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(* Title: HOL/Tools/Sledgehammer/sledgehammer_mash.ML
Author: Jasmin Blanchette, TU Muenchen
Author: Cezary Kaliszyk, University of Innsbruck
Sledgehammer's machine-learning-based relevance filter (MaSh).
*)
signature SLEDGEHAMMER_MASH =
sig
type stature = ATP_Problem_Generate.stature
type raw_fact = Sledgehammer_Fact.raw_fact
type fact = Sledgehammer_Fact.fact
type fact_override = Sledgehammer_Fact.fact_override
type params = Sledgehammer_Prover.params
type prover_result = Sledgehammer_Prover.prover_result
val trace : bool Config.T
val duplicates : bool Config.T
val MePoN : string
val MaShN : string
val MeShN : string
val mepoN : string
val mashN : string
val meshN : string
val unlearnN : string
val learn_isarN : string
val learn_proverN : string
val relearn_isarN : string
val relearn_proverN : string
val fact_filters : string list
val encode_str : string -> string
val encode_strs : string list -> string
val decode_str : string -> string
val decode_strs : string -> string list
datatype mash_algorithm =
MaSh_NB
| MaSh_kNN
| MaSh_NB_kNN
| MaSh_NB_Ext
| MaSh_kNN_Ext
val is_mash_enabled : unit -> bool
val the_mash_algorithm : unit -> mash_algorithm
val str_of_mash_algorithm : mash_algorithm -> string
val mesh_facts : ('a list -> 'a list) -> ('a * 'a -> bool) -> int ->
(real * (('a * real) list * 'a list)) list -> 'a list
val nickname_of_thm : thm -> string
val find_suggested_facts : Proof.context -> ('b * thm) list -> string list -> ('b * thm) list
val crude_thm_ord : Proof.context -> thm ord
val thm_less : thm * thm -> bool
val goal_of_thm : theory -> thm -> thm
val run_prover_for_mash : Proof.context -> params -> string -> string -> fact list -> thm ->
prover_result
val features_of : Proof.context -> string -> stature -> term list -> string list
val trim_dependencies : string list -> string list option
val isar_dependencies_of : string Symtab.table * string Symtab.table -> thm -> string list option
val prover_dependencies_of : Proof.context -> params -> string -> int -> raw_fact list ->
string Symtab.table * string Symtab.table -> thm -> bool * string list
val attach_parents_to_facts : ('a * thm) list -> ('a * thm) list ->
(string list * ('a * thm)) list
val num_extra_feature_facts : int
val extra_feature_factor : real
val weight_facts_smoothly : 'a list -> ('a * real) list
val weight_facts_steeply : 'a list -> ('a * real) list
val find_mash_suggestions : Proof.context -> int -> string list -> ('a * thm) list ->
('a * thm) list -> ('a * thm) list -> ('a * thm) list * ('a * thm) list
val mash_suggested_facts : Proof.context -> string -> params -> int -> term list -> term ->
raw_fact list -> fact list * fact list
val mash_unlearn : Proof.context -> unit
val mash_learn_proof : Proof.context -> params -> term -> thm list -> unit
val mash_learn_facts : Proof.context -> params -> string -> int -> bool -> Time.time ->
raw_fact list -> string
val mash_learn : Proof.context -> params -> fact_override -> thm list -> bool -> unit
val mash_can_suggest_facts : Proof.context -> bool
val mash_can_suggest_facts_fast : Proof.context -> bool
val generous_max_suggestions : int -> int
val mepo_weight : real
val mash_weight : real
val relevant_facts : Proof.context -> params -> string -> int -> fact_override -> term list ->
term -> raw_fact list -> (string * fact list) list
end;
structure Sledgehammer_MaSh : SLEDGEHAMMER_MASH =
struct
open ATP_Util
open ATP_Problem_Generate
open Sledgehammer_Util
open Sledgehammer_Fact
open Sledgehammer_Prover
open Sledgehammer_Prover_Minimize
open Sledgehammer_MePo
val anonymous_proof_prefix = "."
val trace = Attrib.setup_config_bool \<^binding>\<open>sledgehammer_mash_trace\<close> (K false)
val duplicates = Attrib.setup_config_bool \<^binding>\<open>sledgehammer_fact_duplicates\<close> (K false)
fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()
fun gen_eq_thm ctxt = if Config.get ctxt duplicates then Thm.eq_thm_strict else Thm.eq_thm_prop
val MePoN = "MePo"
val MaShN = "MaSh"
val MeShN = "MeSh"
val mepoN = "mepo"
val mashN = "mash"
val meshN = "mesh"
val fact_filters = [meshN, mepoN, mashN]
val unlearnN = "unlearn"
val learn_isarN = "learn_isar"
val learn_proverN = "learn_prover"
val relearn_isarN = "relearn_isar"
val relearn_proverN = "relearn_prover"
fun map_array_at ary f i = Array.update (ary, i, f (Array.sub (ary, i)))
type xtab = int * int Symtab.table
val empty_xtab = (0, Symtab.empty)
fun add_to_xtab key (next, tab) = (next + 1, Symtab.update_new (key, next) tab)
fun maybe_add_to_xtab key = perhaps (try (add_to_xtab key))
fun state_file () = Path.expand (Path.explode "$ISABELLE_HOME_USER/mash_state")
val remove_state_file = try File.rm o state_file
datatype mash_algorithm =
MaSh_NB
| MaSh_kNN
| MaSh_NB_kNN
| MaSh_NB_Ext
| MaSh_kNN_Ext
fun mash_algorithm () =
(case Options.default_string \<^system_option>\<open>MaSh\<close> of
"yes" => SOME MaSh_NB_kNN
| "sml" => SOME MaSh_NB_kNN
| "nb" => SOME MaSh_NB
| "knn" => SOME MaSh_kNN
| "nb_knn" => SOME MaSh_NB_kNN
| "nb_ext" => SOME MaSh_NB_Ext
| "knn_ext" => SOME MaSh_kNN_Ext
| "none" => NONE
| "" => NONE
| algorithm => (warning ("Unknown MaSh algorithm: " ^ quote algorithm); NONE))
val is_mash_enabled = is_some o mash_algorithm
val the_mash_algorithm = the_default MaSh_NB_kNN o mash_algorithm
fun str_of_mash_algorithm MaSh_NB = "nb"
| str_of_mash_algorithm MaSh_kNN = "knn"
| str_of_mash_algorithm MaSh_NB_kNN = "nb_knn"
| str_of_mash_algorithm MaSh_NB_Ext = "nb_ext"
| str_of_mash_algorithm MaSh_kNN_Ext = "knn_ext"
fun scaled_avg [] = 0
| scaled_avg xs = Real.ceil (100000000.0 * fold (curry (op +)) xs 0.0) div length xs
fun avg [] = 0.0
| avg xs = fold (curry (op +)) xs 0.0 / Real.fromInt (length xs)
fun normalize_scores _ [] = []
| normalize_scores max_facts xs =
map (apsnd (curry (op *) (1.0 / avg (map snd (take max_facts xs))))) xs
fun mesh_facts maybe_distinct _ max_facts [(_, (sels, unks))] =
map fst (take max_facts sels) @ take (max_facts - length sels) unks
|> maybe_distinct
| mesh_facts _ fact_eq max_facts mess =
let
val mess = mess |> map (apsnd (apfst (normalize_scores max_facts)))
fun score_in fact (global_weight, (sels, unks)) =
let val score_at = try (nth sels) #> Option.map (fn (_, score) => global_weight * score) in
(case find_index (curry fact_eq fact o fst) sels of
~1 => if member fact_eq unks fact then NONE else SOME 0.0
| rank => score_at rank)
end
fun weight_of fact = mess |> map_filter (score_in fact) |> scaled_avg
in
fold (union fact_eq o map fst o take max_facts o fst o snd) mess []
|> map (`weight_of) |> sort (int_ord o apply2 fst o swap)
|> map snd |> take max_facts
end
fun smooth_weight_of_fact rank = Math.pow (1.3, 15.5 - 0.2 * Real.fromInt rank) + 15.0 (* FUDGE *)
fun steep_weight_of_fact rank = Math.pow (0.62, log2 (Real.fromInt (rank + 1))) (* FUDGE *)
fun weight_facts_smoothly facts = facts ~~ map smooth_weight_of_fact (0 upto length facts - 1)
fun weight_facts_steeply facts = facts ~~ map steep_weight_of_fact (0 upto length facts - 1)
fun sort_array_suffix cmp needed a =
let
exception BOTTOM of int
val al = Array.length a
fun maxson l i =
let val i31 = i + i + i + 1 in
if i31 + 2 < l then
let val x = Unsynchronized.ref i31 in
if is_less (cmp (Array.sub (a, i31), Array.sub (a, i31 + 1))) then x := i31 + 1 else ();
if is_less (cmp (Array.sub (a, !x), Array.sub (a, i31 + 2))) then x := i31 + 2 else ();
!x
end
else
if i31 + 1 < l andalso is_less (cmp (Array.sub (a, i31), Array.sub (a, i31 + 1)))
then i31 + 1 else if i31 < l then i31 else raise BOTTOM i
end
fun trickledown l i e =
let val j = maxson l i in
if is_greater (cmp (Array.sub (a, j), e)) then
(Array.update (a, i, Array.sub (a, j)); trickledown l j e)
else
Array.update (a, i, e)
end
fun trickle l i e = trickledown l i e handle BOTTOM i => Array.update (a, i, e)
fun bubbledown l i =
let val j = maxson l i in
Array.update (a, i, Array.sub (a, j));
bubbledown l j
end
fun bubble l i = bubbledown l i handle BOTTOM i => i
fun trickleup i e =
let val father = (i - 1) div 3 in
if is_less (cmp (Array.sub (a, father), e)) then
(Array.update (a, i, Array.sub (a, father));
if father > 0 then trickleup father e else Array.update (a, 0, e))
else
Array.update (a, i, e)
end
fun for i = if i < 0 then () else (trickle al i (Array.sub (a, i)); for (i - 1))
fun for2 i =
if i < Integer.max 2 (al - needed) then
()
else
let val e = Array.sub (a, i) in
Array.update (a, i, Array.sub (a, 0));
trickleup (bubble i 0) e;
for2 (i - 1)
end
in
for (((al + 1) div 3) - 1);
for2 (al - 1);
if al > 1 then
let val e = Array.sub (a, 1) in
Array.update (a, 1, Array.sub (a, 0));
Array.update (a, 0, e)
end
else
()
end
fun rev_sort_list_prefix cmp needed xs =
let val ary = Array.fromList xs in
sort_array_suffix cmp needed ary;
Array.foldl (op ::) [] ary
end
(*** Convenience functions for synchronized access ***)
fun synchronized_timed_value var time_limit =
Synchronized.timed_access var time_limit (fn value => SOME (value, value))
fun synchronized_timed_change_result var time_limit f =
Synchronized.timed_access var time_limit (SOME o f)
fun synchronized_timed_change var time_limit f =
synchronized_timed_change_result var time_limit (fn x => ((), f x))
fun mash_time_limit _ = SOME (seconds 0.1)
(*** Isabelle-agnostic machine learning ***)
structure MaSh =
struct
fun select_fact_idxs (big_number : real) recommends =
List.app (fn at =>
let val (j, ov) = Array.sub (recommends, at) in
Array.update (recommends, at, (j, big_number + ov))
end)
fun wider_array_of_vector init vec =
let val ary = Array.array init in
Array.copyVec {src = vec, dst = ary, di = 0};
ary
end
val nb_def_prior_weight = 1000 (* FUDGE *)
fun learn_facts (tfreq0, sfreq0, dffreq0) num_facts0 num_facts num_feats depss featss =
let
val tfreq = wider_array_of_vector (num_facts, 0) tfreq0
val sfreq = wider_array_of_vector (num_facts, Inttab.empty) sfreq0
val dffreq = wider_array_of_vector (num_feats, 0) dffreq0
fun learn_one th feats deps =
let
fun add_th weight t =
let
val im = Array.sub (sfreq, t)
fun fold_fn s = Inttab.map_default (s, 0) (Integer.add weight)
in
map_array_at tfreq (Integer.add weight) t;
Array.update (sfreq, t, fold fold_fn feats im)
end
val add_sym = map_array_at dffreq (Integer.add 1)
in
add_th nb_def_prior_weight th;
List.app (add_th 1) deps;
List.app add_sym feats
end
fun for i =
if i = num_facts then ()
else (learn_one i (Vector.sub (featss, i)) (Vector.sub (depss, i)); for (i + 1))
in
for num_facts0;
(Array.vector tfreq, Array.vector sfreq, Array.vector dffreq)
end
fun naive_bayes (tfreq, sfreq, dffreq) num_facts max_suggs fact_idxs goal_feats =
let
val tau = 0.2 (* FUDGE *)
val pos_weight = 5.0 (* FUDGE *)
val def_val = ~18.0 (* FUDGE *)
val init_val = 30.0 (* FUDGE *)
val ln_afreq = Math.ln (Real.fromInt num_facts)
val idf = Vector.map (fn i => ln_afreq - Math.ln (Real.fromInt i)) dffreq
fun tfidf feat = Vector.sub (idf, feat)
fun log_posterior i =
let
val tfreq = Real.fromInt (Vector.sub (tfreq, i))
fun add_feat (f, fw0) (res, sfh) =
(case Inttab.lookup sfh f of
SOME sf =>
(res + fw0 * tfidf f * Math.ln (pos_weight * Real.fromInt sf / tfreq),
Inttab.delete f sfh)
| NONE => (res + fw0 * tfidf f * def_val, sfh))
val (res, sfh) = fold add_feat goal_feats (init_val * Math.ln tfreq, Vector.sub (sfreq, i))
fun fold_sfh (f, sf) sow =
sow + tfidf f * Math.ln (1.0 - Real.fromInt (sf - 1) / tfreq)
val sum_of_weights = Inttab.fold fold_sfh sfh 0.0
in
res + tau * sum_of_weights
end
val posterior = Array.tabulate (num_facts, (fn j => (j, log_posterior j)))
fun ret at acc =
if at = num_facts then acc else ret (at + 1) (Array.sub (posterior, at) :: acc)
in
select_fact_idxs 100000.0 posterior fact_idxs;
sort_array_suffix (Real.compare o apply2 snd) max_suggs posterior;
ret (Integer.max 0 (num_facts - max_suggs)) []
end
val initial_k = 0
fun k_nearest_neighbors dffreq num_facts num_feats depss featss max_suggs fact_idxs goal_feats =
let
exception EXIT of unit
val ln_afreq = Math.ln (Real.fromInt num_facts)
fun tfidf feat = ln_afreq - Math.ln (Real.fromInt (Vector.sub (dffreq, feat)))
val overlaps_sqr = Array.tabulate (num_facts, rpair 0.0)
val feat_facts = Array.array (num_feats, [])
val _ = Vector.foldl (fn (feats, fact) =>
(List.app (map_array_at feat_facts (cons fact)) feats; fact + 1)) 0 featss
fun do_feat (s, sw0) =
let
val sw = sw0 * tfidf s
val w6 = Math.pow (sw, 6.0 (* FUDGE *))
fun inc_overlap j =
let val (_, ov) = Array.sub (overlaps_sqr, j) in
Array.update (overlaps_sqr, j, (j, w6 + ov))
end
in
List.app inc_overlap (Array.sub (feat_facts, s))
end
val _ = List.app do_feat goal_feats
val _ = sort_array_suffix (Real.compare o apply2 snd) num_facts overlaps_sqr
val no_recommends = Unsynchronized.ref 0
val recommends = Array.tabulate (num_facts, rpair 0.0)
val age = Unsynchronized.ref 500000000.0
fun inc_recommend v j =
let val (_, ov) = Array.sub (recommends, j) in
if ov <= 0.0 then
(no_recommends := !no_recommends + 1; Array.update (recommends, j, (j, !age + ov)))
else
Array.update (recommends, j, (j, v + ov))
end
val k = Unsynchronized.ref 0
fun do_k k =
if k >= num_facts then
raise EXIT ()
else
let
val deps_factor = 2.7 (* FUDGE *)
val (j, o2) = Array.sub (overlaps_sqr, num_facts - k - 1)
val _ = inc_recommend o2 j
val ds = Vector.sub (depss, j)
val l = Real.fromInt (length ds)
in
List.app (inc_recommend (deps_factor * o2 / l)) ds
end
fun while1 () =
if !k = initial_k + 1 then () else (do_k (!k); k := !k + 1; while1 ())
handle EXIT () => ()
fun while2 () =
if !no_recommends >= max_suggs then ()
else (do_k (!k); k := !k + 1; age := !age - 10000.0; while2 ())
handle EXIT () => ()
fun ret acc at =
if at = num_facts then acc else ret (Array.sub (recommends, at) :: acc) (at + 1)
in
while1 ();
while2 ();
select_fact_idxs 1000000000.0 recommends fact_idxs;
sort_array_suffix (Real.compare o apply2 snd) max_suggs recommends;
ret [] (Integer.max 0 (num_facts - max_suggs))
end
(* experimental *)
fun external_tool tool max_suggs learns goal_feats =
let
val ser = string_of_int (serial ()) (* poor person's attempt at thread-safety *)
val ocs = TextIO.openOut ("adv_syms" ^ ser)
val ocd = TextIO.openOut ("adv_deps" ^ ser)
val ocq = TextIO.openOut ("adv_seq" ^ ser)
val occ = TextIO.openOut ("adv_conj" ^ ser)
fun os oc s = TextIO.output (oc, s)
fun ol _ _ _ [] = ()
| ol _ f _ [e] = f e
| ol oc f sep (h :: t) = (f h; os oc sep; ol oc f sep t)
fun do_learn (name, feats, deps) =
(os ocs name; os ocs ":"; ol ocs (os ocs o quote) ", " feats; os ocs "\n";
os ocd name; os ocd ":"; ol ocd (os ocd) " " deps; os ocd "\n"; os ocq name; os ocq "\n")
fun forkexec no =
let
val cmd =
"~/misc/" ^ tool ^ " adv_syms" ^ ser ^ " adv_deps" ^ ser ^ " " ^ string_of_int no ^
" adv_seq" ^ ser ^ " < adv_conj" ^ ser
in
fst (Isabelle_System.bash_output cmd)
|> space_explode " "
|> filter_out (curry (op =) "")
end
in
(List.app do_learn learns; ol occ (os occ o quote) ", " (map fst goal_feats);
TextIO.closeOut ocs; TextIO.closeOut ocd; TextIO.closeOut ocq; TextIO.closeOut occ;
forkexec max_suggs)
end
fun k_nearest_neighbors_ext max_suggs =
external_tool ("newknn/knn" ^ " " ^ string_of_int initial_k) max_suggs
fun naive_bayes_ext max_suggs = external_tool "predict/nbayes" max_suggs
fun query_external ctxt algorithm max_suggs learns goal_feats =
(trace_msg ctxt (fn () => "MaSh query external " ^ commas (map fst goal_feats));
(case algorithm of
MaSh_NB_Ext => naive_bayes_ext max_suggs learns goal_feats
| MaSh_kNN_Ext => k_nearest_neighbors_ext max_suggs learns goal_feats))
fun query_internal ctxt algorithm num_facts num_feats (fact_names, featss, depss)
(freqs as (_, _, dffreq)) fact_idxs max_suggs goal_feats int_goal_feats =
let
fun nb () =
naive_bayes freqs num_facts max_suggs fact_idxs int_goal_feats
|> map fst
fun knn () =
k_nearest_neighbors dffreq num_facts num_feats depss featss max_suggs fact_idxs int_goal_feats
|> map fst
in
(trace_msg ctxt (fn () => "MaSh query internal " ^ commas (map fst goal_feats) ^ " from {" ^
elide_string 1000 (space_implode " " (Vector.foldr (op ::) [] fact_names)) ^ "}");
(case algorithm of
MaSh_NB => nb ()
| MaSh_kNN => knn ()
| MaSh_NB_kNN =>
mesh_facts I (op =) max_suggs
[(0.5 (* FUDGE *), (weight_facts_steeply (nb ()), [])),
(0.5 (* FUDGE *), (weight_facts_steeply (knn ()), []))])
|> map (curry Vector.sub fact_names))
end
end;
(*** Persistent, stringly-typed state ***)
fun meta_char c =
if Char.isAlphaNum c orelse c = #"_" orelse c = #"." orelse c = #"(" orelse c = #")" orelse
c = #"," orelse c = #"'" then
String.str c
else
(* fixed width, in case more digits follow *)
"%" ^ stringN_of_int 3 (Char.ord c)
fun unmeta_chars accum [] = String.implode (rev accum)
| unmeta_chars accum (#"%" :: d1 :: d2 :: d3 :: cs) =
(case Int.fromString (String.implode [d1, d2, d3]) of
SOME n => unmeta_chars (Char.chr n :: accum) cs
| NONE => "" (* error *))
| unmeta_chars _ (#"%" :: _) = "" (* error *)
| unmeta_chars accum (c :: cs) = unmeta_chars (c :: accum) cs
val encode_str = String.translate meta_char
val encode_strs = map encode_str #> space_implode " "
fun decode_str s =
if String.isSubstring "%" s then unmeta_chars [] (String.explode s) else s;
fun decode_strs s =
space_explode " " s |> String.isSubstring "%" s ? map decode_str;
datatype proof_kind = Isar_Proof | Automatic_Proof | Isar_Proof_wegen_Prover_Flop
fun str_of_proof_kind Isar_Proof = "i"
| str_of_proof_kind Automatic_Proof = "a"
| str_of_proof_kind Isar_Proof_wegen_Prover_Flop = "x"
fun proof_kind_of_str "a" = Automatic_Proof
| proof_kind_of_str "x" = Isar_Proof_wegen_Prover_Flop
| proof_kind_of_str _ (* "i" *) = Isar_Proof
fun add_edge_to name parent =
Graph.default_node (parent, (Isar_Proof, [], []))
#> Graph.add_edge (parent, name)
fun add_node kind name parents feats deps (accum as (access_G, (fact_xtab, feat_xtab), learns)) =
let val fact_xtab' = add_to_xtab name fact_xtab in
((Graph.new_node (name, (kind, feats, deps)) access_G
handle Graph.DUP _ => Graph.map_node name (K (kind, feats, deps)) access_G)
|> fold (add_edge_to name) parents,
(fact_xtab', fold maybe_add_to_xtab feats feat_xtab),
(name, feats, deps) :: learns)
end
handle Symtab.DUP _ => accum (* robustness (in case the state file violates the invariant) *)
fun try_graph ctxt when def f =
f ()
handle
Graph.CYCLES (cycle :: _) =>
(trace_msg ctxt (fn () => "Cycle involving " ^ commas cycle ^ " when " ^ when); def)
| Graph.DUP name =>
(trace_msg ctxt (fn () => "Duplicate fact " ^ quote name ^ " when " ^ when); def)
| Graph.UNDEF name =>
(trace_msg ctxt (fn () => "Unknown fact " ^ quote name ^ " when " ^ when); def)
| exn =>
if Exn.is_interrupt exn then
Exn.reraise exn
else
(trace_msg ctxt (fn () => "Internal error when " ^ when ^ ":\n" ^ Runtime.exn_message exn);
def)
fun graph_info G =
string_of_int (length (Graph.keys G)) ^ " node(s), " ^
string_of_int (fold (Integer.add o length o snd) (Graph.dest G) 0) ^ " edge(s), " ^
string_of_int (length (Graph.maximals G)) ^ " maximal"
type ffds = string vector * int list vector * int list vector
type freqs = int vector * int Inttab.table vector * int vector
type mash_state =
{access_G : (proof_kind * string list * string list) Graph.T,
xtabs : xtab * xtab,
ffds : ffds,
freqs : freqs,
dirty_facts : string list option}
val empty_xtabs = (empty_xtab, empty_xtab)
val empty_ffds = (Vector.fromList [], Vector.fromList [], Vector.fromList []) : ffds
val empty_freqs = (Vector.fromList [], Vector.fromList [], Vector.fromList []) : freqs
val empty_state =
{access_G = Graph.empty,
xtabs = empty_xtabs,
ffds = empty_ffds,
freqs = empty_freqs,
dirty_facts = SOME []} : mash_state
fun recompute_ffds_freqs_from_learns (learns : (string * string list * string list) list)
((num_facts, fact_tab), (num_feats, feat_tab)) num_facts0 (fact_names0, featss0, depss0) freqs0 =
let
val fact_names = Vector.concat [fact_names0, Vector.fromList (map #1 learns)]
val featss = Vector.concat [featss0,
Vector.fromList (map (map_filter (Symtab.lookup feat_tab) o #2) learns)]
val depss = Vector.concat [depss0,
Vector.fromList (map (map_filter (Symtab.lookup fact_tab) o #3) learns)]
in
((fact_names, featss, depss),
MaSh.learn_facts freqs0 num_facts0 num_facts num_feats depss featss)
end
fun reorder_learns (num_facts, fact_tab) learns =
let val ary = Array.array (num_facts, ("", [], [])) in
List.app (fn learn as (fact, _, _) =>
Array.update (ary, the (Symtab.lookup fact_tab fact), learn))
learns;
Array.foldr (op ::) [] ary
end
fun recompute_ffds_freqs_from_access_G access_G (xtabs as (fact_xtab, _)) =
let
val learns =
Graph.schedule (fn _ => fn (fact, (_, feats, deps)) => (fact, feats, deps)) access_G
|> reorder_learns fact_xtab
in
recompute_ffds_freqs_from_learns learns xtabs 0 empty_ffds empty_freqs
end
local
val version = "*** MaSh version 20190121 ***"
exception FILE_VERSION_TOO_NEW of unit
fun extract_node line =
(case space_explode ":" line of
[head, tail] =>
(case (space_explode " " head, map (unprefix " ") (space_explode ";" tail)) of
([kind, name], [parents, feats, deps]) =>
SOME (proof_kind_of_str kind, decode_str name, decode_strs parents, decode_strs feats,
decode_strs deps)
| _ => NONE)
| _ => NONE)
fun would_load_state (memory_time, _) =
let val path = state_file () in
(case try OS.FileSys.modTime (File.platform_path path) of
NONE => false
| SOME disk_time => memory_time < disk_time)
end;
fun load_state ctxt (time_state as (memory_time, _)) =
let val path = state_file () in
(case try OS.FileSys.modTime (File.platform_path path) of
NONE => time_state
| SOME disk_time =>
if memory_time >= disk_time then
time_state
else
(disk_time,
(case try File.read_lines path of
SOME (version' :: node_lines) =>
let
fun extract_line_and_add_node line =
(case extract_node line of
NONE => I (* should not happen *)
| SOME (kind, name, parents, feats, deps) => add_node kind name parents feats deps)
val empty_G_etc = (Graph.empty, empty_xtabs, [])
val (access_G, xtabs, rev_learns) =
(case string_ord (version', version) of
EQUAL =>
try_graph ctxt "loading state" empty_G_etc
(fn () => fold extract_line_and_add_node node_lines empty_G_etc)
| LESS => (remove_state_file (); empty_G_etc) (* cannot parse old file *)
| GREATER => raise FILE_VERSION_TOO_NEW ())
val (ffds, freqs) =
recompute_ffds_freqs_from_learns (rev rev_learns) xtabs 0 empty_ffds empty_freqs
in
trace_msg ctxt (fn () => "Loaded fact graph (" ^ graph_info access_G ^ ")");
{access_G = access_G, xtabs = xtabs, ffds = ffds, freqs = freqs, dirty_facts = SOME []}
end
| _ => empty_state)))
end
fun str_of_entry (kind, name, parents, feats, deps) =
str_of_proof_kind kind ^ " " ^ encode_str name ^ ": " ^ encode_strs parents ^ "; " ^
encode_strs feats ^ "; " ^ encode_strs deps ^ "\n"
fun save_state _ (time_state as (_, {dirty_facts = SOME [], ...})) = time_state
| save_state ctxt (memory_time, {access_G, xtabs, ffds, freqs, dirty_facts}) =
let
fun append_entry (name, ((kind, feats, deps), (parents, _))) =
cons (kind, name, Graph.Keys.dest parents, feats, deps)
val path = state_file ()
val dirty_facts' =
(case try OS.FileSys.modTime (File.platform_path path) of
NONE => NONE
| SOME disk_time => if disk_time <= memory_time then dirty_facts else NONE)
val (banner, entries) =
(case dirty_facts' of
SOME names => (NONE, fold (append_entry o Graph.get_entry access_G) names [])
| NONE => (SOME (version ^ "\n"), Graph.fold append_entry access_G []))
in
(case banner of SOME s => File.write path s | NONE => ();
entries |> chunk_list 500 |> List.app (File.append path o implode o map str_of_entry))
handle IO.Io _ => ();
trace_msg ctxt (fn () =>
"Saved fact graph (" ^ graph_info access_G ^
(case dirty_facts of
SOME dirty_facts => "; " ^ string_of_int (length dirty_facts) ^ " dirty fact(s)"
| _ => "") ^ ")");
(Time.now (),
{access_G = access_G, xtabs = xtabs, ffds = ffds, freqs = freqs, dirty_facts = SOME []})
end
val global_state = Synchronized.var "Sledgehammer_MaSh.global_state" (Time.zeroTime, empty_state)
in
fun map_state ctxt f =
(trace_msg ctxt (fn () => "Changing MaSh state");
synchronized_timed_change global_state mash_time_limit
(load_state ctxt ##> f #> save_state ctxt))
|> ignore
handle FILE_VERSION_TOO_NEW () => ()
fun peek_state ctxt =
(trace_msg ctxt (fn () => "Peeking at MaSh state");
(case synchronized_timed_value global_state mash_time_limit of
NONE => NONE
| SOME state => if would_load_state state then NONE else SOME state))
fun get_state ctxt =
(trace_msg ctxt (fn () => "Retrieving MaSh state");
synchronized_timed_change_result global_state mash_time_limit
(perhaps (try (load_state ctxt)) #> `snd))
fun clear_state ctxt =
(trace_msg ctxt (fn () => "Clearing MaSh state");
Synchronized.change global_state (fn _ => (remove_state_file (); (Time.zeroTime, empty_state))))
end
(*** Isabelle helpers ***)
fun crude_printed_term size t =
let
fun term _ (res, 0) = (res, 0)
| term (t $ u) (res, size) =
let
val (res, size) = term t (res ^ "(", size)
val (res, size) = term u (res ^ " ", size)
in
(res ^ ")", size)
end
| term (Abs (s, _, t)) (res, size) = term t (res ^ "%" ^ s ^ ".", size - 1)
| term (Bound n) (res, size) = (res ^ "#" ^ string_of_int n, size - 1)
| term (Const (s, _)) (res, size) = (res ^ Long_Name.base_name s, size - 1)
| term (Free (s, _)) (res, size) = (res ^ s, size - 1)
| term (Var ((s, _), _)) (res, size) = (res ^ s, size - 1)
in
fst (term t ("", size))
end
fun nickname_of_thm th =
if Thm.has_name_hint th then
let val hint = Thm.get_name_hint th in
(* There must be a better way to detect local facts. *)
(case Long_Name.dest_local hint of
SOME suf =>
Long_Name.implode [Thm.theory_name th, suf, crude_printed_term 25 (Thm.prop_of th)]
| NONE => hint)
end
else
crude_printed_term 50 (Thm.prop_of th)
fun find_suggested_facts ctxt facts =
let
fun add (fact as (_, th)) = Symtab.default (nickname_of_thm th, fact)
val tab = fold add facts Symtab.empty
fun lookup nick =
Symtab.lookup tab nick
|> tap (fn NONE => trace_msg ctxt (fn () => "Cannot find " ^ quote nick) | _ => ())
in map_filter lookup end
fun free_feature_of s = "f" ^ s
fun thy_feature_of s = "y" ^ s
fun type_feature_of s = "t" ^ s
fun class_feature_of s = "s" ^ s
val local_feature = "local"
fun crude_thm_ord ctxt =
let
val ancestor_lengths =
fold (fn thy => Symtab.update (Context.theory_name thy, length (Context.ancestors_of thy)))
(Theory.nodes_of (Proof_Context.theory_of ctxt)) Symtab.empty
val ancestor_length = Symtab.lookup ancestor_lengths o Context.theory_id_name
fun crude_theory_ord p =
if Context.eq_thy_id p then EQUAL
else if Context.proper_subthy_id p then LESS
else if Context.proper_subthy_id (swap p) then GREATER
else
(case apply2 ancestor_length p of
(SOME m, SOME n) =>
(case int_ord (m, n) of
EQUAL => string_ord (apply2 Context.theory_id_name p)
| ord => ord)
| _ => string_ord (apply2 Context.theory_id_name p))
in
fn p =>
(case crude_theory_ord (apply2 Thm.theory_id p) of
EQUAL =>
(* The hack below is necessary because of odd dependencies that are not reflected in the theory
comparison. *)
let val q = apply2 nickname_of_thm p in
(* Hack to put "xxx_def" before "xxxI" and "xxxE" *)
(case bool_ord (apply2 (String.isSuffix "_def") (swap q)) of
EQUAL => string_ord q
| ord => ord)
end
| ord => ord)
end;
val thm_less_eq = Context.subthy_id o apply2 Thm.theory_id
fun thm_less p = thm_less_eq p andalso not (thm_less_eq (swap p))
val freezeT = Type.legacy_freeze_type
fun freeze (t $ u) = freeze t $ freeze u
| freeze (Abs (s, T, t)) = Abs (s, freezeT T, freeze t)
| freeze (Var ((s, _), T)) = Free (s, freezeT T)
| freeze (Const (s, T)) = Const (s, freezeT T)
| freeze (Free (s, T)) = Free (s, freezeT T)
| freeze t = t
fun goal_of_thm thy = Thm.prop_of #> freeze #> Thm.global_cterm_of thy #> Goal.init
fun run_prover_for_mash ctxt params prover goal_name facts goal =
let
val problem =
{comment = "Goal: " ^ goal_name, state = Proof.init ctxt, goal = goal, subgoal = 1,
subgoal_count = 1, factss = [("", facts)], found_proof = I}
in
get_minimizing_prover ctxt MaSh (K ()) prover params problem
end
val bad_types = [\<^type_name>\<open>prop\<close>, \<^type_name>\<open>bool\<close>, \<^type_name>\<open>fun\<close>]
val crude_str_of_sort = space_implode "," o map Long_Name.base_name o subtract (op =) \<^sort>\<open>type\<close>
fun crude_str_of_typ (Type (s, [])) = Long_Name.base_name s
| crude_str_of_typ (Type (s, Ts)) = Long_Name.base_name s ^ implode (map crude_str_of_typ Ts)
| crude_str_of_typ (TFree (_, S)) = crude_str_of_sort S
| crude_str_of_typ (TVar (_, S)) = crude_str_of_sort S
fun maybe_singleton_str "" = []
| maybe_singleton_str s = [s]
val max_pat_breadth = 5 (* FUDGE *)
fun term_features_of ctxt thy_name term_max_depth type_max_depth ts =
let
val thy = Proof_Context.theory_of ctxt
val fixes = map snd (Variable.dest_fixes ctxt)
val classes = Sign.classes_of thy
fun add_classes \<^sort>\<open>type\<close> = I
| add_classes S =
fold (`(Sorts.super_classes classes)
#> swap #> op ::
#> subtract (op =) \<^sort>\<open>type\<close>
#> map class_feature_of
#> union (op =)) S
fun pattify_type 0 _ = []
| pattify_type _ (Type (s, [])) = if member (op =) bad_types s then [] else [s]
| pattify_type depth (Type (s, U :: Ts)) =
let
val T = Type (s, Ts)
val ps = take max_pat_breadth (pattify_type depth T)
val qs = take max_pat_breadth ("" :: pattify_type (depth - 1) U)
in
map_product (fn p => fn "" => p | q => p ^ "(" ^ q ^ ")") ps qs
end
| pattify_type _ (TFree (_, S)) = maybe_singleton_str (crude_str_of_sort S)
| pattify_type _ (TVar (_, S)) = maybe_singleton_str (crude_str_of_sort S)
fun add_type_pat depth T =
union (op =) (map type_feature_of (pattify_type depth T))
fun add_type_pats 0 _ = I
| add_type_pats depth t = add_type_pat depth t #> add_type_pats (depth - 1) t
fun add_type T =
add_type_pats type_max_depth T
#> fold_atyps_sorts (add_classes o snd) T
fun add_subtypes (T as Type (_, Ts)) = add_type T #> fold add_subtypes Ts
| add_subtypes T = add_type T
fun pattify_term _ 0 _ = []
| pattify_term _ _ (Const (s, _)) =
if is_widely_irrelevant_const s then [] else [s]
| pattify_term _ _ (Free (s, T)) =
maybe_singleton_str (crude_str_of_typ T)
|> (if member (op =) fixes s then cons (free_feature_of (Long_Name.append thy_name s))
else I)
| pattify_term _ _ (Var (_, T)) =
maybe_singleton_str (crude_str_of_typ T)
| pattify_term Ts _ (Bound j) =
maybe_singleton_str (crude_str_of_typ (nth Ts j))
| pattify_term Ts depth (t $ u) =
let
val ps = take max_pat_breadth (pattify_term Ts depth t)
val qs = take max_pat_breadth ("" :: pattify_term Ts (depth - 1) u)
in
map_product (fn p => fn "" => p | q => p ^ "(" ^ q ^ ")") ps qs
end
| pattify_term _ _ _ = []
fun add_term_pat Ts = union (op =) oo pattify_term Ts
fun add_term_pats _ 0 _ = I
| add_term_pats Ts depth t = add_term_pat Ts depth t #> add_term_pats Ts (depth - 1) t
fun add_term Ts = add_term_pats Ts term_max_depth
fun add_subterms Ts t =
(case strip_comb t of
(Const (s, T), args) =>
(not (is_widely_irrelevant_const s) ? add_term Ts t)
#> add_subtypes T #> fold (add_subterms Ts) args
| (head, args) =>
(case head of
Free (_, T) => add_term Ts t #> add_subtypes T
| Var (_, T) => add_subtypes T
| Abs (_, T, body) => add_subtypes T #> add_subterms (T :: Ts) body
| _ => I)
#> fold (add_subterms Ts) args)
in
fold (add_subterms []) ts []
end
val term_max_depth = 2
val type_max_depth = 1
(* TODO: Generate type classes for types? *)
fun features_of ctxt thy_name (scope, _) ts =
thy_feature_of thy_name ::
term_features_of ctxt thy_name term_max_depth type_max_depth ts
|> scope <> Global ? cons local_feature
(* Too many dependencies is a sign that a decision procedure is at work. There is not much to learn
from such proofs. *)
val max_dependencies = 20 (* FUDGE *)
val prover_default_max_facts = 25 (* FUDGE *)
(* "type_definition_xxx" facts are characterized by their use of "CollectI". *)
val typedef_dep = nickname_of_thm @{thm CollectI}
(* Mysterious parts of the class machinery create lots of proofs that refer exclusively to
"someI_ex" (and to some internal constructions). *)
val class_some_dep = nickname_of_thm @{thm someI_ex}
val fundef_ths =
@{thms fundef_ex1_existence fundef_ex1_uniqueness fundef_ex1_iff fundef_default_value}
|> map nickname_of_thm
(* "Rep_xxx_inject", "Abs_xxx_inverse", etc., are derived using these facts. *)
val typedef_ths =
@{thms type_definition.Abs_inverse type_definition.Rep_inverse type_definition.Rep
type_definition.Rep_inject type_definition.Abs_inject type_definition.Rep_cases
type_definition.Abs_cases type_definition.Rep_induct type_definition.Abs_induct
type_definition.Rep_range type_definition.Abs_image}
|> map nickname_of_thm
fun is_size_def [dep] th =
(case first_field ".rec" dep of
SOME (pref, _) =>
(case first_field ".size" (nickname_of_thm th) of
SOME (pref', _) => pref = pref'
| NONE => false)
| NONE => false)
| is_size_def _ _ = false
fun trim_dependencies deps =
if length deps > max_dependencies then NONE else SOME deps
fun isar_dependencies_of name_tabs th =
thms_in_proof max_dependencies (SOME name_tabs) th
|> Option.map (fn deps =>
if deps = [typedef_dep] orelse deps = [class_some_dep] orelse
exists (member (op =) fundef_ths) deps orelse exists (member (op =) typedef_ths) deps orelse
is_size_def deps th then
[]
else
deps)
fun prover_dependencies_of ctxt (params as {verbose, max_facts, ...}) prover auto_level facts
name_tabs th =
(case isar_dependencies_of name_tabs th of
SOME [] => (false, [])
| isar_deps0 =>
let
val isar_deps = these isar_deps0
val thy = Proof_Context.theory_of ctxt
val goal = goal_of_thm thy th
val name = nickname_of_thm th
val (_, hyp_ts, concl_t) = ATP_Util.strip_subgoal goal 1 ctxt
val facts = facts |> filter (fn (_, th') => thm_less (th', th))
fun nickify ((_, stature), th) = ((nickname_of_thm th, stature), th)
fun is_dep dep (_, th) = (nickname_of_thm th = dep)
fun add_isar_dep facts dep accum =
if exists (is_dep dep) accum then
accum
else
(case find_first (is_dep dep) facts of
SOME ((_, status), th) => accum @ [(("", status), th)]
| NONE => accum (* should not happen *))
val mepo_facts =
facts
|> mepo_suggested_facts ctxt params (max_facts |> the_default prover_default_max_facts) NONE
hyp_ts concl_t
val facts =
mepo_facts
|> fold (add_isar_dep facts) isar_deps
|> map nickify
val num_isar_deps = length isar_deps
in
if verbose andalso auto_level = 0 then
writeln ("MaSh: " ^ quote prover ^ " on " ^ quote name ^ " with " ^
string_of_int num_isar_deps ^ " + " ^ string_of_int (length facts - num_isar_deps) ^
" facts")
else
();
(case run_prover_for_mash ctxt params prover name facts goal of
{outcome = NONE, used_facts, ...} =>
(if verbose andalso auto_level = 0 then
let val num_facts = length used_facts in
writeln ("Found proof with " ^ string_of_int num_facts ^ " fact" ^
plural_s num_facts)
end
else
();
(true, map fst used_facts))
| _ => (false, isar_deps))
end)
(*** High-level communication with MaSh ***)
(* In the following functions, chunks are risers w.r.t. "thm_less_eq". *)
fun chunks_and_parents_for chunks th =
let
fun insert_parent new parents =
let val parents = parents |> filter_out (fn p => thm_less_eq (p, new)) in
parents |> forall (fn p => not (thm_less_eq (new, p))) parents ? cons new
end
fun rechunk seen (rest as th' :: ths) =
if thm_less_eq (th', th) then (rev seen, rest)
else rechunk (th' :: seen) ths
fun do_chunk [] accum = accum
| do_chunk (chunk as hd_chunk :: _) (chunks, parents) =
if thm_less_eq (hd_chunk, th) then
(chunk :: chunks, insert_parent hd_chunk parents)
else if thm_less_eq (List.last chunk, th) then
let val (front, back as hd_back :: _) = rechunk [] chunk in
(front :: back :: chunks, insert_parent hd_back parents)
end
else
(chunk :: chunks, parents)
in
fold_rev do_chunk chunks ([], [])
|>> cons []
||> map nickname_of_thm
end
fun attach_parents_to_facts _ [] = []
| attach_parents_to_facts old_facts (facts as (_, th) :: _) =
let
fun do_facts _ [] = []
| do_facts (_, parents) [fact] = [(parents, fact)]
| do_facts (chunks, parents)
((fact as (_, th)) :: (facts as (_, th') :: _)) =
let
val chunks = app_hd (cons th) chunks
val chunks_and_parents' =
if thm_less_eq (th, th') andalso
Thm.theory_name th = Thm.theory_name th'
then (chunks, [nickname_of_thm th])
else chunks_and_parents_for chunks th'
in
(parents, fact) :: do_facts chunks_and_parents' facts
end
in
old_facts @ facts
|> do_facts (chunks_and_parents_for [[]] th)
|> drop (length old_facts)
end
fun is_fact_in_graph access_G = can (Graph.get_node access_G) o nickname_of_thm
val chained_feature_factor = 0.5 (* FUDGE *)
val extra_feature_factor = 0.1 (* FUDGE *)
val num_extra_feature_facts = 10 (* FUDGE *)
val max_proximity_facts = 100 (* FUDGE *)
fun find_mash_suggestions ctxt max_facts suggs facts chained raw_unknown =
let
val inter_fact = inter (eq_snd Thm.eq_thm_prop)
val raw_mash = find_suggested_facts ctxt facts suggs
val proximate = take max_proximity_facts facts
val unknown_chained = inter_fact raw_unknown chained
val unknown_proximate = inter_fact raw_unknown proximate
val mess =
[(0.9 (* FUDGE *), (map (rpair 1.0) unknown_chained, [])),
(0.4 (* FUDGE *), (weight_facts_smoothly unknown_proximate, [])),
(0.1 (* FUDGE *), (weight_facts_steeply raw_mash, raw_unknown))]
val unknown = raw_unknown
|> fold (subtract (eq_snd Thm.eq_thm_prop)) [unknown_chained, unknown_proximate]
in
(mesh_facts (fact_distinct (op aconv)) (eq_snd (gen_eq_thm ctxt)) max_facts mess, unknown)
end
fun mash_suggested_facts ctxt thy_name ({debug, ...} : params) max_suggs hyp_ts concl_t facts =
let
val algorithm = the_mash_algorithm ()
val facts = facts
|> rev_sort_list_prefix (crude_thm_ord ctxt o apply2 snd)
(Int.max (num_extra_feature_facts, max_proximity_facts))
val chained = filter (fn ((_, (scope, _)), _) => scope = Chained) facts
fun fact_has_right_theory (_, th) = thy_name = Thm.theory_name th
fun chained_or_extra_features_of factor (((_, stature), th), weight) =
[Thm.prop_of th]
|> features_of ctxt (Thm.theory_name th) stature
|> map (rpair (weight * factor))
in
(case get_state ctxt of
NONE => ([], [])
| SOME {access_G, xtabs = ((num_facts, fact_tab), (num_feats, feat_tab)), ffds, freqs, ...} =>
let
val goal_feats0 =
features_of ctxt thy_name (Local, General) (concl_t :: hyp_ts)
val chained_feats = chained
|> map (rpair 1.0)
|> map (chained_or_extra_features_of chained_feature_factor)
|> rpair [] |-> fold (union (eq_fst (op =)))
val extra_feats = facts
|> take (Int.max (0, num_extra_feature_facts - length chained))
|> filter fact_has_right_theory
|> weight_facts_steeply
|> map (chained_or_extra_features_of extra_feature_factor)
|> rpair [] |-> fold (union (eq_fst (op =)))
val goal_feats =
fold (union (eq_fst (op =))) [chained_feats, extra_feats] (map (rpair 1.0) goal_feats0)
|> debug ? sort (Real.compare o swap o apply2 snd)
val fact_idxs = map_filter (Symtab.lookup fact_tab o nickname_of_thm o snd) facts
val suggs =
if algorithm = MaSh_NB_Ext orelse algorithm = MaSh_kNN_Ext then
let
val learns =
Graph.schedule (fn _ => fn (fact, (_, feats, deps)) => (fact, feats, deps))
access_G
in
MaSh.query_external ctxt algorithm max_suggs learns goal_feats
end
else
let
val int_goal_feats =
map_filter (fn (s, w) => Option.map (rpair w) (Symtab.lookup feat_tab s)) goal_feats
in
MaSh.query_internal ctxt algorithm num_facts num_feats ffds freqs fact_idxs max_suggs
goal_feats int_goal_feats
end
val unknown = filter_out (is_fact_in_graph access_G o snd) facts
in
find_mash_suggestions ctxt max_suggs suggs facts chained unknown
|> apply2 (map fact_of_raw_fact)
end)
end
fun mash_unlearn ctxt = (clear_state ctxt; writeln "Reset MaSh")
fun learn_wrt_access_graph ctxt (name, parents, feats, deps)
(accum as (access_G, (fact_xtab, feat_xtab))) =
let
fun maybe_learn_from from (accum as (parents, access_G)) =
try_graph ctxt "updating graph" accum (fn () =>
(from :: parents, Graph.add_edge_acyclic (from, name) access_G))
val access_G = access_G |> Graph.default_node (name, (Isar_Proof, feats, deps))
val (parents, access_G) = ([], access_G) |> fold maybe_learn_from parents
val (deps, _) = ([], access_G) |> fold maybe_learn_from deps
val fact_xtab = add_to_xtab name fact_xtab
val feat_xtab = fold maybe_add_to_xtab feats feat_xtab
in
(SOME (name, parents, feats, deps), (access_G, (fact_xtab, feat_xtab)))
end
handle Symtab.DUP _ => (NONE, accum) (* facts sometimes have the same name, confusingly *)
fun relearn_wrt_access_graph ctxt (name, deps) access_G =
let
fun maybe_relearn_from from (accum as (parents, access_G)) =
try_graph ctxt "updating graph" accum (fn () =>
(from :: parents, Graph.add_edge_acyclic (from, name) access_G))
val access_G =
access_G |> Graph.map_node name (fn (_, feats, _) => (Automatic_Proof, feats, deps))
val (deps, _) = ([], access_G) |> fold maybe_relearn_from deps
in
((name, deps), access_G)
end
fun flop_wrt_access_graph name =
Graph.map_node name (fn (_, feats, deps) => (Isar_Proof_wegen_Prover_Flop, feats, deps))
val learn_timeout_slack = 20.0
fun launch_thread timeout task =
let
val hard_timeout = time_mult learn_timeout_slack timeout
val birth_time = Time.now ()
val death_time = birth_time + hard_timeout
val desc = ("Machine learner for Sledgehammer", "")
in
Async_Manager_Legacy.thread MaShN birth_time death_time desc task
end
fun anonymous_proof_name () =
Date.fmt (anonymous_proof_prefix ^ "%Y%m%d.%H%M%S.") (Date.fromTimeLocal (Time.now ())) ^
serial_string ()
fun mash_learn_proof ctxt ({timeout, ...} : params) t used_ths =
if not (null used_ths) andalso is_mash_enabled () then
launch_thread timeout (fn () =>
let
val thy = Proof_Context.theory_of ctxt
val feats = features_of ctxt (Context.theory_name thy) (Local, General) [t]
in
map_state ctxt
(fn {access_G, xtabs as ((num_facts0, _), _), ffds, freqs, dirty_facts} =>
let
val deps = used_ths
|> filter (is_fact_in_graph access_G)
|> map nickname_of_thm
val name = anonymous_proof_name ()
val (access_G', xtabs', rev_learns) =
add_node Automatic_Proof name [] (* ignore parents *) feats deps
(access_G, xtabs, [])
val (ffds', freqs') =
recompute_ffds_freqs_from_learns (rev rev_learns) xtabs' num_facts0 ffds freqs
in
{access_G = access_G', xtabs = xtabs', ffds = ffds', freqs = freqs',
dirty_facts = Option.map (cons name) dirty_facts}
end);
(true, "")
end)
else
()
fun sendback sub = Active.sendback_markup_command (sledgehammerN ^ " " ^ sub)
val commit_timeout = seconds 30.0
(* The timeout is understood in a very relaxed fashion. *)
fun mash_learn_facts ctxt (params as {debug, verbose, ...}) prover auto_level run_prover
learn_timeout facts =
let
val timer = Timer.startRealTimer ()
fun next_commit_time () = Timer.checkRealTimer timer + commit_timeout
in
(case get_state ctxt of
NONE => "MaSh is busy\nPlease try again later"
| SOME {access_G, ...} =>
let
val is_in_access_G = is_fact_in_graph access_G o snd
val no_new_facts = forall is_in_access_G facts
in
if no_new_facts andalso not run_prover then
if auto_level < 2 then
"No new " ^ (if run_prover then "automatic" else "Isar") ^ " proofs to learn" ^
(if auto_level = 0 andalso not run_prover then
"\n\nHint: Try " ^ sendback learn_proverN ^ " to learn from an automatic prover"
else
"")
else
""
else
let
val name_tabs = build_name_tables nickname_of_thm facts
fun deps_of status th =
if status = Non_Rec_Def orelse status = Rec_Def then
SOME []
else if run_prover then
prover_dependencies_of ctxt params prover auto_level facts name_tabs th
|> (fn (false, _) => NONE | (true, deps) => trim_dependencies deps)
else
isar_dependencies_of name_tabs th
fun do_commit [] [] [] state = state
| do_commit learns relearns flops
{access_G, xtabs as ((num_facts0, _), _), ffds, freqs, dirty_facts} =
let
val was_empty = Graph.is_empty access_G
val (learns, (access_G', xtabs')) =
fold_map (learn_wrt_access_graph ctxt) learns (access_G, xtabs)
|>> map_filter I
val (relearns, access_G'') =
fold_map (relearn_wrt_access_graph ctxt) relearns access_G'
val access_G''' = access_G'' |> fold flop_wrt_access_graph flops
val dirty_facts' =
(case (was_empty, dirty_facts) of
(false, SOME names) => SOME (map #1 learns @ map #1 relearns @ names)
| _ => NONE)
val (ffds', freqs') =
if null relearns then
recompute_ffds_freqs_from_learns
(map (fn (name, _, feats, deps) => (name, feats, deps)) learns) xtabs'
num_facts0 ffds freqs
else
recompute_ffds_freqs_from_access_G access_G''' xtabs'
in
{access_G = access_G''', xtabs = xtabs', ffds = ffds', freqs = freqs',
dirty_facts = dirty_facts'}
end
fun commit last learns relearns flops =
(if debug andalso auto_level = 0 then writeln "Committing..." else ();
map_state ctxt (do_commit (rev learns) relearns flops);
if not last andalso auto_level = 0 then
let val num_proofs = length learns + length relearns in
writeln ("Learned " ^ string_of_int num_proofs ^ " " ^
(if run_prover then "automatic" else "Isar") ^ " proof" ^
plural_s num_proofs ^ " in the last " ^ string_of_time commit_timeout)
end
else
())
fun learn_new_fact _ (accum as (_, (_, _, true))) = accum
| learn_new_fact (parents, ((_, stature as (_, status)), th))
(learns, (num_nontrivial, next_commit, _)) =
let
val name = nickname_of_thm th
val feats = features_of ctxt (Thm.theory_name th) stature [Thm.prop_of th]
val deps = these (deps_of status th)
val num_nontrivial = num_nontrivial |> not (null deps) ? Integer.add 1
val learns = (name, parents, feats, deps) :: learns
val (learns, next_commit) =
if Timer.checkRealTimer timer > next_commit then
(commit false learns [] []; ([], next_commit_time ()))
else
(learns, next_commit)
val timed_out = Timer.checkRealTimer timer > learn_timeout
in
(learns, (num_nontrivial, next_commit, timed_out))
end
val (num_new_facts, num_nontrivial) =
if no_new_facts then
(0, 0)
else
let
val new_facts = facts
|> sort (crude_thm_ord ctxt o apply2 snd)
|> map (pair []) (* ignore parents *)
|> filter_out (is_in_access_G o snd)
val (learns, (num_nontrivial, _, _)) =
([], (0, next_commit_time (), false))
|> fold learn_new_fact new_facts
in
commit true learns [] []; (length new_facts, num_nontrivial)
end
fun relearn_old_fact _ (accum as (_, (_, _, true))) = accum
| relearn_old_fact ((_, (_, status)), th)
((relearns, flops), (num_nontrivial, next_commit, _)) =
let
val name = nickname_of_thm th
val (num_nontrivial, relearns, flops) =
(case deps_of status th of
SOME deps => (num_nontrivial + 1, (name, deps) :: relearns, flops)
| NONE => (num_nontrivial, relearns, name :: flops))
val (relearns, flops, next_commit) =
if Timer.checkRealTimer timer > next_commit then
(commit false [] relearns flops; ([], [], next_commit_time ()))
else
(relearns, flops, next_commit)
val timed_out = Timer.checkRealTimer timer > learn_timeout
in
((relearns, flops), (num_nontrivial, next_commit, timed_out))
end
val num_nontrivial =
if not run_prover then
num_nontrivial
else
let
val max_isar = 1000 * max_dependencies
fun priority_of th =
Random.random_range 0 max_isar +
(case try (Graph.get_node access_G) (nickname_of_thm th) of
SOME (Isar_Proof, _, deps) => ~100 * length deps
| SOME (Automatic_Proof, _, _) => 2 * max_isar
| SOME (Isar_Proof_wegen_Prover_Flop, _, _) => max_isar
| NONE => 0)
val old_facts = facts
|> filter is_in_access_G
|> map (`(priority_of o snd))
|> sort (int_ord o apply2 fst)
|> map snd
val ((relearns, flops), (num_nontrivial, _, _)) =
(([], []), (num_nontrivial, next_commit_time (), false))
|> fold relearn_old_fact old_facts
in
commit true [] relearns flops; num_nontrivial
end
in
if verbose orelse auto_level < 2 then
"Learned " ^ string_of_int num_new_facts ^ " fact" ^ plural_s num_new_facts ^
" and " ^ string_of_int num_nontrivial ^ " nontrivial " ^
(if run_prover then "automatic and " else "") ^ "Isar proof" ^
plural_s num_nontrivial ^
(if verbose then " in " ^ string_of_time (Timer.checkRealTimer timer) else "")
else
""
end
end)
end
fun mash_learn ctxt (params as {provers, timeout, ...}) fact_override chained run_prover =
let
val css = Sledgehammer_Fact.clasimpset_rule_table_of ctxt
val ctxt = ctxt |> Config.put instantiate_inducts false
val facts =
nearly_all_facts ctxt false fact_override Keyword.empty_keywords css chained [] \<^prop>\<open>True\<close>
|> sort (crude_thm_ord ctxt o apply2 snd o swap)
val num_facts = length facts
val prover = hd provers
fun learn auto_level run_prover =
mash_learn_facts ctxt params prover auto_level run_prover one_year facts
|> writeln
in
if run_prover then
(writeln ("MaShing through " ^ string_of_int num_facts ^ " fact" ^
plural_s num_facts ^ " for automatic proofs (" ^ quote prover ^ " timeout: " ^
string_of_time timeout ^ ").\n\nCollecting Isar proofs first...");
learn 1 false;
writeln "Now collecting automatic proofs\n\
\This may take several hours; you can safely stop the learning process at any point";
learn 0 true)
else
(writeln ("MaShing through " ^ string_of_int num_facts ^ " fact" ^
plural_s num_facts ^ " for Isar proofs...");
learn 0 false)
end
fun mash_can_suggest_facts ctxt =
(case get_state ctxt of
NONE => false
| SOME {access_G, ...} => not (Graph.is_empty access_G))
fun mash_can_suggest_facts_fast ctxt =
(case peek_state ctxt of
NONE => false
| SOME (_, {access_G, ...}) => not (Graph.is_empty access_G))
(* Generate more suggestions than requested, because some might be thrown out later for various
reasons (e.g., duplicates). *)
fun generous_max_suggestions max_facts = 2 * max_facts + 25 (* FUDGE *)
val mepo_weight = 0.5 (* FUDGE *)
val mash_weight = 0.5 (* FUDGE *)
val max_facts_to_learn_before_query = 100 (* FUDGE *)
(* The threshold should be large enough so that MaSh does not get activated for Auto Sledgehammer. *)
val min_secs_for_learning = 10
fun relevant_facts ctxt (params as {verbose, learn, fact_filter, timeout, ...}) prover
max_facts ({add, only, ...} : fact_override) hyp_ts concl_t facts =
if not (subset (op =) (the_list fact_filter, fact_filters)) then
error ("Unknown fact filter: " ^ quote (the fact_filter))
else if only then
[("", map fact_of_raw_fact facts)]
else if max_facts <= 0 orelse null facts then
[("", [])]
else
let
val thy_name = Context.theory_name (Proof_Context.theory_of ctxt)
fun maybe_launch_thread exact min_num_facts_to_learn =
if not (Async_Manager_Legacy.has_running_threads MaShN) andalso
Time.toSeconds timeout >= min_secs_for_learning then
let val timeout = time_mult learn_timeout_slack timeout in
(if verbose then
writeln ("Started MaShing through " ^
(if exact then "" else "up to ") ^ string_of_int min_num_facts_to_learn ^
" fact" ^ plural_s min_num_facts_to_learn ^ " in the background")
else
());
launch_thread timeout
(fn () => (true, mash_learn_facts ctxt params prover 2 false timeout facts))
end
else
()
val mash_enabled = is_mash_enabled ()
val mash_fast = mash_can_suggest_facts_fast ctxt
fun please_learn () =
if mash_fast then
(case get_state ctxt of
NONE => maybe_launch_thread false (length facts)
| SOME {access_G, xtabs = ((num_facts0, _), _), ...} =>
let
val is_in_access_G = is_fact_in_graph access_G o snd
val min_num_facts_to_learn = length facts - num_facts0
in
if min_num_facts_to_learn <= max_facts_to_learn_before_query then
(case length (filter_out is_in_access_G facts) of
0 => ()
| num_facts_to_learn =>
if num_facts_to_learn <= max_facts_to_learn_before_query then
mash_learn_facts ctxt params prover 2 false timeout facts
|> (fn "" => () | s => writeln (MaShN ^ ": " ^ s))
else
maybe_launch_thread true num_facts_to_learn)
else
maybe_launch_thread false min_num_facts_to_learn
end)
else
maybe_launch_thread false (length facts)
val _ =
if learn andalso mash_enabled andalso fact_filter <> SOME mepoN then please_learn () else ()
val effective_fact_filter =
(case fact_filter of
SOME ff => ff
| NONE => if mash_enabled andalso mash_fast then meshN else mepoN)
val unique_facts = drop_duplicate_facts facts
val add_ths = Attrib.eval_thms ctxt add
fun in_add (_, th) = member Thm.eq_thm_prop add_ths th
fun add_and_take accepts =
(case add_ths of
[] => accepts
| _ =>
(unique_facts |> filter in_add |> map fact_of_raw_fact) @ (accepts |> filter_out in_add))
|> take max_facts
fun mepo () =
(mepo_suggested_facts ctxt params max_facts NONE hyp_ts concl_t unique_facts
|> weight_facts_steeply, [])
fun mash () =
mash_suggested_facts ctxt thy_name params (generous_max_suggestions max_facts) hyp_ts
concl_t facts
|>> weight_facts_steeply
val mess =
(* the order is important for the "case" expression below *)
[] |> effective_fact_filter <> mepoN ? cons (mash_weight, mash)
|> effective_fact_filter <> mashN ? cons (mepo_weight, mepo)
|> Par_List.map (apsnd (fn f => f ()))
val mesh =
mesh_facts (fact_distinct (op aconv)) (eq_snd (gen_eq_thm ctxt)) max_facts mess
|> add_and_take
in
(case (fact_filter, mess) of
(NONE, [(_, (mepo, _)), (_, (mash, _))]) =>
[(meshN, mesh),
(mepoN, mepo |> map fst |> add_and_take),
(mashN, mash |> map fst |> add_and_take)]
| _ => [(effective_fact_filter, mesh)])
end
end;
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