i31 + 1))) then x := i31 + 1 else ();

             if is_less (cmp (Array.sub (a, !x), Array.sub (a, i31 + 2))) then x := i31 + 2 else ();

             !x

           end

         else

           if i31 + 1 < l andalso is_less (cmp (Array.sub (a, i31), Array.sub (a, i31 + 1)))

           then i31 + 1 else if i31 < l then i31 else raise BOTTOM i

       end

     fun trickledown l i e =

       let val j = maxson l i in

         if is_greater (cmp (Array.sub (a, j), e)) then

           (Array.update (a, i, Array.sub (a, j)); trickledown l j e)

         else

           Array.update (a, i, e)

       end

     fun trickle l i e = trickledown l i e handle BOTTOM i => Array.update (a, i, e)

     fun bubbledown l i =

       let val j = maxson l i in

         Array.update (a, i, Array.sub (a, j));

         bubbledown l j

       end

     fun bubble l i = bubbledown l i handle BOTTOM i => i

     fun trickleup i e =

       let val father = (i - 1) div 3 in

         if is_less (cmp (Array.sub (a, father), e)) then

           (Array.update (a, i, Array.sub (a, father));

            if father > 0 then trickleup father e else Array.update (a, 0, e))

         else

           Array.update (a, i, e)

       end

     fun for i = if i < 0 then () else (trickle al i (Array.sub (a, i)); for (i - 1))

     fun for2 i =

       if i < Integer.max 2 (al - needed) then

         ()

       else

         let val e = Array.sub (a, i) in

           Array.update (a, i, Array.sub (a, 0));

           trickleup (bubble i 0) e;

           for2 (i - 1)

         end

   in

     for (((al + 1) div 3) - 1);

     for2 (al - 1);

     if al > 1 then

       let val e = Array.sub (a, 1) in

         Array.update (a, 1, Array.sub (a, 0));

         Array.update (a, 0, e)

       end

     else

       ()

   end

 fun rev_sort_list_prefix cmp needed xs =

   let val ary = Array.fromList xs in

     sort_array_suffix cmp needed ary;

     Array.foldl (op ::) [] ary

   end

 (*** Convenience functions for synchronized access ***)

 fun synchronized_timed_value var time_limit =

   Synchronized.timed_access var time_limit (fn value => SOME (value, value))

 fun synchronized_timed_change_result var time_limit f =

   Synchronized.timed_access var time_limit (SOME o f)

 fun synchronized_timed_change var time_limit f =

   synchronized_timed_change_result var time_limit (fn x => ((), f x))

 fun mash_time_limit _ = SOME (seconds 0.1)

 (*** Isabelle-agnostic machine learning ***)

 structure MaSh =

 struct

 fun select_fact_idxs (big_number : real) recommends =

   List.app (fn at =>

     let val (j, ov) = Array.sub (recommends, at) in

       Array.update (recommends, at, (j, big_number + ov))

     end)

 fun wider_array_of_vector init vec =

   let val ary = Array.array init in

     Array.copyVec {src = vec, dst = ary, di = 0};

     ary

   end

 val nb_def_prior_weight = 1000 (* FUDGE *)

 fun learn_facts (tfreq0, sfreq0, dffreq0) num_facts0 num_facts num_feats depss featss =

   let

     val tfreq = wider_array_of_vector (num_facts, 0) tfreq0

     val sfreq = wider_array_of_vector (num_facts, Inttab.empty) sfreq0

     val dffreq = wider_array_of_vector (num_feats, 0) dffreq0

     fun learn_one th feats deps =

       let

         fun add_th weight t =

           let

             val im = Array.sub (sfreq, t)

             fun fold_fn s = Inttab.map_default (s, 0) (Integer.add weight)

           in

             map_array_at tfreq (Integer.add weight) t;

             Array.update (sfreq, t, fold fold_fn feats im)

           end

         val add_sym = map_array_at dffreq (Integer.add 1)

       in

         add_th nb_def_prior_weight th;

         List.app (add_th 1) deps;

         List.app add_sym feats

       end

     fun for i =

       if i = num_facts then ()

       else (learn_one i (Vector.sub (featss, i)) (Vector.sub (depss, i)); for (i + 1))

   in

     for num_facts0;

     (Array.vector tfreq, Array.vector sfreq, Array.vector dffreq)

   end

 fun naive_bayes (tfreq, sfreq, dffreq) num_facts max_suggs fact_idxs goal_feats =

   let

     val tau = 0.2 (* FUDGE *)

     val pos_weight = 5.0 (* FUDGE *)

     val def_val = ~18.0 (* FUDGE *)

     val init_val = 30.0 (* FUDGE *)

     val ln_afreq = Math.ln (Real.fromInt num_facts)

     val idf = Vector.map (fn i => ln_afreq - Math.ln (Real.fromInt i)) dffreq

     fun tfidf feat = Vector.sub (idf, feat)

     fun log_posterior i =

       let

         val tfreq = Real.fromInt (Vector.sub (tfreq, i))

         fun add_feat (f, fw0) (res, sfh) =

           (case Inttab.lookup sfh f of

             SOME sf =>

             (res + fw0 * tfidf f * Math.ln (pos_weight * Real.fromInt sf / tfreq),

              Inttab.delete f sfh)

           | NONE => (res + fw0 * tfidf f * def_val, sfh))

         val (res, sfh) = fold add_feat goal_feats (init_val * Math.ln tfreq, Vector.sub (sfreq, i))

         fun fold_sfh (f, sf) sow =

           sow + tfidf f * Math.ln (1.0 - Real.fromInt (sf - 1) / tfreq)

         val sum_of_weights = Inttab.fold fold_sfh sfh 0.0

       in

         res + tau * sum_of_weights

       end

     val posterior = Array.tabulate (num_facts, (fn j => (j, log_posterior j)))

     fun ret at acc =

       if at = num_facts then acc else ret (at + 1) (Array.sub (posterior, at) :: acc)

   in

     select_fact_idxs 100000.0 posterior fact_idxs;

     sort_array_suffix (Real.compare o apply2 snd) max_suggs posterior;

     ret (Integer.max 0 (num_facts - max_suggs)) []

   end

 val initial_k = 0

 fun k_nearest_neighbors dffreq num_facts num_feats depss featss max_suggs fact_idxs goal_feats =

   let

     exception EXIT of unit

     val ln_afreq = Math.ln (Real.fromInt num_facts)

     fun tfidf feat = ln_afreq - Math.ln (Real.fromInt (Vector.sub (dffreq, feat)))

     val overlaps_sqr = Array.tabulate (num_facts, rpair 0.0)

     val feat_facts = Array.array (num_feats, [])

     val _ = Vector.foldl (fn (feats, fact) =>

       (List.app (map_array_at feat_facts (cons fact)) feats; fact + 1)) 0 featss

     fun do_feat (s, sw0) =

       let

         val sw = sw0 * tfidf s

         val w6 = Math.pow (sw, 6.0 (* FUDGE *))

         fun inc_overlap j =

           let val (_, ov) = Array.sub (overlaps_sqr, j) in

             Array.update (overlaps_sqr, j, (j, w6 + ov))

           end

       in

         List.app inc_overlap (Array.sub (feat_facts, s))

       end

     val _ = List.app do_feat goal_feats

     val _ = sort_array_suffix (Real.compare o apply2 snd) num_facts overlaps_sqr

     val no_recommends = Unsynchronized.ref 0

     val recommends = Array.tabulate (num_facts, rpair 0.0)

     val age = Unsynchronized.ref 500000000.0

     fun inc_recommend v j =

       let val (_, ov) = Array.sub (recommends, j) in

         if ov <= 0.0 then

           (no_recommends := !no_recommends + 1; Array.update (recommends, j, (j, !age + ov)))

         else

           Array.update (recommends, j, (j, v + ov))

       end

     val k = Unsynchronized.ref 0

     fun do_k k =

       if k >= num_facts then

         raise EXIT ()

       else

         let

           val deps_factor = 2.7 (* FUDGE *)

           val (j, o2) = Array.sub (overlaps_sqr, num_facts - k - 1)

           val _ = inc_recommend o2 j

           val ds = Vector.sub (depss, j)

           val l = Real.fromInt (length ds)

         in

           List.app (inc_recommend (deps_factor * o2 / l)) ds

         end

     fun while1 () =

       if !k = initial_k + 1 then () else (do_k (!k); k := !k + 1; while1 ())

       handle EXIT () => ()

     fun while2 () =

       if !no_recommends >= max_suggs then ()

       else (do_k (!k); k := !k + 1; age := !age - 10000.0; while2 ())

       handle EXIT () => ()

     fun ret acc at =

       if at = num_facts then acc else ret (Array.sub (recommends, at) :: acc) (at + 1)

   in

     while1 ();

     while2 ();

     select_fact_idxs 1000000000.0 recommends fact_idxs;

     sort_array_suffix (Real.compare o apply2 snd) max_suggs recommends;

     ret [] (Integer.max 0 (num_facts - max_suggs))

   end

 (* experimental *)

 fun external_tool tool max_suggs learns goal_feats =

   let

     val ser = string_of_int (serial ()) (* poor person's attempt at thread-safety *)

     val ocs = TextIO.openOut ("adv_syms" ^ ser)

     val ocd = TextIO.openOut ("adv_deps" ^ ser)

     val ocq = TextIO.openOut ("adv_seq" ^ ser)

     val occ = TextIO.openOut ("adv_conj" ^ ser)

     fun os oc s = TextIO.output (oc, s)

     fun ol _ _ _ [] = ()

       | ol _ f _ [e] = f e

       | ol oc f sep (h :: t) = (f h; os oc sep; ol oc f sep t)

     fun do_learn (name, feats, deps) =

       (os ocs name; os ocs ":"; ol ocs (os ocs o quote) ", " feats; os ocs "\n";

        os ocd name; os ocd ":"; ol ocd (os ocd) " " deps; os ocd "\n"; os ocq name; os ocq "\n")

     fun forkexec no =

       let

         val cmd =

           "~/misc/" ^ tool ^ " adv_syms" ^ ser ^ " adv_deps" ^ ser ^ " " ^ string_of_int no ^

           " adv_seq" ^ ser ^ " < adv_conj" ^ ser

       in

         fst (Isabelle_System.bash_output cmd)

         |> space_explode " "

         |> filter_out (curry (op =) "")

       end

   in

     (List.app do_learn learns; ol occ (os occ o quote) ", " (map fst goal_feats);

      TextIO.closeOut ocs; TextIO.closeOut ocd; TextIO.closeOut ocq; TextIO.closeOut occ;

      forkexec max_suggs)

   end

 fun k_nearest_neighbors_ext max_suggs =

   external_tool ("newknn/knn" ^ " " ^ string_of_int initial_k) max_suggs

 fun naive_bayes_ext max_suggs = external_tool "predict/nbayes" max_suggs

 fun query_external ctxt algorithm max_suggs learns goal_feats =

   (trace_msg ctxt (fn () => "MaSh query external " ^ commas (map fst goal_feats));

    (case algorithm of

      MaSh_NB_Ext => naive_bayes_ext max_suggs learns goal_feats

    | MaSh_kNN_Ext => k_nearest_neighbors_ext max_suggs learns goal_feats))

 fun query_internal ctxt algorithm num_facts num_feats (fact_names, featss, depss)

     (freqs as (_, _, dffreq)) fact_idxs max_suggs goal_feats int_goal_feats =

   let

     fun nb () =

       naive_bayes freqs num_facts max_suggs fact_idxs int_goal_feats

       |> map fst

     fun knn () =

       k_nearest_neighbors dffreq num_facts num_feats depss featss max_suggs fact_idxs int_goal_feats

       |> map fst

   in

     (trace_msg ctxt (fn () => "MaSh query internal " ^ commas (map fst goal_feats) ^ " from {" ^

        elide_string 1000 (space_implode " " (Vector.foldr (op ::) [] fact_names)) ^ "}");

      (case algorithm of

        MaSh_NB => nb ()

      | MaSh_kNN => knn ()

      | MaSh_NB_kNN =>

        mesh_facts I (op =) max_suggs

          [(0.5 (* FUDGE *), (weight_facts_steeply (nb ()), [])),

           (0.5 (* FUDGE *), (weight_facts_steeply (knn ()), []))])

      |> map (curry Vector.sub fact_names))

    end

 end;

 (*** Persistent, stringly-typed state ***)

 fun meta_char c =

   if Char.isAlphaNum c orelse 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 encode_str = String.translate meta_char

 val encode_strs = map encode_str #> space_implode " "

 fun decode_str s =

   if String.isSubstring "%" s then unmeta_chars [] (String.explode s) else s;

 fun decode_strs s =

   space_explode " " s |> String.isSubstring "%" s ? map decode_str;

 datatype proof_kind = Isar_Proof | Automatic_Proof | Isar_Proof_wegen_Prover_Flop

 fun str_of_proof_kind Isar_Proof = "i"

   | str_of_proof_kind Automatic_Proof = "a"

   | str_of_proof_kind Isar_Proof_wegen_Prover_Flop = "x"

 fun proof_kind_of_str "a" = Automatic_Proof

   | proof_kind_of_str "x" = Isar_Proof_wegen_Prover_Flop

   | proof_kind_of_str _ (* "i" *) = Isar_Proof

 fun add_edge_to name parent =

   Graph.default_node (parent, (Isar_Proof, [], []))

   #> Graph.add_edge (parent, name)

 fun add_node kind name parents feats deps (accum as (access_G, (fact_xtab, feat_xtab), learns)) =

   let val fact_xtab' = add_to_xtab name fact_xtab in

     ((Graph.new_node (name, (kind, feats, deps)) access_G

       handle Graph.DUP _ => Graph.map_node name (K (kind, feats, deps)) access_G)

      |> fold (add_edge_to name) parents,

      (fact_xtab', fold maybe_add_to_xtab feats feat_xtab),

      (name, feats, deps) :: learns)

   end

   handle Symtab.DUP _ => accum (* robustness (in case the state file violates the invariant) *)

 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

       Exn.reraise exn

     else

       (trace_msg ctxt (fn () => "Internal error when " ^ when ^ ":\n" ^ Runtime.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.maximals G)) ^ " maximal"

 type ffds = string vector * int list vector * int list vector

 type freqs = int vector * int Inttab.table vector * int vector

 type mash_state =

   {access_G : (proof_kind * string list * string list) Graph.T,

    xtabs : xtab * xtab,

    ffds : ffds,

    freqs : freqs,

    dirty_facts : string list option}

 val empty_xtabs = (empty_xtab, empty_xtab)

 val empty_ffds = (Vector.fromList [], Vector.fromList [], Vector.fromList []) : ffds

 val empty_freqs = (Vector.fromList [], Vector.fromList [], Vector.fromList []) : freqs

 val empty_state =

   {access_G = Graph.empty,

    xtabs = empty_xtabs,

    ffds = empty_ffds,

    freqs = empty_freqs,

    dirty_facts = SOME []} : mash_state

 fun recompute_ffds_freqs_from_learns (learns : (string * string list * string list) list)

     ((num_facts, fact_tab), (num_feats, feat_tab)) num_facts0 (fact_names0, featss0, depss0) freqs0 =

   let

     val fact_names = Vector.concat [fact_names0, Vector.fromList (map #1 learns)]

     val featss = Vector.concat [featss0,

       Vector.fromList (map (map_filter (Symtab.lookup feat_tab) o #2) learns)]

     val depss = Vector.concat [depss0,

       Vector.fromList (map (map_filter (Symtab.lookup fact_tab) o #3) learns)]

   in

     ((fact_names, featss, depss),

      MaSh.learn_facts freqs0 num_facts0 num_facts num_feats depss featss)

   end

 fun reorder_learns (num_facts, fact_tab) learns =

   let val ary = Array.array (num_facts, ("", [], [])) in

     List.app (fn learn as (fact, _, _) =>

         Array.update (ary, the (Symtab.lookup fact_tab fact), learn))

       learns;

     Array.foldr (op ::) [] ary

   end

 fun recompute_ffds_freqs_from_access_G access_G (xtabs as (fact_xtab, _)) =

   let

     val learns =

       Graph.schedule (fn _ => fn (fact, (_, feats, deps)) => (fact, feats, deps)) access_G

       |> reorder_learns fact_xtab

   in

     recompute_ffds_freqs_from_learns learns xtabs 0 empty_ffds empty_freqs

   end

 local

 val version = "*** MaSh version 20190121 ***"

 exception FILE_VERSION_TOO_NEW of unit

 fun extract_node line =

   (case space_explode ":" line of

     [head, tail] =>

     (case (space_explode " " head, map (unprefix " ") (space_explode ";" tail)) of

       ([kind, name], [parents, feats, deps]) =>

       SOME (proof_kind_of_str kind, decode_str name, decode_strs parents, decode_strs feats,

         decode_strs deps)

     | _ => NONE)

   | _ => NONE)

 fun would_load_state (memory_time, _) =

   let val path = state_file () in

     (case try OS.FileSys.modTime (File.platform_path path) of

       NONE => false

     | SOME disk_time => memory_time < disk_time)

   end;

 fun load_state ctxt (time_state as (memory_time, _)) =

   let val path = state_file () in

     (case try OS.FileSys.modTime (File.platform_path path) of

       NONE => time_state

     | SOME disk_time =>

       if memory_time >= disk_time then

         time_state

       else

         (disk_time,

          (case try File.read_lines path of

            SOME (version' :: node_lines) =>

            let

              fun extract_line_and_add_node line =

                (case extract_node line of

                  NONE => I (* should not happen *)

                | SOME (kind, name, parents, feats, deps) => add_node kind name parents feats deps)

              val empty_G_etc = (Graph.empty, empty_xtabs, [])

              val (access_G, xtabs, rev_learns) =

                (case string_ord (version', version) of

                  EQUAL =>

                  try_graph ctxt "loading state" empty_G_etc

                    (fn () => fold extract_line_and_add_node node_lines empty_G_etc)

                | LESS => (remove_state_file (); empty_G_etc) (* cannot parse old file *)

                | GREATER => raise FILE_VERSION_TOO_NEW ())

              val (ffds, freqs) =

                recompute_ffds_freqs_from_learns (rev rev_learns) xtabs 0 empty_ffds empty_freqs

            in

              trace_msg ctxt (fn () => "Loaded fact graph (" ^ graph_info access_G ^ ")");

              {access_G = access_G, xtabs = xtabs, ffds = ffds, freqs = freqs, dirty_facts = SOME []}

            end

          | _ => empty_state)))

   end

 fun str_of_entry (kind, name, parents, feats, deps) =

   str_of_proof_kind kind ^ " " ^ encode_str name ^ ": " ^ encode_strs parents ^ "; " ^

   encode_strs feats ^ "; " ^ encode_strs deps ^ "\n"

 fun save_state _ (time_state as (_, {dirty_facts = SOME [], ...})) = time_state

   | save_state ctxt (memory_time, {access_G, xtabs, ffds, freqs, dirty_facts}) =

     let

       fun append_entry (name, ((kind, feats, deps), (parents, _))) =

         cons (kind, name, Graph.Keys.dest parents, feats, deps)

       val path = state_file ()

       val dirty_facts' =

         (case try OS.FileSys.modTime (File.platform_path path) of

           NONE => NONE

         | SOME disk_time => if disk_time <= memory_time then dirty_facts else NONE)

       val (banner, entries) =

         (case dirty_facts' of

           SOME names => (NONE, fold (append_entry o Graph.get_entry access_G) names [])

         | NONE => (SOME (version ^ "\n"), Graph.fold append_entry access_G []))

     in

       (case banner of SOME s => File.write path s | NONE => ();

        entries |> chunk_list 500 |> List.app (File.append path o implode o map str_of_entry))

       handle IO.Io _ => ();

       trace_msg ctxt (fn () =>

         "Saved fact graph (" ^ graph_info access_G ^

         (case dirty_facts of

           SOME dirty_facts => "; " ^ string_of_int (length dirty_facts) ^ " dirty fact(s)"

         | _ => "") ^  ")");

       (Time.now (),

        {access_G = access_G, xtabs = xtabs, ffds = ffds, freqs = freqs, dirty_facts = SOME []})

     end

 val global_state = Synchronized.var "Sledgehammer_MaSh.global_state" (Time.zeroTime, empty_state)

 in

 fun map_state ctxt f =

   (trace_msg ctxt (fn () => "Changing MaSh state");

    synchronized_timed_change global_state mash_time_limit

      (load_state ctxt ##> f #> save_state ctxt))

   |> ignore

   handle FILE_VERSION_TOO_NEW () => ()

 fun peek_state ctxt =

   (trace_msg ctxt (fn () => "Peeking at MaSh state");

    (case synchronized_timed_value global_state mash_time_limit of

      NONE => NONE

    | SOME state => if would_load_state state then NONE else SOME state))

 fun get_state ctxt =

   (trace_msg ctxt (fn () => "Retrieving MaSh state");

    synchronized_timed_change_result global_state mash_time_limit

      (perhaps (try (load_state ctxt)) #> `snd))

 fun clear_state ctxt =

   (trace_msg ctxt (fn () => "Clearing MaSh state");

    Synchronized.change global_state (fn _ => (remove_state_file (); (Time.zeroTime, empty_state))))

 end

 (*** Isabelle helpers ***)

 fun crude_printed_term size t =

   let

     fun term _ (res, 0) = (res, 0)

       | term (t $ u) (res, size) =

         let

           val (res, size) = term t (res ^ "(", size)

           val (res, size) = term u (res ^ " ", size)

         in

           (res ^ ")", size)

         end

       | term (Abs (s, _, t)) (res, size) = term t (res ^ "%" ^ s ^ ".", size - 1)

       | term (Bound n) (res, size) = (res ^ "#" ^ string_of_int n, size - 1)

       | term (Const (s, _)) (res, size) = (res ^ Long_Name.base_name s, size - 1)

       | term (Free (s, _)) (res, size) = (res ^ s, size - 1)

       | term (Var ((s, _), _)) (res, size) = (res ^ s, size - 1)

   in

     fst (term t ("", size))

   end

 fun nickname_of_thm th =

   if Thm.has_name_hint th then

     let val hint = Thm.get_name_hint th in

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

       (case Long_Name.dest_local hint of

         SOME suf =>

         Long_Name.implode [Thm.theory_name th, suf, crude_printed_term 25 (Thm.prop_of th)]

       | NONE => hint)

     end

   else

     crude_printed_term 50 (Thm.prop_of th)

 fun find_suggested_facts ctxt facts =

   let

     fun add (fact as (_, th)) = Symtab.default (nickname_of_thm th, fact)

     val tab = fold add facts Symtab.empty

     fun lookup nick =

       Symtab.lookup tab nick

       |> tap (fn NONE => trace_msg ctxt (fn () => "Cannot find " ^ quote nick) | _ => ())

   in map_filter lookup end

 fun free_feature_of s = "f" ^ s

 fun thy_feature_of s = "y" ^ s

 fun type_feature_of s = "t" ^ s

 fun class_feature_of s = "s" ^ s

 val local_feature = "local"

 fun crude_thm_ord ctxt =

   let

     val ancestor_lengths =

       fold (fn thy => Symtab.update (Context.theory_name thy, length (Context.ancestors_of thy)))

         (Theory.nodes_of (Proof_Context.theory_of ctxt)) Symtab.empty

     val ancestor_length = Symtab.lookup ancestor_lengths o Context.theory_id_name

     fun crude_theory_ord p =

       if Context.eq_thy_id p then EQUAL

       else if Context.proper_subthy_id p then LESS

       else if Context.proper_subthy_id (swap p) then GREATER

       else

         (case apply2 ancestor_length p of

           (SOME m, SOME n) =>

             (case int_ord (m, n) of

               EQUAL => string_ord (apply2 Context.theory_id_name p)

             | ord => ord)

         | _ => string_ord (apply2 Context.theory_id_name p))

   in

     fn p =>

       (case crude_theory_ord (apply2 Thm.theory_id p) of

         EQUAL =>

         (* The hack below is necessary because of odd dependencies that are not reflected in the theory

            comparison. *)

         let val q = apply2 nickname_of_thm p in

           (* Hack to put "xxx_def" before "xxxI" and "xxxE" *)

           (case bool_ord (apply2 (String.isSuffix "_def") (swap q)) of

             EQUAL => string_ord q

           | ord => ord)

         end

       | ord => ord)

   end;

 val thm_less_eq = Context.subthy_id o apply2 Thm.theory_id

 fun thm_less p = thm_less_eq p andalso not (thm_less_eq (swap p))

 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 = Thm.prop_of #> freeze #> Thm.global_cterm_of thy #> Goal.init

 fun run_prover_for_mash ctxt params prover goal_name facts goal =

   let

     val problem =

       {comment = "Goal: " ^ goal_name, state = Proof.init ctxt, goal = goal, subgoal = 1,

        subgoal_count = 1, factss = [("", facts)], found_proof = I}

   in

     get_minimizing_prover ctxt MaSh (K ()) prover params problem

   end

 val bad_types = [\<^type_name>\<open>prop\<close>, \<^type_name>\<open>bool\<close>, \<^type_name>\<open>fun\<close>]

 val crude_str_of_sort = space_implode "," o map Long_Name.base_name o subtract (op =) \<^sort>\<open>type\<close>

 fun crude_str_of_typ (Type (s, [])) = Long_Name.base_name s

   | crude_str_of_typ (Type (s, Ts)) = Long_Name.base_name s ^ implode (map crude_str_of_typ Ts)

   | crude_str_of_typ (TFree (_, S)) = crude_str_of_sort S

   | crude_str_of_typ (TVar (_, S)) = crude_str_of_sort S

 fun maybe_singleton_str "" = []

   | maybe_singleton_str s = [s]

 val max_pat_breadth = 5 (* FUDGE *)

 fun term_features_of ctxt thy_name term_max_depth type_max_depth ts =

   let

     val thy = Proof_Context.theory_of ctxt

     val fixes = map snd (Variable.dest_fixes ctxt)

     val classes = Sign.classes_of thy

     fun add_classes \<^sort>\<open>type\<close> = I

       | add_classes S =

         fold (`(Sorts.super_classes classes)

           #> swap #> op ::

           #> subtract (op =) \<^sort>\<open>type\<close>

           #> map class_feature_of

           #> union (op =)) S

     fun pattify_type 0 _ = []

       | pattify_type _ (Type (s, [])) = if member (op =) bad_types s then [] else [s]

       | pattify_type depth (Type (s, U :: Ts)) =

         let

           val T = Type (s, Ts)

           val ps = take max_pat_breadth (pattify_type depth T)

           val qs = take max_pat_breadth ("" :: pattify_type (depth - 1) U)

         in

           map_product (fn p => fn "" => p | q => p ^ "(" ^ q ^ ")") ps qs

         end

       | pattify_type _ (TFree (_, S)) = maybe_singleton_str (crude_str_of_sort S)

       | pattify_type _ (TVar (_, S)) = maybe_singleton_str (crude_str_of_sort S)

     fun add_type_pat depth T =

       union (op =) (map type_feature_of (pattify_type depth T))

     fun add_type_pats 0 _ = I

       | add_type_pats depth t = add_type_pat depth t #> add_type_pats (depth - 1) t

     fun add_type T =

       add_type_pats type_max_depth T

       #> fold_atyps_sorts (add_classes o snd) T

     fun add_subtypes (T as Type (_, Ts)) = add_type T #> fold add_subtypes Ts

       | add_subtypes T = add_type T

     fun pattify_term _ 0 _ = []

       | pattify_term _ _ (Const (s, _)) =

         if is_widely_irrelevant_const s then [] else [s]

       | pattify_term _ _ (Free (s, T)) =

         maybe_singleton_str (crude_str_of_typ T)

         |> (if member (op =) fixes s then cons (free_feature_of (Long_Name.append thy_name s))

             else I)

       | pattify_term _ _ (Var (_, T)) =

         maybe_singleton_str (crude_str_of_typ T)

       | pattify_term Ts _ (Bound j) =

         maybe_singleton_str (crude_str_of_typ (nth Ts j))

       | pattify_term Ts depth (t $ u) =

         let

           val ps = take max_pat_breadth (pattify_term Ts depth t)

           val qs = take max_pat_breadth ("" :: pattify_term Ts (depth - 1) u)

         in

           map_product (fn p => fn "" => p | q => p ^ "(" ^ q ^ ")") ps qs

         end

       | pattify_term _ _ _ = []

     fun add_term_pat Ts = union (op =) oo pattify_term Ts

     fun add_term_pats _ 0 _ = I

       | add_term_pats Ts depth t = add_term_pat Ts depth t #> add_term_pats Ts (depth - 1) t

     fun add_term Ts = add_term_pats Ts term_max_depth

     fun add_subterms Ts t =

       (case strip_comb t of

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

         (not (is_widely_irrelevant_const s) ? add_term Ts t)

         #> add_subtypes T #> fold (add_subterms Ts) args

       | (head, args) =>

         (case head of

            Free (_, T) => add_term Ts t #> add_subtypes T

          | Var (_, T) => add_subtypes T

          | Abs (_, T, body) => add_subtypes T #> add_subterms (T :: Ts) body

          | _ => I)

         #> fold (add_subterms Ts) args)

   in

     fold (add_subterms []) ts []

   end

 val term_max_depth = 2

 val type_max_depth = 1

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

 fun features_of ctxt thy_name (scope, _) ts =

   thy_feature_of thy_name ::

   term_features_of ctxt thy_name term_max_depth type_max_depth ts

   |> scope <> Global ? cons local_feature

 (* Too many dependencies is a sign that a decision procedure is at work. There is not much to learn

    from such proofs. *)

 val max_dependencies = 20 (* FUDGE *)

 val prover_default_max_facts = 25 (* FUDGE *)

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

 val typedef_dep = nickname_of_thm @{thm CollectI}

 (* Mysterious parts of the class machinery create lots of proofs that refer exclusively to

    "someI_ex" (and to some internal constructions). *)

 val class_some_dep = nickname_of_thm @{thm someI_ex}

 val fundef_ths =

   @{thms fundef_ex1_existence fundef_ex1_uniqueness fundef_ex1_iff fundef_default_value}

   |> map nickname_of_thm

 (* "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_thm

 fun is_size_def [dep] th =

     (case first_field ".rec" dep of

       SOME (pref, _) =>

       (case first_field ".size" (nickname_of_thm th) of

         SOME (pref', _) => pref = pref'

       | NONE => false)

     | NONE => false)

   | is_size_def _ _ = false

 fun trim_dependencies deps =

   if length deps > max_dependencies then NONE else SOME deps

 fun isar_dependencies_of name_tabs th =

   thms_in_proof max_dependencies (SOME name_tabs) th

   |> Option.map (fn deps =>

     if deps = [typedef_dep] orelse deps = [class_some_dep] orelse

         exists (member (op =) fundef_ths) deps orelse exists (member (op =) typedef_ths) deps orelse

         is_size_def deps th then

       []

     else

       deps)

 fun prover_dependencies_of ctxt (params as {verbose, max_facts, ...}) prover auto_level facts

     name_tabs th =

   (case isar_dependencies_of name_tabs th of

     SOME [] => (false, [])

   | isar_deps0 =>

     let

       val isar_deps = these isar_deps0

       val thy = Proof_Context.theory_of ctxt

       val goal = goal_of_thm thy th

       val name = nickname_of_thm th

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

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

       fun nickify ((_, stature), th) = ((nickname_of_thm th, stature), th)

       fun is_dep dep (_, th) = (nickname_of_thm 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 ((_, status), th) => accum @ [(("", status), th)]

           | NONE => accum (* should not happen *))

       val mepo_facts =

         facts

         |> mepo_suggested_facts ctxt params (max_facts |> the_default prover_default_max_facts) NONE

              hyp_ts concl_t

       val facts =

         mepo_facts

         |> fold (add_isar_dep facts) isar_deps

         |> map nickify

       val num_isar_deps = length isar_deps

     in

       if verbose andalso auto_level = 0 then

         writeln ("MaSh: " ^ quote prover ^ " on " ^ quote name ^ " with " ^

           string_of_int num_isar_deps ^ " + " ^ string_of_int (length facts - num_isar_deps) ^

           " facts")

       else

         ();

       (case run_prover_for_mash ctxt params prover name facts goal of

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

         (if verbose andalso auto_level = 0 then

            let val num_facts = length used_facts in

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

                plural_s num_facts)

            end

          else

            ();

          (true, map fst used_facts))

       | _ => (false, isar_deps))

     end)

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

 (* In the following functions, chunks are risers w.r.t. "thm_less_eq". *)

 fun chunks_and_parents_for chunks th =

   let

     fun insert_parent new parents =

       let val parents = parents |> filter_out (fn p => thm_less_eq (p, new)) in

         parents |> forall (fn p => not (thm_less_eq (new, p))) parents ? cons new

       end

     fun rechunk seen (rest as th' :: ths) =

       if thm_less_eq (th', th) then (rev seen, rest)

       else rechunk (th' :: seen) ths

     fun do_chunk [] accum = accum

       | do_chunk (chunk as hd_chunk :: _) (chunks, parents) =

         if thm_less_eq (hd_chunk, th) then

           (chunk :: chunks, insert_parent hd_chunk parents)

         else if thm_less_eq (List.last chunk, th) then

           let val (front, back as hd_back :: _) = rechunk [] chunk in

             (front :: back :: chunks, insert_parent hd_back parents)

           end

         else

           (chunk :: chunks, parents)

   in

     fold_rev do_chunk chunks ([], [])

     |>> cons []

     ||> map nickname_of_thm

   end

 fun attach_parents_to_facts _ [] = []

   | attach_parents_to_facts old_facts (facts as (_, th) :: _) =

     let

       fun do_facts _ [] = []

         | do_facts (_, parents) [fact] = [(parents, fact)]

         | do_facts (chunks, parents)

                    ((fact as (_, th)) :: (facts as (_, th') :: _)) =

           let

             val chunks = app_hd (cons th) chunks

             val chunks_and_parents' =

               if thm_less_eq (th, th') andalso

                 Thm.theory_name th = Thm.theory_name th'

               then (chunks, [nickname_of_thm th])

               else chunks_and_parents_for chunks th'

           in

             (parents, fact) :: do_facts chunks_and_parents' facts

           end

     in

       old_facts @ facts

       |> do_facts (chunks_and_parents_for [[]] th)

       |> drop (length old_facts)

     end

 fun is_fact_in_graph access_G = can (Graph.get_node access_G) o nickname_of_thm

 val chained_feature_factor = 0.5 (* FUDGE *)

 val extra_feature_factor = 0.1 (* FUDGE *)

 val num_extra_feature_facts = 10 (* FUDGE *)

 val max_proximity_facts = 100 (* FUDGE *)

 fun find_mash_suggestions ctxt max_facts suggs facts chained raw_unknown =

   let

     val inter_fact = inter (eq_snd Thm.eq_thm_prop)

     val raw_mash = find_suggested_facts ctxt facts suggs

     val proximate = take max_proximity_facts facts

     val unknown_chained = inter_fact raw_unknown chained

     val unknown_proximate = inter_fact raw_unknown proximate

     val mess =

       [(0.9 (* FUDGE *), (map (rpair 1.0) unknown_chained, [])),

        (0.4 (* FUDGE *), (weight_facts_smoothly unknown_proximate, [])),

        (0.1 (* FUDGE *), (weight_facts_steeply raw_mash, raw_unknown))]

     val unknown = raw_unknown

       |> fold (subtract (eq_snd Thm.eq_thm_prop)) [unknown_chained, unknown_proximate]

   in

     (mesh_facts (fact_distinct (op aconv)) (eq_snd (gen_eq_thm ctxt)) max_facts mess, unknown)

   end

 fun mash_suggested_facts ctxt thy_name ({debug, ...} : params) max_suggs hyp_ts concl_t facts =

   let

     val algorithm = the_mash_algorithm ()

     val facts = facts

       |> rev_sort_list_prefix (crude_thm_ord ctxt o apply2 snd)

         (Int.max (num_extra_feature_facts, max_proximity_facts))

     val chained = filter (fn ((_, (scope, _)), _) => scope = Chained) facts

     fun fact_has_right_theory (_, th) = thy_name = Thm.theory_name th

     fun chained_or_extra_features_of factor (((_, stature), th), weight) =

       [Thm.prop_of th]

       |> features_of ctxt (Thm.theory_name th) stature

       |> map (rpair (weight * factor))

   in

     (case get_state ctxt of

       NONE => ([], [])

     | SOME {access_G, xtabs = ((num_facts, fact_tab), (num_feats, feat_tab)), ffds, freqs, ...} =>

       let

         val goal_feats0 =

           features_of ctxt thy_name (Local, General) (concl_t :: hyp_ts)

         val chained_feats = chained

           |> map (rpair 1.0)

           |> map (chained_or_extra_features_of chained_feature_factor)

           |> rpair [] |-> fold (union (eq_fst (op =)))

         val extra_feats = facts

           |> take (Int.max (0, num_extra_feature_facts - length chained))

           |> filter fact_has_right_theory

           |> weight_facts_steeply

           |> map (chained_or_extra_features_of extra_feature_factor)

           |> rpair [] |-> fold (union (eq_fst (op =)))

         val goal_feats =

           fold (union (eq_fst (op =))) [chained_feats, extra_feats] (map (rpair 1.0) goal_feats0)

           |> debug ? sort (Real.compare o swap o apply2 snd)

         val fact_idxs = map_filter (Symtab.lookup fact_tab o nickname_of_thm o snd) facts

         val suggs =

           if algorithm = MaSh_NB_Ext orelse algorithm = MaSh_kNN_Ext then

             let

               val learns =

                 Graph.schedule (fn _ => fn (fact, (_, feats, deps)) => (fact, feats, deps))

                   access_G

             in

               MaSh.query_external ctxt algorithm max_suggs learns goal_feats

             end

           else

             let

               val int_goal_feats =

                 map_filter (fn (s, w) => Option.map (rpair w) (Symtab.lookup feat_tab s)) goal_feats

             in

               MaSh.query_internal ctxt algorithm num_facts num_feats ffds freqs fact_idxs max_suggs

                 goal_feats int_goal_feats

             end

         val unknown = filter_out (is_fact_in_graph access_G o snd) facts

       in

         find_mash_suggestions ctxt max_suggs suggs facts chained unknown

         |> apply2 (map fact_of_raw_fact)

       end)

   end

 fun mash_unlearn ctxt = (clear_state ctxt; writeln "Reset MaSh")

 fun learn_wrt_access_graph ctxt (name, parents, feats, deps)

     (accum as (access_G, (fact_xtab, feat_xtab))) =

   let

     fun maybe_learn_from from (accum as (parents, access_G)) =

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

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

     val access_G = access_G |> Graph.default_node (name, (Isar_Proof, feats, deps))

     val (parents, access_G) = ([], access_G) |> fold maybe_learn_from parents

     val (deps, _) = ([], access_G) |> fold maybe_learn_from deps

     val fact_xtab = add_to_xtab name fact_xtab

     val feat_xtab = fold maybe_add_to_xtab feats feat_xtab

   in

     (SOME (name, parents, feats, deps), (access_G, (fact_xtab, feat_xtab)))

   end

   handle Symtab.DUP _ => (NONE, accum) (* facts sometimes have the same name, confusingly *)

 fun relearn_wrt_access_graph ctxt (name, deps) access_G =

   let

     fun maybe_relearn_from from (accum as (parents, access_G)) =

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

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

     val access_G =

       access_G |> Graph.map_node name (fn (_, feats, _) => (Automatic_Proof, feats, deps))

     val (deps, _) = ([], access_G) |> fold maybe_relearn_from deps

   in

     ((name, deps), access_G)

   end

 fun flop_wrt_access_graph name =

   Graph.map_node name (fn (_, feats, deps) => (Isar_Proof_wegen_Prover_Flop, feats, deps))

 val learn_timeout_slack = 20.0

 fun launch_thread timeout task =

   let

     val hard_timeout = time_mult learn_timeout_slack timeout

     val birth_time = Time.now ()

     val death_time = birth_time + hard_timeout

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

   in

     Async_Manager_Legacy.thread MaShN birth_time death_time desc task

   end

 fun anonymous_proof_name () =

   Date.fmt (anonymous_proof_prefix ^ "%Y%m%d.%H%M%S.") (Date.fromTimeLocal (Time.now ())) ^

   serial_string ()

 fun mash_learn_proof ctxt ({timeout, ...} : params) t used_ths =

   if not (null used_ths) andalso is_mash_enabled () then

     launch_thread timeout (fn () =>

       let

         val thy = Proof_Context.theory_of ctxt

         val feats = features_of ctxt (Context.theory_name thy) (Local, General) [t]

       in

         map_state ctxt

           (fn {access_G, xtabs as ((num_facts0, _), _), ffds, freqs, dirty_facts} =>

              let

                val deps = used_ths

                  |> filter (is_fact_in_graph access_G)

                  |> map nickname_of_thm

                val name = anonymous_proof_name ()

                val (access_G', xtabs', rev_learns) =

                  add_node Automatic_Proof name [] (* ignore parents *) feats deps

                    (access_G, xtabs, [])

                val (ffds', freqs') =

                  recompute_ffds_freqs_from_learns (rev rev_learns) xtabs' num_facts0 ffds freqs

              in

                {access_G = access_G', xtabs = xtabs', ffds = ffds', freqs = freqs',

                 dirty_facts = Option.map (cons name) dirty_facts}

              end);

         (true, "")

       end)

   else

     ()

 fun sendback sub = Active.sendback_markup_command (sledgehammerN ^ " " ^ sub)

 val commit_timeout = seconds 30.0

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

 fun mash_learn_facts ctxt (params as {debug, verbose, ...}) prover auto_level run_prover

     learn_timeout facts =

   let

     val timer = Timer.startRealTimer ()

     fun next_commit_time () = Timer.checkRealTimer timer + commit_timeout

   in

     (case get_state ctxt of

       NONE => "MaSh is busy\nPlease try again later"

     | SOME {access_G, ...} =>

       let

         val is_in_access_G = is_fact_in_graph access_G o snd

         val no_new_facts = forall is_in_access_G facts

       in

         if no_new_facts andalso not run_prover then

           if auto_level < 2 then

             "No new " ^ (if run_prover then "automatic" else "Isar") ^ " proofs to learn" ^

             (if auto_level = 0 andalso not run_prover then

                "\n\nHint: Try " ^ sendback learn_proverN ^ " to learn from an automatic prover"

              else

                "")

           else

             ""

         else

           let

             val name_tabs = build_name_tables nickname_of_thm facts

             fun deps_of status th =

               if status = Non_Rec_Def orelse status = Rec_Def then

                 SOME []

               else if run_prover then

                 prover_dependencies_of ctxt params prover auto_level facts name_tabs th

                 |> (fn (false, _) => NONE | (true, deps) => trim_dependencies deps)

               else

                 isar_dependencies_of name_tabs th

             fun do_commit [] [] [] state = state

               | do_commit learns relearns flops

                   {access_G, xtabs as ((num_facts0, _), _), ffds, freqs, dirty_facts} =

                 let

                   val was_empty = Graph.is_empty access_G

                   val (learns, (access_G', xtabs')) =

                     fold_map (learn_wrt_access_graph ctxt) learns (access_G, xtabs)

                     |>> map_filter I

                   val (relearns, access_G'') =

                     fold_map (relearn_wrt_access_graph ctxt) relearns access_G'

                   val access_G''' = access_G'' |> fold flop_wrt_access_graph flops

                   val dirty_facts' =

                     (case (was_empty, dirty_facts) of

                       (false, SOME names) => SOME (map #1 learns @ map #1 relearns @ names)

                     | _ => NONE)

                   val (ffds', freqs') =

                     if null relearns then

                       recompute_ffds_freqs_from_learns

                         (map (fn (name, _, feats, deps) => (name, feats, deps)) learns) xtabs'

                         num_facts0 ffds freqs

                     else

                       recompute_ffds_freqs_from_access_G access_G''' xtabs'

                 in

                   {access_G = access_G''', xtabs = xtabs', ffds = ffds', freqs = freqs',

                    dirty_facts = dirty_facts'}

                 end

             fun commit last learns relearns flops =

               (if debug andalso auto_level = 0 then writeln "Committing..." else ();

                map_state ctxt (do_commit (rev learns) relearns flops);

                if not last andalso auto_level = 0 then

                  let val num_proofs = length learns + length relearns in

                    writeln ("Learned " ^ string_of_int num_proofs ^ " " ^

                      (if run_prover then "automatic" else "Isar") ^ " proof" ^

                      plural_s num_proofs ^ " in the last " ^ string_of_time commit_timeout)

                  end

                else

                  ())

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

               | learn_new_fact (parents, ((_, stature as (_, status)), th))

                   (learns, (num_nontrivial, next_commit, _)) =

                 let

                   val name = nickname_of_thm th

                   val feats = features_of ctxt (Thm.theory_name th) stature [Thm.prop_of th]

                   val deps = these (deps_of status th)

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

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

                   val (learns, next_commit) =

                     if Timer.checkRealTimer timer > next_commit then

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

                     else

                       (learns, next_commit)

                   val timed_out = Timer.checkRealTimer timer > learn_timeout

                 in

                   (learns, (num_nontrivial, next_commit, timed_out))

                 end

             val (num_new_facts, num_nontrivial) =

               if no_new_facts then

                 (0, 0)

               else

                 let

                   val new_facts = facts

                     |> sort (crude_thm_ord ctxt o apply2 snd)

                     |> map (pair []) (* ignore parents *)

                     |> filter_out (is_in_access_G o snd)

                   val (learns, (num_nontrivial, _, _)) =

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

                     |> fold learn_new_fact new_facts

                 in

                   commit true learns [] []; (length new_facts, num_nontrivial)

                 end

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

               | relearn_old_fact ((_, (_, status)), th)

                   ((relearns, flops), (num_nontrivial, next_commit, _)) =

                 let

                   val name = nickname_of_thm th

                   val (num_nontrivial, relearns, flops) =

                     (case deps_of status th of

                       SOME deps => (num_nontrivial + 1, (name, deps) :: relearns, flops)

                     | NONE => (num_nontrivial, relearns, name :: flops))

                   val (relearns, flops, next_commit) =

                     if Timer.checkRealTimer timer > next_commit then

                       (commit false [] relearns flops; ([], [], next_commit_time ()))

                     else

                       (relearns, flops, next_commit)

                   val timed_out = Timer.checkRealTimer timer > learn_timeout

                 in

                   ((relearns, flops), (num_nontrivial, next_commit, timed_out))

                 end

             val num_nontrivial =

               if not run_prover then

                 num_nontrivial

               else

                 let

                   val max_isar = 1000 * max_dependencies

                   fun priority_of th =

                     Random.random_range 0 max_isar +

                     (case try (Graph.get_node access_G) (nickname_of_thm th) of

                       SOME (Isar_Proof, _, deps) => ~100 * length deps

                     | SOME (Automatic_Proof, _, _) => 2 * max_isar

                     | SOME (Isar_Proof_wegen_Prover_Flop, _, _) => max_isar

                     | NONE => 0)

                   val old_facts = facts

                     |> filter is_in_access_G

                     |> map (`(priority_of o snd))

                     |> sort (int_ord o apply2 fst)

                     |> map snd

                   val ((relearns, flops), (num_nontrivial, _, _)) =

                     (([], []), (num_nontrivial, next_commit_time (), false))

                     |> fold relearn_old_fact old_facts

                 in

                   commit true [] relearns flops; num_nontrivial

                 end

           in

             if verbose orelse auto_level < 2 then

               "Learned " ^ string_of_int num_new_facts ^ " fact" ^ plural_s num_new_facts ^

               " and " ^ string_of_int num_nontrivial ^ " nontrivial " ^

               (if run_prover then "automatic and " else "") ^ "Isar proof" ^

               plural_s num_nontrivial ^

               (if verbose then " in " ^ string_of_time (Timer.checkRealTimer timer) else "")

             else

               ""

           end

       end)

   end

 fun mash_learn ctxt (params as {provers, timeout, ...}) fact_override chained run_prover =

   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 Keyword.empty_keywords css chained [] \<^prop>\<open>True\<close>

       |> sort (crude_thm_ord ctxt o apply2 snd o swap)

     val num_facts = length facts

     val prover = hd provers

     fun learn auto_level run_prover =

       mash_learn_facts ctxt params prover auto_level run_prover one_year facts

       |> writeln

   in

     if run_prover then

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

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

          string_of_time timeout ^ ").\n\nCollecting Isar proofs first...");

        learn 1 false;

        writeln "Now collecting automatic proofs\n\

          \This may take several hours; you can safely stop the learning process at any point";

        learn 0 true)

     else

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

          plural_s num_facts ^ " for Isar proofs...");

        learn 0 false)

   end

 fun mash_can_suggest_facts ctxt =

   (case get_state ctxt of

     NONE => false

   | SOME {access_G, ...} => not (Graph.is_empty access_G))

 fun mash_can_suggest_facts_fast ctxt =

   (case peek_state ctxt of

     NONE => false

   | SOME (_, {access_G, ...}) => not (Graph.is_empty access_G))

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

    reasons (e.g., duplicates). *)

 fun generous_max_suggestions max_facts = 2 * max_facts + 25 (* FUDGE *)

 val mepo_weight = 0.5 (* FUDGE *)

 val mash_weight = 0.5 (* FUDGE *)

 val max_facts_to_learn_before_query = 100 (* FUDGE *)

 (* The threshold should be large enough so that MaSh does not get activated for Auto Sledgehammer. *)

 val min_secs_for_learning = 10

 fun relevant_facts ctxt (params as {verbose, 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

     [("", map fact_of_raw_fact facts)]

   else if max_facts <= 0 orelse null facts then

     [("", [])]

   else

     let

       val thy_name = Context.theory_name (Proof_Context.theory_of ctxt)

       fun maybe_launch_thread exact min_num_facts_to_learn =

         if not (Async_Manager_Legacy.has_running_threads MaShN) andalso

            Time.toSeconds timeout >= min_secs_for_learning then

           let val timeout = time_mult learn_timeout_slack timeout in

             (if verbose then

                writeln ("Started MaShing through " ^

                  (if exact then "" else "up to ") ^ string_of_int min_num_facts_to_learn ^

                  " fact" ^ plural_s min_num_facts_to_learn ^ " in the background")

              else

                ());

             launch_thread timeout

               (fn () => (true, mash_learn_facts ctxt params prover 2 false timeout facts))

           end

         else

           ()

       val mash_enabled = is_mash_enabled ()

       val mash_fast = mash_can_suggest_facts_fast ctxt

       fun please_learn () =

         if mash_fast then

           (case get_state ctxt of

             NONE => maybe_launch_thread false (length facts)

           | SOME {access_G, xtabs = ((num_facts0, _), _), ...} =>

             let

               val is_in_access_G = is_fact_in_graph access_G o snd

               val min_num_facts_to_learn = length facts - num_facts0

             in

               if min_num_facts_to_learn <= max_facts_to_learn_before_query then

                 (case length (filter_out is_in_access_G facts) of

                   0 => ()

                 | num_facts_to_learn =>

                   if num_facts_to_learn <= max_facts_to_learn_before_query then

                     mash_learn_facts ctxt params prover 2 false timeout facts

                     |> (fn "" => () | s => writeln (MaShN ^ ": " ^ s))

                   else

                     maybe_launch_thread true num_facts_to_learn)

               else

                 maybe_launch_thread false min_num_facts_to_learn

             end)

         else

           maybe_launch_thread false (length facts)

       val _ =

         if learn andalso mash_enabled andalso fact_filter <> SOME mepoN then please_learn () else ()

       val effective_fact_filter =

         (case fact_filter of

           SOME ff => ff

         | NONE => if mash_enabled andalso mash_fast then meshN else mepoN)

       val unique_facts = drop_duplicate_facts facts

       val add_ths = Attrib.eval_thms ctxt add

       fun in_add (_, th) = member Thm.eq_thm_prop add_ths th

       fun add_and_take accepts =

         (case add_ths of

            [] => accepts

          | _ =>

            (unique_facts |> filter in_add |> map fact_of_raw_fact) @ (accepts |> filter_out in_add))

         |> take max_facts

       fun mepo () =

         (mepo_suggested_facts ctxt params max_facts NONE hyp_ts concl_t unique_facts

          |> weight_facts_steeply, [])

       fun mash () =

         mash_suggested_facts ctxt thy_name params (generous_max_suggestions max_facts) hyp_ts

           concl_t facts

         |>> weight_facts_steeply

       val mess =

         (* the order is important for the "case" expression below *)

         [] |> effective_fact_filter <> mepoN ? cons (mash_weight, mash)

            |> effective_fact_filter <> mashN ? cons (mepo_weight, mepo)

            |> Par_List.map (apsnd (fn f => f ()))

       val mesh =

         mesh_facts (fact_distinct (op aconv)) (eq_snd (gen_eq_thm ctxt)) max_facts mess

         |> add_and_take

     in

       (case (fact_filter, mess) of

         (NONE, [(_, (mepo, _)), (_, (mash, _))]) =>

         [(meshN, mesh),

          (mepoN, mepo |> map fst |> add_and_take),

          (mashN, mash |> map fst |> add_and_take)]

       | _ => [(effective_fact_filter, mesh)])

     end

 end;