(* Title: HOL/Tools/Sledgehammer/sledgehammer_mash.ML
Author: Jasmin Blanchette, TU Muenchen
Author: Cezary Kaliszyk, University of Innsbruck
Sledgehammer's machine-learning-based relevance filter (MaSh).
*)
signature SLEDGEHAMMER_MASH =
sig
type stature = ATP_Problem_Generate.stature
type raw_fact = Sledgehammer_Fact.raw_fact
type fact = Sledgehammer_Fact.fact
type fact_override = Sledgehammer_Fact.fact_override
type params = Sledgehammer_Prover.params
type prover_result = Sledgehammer_Prover.prover_result
val trace : bool Config.T
val duplicates : bool Config.T
val MePoN : string
val MaShN : string
val MeShN : string
val mepoN : string
val mashN : string
val meshN : string
val unlearnN : string
val learn_isarN : string
val learn_proverN : string
val relearn_isarN : string
val relearn_proverN : string
val fact_filters : string list
val encode_str : string -> string
val encode_strs : string list -> string
val decode_str : string -> string
val decode_strs : string -> string list
val encode_features : (string * real) list -> string
val extract_suggestions : string -> string * (string * real) list
datatype mash_engine =
MaSh_Py
| MaSh_SML_kNN
| MaSh_SML_kNN_Cpp
| MaSh_SML_NB of bool * bool
| MaSh_SML_NB_Cpp
| MaSh_SML_NB_Py
val is_mash_enabled : unit -> bool
val the_mash_engine : unit -> mash_engine
structure MaSh_Py :
sig
val unlearn : Proof.context -> bool -> unit
val learn : Proof.context -> bool -> bool ->
(string * string list * string list * string list) list -> unit
val relearn : Proof.context -> bool -> bool -> (string * string list) list -> unit
val query : Proof.context -> bool -> int ->
(string * string list * string list * string list) list * string list * string list
* (string * real) list ->
(string * real) list
end
structure MaSh_SML :
sig
val k_nearest_neighbors : int -> int -> (int -> int list) -> (int -> (int * real) list) ->
int -> (int * real) list -> (int * real) list
val naive_bayes : (bool * bool) -> int -> int -> (int -> int list) -> (int -> int list) ->
int -> int -> (int * real) list -> (int * real) list
val naive_bayes_py : Proof.context -> bool -> int -> int -> (int -> int list) ->
(int -> int list) -> int -> int -> (int * real) list -> (int * real) list
val query : Proof.context -> bool -> mash_engine -> string list -> int ->
(string * (string * real) list * string list) list * string list * (string * real) list ->
string list
end
val mash_unlearn : Proof.context -> params -> unit
val nickname_of_thm : thm -> string
val find_suggested_facts : Proof.context -> ('b * thm) list -> string list -> ('b * thm) list
val mesh_facts : ('a * 'a -> bool) -> int -> (real * (('a * real) list * 'a list)) list -> 'a list
val crude_thm_ord : thm * thm -> order
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 -> theory -> int -> int Symtab.table -> stature -> term list ->
(string * real) list
val trim_dependencies : string list -> string list option
val isar_dependencies_of : string Symtab.table * string Symtab.table -> thm -> string list
val prover_dependencies_of : Proof.context -> params -> string -> int -> raw_fact list ->
string Symtab.table * string Symtab.table -> thm -> bool * string list
val attach_parents_to_facts : ('a * thm) list -> ('a * thm) list ->
(string list * ('a * thm)) list
val num_extra_feature_facts : int
val extra_feature_factor : real
val weight_facts_smoothly : 'a list -> ('a * real) list
val weight_facts_steeply : 'a list -> ('a * real) list
val find_mash_suggestions : Proof.context -> int -> string list -> ('b * thm) list ->
('b * thm) list -> ('b * thm) list -> ('b * thm) list * ('b * thm) list
val add_const_counts : term -> int Symtab.table -> int Symtab.table
val mash_suggested_facts : Proof.context -> params -> int -> term list -> term -> raw_fact list ->
fact list * fact list
val mash_learn_proof : Proof.context -> params -> term -> ('a * thm) list -> thm list -> unit
val mash_learn_facts : Proof.context -> params -> string -> bool -> int -> bool -> Time.time ->
raw_fact list -> string
val mash_learn : Proof.context -> params -> fact_override -> thm list -> bool -> unit
val mash_can_suggest_facts : Proof.context -> bool -> bool
val generous_max_suggestions : int -> int
val mepo_weight : real
val mash_weight : real
val relevant_facts : Proof.context -> params -> string -> int -> fact_override -> term list ->
term -> raw_fact list -> (string * fact list) list
val kill_learners : Proof.context -> params -> unit
val running_learners : unit -> unit
end;
structure Sledgehammer_MaSh : SLEDGEHAMMER_MASH =
struct
open ATP_Util
open ATP_Problem_Generate
open Sledgehammer_Util
open Sledgehammer_Fact
open Sledgehammer_Prover
open Sledgehammer_Prover_Minimize
open Sledgehammer_MePo
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 mash_state_dir () = Path.explode "$ISABELLE_HOME_USER/mash" |> tap Isabelle_System.mkdir
fun mash_state_file () = Path.append (mash_state_dir ()) (Path.explode "state")
fun wipe_out_mash_state_dir () =
let val path = mash_state_dir () in
try (File.fold_dir (fn file => fn _ => try File.rm (Path.append path (Path.basic file))) path)
NONE;
()
end
datatype mash_engine =
MaSh_Py
| MaSh_SML_kNN
| MaSh_SML_kNN_Cpp
| MaSh_SML_NB of bool * bool
| MaSh_SML_NB_Cpp
| MaSh_SML_NB_Py
val default_MaSh_SML_NB = MaSh_SML_NB (false, true)
fun mash_engine () =
let val flag1 = Options.default_string @{system_option MaSh} in
(case if flag1 <> "none" (* default *) then flag1 else getenv "MASH" of
"yes" => SOME default_MaSh_SML_NB
| "py" => SOME MaSh_Py
| "sml" => SOME default_MaSh_SML_NB
| "sml_knn" => SOME MaSh_SML_kNN
| "sml_knn_cpp" => SOME MaSh_SML_kNN_Cpp
| "sml_nb" => SOME default_MaSh_SML_NB
| "sml_nbCC" => SOME (MaSh_SML_NB (false, false))
| "sml_nbCD" => SOME (MaSh_SML_NB (false, true))
| "sml_nbDC" => SOME (MaSh_SML_NB (true, false))
| "sml_nbDD" => SOME (MaSh_SML_NB (true, true))
| "sml_nb_cpp" => SOME MaSh_SML_NB_Cpp
| "sml_nb_py" => SOME MaSh_SML_NB_Py
| _ => NONE)
end
val is_mash_enabled = is_some o mash_engine
val the_mash_engine = the_default default_MaSh_SML_NB o mash_engine
(*** Low-level communication with the Python version of MaSh ***)
val save_models_arg = "--saveModels"
val shutdown_server_arg = "--shutdownServer"
fun wipe_out_file file = ignore (try (File.rm o Path.explode) file)
fun write_file banner (xs, f) path =
(case banner of SOME s => File.write path s | NONE => ();
xs |> chunk_list 500 |> List.app (File.append path o implode o map f))
handle IO.Io _ => ()
fun run_mash_tool ctxt overlord extra_args background write_cmds read_suggs =
let
val (temp_dir, serial) =
if overlord then (getenv "ISABELLE_HOME_USER", "")
else (getenv "ISABELLE_TMP", serial_string ())
val log_file = temp_dir ^ "/mash_log" ^ serial
val err_file = temp_dir ^ "/mash_err" ^ serial
val sugg_file = temp_dir ^ "/mash_suggs" ^ serial
val sugg_path = Path.explode sugg_file
val cmd_file = temp_dir ^ "/mash_commands" ^ serial
val cmd_path = Path.explode cmd_file
val model_dir = File.shell_path (mash_state_dir ())
val command =
"cd \"$ISABELLE_SLEDGEHAMMER_MASH\"/src; \
\PYTHONDONTWRITEBYTECODE=y ./mash.py\
\ --quiet\
\ --port=$MASH_PORT\
\ --outputDir " ^ model_dir ^
" --modelFile=" ^ model_dir ^ "/model.pickle\
\ --dictsFile=" ^ model_dir ^ "/dict.pickle\
\ --log " ^ log_file ^
" --inputFile " ^ cmd_file ^
" --predictions " ^ sugg_file ^
(if extra_args = [] then "" else " " ^ space_implode " " extra_args) ^ " >& " ^ err_file ^
(if background then " &" else "")
fun run_on () =
(Isabelle_System.bash command
|> tap (fn _ =>
(case try File.read (Path.explode err_file) |> the_default "" of
"" => trace_msg ctxt (K "Done")
| s => warning ("MaSh error: " ^ elide_string 1000 s)));
read_suggs (fn () => try File.read_lines sugg_path |> these))
fun clean_up () =
if overlord then () else List.app wipe_out_file [err_file, sugg_file, cmd_file]
in
write_file (SOME "") ([], K "") sugg_path;
write_file (SOME "") write_cmds cmd_path;
trace_msg ctxt (fn () => "Running " ^ command);
with_cleanup clean_up run_on ()
end
fun meta_char c =
if Char.isAlphaNum c orelse c = #"_" orelse c = #"." orelse c = #"(" orelse c = #")" orelse
c = #"," then
String.str c
else
(* fixed width, in case more digits follow *)
"%" ^ stringN_of_int 3 (Char.ord c)
fun unmeta_chars accum [] = String.implode (rev accum)
| unmeta_chars accum (#"%" :: d1 :: d2 :: d3 :: cs) =
(case Int.fromString (String.implode [d1, d2, d3]) of
SOME n => unmeta_chars (Char.chr n :: accum) cs
| NONE => "" (* error *))
| unmeta_chars _ (#"%" :: _) = "" (* error *)
| unmeta_chars accum (c :: cs) = unmeta_chars (c :: accum) cs
val encode_str = String.translate meta_char
val decode_str = String.explode #> unmeta_chars []
val encode_strs = map encode_str #> space_implode " "
val decode_strs = space_explode " " #> filter_out (curry (op =) "") #> map decode_str
(* Avoid scientific notation *)
fun safe_str_of_real r =
if r < 0.00001 then "0.00001"
else if r >= 1000000.0 then "1000000"
else Markup.print_real r
fun encode_feature (names, weight) =
encode_str names ^ (if Real.== (weight, 1.0) then "" else "=" ^ safe_str_of_real weight)
fun decode_feature s =
(case space_explode "=" s of
[feat, weight] => (decode_str feat, Real.fromString weight |> the_default 1.0)
| _ => (decode_str s, 1.0))
val encode_features = map encode_feature #> space_implode " "
val decode_features = space_explode " " #> map decode_feature
fun str_of_learn (name, parents, feats, deps) =
"! " ^ encode_str name ^ ": " ^ encode_strs parents ^ "; " ^ encode_strs feats ^ "; " ^
encode_strs deps ^ "\n"
fun str_of_relearn (name, deps) = "p " ^ encode_str name ^ ": " ^ encode_strs deps ^ "\n"
fun str_of_query max_suggs (learns, hints, parents, feats) =
implode (map str_of_learn learns) ^
"? " ^ string_of_int max_suggs ^ " # " ^ encode_strs parents ^ "; " ^ encode_features feats ^
(if null hints then "" else "; " ^ encode_strs hints) ^ "\n"
(* The suggested weights do not make much sense. *)
fun extract_suggestion sugg =
(case space_explode "=" sugg of
[name, weight] => SOME (decode_str name, Real.fromString weight |> the_default 1.0)
| [name] => SOME (decode_str name, 1.0)
| _ => NONE)
fun extract_suggestions line =
(case space_explode ":" line of
[goal, suggs] => (decode_str goal, map_filter extract_suggestion (space_explode " " suggs))
| _ => ("", []))
structure MaSh_Py =
struct
fun shutdown ctxt overlord =
(trace_msg ctxt (K "MaSh_Py shutdown");
run_mash_tool ctxt overlord [shutdown_server_arg] false ([], K "") (K ()))
fun save ctxt overlord =
(trace_msg ctxt (K "MaSh_Py save");
run_mash_tool ctxt overlord [save_models_arg] true ([], K "") (K ()))
fun unlearn ctxt overlord =
(trace_msg ctxt (K "MaSh_Py unlearn");
shutdown ctxt overlord;
wipe_out_mash_state_dir ())
fun learn _ _ _ [] = ()
| learn ctxt overlord save learns =
(trace_msg ctxt (fn () =>
"MaSh_Py learn {" ^ elide_string 1000 (space_implode " " (map #1 learns)) ^ "}");
run_mash_tool ctxt overlord ([] |> save ? cons save_models_arg) false (learns, str_of_learn)
(K ()))
fun relearn _ _ _ [] = ()
| relearn ctxt overlord save relearns =
(trace_msg ctxt (fn () => "MaSh_Py relearn " ^
elide_string 1000 (space_implode " " (map #1 relearns)));
run_mash_tool ctxt overlord ([] |> save ? cons save_models_arg) false
(relearns, str_of_relearn) (K ()))
fun query ctxt overlord max_suggs (query as (_, _, _, feats)) =
(trace_msg ctxt (fn () => "MaSh_Py query " ^ encode_features feats);
run_mash_tool ctxt overlord [] false ([query], str_of_query max_suggs) (fn suggs =>
(case suggs () of [] => [] | suggs => snd (extract_suggestions (List.last suggs))))
handle List.Empty => [])
end;
(*** Standard ML version of MaSh ***)
structure MaSh_SML =
struct
exception BOTTOM of int
fun heap cmp bnd a =
let
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 cmp (Array.sub (a, i31), Array.sub (a, i31 + 1)) = LESS then x := i31 + 1 else ();
if cmp (Array.sub (a, !x), Array.sub (a, i31 + 2)) = LESS then x := i31 + 2 else ();
!x
end
else
if i31 + 1 < l andalso cmp (Array.sub (a, i31), Array.sub (a, i31 + 1)) = LESS
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 cmp (Array.sub (a, j), e) = GREATER 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 cmp (Array.sub (a, father), e) = LESS 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
val l = Array.length a
fun for i = if i < 0 then () else (trickle l i (Array.sub (a, i)); for (i - 1))
fun for2 i =
if i < Integer.max 2 (l - bnd) 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 (((l + 1) div 3) - 1);
for2 (l - 1);
if l > 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
(*
num_facts = maximum number of theorems to check dependencies and symbols
num_visible_facts = do not return theorems over or equal to this number.
Must satisfy: num_visible_facts <= num_facts.
get_deps = returns dependencies of a theorem
get_sym_ths = get theorems that have this feature
max_suggs = number of suggestions to return
feats = features of the goal
*)
fun k_nearest_neighbors num_facts num_visible_facts get_deps get_sym_ths max_suggs feats =
let
val number_of_nearest_neighbors = 40 (* FUDGE *)
(* Can be later used for TFIDF *)
fun sym_wght _ = 1.0
val overlaps_sqr = Array.tabulate (num_facts, rpair 0.0)
fun inc_overlap j v =
let
val ov = snd (Array.sub (overlaps_sqr, j))
in
Array.update (overlaps_sqr, j, (j, v + ov))
end
fun do_feat (s, con_wght) =
let
val sw = sym_wght s
val w2 = sw * sw * con_wght
fun do_th (j, prem_wght) = if j < num_facts then inc_overlap j (w2 * prem_wght) else ()
in
List.app do_th (get_sym_ths s)
end
val _ = List.app do_feat feats
val _ = heap (Real.compare o pairself snd) number_of_nearest_neighbors overlaps_sqr
val recommends = Array.tabulate (num_visible_facts, rpair 0.0)
fun inc_recommend j v =
if j >= num_visible_facts then ()
else Array.update (recommends, j, (j, v + snd (Array.sub (recommends, j))))
fun for k =
if k = number_of_nearest_neighbors orelse k >= num_visible_facts then
()
else
let
val (j, o2) = Array.sub (overlaps_sqr, num_facts - k - 1)
val o1 = Math.sqrt o2
val _ = inc_recommend j o1
val ds = get_deps j
val l = Real.fromInt (length ds)
in
List.app (fn d => inc_recommend d (o1 / l)) ds; for (k + 1)
end
fun ret acc at =
if at = Array.length recommends then acc else ret (Array.sub (recommends, at) :: acc) (at + 1)
in
for 0;
heap (Real.compare o pairself snd) max_suggs recommends;
ret [] (Integer.max 0 (num_visible_facts - max_suggs))
end
val nb_def_prior_weight = 21 (* FUDGE *)
(* TODO: Either use IDF or don't use it. See commented out code portions below. *)
fun naive_bayes_learn num_facts get_deps get_feats num_feats =
let
val tfreq = Array.array (num_facts, 0)
val sfreq = Array.array (num_facts, Inttab.empty)
(* val dffreq = Array.array (num_feats, 0) *)
fun learn th feats deps =
let
fun add_th weight t =
let
val im = Array.sub (sfreq, t)
fun fold_fn s sf = Inttab.update (s, weight + the_default 0 (Inttab.lookup im s)) sf
in
Array.update (tfreq, t, weight + Array.sub (tfreq, t));
Array.update (sfreq, t, fold fold_fn feats im)
end
(* fun add_sym s = Array.update (dffreq, s, 1 + Array.sub (dffreq, s)) *)
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 i (get_feats i) (get_deps i); for (i + 1))
in
for 0; (Array.vector tfreq, Array.vector sfreq (*, Array.vector dffreq *))
end
fun naive_bayes_query (kuehlwein_log, kuehlwein_params) _ (* num_facts *) num_visible_facts
max_suggs feats (tfreq, sfreq (*, dffreq*)) =
let
val tau = if kuehlwein_params then 0.05 else 0.02 (* FUDGE *)
val pos_weight = if kuehlwein_params then 10.0 else 2.0 (* FUDGE *)
val def_val = ~15.0 (* FUDGE *)
(*
val afreq = Real.fromInt num_facts
fun tfidf feat = Math.ln afreq - Math.ln (Real.fromInt (Vector.sub (dffreq, feat)))
*)
fun tfidf _ = 1.0
fun log_posterior i =
let
val tfreq = Real.fromInt (Vector.sub (tfreq, i))
fun fold_feats (f, fw) (res, sfh) =
(case Inttab.lookup sfh f of
SOME sf =>
(res + tfidf f * fw * Math.ln (pos_weight * Real.fromInt sf / tfreq),
Inttab.delete f sfh)
| NONE => (res + fw * def_val, sfh))
val (res, sfh) = fold fold_feats feats (Math.ln tfreq, Vector.sub (sfreq, i))
val fold_sfh =
if kuehlwein_log then
(fn (f, sf) => fn sow => sow - tfidf f * Math.ln (Real.fromInt sf / tfreq))
else
(fn (f, sf) => fn sow =>
sow + tfidf f * Math.ln (1.0 + (1.0 - Real.fromInt sf) / tfreq))
val sum_of_weights = Inttab.fold fold_sfh sfh 0.0
in
res + tau * sum_of_weights
end
val posterior = Array.tabulate (num_visible_facts, (fn j => (j, log_posterior j)))
fun ret acc at =
if at = num_visible_facts then acc else ret (Array.sub (posterior, at) :: acc) (at + 1)
in
heap (Real.compare o pairself snd) max_suggs posterior;
ret [] (Integer.max 0 (num_visible_facts - max_suggs))
end
fun naive_bayes opts num_facts num_visible_facts get_deps get_feats num_feats max_suggs feats =
naive_bayes_learn num_facts get_deps get_feats num_feats
|> naive_bayes_query opts num_facts num_visible_facts max_suggs feats
(* experimental *)
fun naive_bayes_py ctxt overlord num_facts num_visible_facts get_deps get_feats num_feats max_suggs
feats =
let
fun name_of_fact j = "f" ^ string_of_int j
fun fact_of_name s = the (Int.fromString (unprefix "f" s))
fun name_of_feature j = "F" ^ string_of_int j
fun parents_of j = if j = 0 then [] else [name_of_fact (j - 1)]
val learns = map (fn j => (name_of_fact j, parents_of j, map name_of_feature (get_feats j),
map name_of_fact (get_deps j))) (0 upto num_facts - 1)
val parents' = parents_of num_visible_facts
val feats' = map (apfst name_of_feature) feats
in
MaSh_Py.unlearn ctxt overlord;
OS.Process.sleep (seconds 2.0); (* hack *)
MaSh_Py.query ctxt overlord max_suggs (learns, [], parents', feats')
|> map (apfst fact_of_name)
end
(* experimental *)
fun c_plus_plus_tool tool max_suggs learns cfeats =
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 (fn (sy, _) => (os ocs "\""; os ocs sy; os ocs "\"")) ", " 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 (fn sy => (os occ "\""; os occ sy; os occ "\"")) ", " cfeats;
TextIO.closeOut ocs; TextIO.closeOut ocd; TextIO.closeOut ocq; TextIO.closeOut occ;
forkexec max_suggs)
end
val cpp_number_of_nearest_neighbors = 10 (* FUDGE *)
val k_nearest_neighbors_cpp =
c_plus_plus_tool ("newknn/knn" ^ " " ^ string_of_int cpp_number_of_nearest_neighbors)
val naive_bayes_cpp = c_plus_plus_tool "predict/nbayes"
fun add_to_xtab key (next, tab, keys) = (next + 1, Symtab.update_new (key, next) tab, key :: keys)
fun map_array_at ary f i = Array.update (ary, i, f (Array.sub (ary, i)))
fun query ctxt overlord engine visible_facts max_suggs (learns0, hints, feats) =
let
val visible_fact_set = Symtab.make_set visible_facts
val learns =
(learns0 |> List.partition (Symtab.defined visible_fact_set o #1) |> op @) @
(if null hints then [] else [(".goal", feats, hints)])
in
if engine = MaSh_SML_kNN_Cpp then
k_nearest_neighbors_cpp max_suggs learns (map fst feats)
else if engine = MaSh_SML_NB_Cpp then
naive_bayes_cpp max_suggs learns (map fst feats)
else
let
val (rev_depss, rev_featss, (num_facts, _, rev_facts), (num_feats, feat_tab, _)) =
fold (fn (fact, feats, deps) =>
fn (rev_depss, rev_featss, fact_xtab as (_, fact_tab, _), feat_xtab) =>
let
fun add_feat (feat, weight) (xtab as (n, tab, _)) =
(case Symtab.lookup tab feat of
SOME i => ((i, weight), xtab)
| NONE => ((n, weight), add_to_xtab feat xtab))
val (feats', feat_xtab') = fold_map add_feat feats feat_xtab
in
(map_filter (Symtab.lookup fact_tab) deps :: rev_depss, feats' :: rev_featss,
add_to_xtab fact fact_xtab, feat_xtab')
end)
learns ([], [], (0, Symtab.empty, []), (0, Symtab.empty, []))
val facts = rev rev_facts
val fact_vec = Vector.fromList facts
val deps_vec = Vector.fromList (rev rev_depss)
val num_visible_facts = length visible_facts
val get_deps = curry Vector.sub deps_vec
in
trace_msg ctxt (fn () => "MaSh_SML query " ^ encode_features feats ^ " from {" ^
elide_string 1000 (space_implode " " (take num_visible_facts facts)) ^ "}");
(if engine = MaSh_SML_kNN then
let
val facts_ary = Array.array (num_feats, [])
val _ =
fold (fn feats => fn fact =>
let val fact' = fact - 1 in
List.app (fn (feat, weight) =>
map_array_at facts_ary (cons (fact', weight)) feat) feats;
fact'
end)
rev_featss num_facts
val get_facts = curry Array.sub facts_ary
val feats' = map_filter (fn (feat, weight) =>
Option.map (rpair weight) (Symtab.lookup feat_tab feat)) feats
in
k_nearest_neighbors num_facts num_visible_facts get_deps get_facts max_suggs feats'
end
else
let
val unweighted_feats_ary = Vector.fromList (map (map fst) (rev rev_featss))
val get_unweighted_feats = curry Vector.sub unweighted_feats_ary
val int_feats = map (apfst (the_default ~1 o Symtab.lookup feat_tab)) feats
in
(case engine of
MaSh_SML_NB opts =>
naive_bayes opts num_facts num_visible_facts get_deps get_unweighted_feats num_feats
max_suggs int_feats
| MaSh_SML_NB_Py => naive_bayes_py ctxt overlord num_facts num_visible_facts get_deps
get_unweighted_feats num_feats max_suggs int_feats)
end)
|> map (curry Vector.sub fact_vec o fst)
end
end
end;
(*** Middle-level communication with MaSh ***)
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 G =
(Graph.new_node (name, (kind, feats, deps)) G
handle Graph.DUP _ => Graph.map_node name (K (kind, feats, deps)) G)
|> fold (add_edge_to name) parents
fun try_graph ctxt when def f =
f ()
handle
Graph.CYCLES (cycle :: _) =>
(trace_msg ctxt (fn () => "Cycle involving " ^ commas cycle ^ " when " ^ when); def)
| Graph.DUP name =>
(trace_msg ctxt (fn () => "Duplicate fact " ^ quote name ^ " when " ^ when); def)
| Graph.UNDEF name =>
(trace_msg ctxt (fn () => "Unknown fact " ^ quote name ^ " when " ^ when); def)
| exn =>
if Exn.is_interrupt exn then
reraise exn
else
(trace_msg ctxt (fn () => "Internal error when " ^ when ^ ":\n" ^ 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 mash_state =
{access_G : (proof_kind * (string * real) list * string list) Graph.T,
num_known_facts : int,
dirty : string list option}
val empty_state = {access_G = Graph.empty, num_known_facts = 0, dirty = SOME []} : mash_state
local
val version = "*** MaSh version 20140519 ***"
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_features feats,
decode_strs deps)
| _ => NONE)
| _ => NONE)
fun load_state ctxt overlord (time_state as (memory_time, _)) =
let val path = mash_state_file () in
(case try OS.FileSys.modTime (Path.implode (Path.expand path)) of
NONE => time_state
| SOME disk_time =>
if Time.>= (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 (access_G, num_known_facts) =
(case string_ord (version', version) of
EQUAL =>
(try_graph ctxt "loading state" Graph.empty (fn () =>
fold extract_line_and_add_node node_lines Graph.empty),
length node_lines)
| LESS =>
(* cannot parse old file *)
(if the_mash_engine () = MaSh_Py then MaSh_Py.unlearn ctxt overlord
else wipe_out_mash_state_dir ();
(Graph.empty, 0))
| GREATER => raise FILE_VERSION_TOO_NEW ())
in
trace_msg ctxt (fn () => "Loaded fact graph (" ^ graph_info access_G ^ ")");
{access_G = access_G, num_known_facts = num_known_facts, dirty = 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_features feats ^ "; " ^ encode_strs deps ^ "\n"
fun save_state _ (time_state as (_, {dirty = SOME [], ...})) = time_state
| save_state ctxt (memory_time, {access_G, num_known_facts, dirty}) =
let
fun append_entry (name, ((kind, feats, deps), (parents, _))) =
cons (kind, name, Graph.Keys.dest parents, feats, deps)
val path = mash_state_file ()
val dirty' =
(case try OS.FileSys.modTime (Path.implode path) of
NONE => NONE
| SOME disk_time => if Time.< (disk_time, memory_time) then dirty else NONE)
val (banner, entries) =
(case dirty' 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
write_file banner (entries, str_of_entry) path;
trace_msg ctxt (fn () =>
"Saved fact graph (" ^ graph_info access_G ^
(case dirty of
SOME dirty => "; " ^ string_of_int (length dirty) ^ " dirty fact(s)"
| _ => "") ^ ")");
(Time.now (), {access_G = access_G, num_known_facts = num_known_facts, dirty = SOME []})
end
val global_state =
Synchronized.var "Sledgehammer_MaSh.global_state" (Time.zeroTime, empty_state)
in
fun map_state ctxt overlord f =
Synchronized.change global_state (load_state ctxt overlord ##> f #> save_state ctxt)
handle FILE_VERSION_TOO_NEW () => ()
fun peek_state ctxt overlord f =
Synchronized.change_result global_state (perhaps (try (load_state ctxt overlord)) #> `snd #>> f)
fun clear_state ctxt overlord =
(* "MaSh_Py.unlearn" also removes the state file *)
Synchronized.change global_state (fn _ =>
(if the_mash_engine () = MaSh_Py then MaSh_Py.unlearn ctxt overlord
else wipe_out_mash_state_dir ();
(Time.zeroTime, empty_state)))
end
fun mash_unlearn ctxt ({overlord, ...} : params) =
(clear_state ctxt overlord; Output.urgent_message "Reset MaSh.")
(*** Isabelle helpers ***)
val local_prefix = "local" ^ Long_Name.separator
fun elided_backquote_thm threshold th =
elide_string threshold (backquote_thm (Proof_Context.init_global (Thm.theory_of_thm th)) th)
val thy_name_of_thm = Context.theory_name o Thm.theory_of_thm
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 try (unprefix local_prefix) hint of
SOME suf =>
thy_name_of_thm th ^ Long_Name.separator ^ suf ^ Long_Name.separator ^
elided_backquote_thm 50 th
| NONE => hint)
end
else
elided_backquote_thm 200 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 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 Real.* (1.0 / avg (map snd (take max_facts xs))))) xs
fun mesh_facts fact_eq max_facts [(_, (sels, unks))] =
distinct fact_eq (map fst (take max_facts sels) @ take (max_facts - length sels) unks)
| 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 swap o pairself fst)
|> map snd |> take max_facts
end
val default_weight = 1.0
fun free_feature_of s = ("f" ^ s, 40.0 (* FUDGE *))
fun thy_feature_of s = ("y" ^ s, 8.0 (* FUDGE *))
fun type_feature_of s = ("t" ^ s, 4.0 (* FUDGE *))
fun class_feature_of s = ("s" ^ s, 1.0 (* FUDGE *))
val local_feature = ("local", 16.0 (* FUDGE *))
fun crude_theory_ord p =
if Theory.subthy p then
if Theory.eq_thy p then EQUAL else LESS
else if Theory.subthy (swap p) then
GREATER
else
(case int_ord (pairself (length o Theory.ancestors_of) p) of
EQUAL => string_ord (pairself Context.theory_name p)
| order => order)
fun crude_thm_ord p =
(case crude_theory_ord (pairself theory_of_thm p) of
EQUAL =>
(* The hack below is necessary because of odd dependencies that are not reflected in the theory
comparison. *)
let val q = pairself nickname_of_thm p in
(* Hack to put "xxx_def" before "xxxI" and "xxxE" *)
(case bool_ord (pairself (String.isSuffix "_def") (swap q)) of
EQUAL => string_ord q
| ord => ord)
end
| ord => ord)
val thm_less_eq = Theory.subthy o pairself theory_of_thm
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 = prop_of #> freeze #> 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)]}
in
get_minimizing_prover ctxt MaSh (K ()) prover params (K (K (K ""))) problem
end
val bad_types = [@{type_name prop}, @{type_name bool}, @{type_name fun}]
val pat_tvar_prefix = "_"
val pat_var_prefix = "_"
(* try "Long_Name.base_name" for shorter names *)
fun massage_long_name s = s
val crude_str_of_sort = space_implode ":" o map massage_long_name o subtract (op =) @{sort type}
fun crude_str_of_typ (Type (s, [])) = massage_long_name s
| crude_str_of_typ (Type (s, Ts)) = massage_long_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 pref s = [pref ^ s]
val max_pat_breadth = 10 (* FUDGE *)
fun term_features_of ctxt thy_name num_facts const_tab 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 massage_long_name
#> map class_feature_of
#> union (eq_fst (op =))) S
fun pattify_type 0 _ = []
| pattify_type _ (Type (s, [])) =
if member (op =) bad_types s then [] else [massage_long_name 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 pat_tvar_prefix (crude_str_of_sort S)
| pattify_type _ (TVar (_, S)) =
maybe_singleton_str pat_tvar_prefix (crude_str_of_sort S)
fun add_type_pat depth T =
union (eq_fst (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
val base_weight_of_const = 16.0 (* FUDGE *)
val weight_of_const =
(if num_facts = 0 orelse Symtab.is_empty const_tab then
K base_weight_of_const
else
fn s =>
let val count = Symtab.lookup const_tab s |> the_default 1 in
base_weight_of_const + Real.fromInt num_facts / Real.fromInt count
end)
fun pattify_term _ 0 _ = []
| pattify_term _ _ (Const (s, _)) =
if is_widely_irrelevant_const s then [] else [(massage_long_name s, weight_of_const s)]
| pattify_term _ _ (Free (s, T)) =
maybe_singleton_str pat_var_prefix (crude_str_of_typ T)
|> map (rpair 1.0)
|> (if member (op =) fixes s then
cons (free_feature_of (massage_long_name
(thy_name ^ Long_Name.separator ^ s)))
else
I)
| pattify_term _ _ (Var (_, T)) =
maybe_singleton_str pat_var_prefix (crude_str_of_typ T) |> map (rpair default_weight)
| pattify_term Ts _ (Bound j) =
maybe_singleton_str pat_var_prefix (crude_str_of_typ (nth Ts j))
|> map (rpair default_weight)
| pattify_term Ts depth (t $ u) =
let
val ps = take max_pat_breadth (pattify_term Ts depth t)
val qs = take max_pat_breadth (("", default_weight) :: pattify_term Ts (depth - 1) u)
in
map_product (fn ppw as (p, pw) =>
fn ("", _) => ppw
| (q, qw) => (p ^ "(" ^ q ^ ")", pw + qw)) ps qs
end
| pattify_term _ _ _ = []
fun add_term_pat Ts = union (eq_fst (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 num_facts const_tab (scope, _) ts =
let val thy_name = Context.theory_name thy in
thy_feature_of thy_name ::
term_features_of ctxt thy_name num_facts const_tab term_max_depth type_max_depth ts
|> scope <> Global ? cons local_feature
end
(* 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
val prover_default_max_facts = 25
(* "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 =
let val deps = thms_in_proof (SOME name_tabs) th in
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
end
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
[] => (false, [])
| isar_deps =>
let
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
Output.urgent_message ("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
Output.urgent_message ("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
thy_name_of_thm th = thy_name_of_thm 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 maximal_wrt_graph G keys =
let
val tab = Symtab.empty |> fold (fn name => Symtab.default (name, ())) keys
fun insert_new seen name = not (Symtab.defined seen name) ? insert (op =) name
fun num_keys keys = Graph.Keys.fold (K (Integer.add 1)) keys 0
fun find_maxes _ (maxs, []) = map snd maxs
| find_maxes seen (maxs, new :: news) =
find_maxes (seen |> num_keys (Graph.imm_succs G new) > 1 ? Symtab.default (new, ()))
(if Symtab.defined tab new then
let
val newp = Graph.all_preds G [new]
fun is_ancestor x yp = member (op =) yp x
val maxs = maxs |> filter (fn (_, max) => not (is_ancestor max newp))
in
if exists (is_ancestor new o fst) maxs then (maxs, news)
else ((newp, new) :: filter_out (fn (_, max) => is_ancestor max newp) maxs, news)
end
else
(maxs, Graph.Keys.fold (insert_new seen) (Graph.imm_preds G new) news))
in
find_maxes Symtab.empty ([], Graph.maximals G)
end
fun maximal_wrt_access_graph access_G facts =
map (nickname_of_thm o snd) facts
|> maximal_wrt_graph access_G
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 *)
(* FUDGE *)
fun weight_of_proximity_fact rank =
Math.pow (1.3, 15.5 - 0.2 * Real.fromInt rank) + 15.0
fun weight_facts_smoothly facts =
facts ~~ map weight_of_proximity_fact (0 upto length facts - 1)
(* FUDGE *)
fun steep_weight_of_fact rank =
Math.pow (0.62, log2 (Real.fromInt (rank + 1)))
fun weight_facts_steeply facts =
facts ~~ map steep_weight_of_fact (0 upto length facts - 1)
val max_proximity_facts = 100
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 (eq_snd (gen_eq_thm ctxt)) max_facts mess, unknown)
end
fun add_const_counts t =
fold (fn s => Symtab.map_default (s, 0) (Integer.add 1)) (Term.add_const_names t [])
fun mash_suggested_facts ctxt ({debug, overlord, ...} : params) max_facts hyp_ts concl_t facts =
let
val thy = Proof_Context.theory_of ctxt
val thy_name = Context.theory_name thy
val engine = the_mash_engine ()
val facts = facts |> sort (crude_thm_ord o pairself snd o swap)
val chained = facts |> filter (fn ((_, (scope, _)), _) => scope = Chained)
val num_facts = length facts
(* Weights appear to hurt kNN more than they help. *)
val const_tab = Symtab.empty |> engine <> MaSh_SML_kNN
? fold (add_const_counts o prop_of o snd) facts
fun fact_has_right_theory (_, th) =
thy_name = Context.theory_name (theory_of_thm th)
fun chained_or_extra_features_of factor (((_, stature), th), weight) =
[prop_of th]
|> features_of ctxt (theory_of_thm th) num_facts const_tab stature
|> map (apsnd (fn r => weight * factor * r))
fun query_args access_G =
let
val parents = maximal_wrt_access_graph access_G facts
val hints = chained
|> filter (is_fact_in_graph access_G o snd)
|> map (nickname_of_thm o snd)
val goal_feats =
features_of ctxt thy num_facts const_tab (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 feats = fold (union (eq_fst (op =))) [chained_feats, extra_feats] goal_feats
|> debug ? sort (Real.compare o swap o pairself snd)
in
(parents, hints, feats)
end
val (access_G, py_suggs) =
peek_state ctxt overlord (fn {access_G, ...} =>
if Graph.is_empty access_G then
(trace_msg ctxt (K "Nothing has been learned yet"); (access_G, []))
else
(access_G,
if engine = MaSh_Py then
let val (parents, hints, feats) = query_args access_G in
MaSh_Py.query ctxt overlord max_facts ([], hints, parents, feats)
|> map fst
end
else
[]))
val sml_suggs =
if engine = MaSh_Py then
[]
else
let
val (parents, hints, feats) = query_args access_G
val visible_facts = Graph.all_preds access_G parents
val learns =
Graph.schedule (fn _ => fn (fact, (_, feats, deps)) => (fact, feats, deps)) access_G
in
MaSh_SML.query ctxt overlord engine visible_facts max_facts (learns, hints, feats)
end
val unknown = filter_out (is_fact_in_graph access_G o snd) facts
in
find_mash_suggestions ctxt max_facts (py_suggs @ sml_suggs) facts chained unknown
|> pairself (map fact_of_raw_fact)
end
fun learn_wrt_access_graph ctxt (name, parents, feats, deps) (learns, G) =
let
fun maybe_learn_from from (accum as (parents, G)) =
try_graph ctxt "updating graph" accum (fn () =>
(from :: parents, Graph.add_edge_acyclic (from, name) G))
val G = G |> Graph.default_node (name, (Isar_Proof, feats, deps))
val (parents, G) = ([], G) |> fold maybe_learn_from parents
val (deps, _) = ([], G) |> fold maybe_learn_from deps
in
((name, parents, map fst feats, deps) :: learns, G)
end
fun relearn_wrt_access_graph ctxt (name, deps) (relearns, G) =
let
fun maybe_relearn_from from (accum as (parents, G)) =
try_graph ctxt "updating graph" accum (fn () =>
(from :: parents, Graph.add_edge_acyclic (from, name) G))
val G = G |> Graph.map_node name (fn (_, feats, _) => (Automatic_Proof, feats, deps))
val (deps, _) = ([], G) |> fold maybe_relearn_from deps
in
((name, deps) :: relearns, G)
end
fun flop_wrt_access_graph name =
Graph.map_node name (fn (_, feats, deps) => (Isar_Proof_wegen_Prover_Flop, feats, deps))
val learn_timeout_slack = 20.0
fun launch_thread timeout task =
let
val hard_timeout = time_mult learn_timeout_slack timeout
val birth_time = Time.now ()
val death_time = Time.+ (birth_time, hard_timeout)
val desc = ("Machine learner for Sledgehammer", "")
in
Async_Manager.thread MaShN birth_time death_time desc task
end
fun learned_proof_name () =
Date.fmt ".%Y%m%d.%H%M%S." (Date.fromTimeLocal (Time.now ())) ^ serial_string ()
fun mash_learn_proof ctxt ({overlord, timeout, ...} : params) t facts used_ths =
if is_mash_enabled () then
launch_thread timeout (fn () =>
let
val thy = Proof_Context.theory_of ctxt
val feats = features_of ctxt thy 0 Symtab.empty (Local, General) [t]
in
map_state ctxt overlord (fn state as {access_G, num_known_facts, dirty} =>
let
val parents = maximal_wrt_access_graph access_G facts
val deps = used_ths
|> filter (is_fact_in_graph access_G)
|> map nickname_of_thm
in
if the_mash_engine () = MaSh_Py then
(MaSh_Py.learn ctxt overlord true [("", parents, map fst feats, deps)]; state)
else
let
val name = learned_proof_name ()
val access_G = access_G |> add_node Automatic_Proof name parents feats deps
in
{access_G = access_G, num_known_facts = num_known_facts + 1,
dirty = Option.map (cons name) dirty}
end
end);
(true, "")
end)
else
()
fun sendback sub =
Active.sendback_markup [Markup.padding_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, overlord, ...}) prover save auto_level
run_prover learn_timeout facts =
let
val timer = Timer.startRealTimer ()
fun next_commit_time () = Time.+ (Timer.checkRealTimer timer, commit_timeout)
val engine = the_mash_engine ()
val {access_G, ...} = peek_state ctxt overlord I
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
|> trim_dependencies
fun do_commit [] [] [] state = state
| do_commit learns relearns flops {access_G, num_known_facts, dirty} =
let
val was_empty = Graph.is_empty access_G
val (learns, access_G) = ([], access_G) |> fold (learn_wrt_access_graph ctxt) learns
val (relearns, access_G) =
([], access_G) |> fold (relearn_wrt_access_graph ctxt) relearns
val access_G = access_G |> fold flop_wrt_access_graph flops
val num_known_facts = num_known_facts + length learns
val dirty =
(case (was_empty, dirty) of
(false, SOME names) => SOME (map #1 learns @ map #1 relearns @ names)
| _ => NONE)
in
if engine = MaSh_Py then
(MaSh_Py.learn ctxt overlord (save andalso null relearns) (rev learns);
MaSh_Py.relearn ctxt overlord save relearns)
else
();
{access_G = access_G, num_known_facts = num_known_facts, dirty = dirty}
end
fun commit last learns relearns flops =
(if debug andalso auto_level = 0 then Output.urgent_message "Committing..." else ();
map_state ctxt overlord (do_commit (rev learns) relearns flops);
if not last andalso auto_level = 0 then
let val num_proofs = length learns + length relearns in
Output.urgent_message ("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, (n, next_commit, _)) =
let
val name = nickname_of_thm th
val feats = features_of ctxt (theory_of_thm th) 0 Symtab.empty stature [prop_of th]
val deps = deps_of status th |> these
val n = n |> not (null deps) ? Integer.add 1
val learns = (name, parents, feats, deps) :: learns
val (learns, next_commit) =
if Time.> (Timer.checkRealTimer timer, next_commit) then
(commit false learns [] []; ([], next_commit_time ()))
else
(learns, next_commit)
val timed_out = Time.> (Timer.checkRealTimer timer, learn_timeout)
in
(learns, (n, next_commit, timed_out))
end
val n =
if no_new_facts then
0
else
let
val new_facts = facts
|> sort (crude_thm_ord o pairself snd)
|> attach_parents_to_facts []
|> filter_out (is_in_access_G o snd)
val (learns, (n, _, _)) =
([], (0, next_commit_time (), false))
|> fold learn_new_fact new_facts
in
commit true learns [] []; n
end
fun relearn_old_fact _ (accum as (_, (_, _, true))) = accum
| relearn_old_fact ((_, (_, status)), th) ((relearns, flops), (n, next_commit, _)) =
let
val name = nickname_of_thm th
val (n, relearns, flops) =
(case deps_of status th of
SOME deps => (n + 1, (name, deps) :: relearns, flops)
| NONE => (n, relearns, name :: flops))
val (relearns, flops, next_commit) =
if Time.> (Timer.checkRealTimer timer, next_commit) then
(commit false [] relearns flops; ([], [], next_commit_time ()))
else
(relearns, flops, next_commit)
val timed_out = Time.> (Timer.checkRealTimer timer, learn_timeout)
in
((relearns, flops), (n, next_commit, timed_out))
end
val n =
if not run_prover then
n
else
let
val max_isar = 1000 * max_dependencies
fun priority_of th =
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 pairself fst)
|> map snd
val ((relearns, flops), (n, _, _)) =
(([], []), (n, next_commit_time (), false))
|> fold relearn_old_fact old_facts
in
commit true [] relearns flops; n
end
in
if verbose orelse auto_level < 2 then
"Learned " ^ string_of_int n ^ " nontrivial " ^
(if run_prover then "automatic and " else "") ^ "Isar proof" ^ plural_s n ^
(if verbose then " in " ^ string_of_time (Timer.checkRealTimer timer) else "") ^ "."
else
""
end
end
fun mash_learn ctxt (params as {provers, timeout, ...}) fact_override chained run_prover =
let
val css = Sledgehammer_Fact.clasimpset_rule_table_of ctxt
val ctxt = ctxt |> Config.put instantiate_inducts false
val facts = nearly_all_facts ctxt false fact_override Symtab.empty css chained [] @{prop True}
|> sort (crude_thm_ord o pairself snd o swap)
val num_facts = length facts
val prover = hd provers
fun learn auto_level run_prover =
mash_learn_facts ctxt params prover true auto_level run_prover one_year facts
|> Output.urgent_message
in
if run_prover then
(Output.urgent_message ("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;
Output.urgent_message "Now collecting automatic proofs. This may take several hours. You \
\can safely stop the learning process at any point.";
learn 0 true)
else
(Output.urgent_message ("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 overlord =
not (Graph.is_empty (#access_G (peek_state ctxt overlord I)))
(* Generate more suggestions than requested, because some might be thrown out later for various
reasons (e.g., duplicates). *)
fun generous_max_suggestions max_facts = 3 * max_facts div 2 + 25
val mepo_weight = 0.5
val mash_weight = 0.5
val max_facts_to_learn_before_query = 100
(* The threshold should be large enough so that MaSh does not get activated for Auto Sledgehammer
and Try. *)
val min_secs_for_learning = 15
fun relevant_facts ctxt (params as {overlord, blocking, learn, fact_filter, timeout, ...}) prover
max_facts ({add, only, ...} : fact_override) hyp_ts concl_t facts =
if not (subset (op =) (the_list fact_filter, fact_filters)) then
error ("Unknown fact filter: " ^ quote (the fact_filter) ^ ".")
else if only then
[("", map fact_of_raw_fact facts)]
else if max_facts <= 0 orelse null facts then
[("", [])]
else
let
fun maybe_launch_thread () =
if not (Async_Manager.has_running_threads MaShN) andalso
Time.toSeconds timeout >= min_secs_for_learning then
let val timeout = time_mult learn_timeout_slack timeout in
launch_thread timeout
(fn () => (true, mash_learn_facts ctxt params prover true 2 false timeout facts))
end
else
()
fun maybe_learn () =
if is_mash_enabled () andalso learn then
let
val {access_G, num_known_facts, ...} = peek_state ctxt overlord I
val is_in_access_G = is_fact_in_graph access_G o snd
in
if length facts - num_known_facts <= max_facts_to_learn_before_query then
(case length (filter_out is_in_access_G facts) of
0 => false
| num_facts_to_learn =>
if num_facts_to_learn <= max_facts_to_learn_before_query then
(mash_learn_facts ctxt params prover false 2 false timeout facts
|> (fn "" => () | s => Output.urgent_message (MaShN ^ ": " ^ s));
true)
else
(maybe_launch_thread (); false))
else
(maybe_launch_thread (); false)
end
else
false
val (save, effective_fact_filter) =
(case fact_filter of
SOME ff => (ff <> mepoN andalso maybe_learn (), ff)
| NONE =>
if is_mash_enabled () then
(maybe_learn (), if mash_can_suggest_facts ctxt overlord then meshN else mepoN)
else
(false, mepoN))
val unique_facts = drop_duplicate_facts facts
val add_ths = Attrib.eval_thms ctxt add
fun in_add (_, th) = member Thm.eq_thm_prop add_ths th
fun add_and_take accepts =
(case add_ths of
[] => accepts
| _ =>
(unique_facts |> filter in_add |> map fact_of_raw_fact) @ (accepts |> filter_out in_add))
|> take max_facts
fun mepo () =
(mepo_suggested_facts ctxt params max_facts NONE hyp_ts concl_t unique_facts
|> weight_facts_steeply, [])
fun mash () =
mash_suggested_facts ctxt 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 (eq_snd (gen_eq_thm ctxt)) max_facts mess |> add_and_take
in
if the_mash_engine () = MaSh_Py andalso save then MaSh_Py.save ctxt overlord else ();
(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
fun kill_learners ctxt ({overlord, ...} : params) =
(Async_Manager.kill_threads MaShN "learner";
if the_mash_engine () = MaSh_Py then MaSh_Py.shutdown ctxt overlord else ())
fun running_learners () = Async_Manager.running_threads MaShN "learner"
end;