1 (* Title: HOL/Tools/Sledgehammer/sledgehammer_mash.ML
2 Author: Jasmin Blanchette, TU Muenchen
4 Sledgehammer's machine-learning-based relevance filter (MaSh).
7 signature SLEDGEHAMMER_MASH =
9 type stature = ATP_Problem_Generate.stature
10 type fact = Sledgehammer_Fact.fact
11 type fact_override = Sledgehammer_Fact.fact_override
12 type params = Sledgehammer_Provers.params
13 type relevance_fudge = Sledgehammer_Provers.relevance_fudge
14 type prover_result = Sledgehammer_Provers.prover_result
16 val trace : bool Config.T
21 val fact_filters : string list
22 val escape_meta : string -> string
23 val escape_metas : string list -> string
24 val unescape_meta : string -> string
25 val unescape_metas : string -> string list
26 val extract_query : string -> string * string list
27 val nickname_of : thm -> string
28 val suggested_facts : string list -> ('a * thm) list -> ('a * thm) list
30 int -> (('a * thm) list * ('a * thm) list) list -> ('a * thm) list
31 val is_likely_tautology_or_too_meta : thm -> bool
32 val theory_ord : theory * theory -> order
33 val thm_ord : thm * thm -> order
35 Proof.context -> string -> theory -> stature -> term list -> string list
36 val isabelle_dependencies_of : unit Symtab.table -> thm -> string list
37 val goal_of_thm : theory -> thm -> thm
38 val run_prover_for_mash :
39 Proof.context -> params -> string -> fact list -> thm -> prover_result
40 val mash_CLEAR : Proof.context -> unit
43 -> (string * string list * string list * string list) list -> unit
45 Proof.context -> bool -> int -> string list * string list -> string list
46 val mash_unlearn : Proof.context -> unit
47 val mash_could_suggest_facts : unit -> bool
48 val mash_can_suggest_facts : Proof.context -> bool
49 val mash_suggest_facts :
50 Proof.context -> params -> string -> int -> term list -> term
51 -> ('a * thm) list -> ('a * thm) list * ('a * thm) list
52 val mash_learn_proof :
53 Proof.context -> params -> string -> term -> ('a * thm) list -> thm list
55 val mash_learn_facts :
56 Proof.context -> params -> Time.time -> fact list -> string
57 val mash_learn : Proof.context -> params -> unit
59 Proof.context -> params -> string -> int -> fact_override -> term list
60 -> term -> fact list -> fact list
61 val kill_learners : unit -> unit
62 val running_learners : unit -> unit
65 structure Sledgehammer_MaSh : SLEDGEHAMMER_MASH =
69 open ATP_Problem_Generate
70 open Sledgehammer_Util
71 open Sledgehammer_Fact
72 open Sledgehammer_Provers
73 open Sledgehammer_Minimize
74 open Sledgehammer_MePo
77 Attrib.setup_config_bool @{binding sledgehammer_mash_trace} (K false)
78 fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()
86 val fact_filters = [meshN, mepoN, mashN]
88 fun mash_home () = getenv "MASH_HOME"
89 fun mash_state_dir () =
90 getenv "ISABELLE_HOME_USER" ^ "/mash"
91 |> tap (Isabelle_System.mkdir o Path.explode)
92 fun mash_state_path () = mash_state_dir () ^ "/state" |> Path.explode
95 (*** Isabelle helpers ***)
98 if Char.isAlphaNum c orelse c = #"_" orelse c = #"." orelse c = #"(" orelse
99 c = #")" orelse c = #"," then
102 (* fixed width, in case more digits follow *)
103 "\\" ^ stringN_of_int 3 (Char.ord c)
105 fun unmeta_chars accum [] = String.implode (rev accum)
106 | unmeta_chars accum (#"\\" :: d1 :: d2 :: d3 :: cs) =
107 (case Int.fromString (String.implode [d1, d2, d3]) of
108 SOME n => unmeta_chars (Char.chr n :: accum) cs
109 | NONE => "" (* error *))
110 | unmeta_chars _ (#"\\" :: _) = "" (* error *)
111 | unmeta_chars accum (c :: cs) = unmeta_chars (c :: accum) cs
113 val escape_meta = String.translate meta_char
114 val escape_metas = map escape_meta #> space_implode " "
115 val unescape_meta = String.explode #> unmeta_chars []
117 space_explode " " #> filter_out (curry (op =) "") #> map unescape_meta
119 fun extract_query line =
120 case space_explode ":" line of
121 [goal_name, suggs] => (unescape_meta goal_name, unescape_metas suggs)
124 fun parent_of_local_thm th =
126 val thy = th |> Thm.theory_of_thm
127 val facts = thy |> Global_Theory.facts_of
128 val space = facts |> Facts.space_of
129 fun id_of s = #id (Name_Space.the_entry space s)
130 fun max_id (s', _) (s, id) =
131 let val id' = id_of s' in if id > id' then (s, id) else (s', id') end
132 in ("", ~1) |> Facts.fold_static max_id facts |> fst end
134 val local_prefix = "local" ^ Long_Name.separator
137 let val hint = Thm.get_name_hint th in
138 (* FIXME: There must be a better way to detect local facts. *)
139 case try (unprefix local_prefix) hint of
141 parent_of_local_thm th ^ Long_Name.separator ^ Long_Name.separator ^ suff
145 fun suggested_facts suggs facts =
147 fun add_fact (fact as (_, th)) = Symtab.default (nickname_of th, fact)
148 val tab = Symtab.empty |> fold add_fact facts
149 in map_filter (Symtab.lookup tab) suggs end
151 (* Ad hoc score function roughly based on Blanchette's Ringberg 2011 data. *)
152 fun score x = Math.pow (1.5, 15.5 - 0.05 * Real.fromInt x) + 15.0
154 fun sum_sq_avg [] = 0
156 Real.ceil (100000.0 * fold (curry (op +) o score) xs 0.0) div length xs
158 fun mesh_facts max_facts [(selected, unknown)] =
159 take max_facts selected @ take (max_facts - length selected) unknown
160 | mesh_facts max_facts mess =
162 val mess = mess |> map (apfst (`length))
163 val fact_eq = Thm.eq_thm o pairself snd
164 fun score_in fact ((sel_len, sels), unks) =
165 case find_index (curry fact_eq fact) sels of
166 ~1 => (case find_index (curry fact_eq fact) unks of
170 fun score_of fact = mess |> map_filter (score_in fact) |> sum_sq_avg
171 val facts = fold (union fact_eq o take max_facts o snd o fst) mess []
173 facts |> map (`score_of) |> sort (int_ord o swap o pairself fst)
174 |> map snd |> take max_facts
177 val thy_feature_prefix = "y_"
179 val thy_feature_name_of = prefix thy_feature_prefix
180 val const_name_of = prefix const_prefix
181 val type_name_of = prefix type_const_prefix
182 val class_name_of = prefix class_prefix
184 fun is_likely_tautology_or_too_meta th =
186 val is_boring_const = member (op =) atp_widely_irrelevant_consts
187 fun is_boring_bool t =
188 not (exists_Const (not o is_boring_const o fst) t) orelse
189 exists_type (exists_subtype (curry (op =) @{typ prop})) t
190 fun is_boring_prop (@{const Trueprop} $ t) = is_boring_bool t
191 | is_boring_prop (@{const "==>"} $ t $ u) =
192 is_boring_prop t andalso is_boring_prop u
193 | is_boring_prop (Const (@{const_name all}, _) $ (Abs (_, _, t)) $ u) =
194 is_boring_prop t andalso is_boring_prop u
195 | is_boring_prop (Const (@{const_name "=="}, _) $ t $ u) =
196 is_boring_bool t andalso is_boring_bool u
197 | is_boring_prop _ = true
199 is_boring_prop (prop_of th) andalso not (Thm.eq_thm_prop (@{thm ext}, th))
203 if Theory.eq_thy p then
205 else if Theory.subthy p then
207 else if Theory.subthy (swap p) then
209 else case int_ord (pairself (length o Theory.ancestors_of) p) of
210 EQUAL => string_ord (pairself Context.theory_name p)
213 val thm_ord = theory_ord o pairself theory_of_thm
215 val bad_types = [@{type_name prop}, @{type_name bool}, @{type_name fun}]
217 fun interesting_terms_types_and_classes ctxt prover term_max_depth
220 fun is_bad_const (x as (s, _)) args =
221 member (op =) atp_logical_consts s orelse
222 fst (is_built_in_const_for_prover ctxt prover x args)
223 fun add_classes @{sort type} = I
224 | add_classes S = union (op =) (map class_name_of S)
225 fun do_add_type (Type (s, Ts)) =
226 (not (member (op =) bad_types s) ? insert (op =) (type_name_of s))
227 #> fold do_add_type Ts
228 | do_add_type (TFree (_, S)) = add_classes S
229 | do_add_type (TVar (_, S)) = add_classes S
230 fun add_type T = type_max_depth >= 0 ? do_add_type T
232 if member (op <>) args "" then s ^ "(" ^ space_implode "," args ^ ")"
234 fun patternify ~1 _ = ""
235 | patternify depth t =
237 (Const (s, _), args) =>
238 mk_app (const_name_of s) (map (patternify (depth - 1)) args)
240 fun add_term_patterns ~1 _ = I
241 | add_term_patterns depth t =
242 insert (op =) (patternify depth t)
243 #> add_term_patterns (depth - 1) t
244 val add_term = add_term_patterns term_max_depth
246 let val (head, args) = strip_comb t in
248 Const (x as (_, T)) =>
249 not (is_bad_const x args) ? (add_term t #> add_type T)
250 | Free (_, T) => add_type T
251 | Var (_, T) => add_type T
252 | Abs (_, T, body) => add_type T #> add_patterns body
254 #> fold add_patterns args
256 in [] |> fold add_patterns ts end
258 fun is_exists (s, _) = (s = @{const_name Ex} orelse s = @{const_name Ex1})
260 val term_max_depth = 1
261 val type_max_depth = 1
263 (* TODO: Generate type classes for types? *)
264 fun features_of ctxt prover thy (scope, status) ts =
265 thy_feature_name_of (Context.theory_name thy) ::
266 interesting_terms_types_and_classes ctxt prover term_max_depth type_max_depth
268 |> forall is_lambda_free ts ? cons "no_lams"
269 |> forall (not o exists_Const is_exists) ts ? cons "no_skos"
270 |> scope <> Global ? cons "local"
273 | Induction => cons "induction"
274 | Intro => cons "intro"
275 | Inductive => cons "inductive"
276 | Elim => cons "elim"
277 | Simp => cons "simp"
280 fun isabelle_dependencies_of all_facts = thms_in_proof (SOME all_facts)
282 val freezeT = Type.legacy_freeze_type
284 fun freeze (t $ u) = freeze t $ freeze u
285 | freeze (Abs (s, T, t)) = Abs (s, freezeT T, freeze t)
286 | freeze (Var ((s, _), T)) = Free (s, freezeT T)
287 | freeze (Const (s, T)) = Const (s, freezeT T)
288 | freeze (Free (s, T)) = Free (s, freezeT T)
291 fun goal_of_thm thy = prop_of #> freeze #> cterm_of thy #> Goal.init
293 fun run_prover_for_mash ctxt params prover facts goal =
296 {state = Proof.init ctxt, goal = goal, subgoal = 1, subgoal_count = 1,
297 facts = facts |> map (apfst (apfst (fn name => name ())))
298 |> map Untranslated_Fact}
299 val prover = get_minimizing_prover ctxt Normal (K ()) prover
300 in prover params (K (K (K ""))) problem end
303 (*** Low-level communication with MaSh ***)
305 fun write_file (xs, f) file =
306 let val path = Path.explode file in
309 |> List.app (File.append path o space_implode "" o map f)
312 fun mash_info overlord =
313 if overlord then (getenv "ISABELLE_HOME_USER", "")
314 else (getenv "ISABELLE_TMP", serial_string ())
316 fun and_rm_files overlord flags files =
320 " && rm -f" ^ flags ^ " -- " ^
321 space_implode " " (map File.shell_quote files)
323 fun run_mash ctxt overlord (temp_dir, serial) async core =
325 val log_file = temp_dir ^ "/mash_log" ^ serial
326 val err_file = temp_dir ^ "/mash_err" ^ serial
328 "(" ^ mash_home () ^ "/mash --quiet --outputDir " ^ mash_state_dir () ^
329 " --log " ^ log_file ^ " " ^ core ^ ") 2>&1 > " ^ err_file ^
330 and_rm_files overlord "" [log_file, err_file] ^
331 (if async then " &" else "")
333 trace_msg ctxt (fn () =>
334 (if async then "Launching " else "Running ") ^ command);
335 write_file ([], K "") log_file;
336 write_file ([], K "") err_file;
337 Isabelle_System.bash command;
338 if not async then trace_msg ctxt (K "Done") else ()
341 fun run_mash_commands ctxt overlord save max_suggs write_cmds read_suggs =
343 val info as (temp_dir, serial) = mash_info overlord
344 val sugg_file = temp_dir ^ "/mash_suggs" ^ serial
345 val cmd_file = temp_dir ^ "/mash_commands" ^ serial
347 write_file ([], K "") sugg_file;
348 write_file write_cmds cmd_file;
349 run_mash ctxt overlord info false
350 ("--inputFile " ^ cmd_file ^ " --predictions " ^ sugg_file ^
351 " --numberOfPredictions " ^ string_of_int max_suggs ^
352 (if save then " --saveModel" else "") ^
353 (and_rm_files overlord "" [sugg_file, cmd_file]));
354 read_suggs (fn () => File.read_lines (Path.explode sugg_file))
357 fun str_of_update (name, parents, feats, deps) =
358 "! " ^ escape_meta name ^ ": " ^ escape_metas parents ^ "; " ^
359 escape_metas feats ^ "; " ^ escape_metas deps ^ "\n"
361 fun str_of_query (parents, feats) =
362 "? " ^ escape_metas parents ^ "; " ^ escape_metas feats
364 fun mash_CLEAR ctxt =
365 let val path = mash_state_dir () |> Path.explode in
366 trace_msg ctxt (K "MaSh CLEAR");
367 File.fold_dir (fn file => fn () =>
368 File.rm (Path.append path (Path.basic file)))
372 fun mash_ADD _ _ [] = ()
373 | mash_ADD ctxt overlord upds =
374 (trace_msg ctxt (fn () => "MaSh ADD " ^
375 elide_string 1000 (space_implode " " (map #1 upds)));
376 run_mash_commands ctxt overlord true 0 (upds, str_of_update) (K ()))
378 fun mash_QUERY ctxt overlord max_suggs (query as (_, feats)) =
379 (trace_msg ctxt (fn () => "MaSh QUERY " ^ space_implode " " feats);
380 run_mash_commands ctxt overlord false max_suggs
381 ([query], str_of_query)
382 (fn suggs => snd (extract_query (List.last (suggs ()))))
383 handle List.Empty => [])
386 (*** High-level communication with MaSh ***)
388 fun try_graph ctxt when def f =
390 handle Graph.CYCLES (cycle :: _) =>
391 (trace_msg ctxt (fn () =>
392 "Cycle involving " ^ commas cycle ^ " when " ^ when); def)
393 | Graph.UNDEF name =>
394 (trace_msg ctxt (fn () =>
395 "Unknown fact " ^ quote name ^ " when " ^ when); def)
397 type mash_state = {fact_graph : unit Graph.T}
399 val empty_state = {fact_graph = Graph.empty}
403 val version = "*** MaSh 0.0 ***"
405 fun load _ (state as (true, _)) = state
407 let val path = mash_state_path () in
409 case try File.read_lines path of
410 SOME (version' :: fact_lines) =>
412 fun add_edge_to name parent =
413 Graph.default_node (parent, ())
414 #> Graph.add_edge (parent, name)
415 fun add_fact_line line =
416 case extract_query line of
417 ("", _) => I (* shouldn't happen *)
419 Graph.default_node (name, ())
420 #> fold (add_edge_to name) parents
422 try_graph ctxt "loading state" Graph.empty (fn () =>
423 Graph.empty |> version' = version
424 ? fold add_fact_line fact_lines)
425 in {fact_graph = fact_graph} end
429 fun save {fact_graph} =
431 val path = mash_state_path ()
432 fun fact_line_for name parents =
433 escape_meta name ^ ": " ^ escape_metas parents
434 val append_fact = File.append path o suffix "\n" oo fact_line_for
436 File.write path (version ^ "\n");
437 Graph.fold (fn (name, ((), (parents, _))) => fn () =>
438 append_fact name (Graph.Keys.dest parents))
443 Synchronized.var "Sledgehammer_MaSh.global_state" (false, empty_state)
447 fun mash_map ctxt f =
448 Synchronized.change global_state (load ctxt ##> (f #> tap save))
451 Synchronized.change_result global_state (load ctxt #> `snd)
453 fun mash_unlearn ctxt =
454 Synchronized.change global_state (fn _ =>
455 (mash_CLEAR ctxt; File.write (mash_state_path ()) "";
456 (true, empty_state)))
460 fun mash_could_suggest_facts () = mash_home () <> ""
461 fun mash_can_suggest_facts ctxt =
462 not (Graph.is_empty (#fact_graph (mash_get ctxt)))
464 fun parents_wrt_facts facts fact_graph =
466 val facts = [] |> fold (cons o nickname_of o snd) facts
467 val tab = Symtab.empty |> fold (fn name => Symtab.update (name, ())) facts
468 fun insert_not_seen seen name =
469 not (member (op =) seen name) ? insert (op =) name
470 fun parents_of _ parents [] = parents
471 | parents_of seen parents (name :: names) =
472 if Symtab.defined tab name then
473 parents_of (name :: seen) (name :: parents) names
475 parents_of (name :: seen) parents
476 (Graph.Keys.fold (insert_not_seen seen)
477 (Graph.imm_preds fact_graph name) names)
478 in parents_of [] [] (Graph.maximals fact_graph) end
480 (* Generate more suggestions than requested, because some might be thrown out
481 later for various reasons and "meshing" gives better results with some
483 fun max_suggs_of max_facts = max_facts + Int.min (200, max_facts)
485 fun is_fact_in_graph fact_graph (_, th) =
486 can (Graph.get_node fact_graph) (nickname_of th)
488 fun mash_suggest_facts ctxt ({overlord, ...} : params) prover max_facts hyp_ts
491 val thy = Proof_Context.theory_of ctxt
492 val fact_graph = #fact_graph (mash_get ctxt)
493 val parents = parents_wrt_facts facts fact_graph
494 val feats = features_of ctxt prover thy (Local, General) (concl_t :: hyp_ts)
496 if Graph.is_empty fact_graph then []
497 else mash_QUERY ctxt overlord (max_suggs_of max_facts) (parents, feats)
498 val selected = facts |> suggested_facts suggs
499 val unknown = facts |> filter_out (is_fact_in_graph fact_graph)
500 in (selected, unknown) end
502 fun update_fact_graph ctxt (name, parents, feats, deps) (upds, graph) =
504 fun maybe_add_from from (accum as (parents, graph)) =
505 try_graph ctxt "updating graph" accum (fn () =>
506 (from :: parents, Graph.add_edge_acyclic (from, name) graph))
507 val graph = graph |> Graph.default_node (name, ())
508 val (parents, graph) = ([], graph) |> fold maybe_add_from parents
509 val (deps, graph) = ([], graph) |> fold maybe_add_from deps
510 in ((name, parents, feats, deps) :: upds, graph) end
512 val learn_timeout_slack = 2.0
514 fun launch_thread timeout task =
516 val hard_timeout = time_mult learn_timeout_slack timeout
517 val birth_time = Time.now ()
518 val death_time = Time.+ (birth_time, hard_timeout)
519 val desc = ("machine learner for Sledgehammer", "")
520 in Async_Manager.launch MaShN birth_time death_time desc task end
522 fun mash_learn_proof ctxt ({overlord, timeout, ...} : params) prover t facts
524 if is_smt_prover ctxt prover then
527 launch_thread timeout
530 val thy = Proof_Context.theory_of ctxt
531 val name = timestamp () ^ " " ^ serial_string () (* freshish *)
532 val feats = features_of ctxt prover thy (Local, General) [t]
533 val deps = used_ths |> map nickname_of
535 mash_map ctxt (fn {fact_graph} =>
537 val parents = parents_wrt_facts facts fact_graph
538 val upds = [(name, parents, feats, deps)]
539 val (upds, fact_graph) =
540 ([], fact_graph) |> fold (update_fact_graph ctxt) upds
542 mash_ADD ctxt overlord upds; {fact_graph = fact_graph}
547 (* Too many dependencies is a sign that a decision procedure is at work. There
548 isn't much too learn from such proofs. *)
549 val max_dependencies = 10
550 val pass1_learn_timeout_factor = 0.75
552 (* The timeout is understood in a very slack fashion. *)
553 fun mash_learn_facts ctxt ({provers, verbose, overlord, ...} : params) timeout
556 val timer = Timer.startRealTimer ()
557 val prover = hd provers
559 Time.> (Timer.checkRealTimer timer, time_mult frac timeout)
560 val {fact_graph} = mash_get ctxt
562 facts |> filter_out (is_fact_in_graph fact_graph)
563 |> sort (thm_ord o pairself snd)
565 if null new_facts then
569 val ths = facts |> map snd
571 ths |> filter_out is_likely_tautology_or_too_meta
572 |> map (rpair () o nickname_of)
574 fun trim_deps deps = if length deps > max_dependencies then [] else deps
575 fun do_fact _ (accum as (_, true)) = accum
576 | do_fact ((_, stature), th) ((parents, upds), false) =
578 val name = nickname_of th
580 features_of ctxt prover (theory_of_thm th) stature [prop_of th]
581 val deps = isabelle_dependencies_of all_names th |> trim_deps
582 val upd = (name, parents, feats, deps)
583 in (([name], upd :: upds), timed_out pass1_learn_timeout_factor) end
584 val parents = parents_wrt_facts facts fact_graph
586 ((parents, []), false) |> fold do_fact new_facts |>> apsnd rev
588 fun trans {fact_graph} =
590 val (upds, fact_graph) =
591 ([], fact_graph) |> fold (update_fact_graph ctxt) upds
592 in (mash_ADD ctxt overlord (rev upds); {fact_graph = fact_graph}) end
596 "Learned " ^ string_of_int n ^ " proof" ^ plural_s n ^
598 " in " ^ string_from_time (Timer.checkRealTimer timer)
606 fun mash_learn ctxt params =
608 val thy = Proof_Context.theory_of ctxt
609 val _ = Output.urgent_message "MaShing..."
610 val css_table = Sledgehammer_Fact.clasimpset_rule_table_of ctxt
611 val facts = all_facts_of thy css_table
613 mash_learn_facts ctxt params infinite_timeout facts
614 |> (fn "" => "Learned nothing." | msg => msg)
615 |> Output.urgent_message
618 (* The threshold should be large enough so that MaSh doesn't kick in for Auto
619 Sledgehammer and Try. *)
620 val min_secs_for_learning = 15
622 fun relevant_facts ctxt (params as {learn, fact_filter, timeout, ...}) prover
623 max_facts ({add, only, ...} : fact_override) hyp_ts concl_t facts =
624 if not (subset (op =) (the_list fact_filter, fact_filters)) then
625 error ("Unknown fact filter: " ^ quote (the fact_filter) ^ ".")
628 else if max_facts <= 0 orelse null facts then
633 if learn andalso not (Async_Manager.has_running_threads MaShN) andalso
634 Time.toSeconds timeout >= min_secs_for_learning then
635 let val timeout = time_mult learn_timeout_slack timeout in
636 launch_thread timeout
637 (fn () => (true, mash_learn_facts ctxt params timeout facts))
643 SOME ff => (() |> ff <> mepoN ? maybe_learn; ff)
645 if is_smt_prover ctxt prover then mepoN
646 else if mash_can_suggest_facts ctxt then (maybe_learn (); meshN)
647 else if mash_could_suggest_facts () then (maybe_learn (); mepoN)
649 val add_ths = Attrib.eval_thms ctxt add
650 fun prepend_facts ths accepts =
651 ((facts |> filter (member Thm.eq_thm_prop ths o snd)) @
652 (accepts |> filter_out (member Thm.eq_thm_prop ths o snd)))
655 iterative_relevant_facts ctxt params prover max_facts NONE hyp_ts
658 mash_suggest_facts ctxt params prover max_facts hyp_ts concl_t facts
660 [] |> (if fact_filter <> mashN then cons (iter (), []) else I)
661 |> (if fact_filter <> mepoN then cons (mash ()) else I)
663 mesh_facts max_facts mess
664 |> not (null add_ths) ? prepend_facts add_ths
667 fun kill_learners () = Async_Manager.kill_threads MaShN "learner"
668 fun running_learners () = Async_Manager.running_threads MaShN "learner"