diff --git a/src/HOL/Tools/Sledgehammer/sledgehammer.ML b/src/HOL/Tools/Sledgehammer/sledgehammer.ML --- a/src/HOL/Tools/Sledgehammer/sledgehammer.ML +++ b/src/HOL/Tools/Sledgehammer/sledgehammer.ML @@ -1,362 +1,362 @@ (* Title: HOL/Tools/Sledgehammer/sledgehammer.ML Author: Fabian Immler, TU Muenchen Author: Makarius Author: Jasmin Blanchette, TU Muenchen Sledgehammer's heart. *) signature SLEDGEHAMMER = sig type stature = ATP_Problem_Generate.stature type fact = Sledgehammer_Fact.fact type fact_override = Sledgehammer_Fact.fact_override type proof_method = Sledgehammer_Proof_Methods.proof_method type play_outcome = Sledgehammer_Proof_Methods.play_outcome type mode = Sledgehammer_Prover.mode type params = Sledgehammer_Prover.params type induction_rules = Sledgehammer_Prover.induction_rules type prover_problem = Sledgehammer_Prover.prover_problem type prover_result = Sledgehammer_Prover.prover_result datatype sledgehammer_outcome = SH_Some of prover_result | SH_Unknown | SH_Timeout | SH_None val short_string_of_sledgehammer_outcome : sledgehammer_outcome -> string val play_one_line_proof : bool -> Time.time -> (string * stature) list -> Proof.state -> int -> proof_method * proof_method list list -> (string * stature) list * (proof_method * play_outcome) val string_of_factss : (string * fact list) list -> string val run_sledgehammer : params -> mode -> (string -> unit) option -> int -> fact_override -> Proof.state -> bool * (sledgehammer_outcome * string) end; structure Sledgehammer : SLEDGEHAMMER = struct open ATP_Util open ATP_Proof open ATP_Problem_Generate open Sledgehammer_Util open Sledgehammer_Fact open Sledgehammer_Proof_Methods open Sledgehammer_Isar_Proof open Sledgehammer_Isar_Preplay open Sledgehammer_Isar_Minimize open Sledgehammer_Prover open Sledgehammer_Prover_ATP open Sledgehammer_Prover_Minimize open Sledgehammer_MaSh datatype sledgehammer_outcome = SH_Some of prover_result | SH_Unknown | SH_Timeout | SH_None fun short_string_of_sledgehammer_outcome (SH_Some _) = "some" | short_string_of_sledgehammer_outcome SH_Unknown = "unknown" | short_string_of_sledgehammer_outcome SH_Timeout = "timeout" | short_string_of_sledgehammer_outcome SH_None = "none" fun alternative f (SOME x) (SOME y) = SOME (f (x, y)) | alternative _ (x as SOME _) NONE = x | alternative _ NONE (y as SOME _) = y | alternative _ NONE NONE = NONE fun max_outcome outcomes = let val result = find_first (fn (SH_Some _, _) => true | _ => false) outcomes val unknown = find_first (fn (SH_Unknown, _) => true | _ => false) outcomes val timeout = find_first (fn (SH_Timeout, _) => true | _ => false) outcomes val none = find_first (fn (SH_None, _) => true | _ => false) outcomes in result |> alternative snd unknown |> alternative snd timeout |> alternative snd none |> the_default (SH_Unknown, "") end fun is_metis_method (Metis_Method _) = true | is_metis_method _ = false fun play_one_line_proof minimize timeout used_facts state i (preferred_meth, methss) = (if timeout = Time.zeroTime then (used_facts, (preferred_meth, Play_Timed_Out Time.zeroTime)) else let val ctxt = Proof.context_of state val fact_names = used_facts |> filter_out (fn (_, (sc, _)) => sc = Chained) |> map fst val {facts = chained, goal, ...} = Proof.goal state val goal_t = Logic.get_goal (Thm.prop_of goal) i fun try_methss [] [] = (used_facts, (preferred_meth, Play_Timed_Out Time.zeroTime)) | try_methss ress [] = (used_facts, (case AList.lookup (op =) ress preferred_meth of SOME play => (preferred_meth, play) | NONE => hd (sort (play_outcome_ord o apply2 snd) (rev ress)))) | try_methss ress (meths :: methss) = let fun mk_step fact_names meths = Prove { qualifiers = [], obtains = [], label = ("", 0), goal = goal_t, subproofs = [], facts = ([], fact_names), proof_methods = meths, comment = ""} in (case preplay_isar_step ctxt chained timeout [] (mk_step fact_names meths) of (res as (meth, Played time)) :: _ => (* if a fact is needed by an ATP, it will be needed by "metis" *) if not minimize orelse is_metis_method meth then (used_facts, res) else let val (time', used_names') = minimized_isar_step ctxt chained time (mk_step fact_names [meth]) ||> (facts_of_isar_step #> snd) val used_facts' = filter (member (op =) used_names' o fst) used_facts in (used_facts', (meth, Played time')) end | ress' => try_methss (ress' @ ress) methss) end in try_methss [] methss end) |> (fn (used_facts, (meth, play)) => (used_facts |> filter_out (fn (_, (sc, _)) => sc = Chained), (meth, play))) -fun launch_prover (params as {verbose, spy, max_facts, induction_rules, ...}) mode only learn +fun launch_prover (params as {verbose, spy, ...}) mode learn (problem as {state, subgoal, factss, ...} : prover_problem) slice name = let val ctxt = Proof.context_of state val _ = spying spy (fn () => (state, subgoal, name, "Launched")) - val induction_rules = the_default Exclude induction_rules fun print_used_facts used_facts used_from = tag_list 1 used_from |> map (fn (j, fact) => fact |> apsnd (K j)) |> filter_used_facts false used_facts |> map (fn ((name, _), j) => name ^ "@" ^ string_of_int j) |> commas |> prefix ("Facts in " ^ name ^ " proof: ") |> writeln fun spying_str_of_res ({outcome = NONE, used_facts, used_from, ...} : prover_result) = let val num_used_facts = length used_facts fun find_indices facts = tag_list 1 facts |> map (fn (j, fact) => fact |> apsnd (K j)) |> filter_used_facts false used_facts |> distinct (eq_fst (op =)) |> map (prefix "@" o string_of_int o snd) fun filter_info (fact_filter, facts) = let val indices = find_indices facts (* "Int.max" is there for robustness -- it shouldn't be necessary *) val unknowns = replicate (Int.max (0, num_used_facts - length indices)) "?" in (commas (indices @ unknowns), fact_filter) end val filter_infos = map filter_info (("actual", used_from) :: factss) |> AList.group (op =) |> map (fn (indices, fact_filters) => commas fact_filters ^ ": " ^ indices) in "Success: Found proof with " ^ string_of_int num_used_facts ^ " fact" ^ plural_s num_used_facts ^ (if num_used_facts = 0 then "" else ": " ^ commas filter_infos) end | spying_str_of_res {outcome = SOME failure, ...} = "Failure: " ^ string_of_atp_failure failure in get_minimizing_prover ctxt mode learn name params problem slice |> verbose ? tap (fn {outcome = NONE, used_facts as _ :: _, used_from, ...} => print_used_facts used_facts used_from | _ => ()) |> spy ? tap (fn res => spying spy (fn () => (state, subgoal, name, spying_str_of_res res))) end fun preplay_prover_result ({ minimize, preplay_timeout, ...} : params) state subgoal (result as {outcome, used_facts, preferred_methss, message, ...} : prover_result) = let val output = if outcome = SOME ATP_Proof.TimedOut then SH_Timeout else if is_some outcome then SH_None else SH_Some result fun output_message () = message (fn () => play_one_line_proof minimize preplay_timeout used_facts state subgoal preferred_methss) in (output, output_message) end fun check_expected_outcome ctxt prover_name expect outcome = let val outcome_code = short_string_of_sledgehammer_outcome outcome in - (* The "expect" argument is deliberately ignored if the prover is - missing so that the "Metis_Examples" can be processed on any - machine. *) + (* The "expect" argument is deliberately ignored if the prover is missing so that + "Metis_Examples" can be processed on any machine. *) if expect = "" orelse outcome_code = expect orelse not (is_prover_installed ctxt prover_name) then () else error ("Unexpected outcome: " ^ quote outcome_code) end -fun launch_prover_and_preplay (params as {debug, timeout, expect, ...}) mode writeln_result only - learn (problem as {state, subgoal, ...}) slice prover_name = +fun launch_prover_and_preplay (params as {debug, timeout, expect, ...}) mode writeln_result learn + (problem as {state, subgoal, ...}) slice prover_name = let val ctxt = Proof.context_of state val hard_timeout = Time.scale 5.0 timeout fun really_go () = - launch_prover params mode only learn problem slice prover_name + launch_prover params mode learn problem slice prover_name |> preplay_prover_result params state subgoal fun go () = if debug then really_go () else (really_go () handle ERROR msg => (SH_Unknown, fn () => "Error: " ^ msg ^ "\n") | exn => if Exn.is_interrupt exn then Exn.reraise exn else (SH_Unknown, fn () => "Internal error:\n" ^ Runtime.exn_message exn ^ "\n")) val (outcome, message) = Timeout.apply hard_timeout go () val () = check_expected_outcome ctxt prover_name expect outcome val message = message () val () = (case outcome of SH_Some _ => the_default writeln writeln_result (prover_name ^ ": " ^ message) | _ => ()) in (outcome, message) end -val auto_try_max_facts_divisor = 2 (* FUDGE *) - fun string_of_facts facts = "Including " ^ string_of_int (length facts) ^ " relevant fact" ^ plural_s (length facts) ^ ": " ^ (facts |> map (fst o fst) |> space_implode " ") fun string_of_factss factss = if forall (null o snd) factss then "Found no relevant facts" else cat_lines (map (fn (filter, facts) => (if filter = "" then "" else filter ^ ": ") ^ string_of_facts facts) factss) fun run_sledgehammer (params as {verbose, spy, provers, induction_rules, max_facts, ...}) mode writeln_result i (fact_override as {only, ...}) state = if null provers then error "No prover is set" else (case subgoal_count state of 0 => (error "No subgoal!"; (false, (SH_None, ""))) | n => let val _ = Proof.assert_backward state val print = if mode = Normal andalso is_none writeln_result then writeln else K () val found_proof = fn prover_name => if mode = Normal then (writeln_result |> the_default writeln) (prover_name ^ " found a proof...") else () val ctxt = Proof.context_of state val inst_inducts = induction_rules = SOME Instantiate val {facts = chained_thms, goal, ...} = Proof.goal state val (_, hyp_ts, concl_t) = strip_subgoal goal i ctxt val _ = (case find_first (not o is_prover_supported ctxt) provers of SOME name => error ("No such prover: " ^ name) | NONE => ()) val _ = print "Sledgehammering..." val _ = spying spy (fn () => (state, i, "***", "Starting " ^ str_of_mode mode ^ " mode")) val ({elapsed, ...}, all_facts) = Timing.timing (nearly_all_facts_of_context ctxt inst_inducts fact_override chained_thms hyp_ts) concl_t val _ = spying spy (fn () => (state, i, "All", "Extracting " ^ string_of_int (length all_facts) ^ " facts from background theory in " ^ string_of_int (Time.toMilliseconds elapsed) ^ " ms")) val spying_str_of_factss = commas o map (fn (filter, facts) => filter ^ ": " ^ string_of_int (length facts)) fun get_factss provers = let val max_max_facts = (case max_facts of SOME n => n | NONE => - 0 |> fold (fn prover => Integer.max (fst (fst (get_default_slice ctxt prover)))) - provers - |> mode = Auto_Try ? (fn n => n div auto_try_max_facts_divisor)) + fold (fn prover => Integer.max (fst (fst (get_default_slice ctxt prover)))) provers + 0) + val ({elapsed, ...}, factss) = Timing.timing (relevant_facts ctxt params (hd provers) max_max_facts fact_override hyp_ts concl_t) all_facts + + val induction_rules = the_default (if only then Include else Exclude) induction_rules + val factss = map (apsnd (maybe_filter_out_induction_rules induction_rules)) factss + val () = spying spy (fn () => (state, i, "All", "Filtering facts in " ^ string_of_int (Time.toMilliseconds elapsed) ^ " ms (MaSh algorithm: " ^ str_of_mash_algorithm (the_mash_algorithm ()) ^ ")")); val () = if verbose then print (string_of_factss factss) else () val () = spying spy (fn () => (state, i, "All", "Selected facts: " ^ spying_str_of_factss factss)) in factss end fun launch_provers () = let val problem = {comment = "", state = state, goal = goal, subgoal = i, subgoal_count = n, factss = get_factss provers, found_proof = found_proof} val learn = mash_learn_proof ctxt params (Thm.prop_of goal) - val launch = launch_prover_and_preplay params mode writeln_result only learn + val launch = launch_prover_and_preplay params mode writeln_result learn in if mode = Auto_Try then (SH_Unknown, "") |> fold (fn prover => fn accum as (SH_Some _, _) => accum | _ => launch problem (get_default_slice ctxt prover) prover) provers else (learn chained_thms; provers |> Par_List.map (fn prover => launch problem (get_default_slice ctxt prover) prover) |> max_outcome) end in (launch_provers () handle Timeout.TIMEOUT _ => (SH_Timeout, "")) |> `(fn (outcome, _) => (case outcome of SH_Some _ => (print "QED"; true) | SH_Timeout => (print "Timed out"; false) | _ => (print "Done"; false))) end) end; diff --git a/src/HOL/Tools/Sledgehammer/sledgehammer_mash.ML b/src/HOL/Tools/Sledgehammer/sledgehammer_mash.ML --- a/src/HOL/Tools/Sledgehammer/sledgehammer_mash.ML +++ b/src/HOL/Tools/Sledgehammer/sledgehammer_mash.ML @@ -1,1638 +1,1638 @@ (* 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 lazy_fact = Sledgehammer_Fact.lazy_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 -> lazy_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 -> lazy_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 -> lazy_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 -> lazy_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>\sledgehammer_mash_trace\ (K false) val duplicates = Attrib.setup_config_bool \<^binding>\sledgehammer_fact_duplicates\ (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>\MaSh\ 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 = map_index (swap o apfst smooth_weight_of_fact) facts fun weight_facts_steeply facts = map_index (swap o apfst steep_weight_of_fact) facts 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 = K ()} val slice = get_default_slice ctxt prover in get_minimizing_prover ctxt MaSh (K ()) prover params problem slice end val bad_types = [\<^type_name>\prop\, \<^type_name>\bool\, \<^type_name>\fun\] val crude_str_of_sort = space_implode "," o map Long_Name.base_name o subtract (op =) \<^sort>\type\ 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>\type\ = I | add_classes S = fold (`(Sorts.super_classes classes) #> swap #> op :: #> subtract (op =) \<^sort>\type\ #> 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_lazy_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.scale learn_timeout_slack timeout val birth_time = Time.now () val death_time = birth_time + Timeout.scale_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, induction_rules, ...}) fact_override chained run_prover = let val css = Sledgehammer_Fact.clasimpset_rule_table_of ctxt val facts = nearly_all_facts ctxt (induction_rules = SOME Instantiate) fact_override Keyword.empty_keywords css chained [] \<^prop>\True\ |> 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_lazy_fact facts)] + [("", map fact_of_lazy_fact (take max_facts 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.scale 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_lazy_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;