1 (* Title: HOL/Tools/Sledgehammer/sledgehammer_mash.ML
2 Author: Jasmin Blanchette, TU Muenchen
3 Author: Cezary Kaliszyk, University of Innsbruck
5 Sledgehammer's machine-learning-based relevance filter (MaSh).
8 signature SLEDGEHAMMER_MASH =
10 type stature = ATP_Problem_Generate.stature
11 type raw_fact = Sledgehammer_Fact.raw_fact
12 type fact = Sledgehammer_Fact.fact
13 type fact_override = Sledgehammer_Fact.fact_override
14 type params = Sledgehammer_Prover.params
15 type prover_result = Sledgehammer_Prover.prover_result
17 val trace : bool Config.T
18 val duplicates : bool Config.T
26 val learn_isarN : string
27 val learn_proverN : string
28 val relearn_isarN : string
29 val relearn_proverN : string
30 val fact_filters : string list
31 val encode_str : string -> string
32 val encode_strs : string list -> string
33 val decode_str : string -> string
34 val decode_strs : string -> string list
35 val encode_features : (string * real) list -> string
36 val extract_suggestions : string -> string * (string * real) list
38 datatype mash_engine =
45 val is_mash_enabled : unit -> bool
46 val the_mash_engine : unit -> mash_engine
48 val mash_unlearn : Proof.context -> params -> unit
49 val nickname_of_thm : thm -> string
50 val find_suggested_facts : Proof.context -> ('b * thm) list -> string list -> ('b * thm) list
51 val mesh_facts : ('a * 'a -> bool) -> int -> (real * (('a * real) list * 'a list)) list -> 'a list
52 val crude_thm_ord : thm * thm -> order
53 val thm_less : thm * thm -> bool
54 val goal_of_thm : theory -> thm -> thm
55 val run_prover_for_mash : Proof.context -> params -> string -> string -> fact list -> thm ->
57 val features_of : Proof.context -> theory -> int -> int Symtab.table -> stature -> term list ->
59 val trim_dependencies : string list -> string list option
60 val isar_dependencies_of : string Symtab.table * string Symtab.table -> thm -> string list option
61 val prover_dependencies_of : Proof.context -> params -> string -> int -> raw_fact list ->
62 string Symtab.table * string Symtab.table -> thm -> bool * string list
63 val attach_parents_to_facts : ('a * thm) list -> ('a * thm) list ->
64 (string list * ('a * thm)) list
65 val num_extra_feature_facts : int
66 val extra_feature_factor : real
67 val weight_facts_smoothly : 'a list -> ('a * real) list
68 val weight_facts_steeply : 'a list -> ('a * real) list
69 val find_mash_suggestions : Proof.context -> int -> string list -> ('b * thm) list ->
70 ('b * thm) list -> ('b * thm) list -> ('b * thm) list * ('b * thm) list
71 val add_const_counts : term -> int Symtab.table -> int Symtab.table
72 val mash_suggested_facts : Proof.context -> params -> int -> term list -> term -> raw_fact list ->
74 val mash_learn_proof : Proof.context -> params -> term -> ('a * thm) list -> thm list -> unit
75 val mash_learn_facts : Proof.context -> params -> string -> bool -> int -> bool -> Time.time ->
76 raw_fact list -> string
77 val mash_learn : Proof.context -> params -> fact_override -> thm list -> bool -> unit
79 val mash_can_suggest_facts : Proof.context -> bool -> bool
80 val generous_max_suggestions : int -> int
81 val mepo_weight : real
82 val mash_weight : real
83 val relevant_facts : Proof.context -> params -> string -> int -> fact_override -> term list ->
84 term -> raw_fact list -> (string * fact list) list
85 val kill_learners : Proof.context -> params -> unit
86 val running_learners : unit -> unit
89 structure Sledgehammer_MaSh : SLEDGEHAMMER_MASH =
93 open ATP_Problem_Generate
94 open Sledgehammer_Util
95 open Sledgehammer_Fact
96 open Sledgehammer_Prover
97 open Sledgehammer_Prover_Minimize
98 open Sledgehammer_MePo
100 val trace = Attrib.setup_config_bool @{binding sledgehammer_mash_trace} (K false)
101 val duplicates = Attrib.setup_config_bool @{binding sledgehammer_fact_duplicates} (K false)
103 fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()
105 fun gen_eq_thm ctxt = if Config.get ctxt duplicates then Thm.eq_thm_strict else Thm.eq_thm_prop
115 val fact_filters = [meshN, mepoN, mashN]
117 val unlearnN = "unlearn"
118 val learn_isarN = "learn_isar"
119 val learn_proverN = "learn_prover"
120 val relearn_isarN = "relearn_isar"
121 val relearn_proverN = "relearn_prover"
123 fun map_array_at ary f i = Array.update (ary, i, f (Array.sub (ary, i)))
125 type xtab = int * int Symtab.table
127 val empty_xtab = (0, Symtab.empty)
129 fun add_to_xtab key (next, tab) = (next + 1, Symtab.update_new (key, next) tab)
130 fun maybe_add_to_xtab key = perhaps (try (add_to_xtab key))
132 fun mash_state_dir () = Path.explode "$ISABELLE_HOME_USER/mash" |> tap Isabelle_System.mkdir
133 fun mash_state_file () = Path.append (mash_state_dir ()) (Path.explode "state")
135 fun wipe_out_mash_state_dir () =
136 let val path = mash_state_dir () in
137 try (File.fold_dir (fn file => fn _ => try File.rm (Path.append path (Path.basic file))) path)
142 datatype mash_engine =
150 let val flag1 = Options.default_string @{system_option MaSh} in
151 (case if flag1 <> "none" (* default *) then flag1 else getenv "MASH" of
152 "yes" => SOME MaSh_SML_NB
153 | "py" => SOME MaSh_Py
154 | "sml" => SOME MaSh_SML_NB
155 | "sml_knn" => SOME MaSh_SML_kNN
156 | "sml_knn_ext" => SOME MaSh_SML_kNN_Ext
157 | "sml_nb" => SOME MaSh_SML_NB
158 | "sml_nb_ext" => SOME MaSh_SML_NB_Ext
162 val is_mash_enabled = is_some o mash_engine
163 val the_mash_engine = the_default MaSh_SML_NB o mash_engine
166 (*** Low-level communication with the Python version of MaSh ***)
168 val save_models_arg = "--saveModels"
169 val shutdown_server_arg = "--shutdownServer"
171 fun wipe_out_file file = ignore (try (File.rm o Path.explode) file)
173 fun write_file banner (xs, f) path =
174 (case banner of SOME s => File.write path s | NONE => ();
175 xs |> chunk_list 500 |> List.app (File.append path o implode o map f))
178 fun run_mash_tool ctxt overlord extra_args background write_cmds read_suggs =
180 val (temp_dir, serial) =
181 if overlord then (getenv "ISABELLE_HOME_USER", "")
182 else (getenv "ISABELLE_TMP", serial_string ())
183 val log_file = temp_dir ^ "/mash_log" ^ serial
184 val err_file = temp_dir ^ "/mash_err" ^ serial
185 val sugg_file = temp_dir ^ "/mash_suggs" ^ serial
186 val sugg_path = Path.explode sugg_file
187 val cmd_file = temp_dir ^ "/mash_commands" ^ serial
188 val cmd_path = Path.explode cmd_file
189 val model_dir = File.shell_path (mash_state_dir ())
192 "cd \"$ISABELLE_SLEDGEHAMMER_MASH\"/src; \
193 \PYTHONDONTWRITEBYTECODE=y ./mash.py\
196 \ --outputDir " ^ model_dir ^
197 " --modelFile=" ^ model_dir ^ "/model.pickle\
198 \ --dictsFile=" ^ model_dir ^ "/dict.pickle\
199 \ --log " ^ log_file ^
200 " --inputFile " ^ cmd_file ^
201 " --predictions " ^ sugg_file ^
202 (if extra_args = [] then "" else " " ^ space_implode " " extra_args) ^ " >& " ^ err_file ^
203 (if background then " &" else "")
206 (Isabelle_System.bash command
208 (case try File.read (Path.explode err_file) |> the_default "" of
209 "" => trace_msg ctxt (K "Done")
210 | s => warning ("MaSh error: " ^ elide_string 1000 s)));
211 read_suggs (fn () => try File.read_lines sugg_path |> these))
214 if overlord then () else List.app wipe_out_file [err_file, sugg_file, cmd_file]
216 write_file (SOME "") ([], K "") sugg_path;
217 write_file (SOME "") write_cmds cmd_path;
218 trace_msg ctxt (fn () => "Running " ^ command);
219 with_cleanup clean_up run_on ()
223 if Char.isAlphaNum c orelse c = #"_" orelse c = #"." orelse c = #"(" orelse c = #")" orelse
227 (* fixed width, in case more digits follow *)
228 "%" ^ stringN_of_int 3 (Char.ord c)
230 fun unmeta_chars accum [] = String.implode (rev accum)
231 | unmeta_chars accum (#"%" :: d1 :: d2 :: d3 :: cs) =
232 (case Int.fromString (String.implode [d1, d2, d3]) of
233 SOME n => unmeta_chars (Char.chr n :: accum) cs
234 | NONE => "" (* error *))
235 | unmeta_chars _ (#"%" :: _) = "" (* error *)
236 | unmeta_chars accum (c :: cs) = unmeta_chars (c :: accum) cs
238 val encode_str = String.translate meta_char
239 val decode_str = String.explode #> unmeta_chars []
241 val encode_strs = map encode_str #> space_implode " "
242 val decode_strs = space_explode " " #> filter_out (curry (op =) "") #> map decode_str
244 (* Avoid scientific notation *)
245 fun safe_str_of_real r =
246 if r < 0.00001 then "0.00001"
247 else if r >= 1000000.0 then "1000000"
248 else Markup.print_real r
250 fun encode_feature (names, weight) =
251 encode_str names ^ (if Real.== (weight, 1.0) then "" else "=" ^ safe_str_of_real weight)
253 val encode_features = map encode_feature #> space_implode " "
255 fun str_of_learn (name, parents, feats, deps) =
256 "! " ^ encode_str name ^ ": " ^ encode_strs parents ^ "; " ^ encode_strs feats ^ "; " ^
257 encode_strs deps ^ "\n"
259 fun str_of_relearn (name, deps) = "p " ^ encode_str name ^ ": " ^ encode_strs deps ^ "\n"
261 fun str_of_query max_suggs (learns, hints, parents, feats) =
262 implode (map str_of_learn learns) ^
263 "? " ^ string_of_int max_suggs ^ " # " ^ encode_strs parents ^ "; " ^ encode_features feats ^
264 (if null hints then "" else "; " ^ encode_strs hints) ^ "\n"
266 (* The suggested weights do not make much sense. *)
267 fun extract_suggestion sugg =
268 (case space_explode "=" sugg of
269 [name, weight] => SOME (decode_str name, Real.fromString weight |> the_default 1.0)
270 | [name] => SOME (decode_str name, 1.0)
273 fun extract_suggestions line =
274 (case space_explode ":" line of
275 [goal, suggs] => (decode_str goal, map_filter extract_suggestion (space_explode " " suggs))
281 fun shutdown ctxt overlord =
282 (trace_msg ctxt (K "MaSh_Py shutdown");
283 run_mash_tool ctxt overlord [shutdown_server_arg] false ([], K "") (K ()))
285 fun save ctxt overlord =
286 (trace_msg ctxt (K "MaSh_Py save");
287 run_mash_tool ctxt overlord [save_models_arg] true ([], K "") (K ()))
289 fun unlearn ctxt overlord =
290 (trace_msg ctxt (K "MaSh_Py unlearn");
291 shutdown ctxt overlord;
292 wipe_out_mash_state_dir ())
294 fun learn _ _ _ [] = ()
295 | learn ctxt overlord save learns =
296 (trace_msg ctxt (fn () =>
297 "MaSh_Py learn {" ^ elide_string 1000 (space_implode " " (map #1 learns)) ^ "}");
298 run_mash_tool ctxt overlord ([] |> save ? cons save_models_arg) false (learns, str_of_learn)
301 fun relearn _ _ _ [] = ()
302 | relearn ctxt overlord save relearns =
303 (trace_msg ctxt (fn () => "MaSh_Py relearn " ^
304 elide_string 1000 (space_implode " " (map #1 relearns)));
305 run_mash_tool ctxt overlord ([] |> save ? cons save_models_arg) false
306 (relearns, str_of_relearn) (K ()))
308 fun query ctxt overlord max_suggs (query as (_, _, _, feats)) =
309 (trace_msg ctxt (fn () => "MaSh_Py query " ^ encode_features feats);
310 run_mash_tool ctxt overlord [] false ([query], str_of_query max_suggs) (fn suggs =>
311 (case suggs () of [] => [] | suggs => snd (extract_suggestions (List.last suggs))))
312 handle List.Empty => [])
317 (*** Standard ML version of MaSh ***)
322 exception BOTTOM of int
324 fun heap cmp bnd al a =
327 let val i31 = i + i + i + 1 in
329 let val x = Unsynchronized.ref i31 in
330 if cmp (Array.sub (a, i31), Array.sub (a, i31 + 1)) = LESS then x := i31 + 1 else ();
331 if cmp (Array.sub (a, !x), Array.sub (a, i31 + 2)) = LESS then x := i31 + 2 else ();
335 if i31 + 1 < l andalso cmp (Array.sub (a, i31), Array.sub (a, i31 + 1)) = LESS
336 then i31 + 1 else if i31 < l then i31 else raise BOTTOM i
339 fun trickledown l i e =
340 let val j = maxson l i in
341 if cmp (Array.sub (a, j), e) = GREATER then
342 (Array.update (a, i, Array.sub (a, j)); trickledown l j e)
344 Array.update (a, i, e)
347 fun trickle l i e = trickledown l i e handle BOTTOM i => Array.update (a, i, e)
350 let val j = maxson l i in
351 Array.update (a, i, Array.sub (a, j));
355 fun bubble l i = bubbledown l i handle BOTTOM i => i
358 let val father = (i - 1) div 3 in
359 if cmp (Array.sub (a, father), e) = LESS then
360 (Array.update (a, i, Array.sub (a, father));
361 if father > 0 then trickleup father e else Array.update (a, 0, e))
363 Array.update (a, i, e)
366 fun for i = if i < 0 then () else (trickle al i (Array.sub (a, i)); for (i - 1))
369 if i < Integer.max 2 (al - bnd) then
372 let val e = Array.sub (a, i) in
373 Array.update (a, i, Array.sub (a, 0));
374 trickleup (bubble i 0) e;
378 for (((al + 1) div 3) - 1);
381 let val e = Array.sub (a, 1) in
382 Array.update (a, 1, Array.sub (a, 0));
383 Array.update (a, 0, e)
389 val number_of_nearest_neighbors = 10 (* FUDGE *)
391 fun select_visible_facts big_number recommends =
393 let val (j, ov) = Array.sub (recommends, at) in
394 Array.update (recommends, at, (j, big_number + ov))
397 exception EXIT of unit
399 fun k_nearest_neighbors dffreq num_facts depss feat_facts max_suggs visible_facts goal_feats =
401 val ln_afreq = Math.ln (Real.fromInt num_facts)
402 fun tfidf feat = ln_afreq - Math.ln (Real.fromInt (Vector.sub (dffreq, feat)))
404 val overlaps_sqr = Array.tabulate (num_facts, rpair 0.0)
406 fun inc_overlap j v =
407 let val ov = snd (Array.sub (overlaps_sqr, j)) in
408 Array.update (overlaps_sqr, j, (j, v + ov))
415 fun do_th j = if j < num_facts then inc_overlap j w2 else ()
417 List.app do_th (Array.sub (feat_facts, s))
420 val _ = List.app do_feat goal_feats
421 val _ = heap (Real.compare o pairself snd) num_facts num_facts overlaps_sqr
422 val no_recommends = Unsynchronized.ref 0
423 val recommends = Array.tabulate (num_facts, rpair 0.0)
424 val age = Unsynchronized.ref 500000000.0
426 fun inc_recommend j v =
427 let val ov = snd (Array.sub (recommends, j)) in
429 (no_recommends := !no_recommends + 1; Array.update (recommends, j, (j, !age + ov)))
430 else if ov < !age + 1000.0 then
431 Array.update (recommends, j, (j, v + ov))
436 val k = Unsynchronized.ref 0
438 if k >= num_facts then
442 val (j, o2) = Array.sub (overlaps_sqr, num_facts - k - 1)
443 val o1 = Math.sqrt o2
444 val _ = inc_recommend j o1
445 val ds = Vector.sub (depss, j)
446 val l = Real.fromInt (length ds)
448 List.app (fn d => inc_recommend d (o1 / l)) ds
452 if !k = number_of_nearest_neighbors then () else (do_k (!k); k := !k + 1; while1 ())
456 if !no_recommends >= max_suggs then ()
457 else (do_k (!k); k := !k + 1; age := !age - 10000.0; while2 ())
461 if at = num_facts then acc else ret (Array.sub (recommends, at) :: acc) (at + 1)
465 select_visible_facts 1000000000.0 recommends visible_facts;
466 heap (Real.compare o pairself snd) max_suggs num_facts recommends;
467 ret [] (Integer.max 0 (num_facts - max_suggs))
470 fun wider_array_of_vector init vec =
471 let val ary = Array.array init in
472 Array.copyVec {src = vec, dst = ary, di = 0};
476 val nb_def_prior_weight = 21 (* FUDGE *)
478 fun learn_facts (tfreq0, sfreq0, dffreq0) num_facts0 num_facts num_feats depss featss =
480 val tfreq = wider_array_of_vector (num_facts, 0) tfreq0
481 val sfreq = wider_array_of_vector (num_facts, Inttab.empty) sfreq0
482 val dffreq = wider_array_of_vector (num_feats, 0) dffreq0
484 fun learn_one th feats deps =
486 fun add_th weight t =
488 val im = Array.sub (sfreq, t)
489 fun fold_fn s = Inttab.map_default (s, 0) (Integer.add weight)
491 map_array_at tfreq (Integer.add weight) t;
492 Array.update (sfreq, t, fold fold_fn feats im)
495 val add_sym = map_array_at dffreq (Integer.add 1)
497 add_th nb_def_prior_weight th;
498 List.app (add_th 1) deps;
499 List.app add_sym feats
503 if i = num_facts then
506 (learn_one (num_facts0 + i) (Vector.sub (featss, i)) (Vector.sub (depss, i));
510 (Array.vector tfreq, Array.vector sfreq, Array.vector dffreq)
513 fun naive_bayes (tfreq, sfreq, dffreq) num_facts max_suggs visible_facts goal_feats =
515 val tau = 0.05 (* FUDGE *)
516 val pos_weight = 10.0 (* FUDGE *)
517 val def_val = ~15.0 (* FUDGE *)
519 val ln_afreq = Math.ln (Real.fromInt num_facts)
520 val idf = Vector.map (fn i => ln_afreq - Math.ln (Real.fromInt i)) dffreq
522 fun tfidf feat = Vector.sub (idf, feat)
524 fun log_posterior i =
526 val tfreq = Real.fromInt (Vector.sub (tfreq, i))
528 fun fold_feats f (res, sfh) =
529 (case Inttab.lookup sfh f of
531 (res + tfidf f * Math.ln (pos_weight * Real.fromInt sf / tfreq),
533 | NONE => (res + tfidf f * def_val, sfh))
535 val (res, sfh) = fold fold_feats goal_feats (Math.ln tfreq, Vector.sub (sfreq, i))
537 fun fold_sfh (f, sf) sow = sow + tfidf f * Math.ln (1.0 + (1.0 - Real.fromInt sf) / tfreq)
539 val sum_of_weights = Inttab.fold fold_sfh sfh 0.0
541 res + tau * sum_of_weights
544 val posterior = Array.tabulate (num_facts, (fn j => (j, log_posterior j)))
547 if at = num_facts then acc else ret (at + 1) (Array.sub (posterior, at) :: acc)
549 select_visible_facts 100000.0 posterior visible_facts;
550 heap (Real.compare o pairself snd) max_suggs num_facts posterior;
551 ret (Integer.max 0 (num_facts - max_suggs)) []
555 fun naive_bayes_py ctxt overlord num_facts depss featss max_suggs goal_feats =
557 fun name_of_fact j = "f" ^ string_of_int j
558 fun fact_of_name s = the (Int.fromString (unprefix "f" s))
559 fun name_of_feature j = "F" ^ string_of_int j
560 fun parents_of j = if j = 0 then [] else [name_of_fact (j - 1)]
562 val learns = map (fn j => (name_of_fact j, parents_of j,
563 map name_of_feature (Vector.sub (featss, j)),
564 map name_of_fact (Vector.sub (depss, j)))) (0 upto num_facts - 1)
565 val parents' = parents_of num_facts
566 val goal_feats' = map (rpair 1.0 o name_of_feature) goal_feats
568 MaSh_Py.unlearn ctxt overlord;
569 OS.Process.sleep (seconds 2.0); (* hack *)
570 MaSh_Py.query ctxt overlord max_suggs (learns, [], parents', goal_feats')
571 |> map (apfst fact_of_name)
575 fun external_tool tool max_suggs learns goal_feats =
577 val ser = string_of_int (serial ()) (* poor person's attempt at thread-safety *)
578 val ocs = TextIO.openOut ("adv_syms" ^ ser)
579 val ocd = TextIO.openOut ("adv_deps" ^ ser)
580 val ocq = TextIO.openOut ("adv_seq" ^ ser)
581 val occ = TextIO.openOut ("adv_conj" ^ ser)
583 fun os oc s = TextIO.output (oc, s)
587 | ol oc f sep (h :: t) = (f h; os oc sep; ol oc f sep t)
589 fun do_learn (name, feats, deps) =
590 (os ocs name; os ocs ":"; ol ocs (os ocs o quote) ", " feats; os ocs "\n";
591 os ocd name; os ocd ":"; ol ocd (os ocd) " " deps; os ocd "\n"; os ocq name; os ocq "\n")
596 "~/misc/" ^ tool ^ " adv_syms" ^ ser ^ " adv_deps" ^ ser ^ " " ^ string_of_int no ^
597 " adv_seq" ^ ser ^ " < adv_conj" ^ ser
599 fst (Isabelle_System.bash_output cmd)
601 |> filter_out (curry (op =) "")
604 (List.app do_learn learns; ol occ (os occ o quote) ", " goal_feats;
605 TextIO.closeOut ocs; TextIO.closeOut ocd; TextIO.closeOut ocq; TextIO.closeOut occ;
609 val k_nearest_neighbors_ext =
610 external_tool ("newknn/knn" ^ " " ^ string_of_int number_of_nearest_neighbors)
611 val naive_bayes_ext = external_tool "predict/nbayes"
613 fun query_external ctxt engine max_suggs learns goal_feats =
614 (trace_msg ctxt (fn () => "MaSh_SML query external " ^ encode_strs goal_feats);
616 MaSh_SML_kNN_Ext => k_nearest_neighbors_ext max_suggs learns goal_feats
617 | MaSh_SML_NB_Ext => naive_bayes_ext max_suggs learns goal_feats))
619 fun query_internal ctxt engine num_facts num_feats (fact_names, featss, depss)
620 (freqs as (_, _, dffreq)) visible_facts max_suggs goal_feats int_goal_feats =
621 (trace_msg ctxt (fn () => "MaSh_SML query internal " ^ encode_strs goal_feats ^ " from {" ^
622 elide_string 1000 (space_implode " " (Vector.foldr (op ::) [] fact_names)) ^ "}");
626 val feat_facts = Array.array (num_feats, [])
628 Vector.foldl (fn (feats, fact) =>
629 (List.app (map_array_at feat_facts (cons fact)) feats; fact + 1))
632 k_nearest_neighbors dffreq num_facts depss feat_facts max_suggs visible_facts int_goal_feats
634 | MaSh_SML_NB => naive_bayes freqs num_facts max_suggs visible_facts int_goal_feats)
635 |> map (curry Vector.sub fact_names o fst))
640 (*** Middle-level communication with MaSh ***)
642 datatype proof_kind = Isar_Proof | Automatic_Proof | Isar_Proof_wegen_Prover_Flop
644 fun str_of_proof_kind Isar_Proof = "i"
645 | str_of_proof_kind Automatic_Proof = "a"
646 | str_of_proof_kind Isar_Proof_wegen_Prover_Flop = "x"
648 fun proof_kind_of_str "a" = Automatic_Proof
649 | proof_kind_of_str "x" = Isar_Proof_wegen_Prover_Flop
650 | proof_kind_of_str _ (* "i" *) = Isar_Proof
652 fun add_edge_to name parent =
653 Graph.default_node (parent, (Isar_Proof, [], []))
654 #> Graph.add_edge (parent, name)
656 fun add_node kind name parents feats deps (access_G, (fact_xtab, feat_xtab), learns) =
657 ((Graph.new_node (name, (kind, feats, deps)) access_G
658 handle Graph.DUP _ => Graph.map_node name (K (kind, feats, deps)) access_G)
659 |> fold (add_edge_to name) parents,
660 (maybe_add_to_xtab name fact_xtab,
661 fold maybe_add_to_xtab feats feat_xtab),
662 (name, feats, deps) :: learns)
664 fun try_graph ctxt when def f =
667 Graph.CYCLES (cycle :: _) =>
668 (trace_msg ctxt (fn () => "Cycle involving " ^ commas cycle ^ " when " ^ when); def)
670 (trace_msg ctxt (fn () => "Duplicate fact " ^ quote name ^ " when " ^ when); def)
671 | Graph.UNDEF name =>
672 (trace_msg ctxt (fn () => "Unknown fact " ^ quote name ^ " when " ^ when); def)
674 if Exn.is_interrupt exn then
677 (trace_msg ctxt (fn () => "Internal error when " ^ when ^ ":\n" ^ Runtime.exn_message exn);
681 string_of_int (length (Graph.keys G)) ^ " node(s), " ^
682 string_of_int (fold (Integer.add o length o snd) (Graph.dest G) 0) ^ " edge(s), " ^
683 string_of_int (length (Graph.maximals G)) ^ " maximal"
686 {access_G : (proof_kind * string list * string list) Graph.T,
688 ffds : string vector * int list vector * int list vector,
689 freqs : int vector * int Inttab.table vector * int vector,
690 dirty_facts : string list option}
692 val empty_xtabs = (empty_xtab, empty_xtab)
693 val empty_ffds = (Vector.fromList [], Vector.fromList [], Vector.fromList [])
694 val empty_freqs = (Vector.fromList [], Vector.fromList [], Vector.fromList [])
697 {access_G = Graph.empty,
701 dirty_facts = SOME []} : mash_state
703 fun recompute_ffds_freqs_from_learns learns ((num_facts, fact_tab), (num_feats, feat_tab))
704 num_facts0 (fact_names0, featss0, depss0) freqs0 =
706 val fact_names = Vector.concat [fact_names0, Vector.fromList (map #1 learns)]
707 val featss = Vector.concat [featss0,
708 Vector.fromList (map (map_filter (Symtab.lookup feat_tab) o #2) learns)]
709 val depss = Vector.concat [depss0,
710 Vector.fromList (map (map_filter (Symtab.lookup fact_tab) o #3) learns)]
712 ((fact_names, featss, depss),
713 MaSh_SML.learn_facts freqs0 num_facts0 num_facts num_feats depss featss)
716 fun reorder_learns (num_facts, fact_tab) learns =
717 let val ary = Array.array (num_facts, ("", [], [])) in
718 List.app (fn learn as (fact, _, _) =>
719 Array.update (ary, the (Symtab.lookup fact_tab fact), learn))
721 Array.foldr (op ::) [] ary
724 fun recompute_ffds_freqs_from_access_G access_G (xtabs as (fact_xtab, _)) =
727 Graph.schedule (fn _ => fn (fact, (_, feats, deps)) => (fact, feats, deps)) access_G
728 |> reorder_learns fact_xtab
730 recompute_ffds_freqs_from_learns learns xtabs 0 empty_ffds empty_freqs
735 val version = "*** MaSh version 20140625 ***"
737 exception FILE_VERSION_TOO_NEW of unit
739 fun extract_node line =
740 (case space_explode ":" line of
742 (case (space_explode " " head, map (unprefix " ") (space_explode ";" tail)) of
743 ([kind, name], [parents, feats, deps]) =>
744 SOME (proof_kind_of_str kind, decode_str name, decode_strs parents, decode_strs feats,
749 fun load_state ctxt overlord (time_state as (memory_time, _)) =
750 let val path = mash_state_file () in
751 (case try OS.FileSys.modTime (Path.implode (Path.expand path)) of
754 if Time.>= (memory_time, disk_time) then
758 (case try File.read_lines path of
759 SOME (version' :: node_lines) =>
761 fun extract_line_and_add_node line =
762 (case extract_node line of
763 NONE => I (* should not happen *)
764 | SOME (kind, name, parents, feats, deps) => add_node kind name parents feats deps)
766 val empty_G_etc = (Graph.empty, empty_xtabs, [])
768 val (access_G, xtabs, rev_learns) =
769 (case string_ord (version', version) of
771 try_graph ctxt "loading state" empty_G_etc
772 (fn () => fold extract_line_and_add_node node_lines empty_G_etc)
774 (* cannot parse old file *)
775 (if the_mash_engine () = MaSh_Py then MaSh_Py.unlearn ctxt overlord
776 else wipe_out_mash_state_dir ();
778 | GREATER => raise FILE_VERSION_TOO_NEW ())
781 recompute_ffds_freqs_from_learns (rev rev_learns) xtabs 0 empty_ffds empty_freqs
783 trace_msg ctxt (fn () => "Loaded fact graph (" ^ graph_info access_G ^ ")");
784 {access_G = access_G, xtabs = xtabs, ffds = ffds, freqs = freqs, dirty_facts = SOME []}
786 | _ => empty_state)))
789 fun str_of_entry (kind, name, parents, feats, deps) =
790 str_of_proof_kind kind ^ " " ^ encode_str name ^ ": " ^ encode_strs parents ^ "; " ^
791 encode_strs feats ^ "; " ^ encode_strs deps ^ "\n"
793 fun save_state _ (time_state as (_, {dirty_facts = SOME [], ...})) = time_state
794 | save_state ctxt (memory_time, {access_G, xtabs, ffds, freqs, dirty_facts}) =
796 fun append_entry (name, ((kind, feats, deps), (parents, _))) =
797 cons (kind, name, Graph.Keys.dest parents, feats, deps)
799 val path = mash_state_file ()
801 (case try OS.FileSys.modTime (Path.implode path) of
803 | SOME disk_time => if Time.< (disk_time, memory_time) then dirty_facts else NONE)
804 val (banner, entries) =
805 (case dirty_facts' of
806 SOME names => (NONE, fold (append_entry o Graph.get_entry access_G) names [])
807 | NONE => (SOME (version ^ "\n"), Graph.fold append_entry access_G []))
809 write_file banner (entries, str_of_entry) path;
810 trace_msg ctxt (fn () =>
811 "Saved fact graph (" ^ graph_info access_G ^
813 SOME dirty_facts => "; " ^ string_of_int (length dirty_facts) ^ " dirty fact(s)"
816 {access_G = access_G, xtabs = xtabs, ffds = ffds, freqs = freqs, dirty_facts = SOME []})
819 val global_state = Synchronized.var "Sledgehammer_MaSh.global_state" (Time.zeroTime, empty_state)
823 fun map_state ctxt overlord f =
824 Synchronized.change global_state (load_state ctxt overlord ##> f #> save_state ctxt)
825 handle FILE_VERSION_TOO_NEW () => ()
827 fun peek_state ctxt overlord f =
828 Synchronized.change_result global_state (perhaps (try (load_state ctxt overlord)) #> `snd #>> f)
830 fun clear_state ctxt overlord =
831 (* "MaSh_Py.unlearn" also removes the state file *)
832 Synchronized.change global_state (fn _ =>
833 (if the_mash_engine () = MaSh_Py then MaSh_Py.unlearn ctxt overlord
834 else wipe_out_mash_state_dir ();
835 (Time.zeroTime, empty_state)))
839 fun mash_unlearn ctxt ({overlord, ...} : params) =
840 (clear_state ctxt overlord; Output.urgent_message "Reset MaSh.")
843 (*** Isabelle helpers ***)
845 val local_prefix = "local" ^ Long_Name.separator
847 fun elided_backquote_thm threshold th =
848 elide_string threshold (backquote_thm (Proof_Context.init_global (Thm.theory_of_thm th)) th)
850 val thy_name_of_thm = Context.theory_name o Thm.theory_of_thm
852 fun nickname_of_thm th =
853 if Thm.has_name_hint th then
854 let val hint = Thm.get_name_hint th in
855 (* There must be a better way to detect local facts. *)
856 (case try (unprefix local_prefix) hint of
858 thy_name_of_thm th ^ Long_Name.separator ^ suf ^ Long_Name.separator ^
859 elided_backquote_thm 50 th
863 elided_backquote_thm 200 th
865 fun find_suggested_facts ctxt facts =
867 fun add (fact as (_, th)) = Symtab.default (nickname_of_thm th, fact)
868 val tab = fold add facts Symtab.empty
870 Symtab.lookup tab nick
871 |> tap (fn NONE => trace_msg ctxt (fn () => "Cannot find " ^ quote nick) | _ => ())
872 in map_filter lookup end
874 fun scaled_avg [] = 0
875 | scaled_avg xs = Real.ceil (100000000.0 * fold (curry (op +)) xs 0.0) div length xs
878 | avg xs = fold (curry (op +)) xs 0.0 / Real.fromInt (length xs)
880 fun normalize_scores _ [] = []
881 | normalize_scores max_facts xs =
882 map (apsnd (curry Real.* (1.0 / avg (map snd (take max_facts xs))))) xs
884 fun mesh_facts fact_eq max_facts [(_, (sels, unks))] =
885 distinct fact_eq (map fst (take max_facts sels) @ take (max_facts - length sels) unks)
886 | mesh_facts fact_eq max_facts mess =
888 val mess = mess |> map (apsnd (apfst (normalize_scores max_facts)))
890 fun score_in fact (global_weight, (sels, unks)) =
891 let val score_at = try (nth sels) #> Option.map (fn (_, score) => global_weight * score) in
892 (case find_index (curry fact_eq fact o fst) sels of
893 ~1 => if member fact_eq unks fact then NONE else SOME 0.0
894 | rank => score_at rank)
897 fun weight_of fact = mess |> map_filter (score_in fact) |> scaled_avg
899 fold (union fact_eq o map fst o take max_facts o fst o snd) mess []
900 |> map (`weight_of) |> sort (int_ord o swap o pairself fst)
901 |> map snd |> take max_facts
904 val default_weight = 1.0
905 fun free_feature_of s = ("f" ^ s, 40.0 (* FUDGE *))
906 fun thy_feature_of s = ("y" ^ s, 8.0 (* FUDGE *))
907 fun type_feature_of s = ("t" ^ s, 4.0 (* FUDGE *))
908 fun class_feature_of s = ("s" ^ s, 1.0 (* FUDGE *))
909 val local_feature = ("local", 16.0 (* FUDGE *))
911 fun crude_theory_ord p =
912 if Theory.subthy p then
913 if Theory.eq_thy p then EQUAL else LESS
914 else if Theory.subthy (swap p) then
917 (case int_ord (pairself (length o Theory.ancestors_of) p) of
918 EQUAL => string_ord (pairself Context.theory_name p)
921 fun crude_thm_ord p =
922 (case crude_theory_ord (pairself theory_of_thm p) of
924 (* The hack below is necessary because of odd dependencies that are not reflected in the theory
926 let val q = pairself nickname_of_thm p in
927 (* Hack to put "xxx_def" before "xxxI" and "xxxE" *)
928 (case bool_ord (pairself (String.isSuffix "_def") (swap q)) of
929 EQUAL => string_ord q
934 val thm_less_eq = Theory.subthy o pairself theory_of_thm
935 fun thm_less p = thm_less_eq p andalso not (thm_less_eq (swap p))
937 val freezeT = Type.legacy_freeze_type
939 fun freeze (t $ u) = freeze t $ freeze u
940 | freeze (Abs (s, T, t)) = Abs (s, freezeT T, freeze t)
941 | freeze (Var ((s, _), T)) = Free (s, freezeT T)
942 | freeze (Const (s, T)) = Const (s, freezeT T)
943 | freeze (Free (s, T)) = Free (s, freezeT T)
946 fun goal_of_thm thy = prop_of #> freeze #> cterm_of thy #> Goal.init
948 fun run_prover_for_mash ctxt params prover goal_name facts goal =
951 {comment = "Goal: " ^ goal_name, state = Proof.init ctxt, goal = goal, subgoal = 1,
952 subgoal_count = 1, factss = [("", facts)]}
954 get_minimizing_prover ctxt MaSh (K ()) prover params (K (K (K ""))) problem
957 val bad_types = [@{type_name prop}, @{type_name bool}, @{type_name fun}]
959 val pat_tvar_prefix = "_"
960 val pat_var_prefix = "_"
962 (* try "Long_Name.base_name" for shorter names *)
963 fun massage_long_name s = s
965 val crude_str_of_sort = space_implode ":" o map massage_long_name o subtract (op =) @{sort type}
967 fun crude_str_of_typ (Type (s, [])) = massage_long_name s
968 | crude_str_of_typ (Type (s, Ts)) = massage_long_name s ^ implode (map crude_str_of_typ Ts)
969 | crude_str_of_typ (TFree (_, S)) = crude_str_of_sort S
970 | crude_str_of_typ (TVar (_, S)) = crude_str_of_sort S
972 fun maybe_singleton_str _ "" = []
973 | maybe_singleton_str pref s = [pref ^ s]
975 val max_pat_breadth = 10 (* FUDGE *)
977 fun term_features_of ctxt thy_name num_facts const_tab term_max_depth type_max_depth ts =
979 val thy = Proof_Context.theory_of ctxt
981 val fixes = map snd (Variable.dest_fixes ctxt)
982 val classes = Sign.classes_of thy
984 fun add_classes @{sort type} = I
986 fold (`(Sorts.super_classes classes)
988 #> subtract (op =) @{sort type} #> map massage_long_name
989 #> map class_feature_of
990 #> union (eq_fst (op =))) S
992 fun pattify_type 0 _ = []
993 | pattify_type _ (Type (s, [])) =
994 if member (op =) bad_types s then [] else [massage_long_name s]
995 | pattify_type depth (Type (s, U :: Ts)) =
998 val ps = take max_pat_breadth (pattify_type depth T)
999 val qs = take max_pat_breadth ("" :: pattify_type (depth - 1) U)
1001 map_product (fn p => fn "" => p | q => p ^ "(" ^ q ^ ")") ps qs
1003 | pattify_type _ (TFree (_, S)) =
1004 maybe_singleton_str pat_tvar_prefix (crude_str_of_sort S)
1005 | pattify_type _ (TVar (_, S)) =
1006 maybe_singleton_str pat_tvar_prefix (crude_str_of_sort S)
1008 fun add_type_pat depth T =
1009 union (eq_fst (op =)) (map type_feature_of (pattify_type depth T))
1011 fun add_type_pats 0 _ = I
1012 | add_type_pats depth t =
1013 add_type_pat depth t #> add_type_pats (depth - 1) t
1016 add_type_pats type_max_depth T
1017 #> fold_atyps_sorts (add_classes o snd) T
1019 fun add_subtypes (T as Type (_, Ts)) = add_type T #> fold add_subtypes Ts
1020 | add_subtypes T = add_type T
1022 val base_weight_of_const = 16.0 (* FUDGE *)
1023 val weight_of_const =
1024 (if num_facts = 0 orelse Symtab.is_empty const_tab then
1025 K base_weight_of_const
1028 let val count = Symtab.lookup const_tab s |> the_default 1 in
1029 base_weight_of_const + Real.fromInt num_facts / Real.fromInt count
1032 fun pattify_term _ 0 _ = []
1033 | pattify_term _ _ (Const (s, _)) =
1034 if is_widely_irrelevant_const s then [] else [(massage_long_name s, weight_of_const s)]
1035 | pattify_term _ _ (Free (s, T)) =
1036 maybe_singleton_str pat_var_prefix (crude_str_of_typ T)
1038 |> (if member (op =) fixes s then
1039 cons (free_feature_of (massage_long_name
1040 (thy_name ^ Long_Name.separator ^ s)))
1043 | pattify_term _ _ (Var (_, T)) =
1044 maybe_singleton_str pat_var_prefix (crude_str_of_typ T) |> map (rpair default_weight)
1045 | pattify_term Ts _ (Bound j) =
1046 maybe_singleton_str pat_var_prefix (crude_str_of_typ (nth Ts j))
1047 |> map (rpair default_weight)
1048 | pattify_term Ts depth (t $ u) =
1050 val ps = take max_pat_breadth (pattify_term Ts depth t)
1051 val qs = take max_pat_breadth (("", default_weight) :: pattify_term Ts (depth - 1) u)
1053 map_product (fn ppw as (p, pw) =>
1055 | (q, qw) => (p ^ "(" ^ q ^ ")", pw + qw)) ps qs
1057 | pattify_term _ _ _ = []
1059 fun add_term_pat Ts = union (eq_fst (op =)) oo pattify_term Ts
1061 fun add_term_pats _ 0 _ = I
1062 | add_term_pats Ts depth t = add_term_pat Ts depth t #> add_term_pats Ts (depth - 1) t
1064 fun add_term Ts = add_term_pats Ts term_max_depth
1066 fun add_subterms Ts t =
1067 (case strip_comb t of
1068 (Const (s, T), args) =>
1069 (not (is_widely_irrelevant_const s) ? add_term Ts t)
1071 #> fold (add_subterms Ts) args
1074 Free (_, T) => add_term Ts t #> add_subtypes T
1075 | Var (_, T) => add_subtypes T
1076 | Abs (_, T, body) => add_subtypes T #> add_subterms (T :: Ts) body
1078 #> fold (add_subterms Ts) args)
1080 fold (add_subterms []) ts []
1083 val term_max_depth = 2
1084 val type_max_depth = 1
1086 (* TODO: Generate type classes for types? *)
1087 fun features_of ctxt thy num_facts const_tab (scope, _) ts =
1088 let val thy_name = Context.theory_name thy in
1089 thy_feature_of thy_name ::
1090 term_features_of ctxt thy_name num_facts const_tab term_max_depth type_max_depth ts
1091 |> scope <> Global ? cons local_feature
1094 (* Too many dependencies is a sign that a decision procedure is at work. There is not much to learn
1095 from such proofs. *)
1096 val max_dependencies = 20
1098 val prover_default_max_facts = 25
1100 (* "type_definition_xxx" facts are characterized by their use of "CollectI". *)
1101 val typedef_dep = nickname_of_thm @{thm CollectI}
1102 (* Mysterious parts of the class machinery create lots of proofs that refer exclusively to
1103 "someI_ex" (and to some internal constructions). *)
1104 val class_some_dep = nickname_of_thm @{thm someI_ex}
1107 @{thms fundef_ex1_existence fundef_ex1_uniqueness fundef_ex1_iff fundef_default_value}
1108 |> map nickname_of_thm
1110 (* "Rep_xxx_inject", "Abs_xxx_inverse", etc., are derived using these facts. *)
1112 @{thms type_definition.Abs_inverse type_definition.Rep_inverse type_definition.Rep
1113 type_definition.Rep_inject type_definition.Abs_inject type_definition.Rep_cases
1114 type_definition.Abs_cases type_definition.Rep_induct type_definition.Abs_induct
1115 type_definition.Rep_range type_definition.Abs_image}
1116 |> map nickname_of_thm
1118 fun is_size_def [dep] th =
1119 (case first_field ".rec" dep of
1121 (case first_field ".size" (nickname_of_thm th) of
1122 SOME (pref', _) => pref = pref'
1125 | is_size_def _ _ = false
1127 fun trim_dependencies deps =
1128 if length deps > max_dependencies then NONE else SOME deps
1130 fun isar_dependencies_of name_tabs th =
1131 thms_in_proof max_dependencies (SOME name_tabs) th
1132 |> Option.map (fn deps =>
1133 if deps = [typedef_dep] orelse deps = [class_some_dep] orelse
1134 exists (member (op =) fundef_ths) deps orelse exists (member (op =) typedef_ths) deps orelse
1135 is_size_def deps th then
1140 fun prover_dependencies_of ctxt (params as {verbose, max_facts, ...}) prover auto_level facts
1142 (case isar_dependencies_of name_tabs th of
1143 SOME [] => (false, [])
1146 val isar_deps = these isar_deps0
1147 val thy = Proof_Context.theory_of ctxt
1148 val goal = goal_of_thm thy th
1149 val name = nickname_of_thm th
1150 val (_, hyp_ts, concl_t) = ATP_Util.strip_subgoal goal 1 ctxt
1151 val facts = facts |> filter (fn (_, th') => thm_less (th', th))
1153 fun nickify ((_, stature), th) = ((nickname_of_thm th, stature), th)
1155 fun is_dep dep (_, th) = nickname_of_thm th = dep
1157 fun add_isar_dep facts dep accum =
1158 if exists (is_dep dep) accum then
1161 (case find_first (is_dep dep) facts of
1162 SOME ((_, status), th) => accum @ [(("", status), th)]
1163 | NONE => accum (* should not happen *))
1167 |> mepo_suggested_facts ctxt params (max_facts |> the_default prover_default_max_facts) NONE
1171 |> fold (add_isar_dep facts) isar_deps
1173 val num_isar_deps = length isar_deps
1175 if verbose andalso auto_level = 0 then
1176 Output.urgent_message ("MaSh: " ^ quote prover ^ " on " ^ quote name ^ " with " ^
1177 string_of_int num_isar_deps ^ " + " ^ string_of_int (length facts - num_isar_deps) ^
1181 (case run_prover_for_mash ctxt params prover name facts goal of
1182 {outcome = NONE, used_facts, ...} =>
1183 (if verbose andalso auto_level = 0 then
1184 let val num_facts = length used_facts in
1185 Output.urgent_message ("Found proof with " ^ string_of_int num_facts ^ " fact" ^
1186 plural_s num_facts ^ ".")
1190 (true, map fst used_facts))
1191 | _ => (false, isar_deps))
1195 (*** High-level communication with MaSh ***)
1197 (* In the following functions, chunks are risers w.r.t. "thm_less_eq". *)
1199 fun chunks_and_parents_for chunks th =
1201 fun insert_parent new parents =
1202 let val parents = parents |> filter_out (fn p => thm_less_eq (p, new)) in
1203 parents |> forall (fn p => not (thm_less_eq (new, p))) parents ? cons new
1206 fun rechunk seen (rest as th' :: ths) =
1207 if thm_less_eq (th', th) then (rev seen, rest)
1208 else rechunk (th' :: seen) ths
1210 fun do_chunk [] accum = accum
1211 | do_chunk (chunk as hd_chunk :: _) (chunks, parents) =
1212 if thm_less_eq (hd_chunk, th) then
1213 (chunk :: chunks, insert_parent hd_chunk parents)
1214 else if thm_less_eq (List.last chunk, th) then
1215 let val (front, back as hd_back :: _) = rechunk [] chunk in
1216 (front :: back :: chunks, insert_parent hd_back parents)
1219 (chunk :: chunks, parents)
1221 fold_rev do_chunk chunks ([], [])
1223 ||> map nickname_of_thm
1226 fun attach_parents_to_facts _ [] = []
1227 | attach_parents_to_facts old_facts (facts as (_, th) :: _) =
1229 fun do_facts _ [] = []
1230 | do_facts (_, parents) [fact] = [(parents, fact)]
1231 | do_facts (chunks, parents)
1232 ((fact as (_, th)) :: (facts as (_, th') :: _)) =
1234 val chunks = app_hd (cons th) chunks
1235 val chunks_and_parents' =
1236 if thm_less_eq (th, th') andalso thy_name_of_thm th = thy_name_of_thm th' then
1237 (chunks, [nickname_of_thm th])
1239 chunks_and_parents_for chunks th'
1241 (parents, fact) :: do_facts chunks_and_parents' facts
1245 |> do_facts (chunks_and_parents_for [[]] th)
1246 |> drop (length old_facts)
1249 fun maximal_wrt_graph G keys =
1251 val tab = Symtab.empty |> fold (fn name => Symtab.default (name, ())) keys
1253 fun insert_new seen name = not (Symtab.defined seen name) ? insert (op =) name
1255 fun num_keys keys = Graph.Keys.fold (K (Integer.add 1)) keys 0
1257 fun find_maxes _ (maxs, []) = map snd maxs
1258 | find_maxes seen (maxs, new :: news) =
1259 find_maxes (seen |> num_keys (Graph.imm_succs G new) > 1 ? Symtab.default (new, ()))
1260 (if Symtab.defined tab new then
1262 val newp = Graph.all_preds G [new]
1263 fun is_ancestor x yp = member (op =) yp x
1264 val maxs = maxs |> filter (fn (_, max) => not (is_ancestor max newp))
1266 if exists (is_ancestor new o fst) maxs then (maxs, news)
1267 else ((newp, new) :: filter_out (fn (_, max) => is_ancestor max newp) maxs, news)
1270 (maxs, Graph.Keys.fold (insert_new seen) (Graph.imm_preds G new) news))
1272 find_maxes Symtab.empty ([], Graph.maximals G)
1275 fun maximal_wrt_access_graph access_G facts =
1276 map (nickname_of_thm o snd) facts
1277 |> maximal_wrt_graph access_G
1279 fun is_fact_in_graph access_G = can (Graph.get_node access_G) o nickname_of_thm
1281 val chained_feature_factor = 0.5 (* FUDGE *)
1282 val extra_feature_factor = 0.1 (* FUDGE *)
1283 val num_extra_feature_facts = 0 (* FUDGE *) (* TODO: keep or eliminate? *)
1286 fun weight_of_proximity_fact rank =
1287 Math.pow (1.3, 15.5 - 0.2 * Real.fromInt rank) + 15.0
1289 fun weight_facts_smoothly facts =
1290 facts ~~ map weight_of_proximity_fact (0 upto length facts - 1)
1293 fun steep_weight_of_fact rank =
1294 Math.pow (0.62, log2 (Real.fromInt (rank + 1)))
1296 fun weight_facts_steeply facts =
1297 facts ~~ map steep_weight_of_fact (0 upto length facts - 1)
1299 val max_proximity_facts = 100
1301 fun find_mash_suggestions ctxt max_facts suggs facts chained raw_unknown =
1303 val inter_fact = inter (eq_snd Thm.eq_thm_prop)
1304 val raw_mash = find_suggested_facts ctxt facts suggs
1305 val proximate = take max_proximity_facts facts
1306 val unknown_chained = inter_fact raw_unknown chained
1307 val unknown_proximate = inter_fact raw_unknown proximate
1309 [(0.9 (* FUDGE *), (map (rpair 1.0) unknown_chained, [])),
1310 (0.4 (* FUDGE *), (weight_facts_smoothly unknown_proximate, [])),
1311 (0.1 (* FUDGE *), (weight_facts_steeply raw_mash, raw_unknown))]
1312 val unknown = raw_unknown
1313 |> fold (subtract (eq_snd Thm.eq_thm_prop)) [unknown_chained, unknown_proximate]
1315 (mesh_facts (eq_snd (gen_eq_thm ctxt)) max_facts mess, unknown)
1318 fun add_const_counts t =
1319 fold (fn s => Symtab.map_default (s, 0) (Integer.add 1)) (Term.add_const_names t [])
1321 fun mash_suggested_facts ctxt ({debug, overlord, ...} : params) max_suggs hyp_ts concl_t facts =
1323 val thy = Proof_Context.theory_of ctxt
1324 val thy_name = Context.theory_name thy
1325 val engine = the_mash_engine ()
1327 val facts = facts |> sort (crude_thm_ord o pairself snd o swap)
1328 val chained = facts |> filter (fn ((_, (scope, _)), _) => scope = Chained)
1329 val num_facts = length facts
1331 (* Weights appear to hurt kNN more than they help. *)
1332 val const_tab = Symtab.empty |> engine <> MaSh_SML_kNN
1333 ? fold (add_const_counts o prop_of o snd) facts
1335 fun fact_has_right_theory (_, th) =
1336 thy_name = Context.theory_name (theory_of_thm th)
1338 fun chained_or_extra_features_of factor (((_, stature), th), weight) =
1340 |> features_of ctxt (theory_of_thm th) num_facts const_tab stature
1341 |> map (apsnd (fn r => weight * factor * r))
1343 fun query_args access_G =
1345 val parents = maximal_wrt_access_graph access_G facts
1347 |> filter (is_fact_in_graph access_G o snd)
1348 |> map (nickname_of_thm o snd)
1351 features_of ctxt thy num_facts const_tab (Local, General) (concl_t :: hyp_ts)
1352 val chained_feats = chained
1354 |> map (chained_or_extra_features_of chained_feature_factor)
1355 |> rpair [] |-> fold (union (eq_fst (op =)))
1358 |> take (Int.max (0, num_extra_feature_facts - length chained))
1359 |> filter fact_has_right_theory
1360 |> weight_facts_steeply
1361 |> map (chained_or_extra_features_of extra_feature_factor)
1362 |> rpair [] |-> fold (union (eq_fst (op =)))
1363 val feats = fold (union (eq_fst (op =))) [chained_feats, extra_feats] goal_feats
1364 |> debug ? sort (Real.compare o swap o pairself snd)
1366 (parents, hints, feats)
1369 val ((access_G, ((num_facts, fact_tab), (num_feats, feat_tab)), ffds, freqs), py_suggs) =
1370 peek_state ctxt overlord (fn {access_G, xtabs, ffds, freqs, ...} =>
1371 ((access_G, xtabs, ffds, freqs),
1372 if Graph.is_empty access_G then
1373 (trace_msg ctxt (K "Nothing has been learned yet"); [])
1374 else if engine = MaSh_Py then
1375 let val (parents, hints, feats) = query_args access_G in
1376 MaSh_Py.query ctxt overlord max_suggs ([], hints, parents, feats)
1383 if engine = MaSh_Py then
1387 val (parents, hints, goal_feats0) = query_args access_G
1388 val goal_feats = map fst goal_feats0
1389 val visible_facts = map_filter (Symtab.lookup fact_tab) (Graph.all_preds access_G parents)
1391 if engine = MaSh_SML_kNN_Ext orelse engine = MaSh_SML_NB_Ext then
1394 Graph.schedule (fn _ => fn (fact, (_, feats, deps)) => (fact, feats, deps)) access_G
1396 MaSh_SML.query_external ctxt engine max_suggs learns goal_feats
1400 val int_goal_feats = map_filter (Symtab.lookup feat_tab) goal_feats
1402 MaSh_SML.query_internal ctxt engine num_facts num_feats ffds freqs visible_facts
1403 max_suggs goal_feats int_goal_feats
1407 val unknown = filter_out (is_fact_in_graph access_G o snd) facts
1409 find_mash_suggestions ctxt max_suggs (py_suggs @ sml_suggs) facts chained unknown
1410 |> pairself (map fact_of_raw_fact)
1413 fun learn_wrt_access_graph ctxt (name, parents, feats, deps) (access_G, (fact_xtab, feat_xtab)) =
1415 fun maybe_learn_from from (accum as (parents, access_G)) =
1416 try_graph ctxt "updating graph" accum (fn () =>
1417 (from :: parents, Graph.add_edge_acyclic (from, name) access_G))
1419 val access_G = access_G |> Graph.default_node (name, (Isar_Proof, feats, deps))
1420 val (parents, access_G) = ([], access_G) |> fold maybe_learn_from parents
1421 val (deps, _) = ([], access_G) |> fold maybe_learn_from deps
1423 val fact_xtab = maybe_add_to_xtab name fact_xtab
1424 val feat_xtab = fold maybe_add_to_xtab feats feat_xtab
1426 ((name, parents, feats, deps), (access_G, (fact_xtab, feat_xtab)))
1429 fun relearn_wrt_access_graph ctxt (name, deps) access_G =
1431 fun maybe_relearn_from from (accum as (parents, access_G)) =
1432 try_graph ctxt "updating graph" accum (fn () =>
1433 (from :: parents, Graph.add_edge_acyclic (from, name) access_G))
1435 access_G |> Graph.map_node name (fn (_, feats, _) => (Automatic_Proof, feats, deps))
1436 val (deps, _) = ([], access_G) |> fold maybe_relearn_from deps
1438 ((name, deps), access_G)
1441 fun flop_wrt_access_graph name =
1442 Graph.map_node name (fn (_, feats, deps) => (Isar_Proof_wegen_Prover_Flop, feats, deps))
1444 val learn_timeout_slack = 20.0
1446 fun launch_thread timeout task =
1448 val hard_timeout = time_mult learn_timeout_slack timeout
1449 val birth_time = Time.now ()
1450 val death_time = Time.+ (birth_time, hard_timeout)
1451 val desc = ("Machine learner for Sledgehammer", "")
1453 Async_Manager.thread MaShN birth_time death_time desc task
1456 fun learned_proof_name () =
1457 Date.fmt ".%Y%m%d.%H%M%S." (Date.fromTimeLocal (Time.now ())) ^ serial_string ()
1459 fun mash_learn_proof ctxt ({overlord, timeout, ...} : params) t facts used_ths =
1460 if is_mash_enabled () then
1461 launch_thread timeout (fn () =>
1463 val thy = Proof_Context.theory_of ctxt
1464 val feats = map fst (features_of ctxt thy 0 Symtab.empty (Local, General) [t])
1466 map_state ctxt overlord
1467 (fn state as {access_G, xtabs as ((num_facts0, _), _), ffds, freqs, dirty_facts} =>
1469 val parents = maximal_wrt_access_graph access_G facts
1471 |> filter (is_fact_in_graph access_G)
1472 |> map nickname_of_thm
1474 if the_mash_engine () = MaSh_Py then
1475 (MaSh_Py.learn ctxt overlord true [("", parents, feats, deps)]; state)
1478 val name = learned_proof_name ()
1479 val (access_G', xtabs', rev_learns) =
1480 add_node Automatic_Proof name parents feats deps (access_G, xtabs, [])
1482 val (ffds', freqs') =
1483 recompute_ffds_freqs_from_learns (rev rev_learns) xtabs' num_facts0 ffds freqs
1485 {access_G = access_G', xtabs = xtabs', ffds = ffds', freqs = freqs',
1486 dirty_facts = Option.map (cons name) dirty_facts}
1494 fun sendback sub = Active.sendback_markup [Markup.padding_command] (sledgehammerN ^ " " ^ sub)
1496 val commit_timeout = seconds 30.0
1498 (* The timeout is understood in a very relaxed fashion. *)
1499 fun mash_learn_facts ctxt (params as {debug, verbose, overlord, ...}) prover save auto_level
1500 run_prover learn_timeout facts =
1502 val timer = Timer.startRealTimer ()
1503 fun next_commit_time () = Time.+ (Timer.checkRealTimer timer, commit_timeout)
1505 val engine = the_mash_engine ()
1506 val {access_G, ...} = peek_state ctxt overlord I
1507 val is_in_access_G = is_fact_in_graph access_G o snd
1508 val no_new_facts = forall is_in_access_G facts
1510 if no_new_facts andalso not run_prover then
1511 if auto_level < 2 then
1512 "No new " ^ (if run_prover then "automatic" else "Isar") ^ " proofs to learn." ^
1513 (if auto_level = 0 andalso not run_prover then
1514 "\n\nHint: Try " ^ sendback learn_proverN ^ " to learn from an automatic prover."
1521 val name_tabs = build_name_tables nickname_of_thm facts
1523 fun deps_of status th =
1524 if status = Non_Rec_Def orelse status = Rec_Def then
1526 else if run_prover then
1527 prover_dependencies_of ctxt params prover auto_level facts name_tabs th
1528 |> (fn (false, _) => NONE | (true, deps) => trim_dependencies deps)
1530 isar_dependencies_of name_tabs th
1532 fun do_commit [] [] [] state = state
1533 | do_commit learns relearns flops
1534 {access_G, xtabs as ((num_facts0, _), _), ffds, freqs, dirty_facts} =
1536 val was_empty = Graph.is_empty access_G
1538 val (learns, (access_G, xtabs)) =
1539 fold_map (learn_wrt_access_graph ctxt) learns (access_G, xtabs)
1540 val (relearns, access_G) =
1541 fold_map (relearn_wrt_access_graph ctxt) relearns access_G
1543 val access_G = access_G |> fold flop_wrt_access_graph flops
1545 (case (was_empty, dirty_facts) of
1546 (false, SOME names) => SOME (map #1 learns @ map #1 relearns @ names)
1549 val (ffds', freqs') =
1550 if null relearns then
1551 recompute_ffds_freqs_from_learns
1552 (map (fn (name, _, feats, deps) => (name, feats, deps)) learns) xtabs num_facts0
1555 recompute_ffds_freqs_from_access_G access_G xtabs
1557 if engine = MaSh_Py then
1558 (MaSh_Py.learn ctxt overlord (save andalso null relearns) learns;
1559 MaSh_Py.relearn ctxt overlord save relearns)
1562 {access_G = access_G, xtabs = xtabs, ffds = ffds', freqs = freqs',
1563 dirty_facts = dirty_facts}
1566 fun commit last learns relearns flops =
1567 (if debug andalso auto_level = 0 then Output.urgent_message "Committing..." else ();
1568 map_state ctxt overlord (do_commit (rev learns) relearns flops);
1569 if not last andalso auto_level = 0 then
1570 let val num_proofs = length learns + length relearns in
1571 Output.urgent_message ("Learned " ^ string_of_int num_proofs ^ " " ^
1572 (if run_prover then "automatic" else "Isar") ^ " proof" ^
1573 plural_s num_proofs ^ " in the last " ^ string_of_time commit_timeout ^ ".")
1578 fun learn_new_fact _ (accum as (_, (_, _, true))) = accum
1579 | learn_new_fact (parents, ((_, stature as (_, status)), th))
1580 (learns, (n, next_commit, _)) =
1582 val name = nickname_of_thm th
1584 map fst (features_of ctxt (theory_of_thm th) 0 Symtab.empty stature [prop_of th])
1585 val deps = deps_of status th |> these
1586 val n = n |> not (null deps) ? Integer.add 1
1587 val learns = (name, parents, feats, deps) :: learns
1588 val (learns, next_commit) =
1589 if Time.> (Timer.checkRealTimer timer, next_commit) then
1590 (commit false learns [] []; ([], next_commit_time ()))
1592 (learns, next_commit)
1593 val timed_out = Time.> (Timer.checkRealTimer timer, learn_timeout)
1595 (learns, (n, next_commit, timed_out))
1599 if no_new_facts then
1603 val new_facts = facts
1604 |> sort (crude_thm_ord o pairself snd)
1605 |> attach_parents_to_facts []
1606 |> filter_out (is_in_access_G o snd)
1607 val (learns, (n, _, _)) =
1608 ([], (0, next_commit_time (), false))
1609 |> fold learn_new_fact new_facts
1611 commit true learns [] []; n
1614 fun relearn_old_fact _ (accum as (_, (_, _, true))) = accum
1615 | relearn_old_fact ((_, (_, status)), th) ((relearns, flops), (n, next_commit, _)) =
1617 val name = nickname_of_thm th
1618 val (n, relearns, flops) =
1619 (case deps_of status th of
1620 SOME deps => (n + 1, (name, deps) :: relearns, flops)
1621 | NONE => (n, relearns, name :: flops))
1622 val (relearns, flops, next_commit) =
1623 if Time.> (Timer.checkRealTimer timer, next_commit) then
1624 (commit false [] relearns flops; ([], [], next_commit_time ()))
1626 (relearns, flops, next_commit)
1627 val timed_out = Time.> (Timer.checkRealTimer timer, learn_timeout)
1629 ((relearns, flops), (n, next_commit, timed_out))
1633 if not run_prover then
1637 val max_isar = 1000 * max_dependencies
1639 fun priority_of th =
1640 random_range 0 max_isar +
1641 (case try (Graph.get_node access_G) (nickname_of_thm th) of
1642 SOME (Isar_Proof, _, deps) => ~100 * length deps
1643 | SOME (Automatic_Proof, _, _) => 2 * max_isar
1644 | SOME (Isar_Proof_wegen_Prover_Flop, _, _) => max_isar
1647 val old_facts = facts
1648 |> filter is_in_access_G
1649 |> map (`(priority_of o snd))
1650 |> sort (int_ord o pairself fst)
1652 val ((relearns, flops), (n, _, _)) =
1653 (([], []), (n, next_commit_time (), false))
1654 |> fold relearn_old_fact old_facts
1656 commit true [] relearns flops; n
1659 if verbose orelse auto_level < 2 then
1660 "Learned " ^ string_of_int n ^ " nontrivial " ^
1661 (if run_prover then "automatic and " else "") ^ "Isar proof" ^ plural_s n ^
1662 (if verbose then " in " ^ string_of_time (Timer.checkRealTimer timer) else "") ^ "."
1668 fun mash_learn ctxt (params as {provers, timeout, ...}) fact_override chained run_prover =
1670 val css = Sledgehammer_Fact.clasimpset_rule_table_of ctxt
1671 val ctxt = ctxt |> Config.put instantiate_inducts false
1672 val facts = nearly_all_facts ctxt false fact_override Symtab.empty css chained [] @{prop True}
1673 |> sort (crude_thm_ord o pairself snd o swap)
1674 val num_facts = length facts
1675 val prover = hd provers
1677 fun learn auto_level run_prover =
1678 mash_learn_facts ctxt params prover true auto_level run_prover one_year facts
1679 |> Output.urgent_message
1682 (Output.urgent_message ("MaShing through " ^ string_of_int num_facts ^ " fact" ^
1683 plural_s num_facts ^ " for automatic proofs (" ^ quote prover ^ " timeout: " ^
1684 string_of_time timeout ^ ").\n\nCollecting Isar proofs first...");
1686 Output.urgent_message "Now collecting automatic proofs. This may take several hours. You \
1687 \can safely stop the learning process at any point.";
1690 (Output.urgent_message ("MaShing through " ^ string_of_int num_facts ^ " fact" ^
1691 plural_s num_facts ^ " for Isar proofs...");
1695 fun mash_can_suggest_facts ctxt overlord =
1696 not (Graph.is_empty (#access_G (peek_state ctxt overlord I)))
1698 (* Generate more suggestions than requested, because some might be thrown out later for various
1699 reasons (e.g., duplicates). *)
1700 fun generous_max_suggestions max_facts = 3 * max_facts div 2 + 25
1702 val mepo_weight = 0.5
1703 val mash_weight = 0.5
1705 val max_facts_to_learn_before_query = 100
1707 (* The threshold should be large enough so that MaSh does not get activated for Auto Sledgehammer
1709 val min_secs_for_learning = 15
1711 fun relevant_facts ctxt (params as {overlord, learn, fact_filter, timeout, ...}) prover max_facts
1712 ({add, only, ...} : fact_override) hyp_ts concl_t facts =
1713 if not (subset (op =) (the_list fact_filter, fact_filters)) then
1714 error ("Unknown fact filter: " ^ quote (the fact_filter) ^ ".")
1716 [("", map fact_of_raw_fact facts)]
1717 else if max_facts <= 0 orelse null facts then
1721 fun maybe_launch_thread () =
1722 if not (Async_Manager.has_running_threads MaShN) andalso
1723 Time.toSeconds timeout >= min_secs_for_learning then
1724 let val timeout = time_mult learn_timeout_slack timeout in
1725 launch_thread timeout
1726 (fn () => (true, mash_learn_facts ctxt params prover true 2 false timeout facts))
1731 fun maybe_learn () =
1732 if is_mash_enabled () andalso learn then
1734 val {access_G, xtabs = ((num_facts0, _), _), ...} = peek_state ctxt overlord I
1735 val is_in_access_G = is_fact_in_graph access_G o snd
1737 if length facts - num_facts0 <= max_facts_to_learn_before_query then
1738 (case length (filter_out is_in_access_G facts) of
1740 | num_facts_to_learn =>
1741 if num_facts_to_learn <= max_facts_to_learn_before_query then
1742 (mash_learn_facts ctxt params prover false 2 false timeout facts
1743 |> (fn "" => () | s => Output.urgent_message (MaShN ^ ": " ^ s));
1746 (maybe_launch_thread (); false))
1748 (maybe_launch_thread (); false)
1753 val (save, effective_fact_filter) =
1754 (case fact_filter of
1755 SOME ff => (ff <> mepoN andalso maybe_learn (), ff)
1757 if is_mash_enabled () then
1758 (maybe_learn (), if mash_can_suggest_facts ctxt overlord then meshN else mepoN)
1762 val unique_facts = drop_duplicate_facts facts
1763 val add_ths = Attrib.eval_thms ctxt add
1765 fun in_add (_, th) = member Thm.eq_thm_prop add_ths th
1767 fun add_and_take accepts =
1771 (unique_facts |> filter in_add |> map fact_of_raw_fact) @ (accepts |> filter_out in_add))
1775 (mepo_suggested_facts ctxt params max_facts NONE hyp_ts concl_t unique_facts
1776 |> weight_facts_steeply, [])
1779 mash_suggested_facts ctxt params (generous_max_suggestions max_facts) hyp_ts concl_t facts
1780 |>> weight_facts_steeply
1783 (* the order is important for the "case" expression below *)
1784 [] |> effective_fact_filter <> mepoN ? cons (mash_weight, mash)
1785 |> effective_fact_filter <> mashN ? cons (mepo_weight, mepo)
1786 |> Par_List.map (apsnd (fn f => f ()))
1787 val mesh = mesh_facts (eq_snd (gen_eq_thm ctxt)) max_facts mess |> add_and_take
1789 if the_mash_engine () = MaSh_Py andalso save then MaSh_Py.save ctxt overlord else ();
1790 (case (fact_filter, mess) of
1791 (NONE, [(_, (mepo, _)), (_, (mash, _))]) =>
1792 [(meshN, mesh), (mepoN, mepo |> map fst |> add_and_take),
1793 (mashN, mash |> map fst |> add_and_take)]
1794 | _ => [(effective_fact_filter, mesh)])
1797 fun kill_learners ctxt ({overlord, ...} : params) =
1798 (Async_Manager.kill_threads MaShN "learner";
1799 if the_mash_engine () = MaSh_Py then MaSh_Py.shutdown ctxt overlord else ())
1801 fun running_learners () = Async_Manager.running_threads MaShN "learner"