(* Title: HOL/Tools/Sledgehammer/sledgehammer_filter_mash.ML
Author: Jasmin Blanchette, TU Muenchen
Sledgehammer's machine-learning-based relevance filter (MaSh).
*)
signature SLEDGEHAMMER_FILTER_MASH =
sig
type status = ATP_Problem_Generate.status
type stature = ATP_Problem_Generate.stature
type fact = Sledgehammer_Fact.fact
type fact_override = Sledgehammer_Fact.fact_override
type params = Sledgehammer_Provers.params
type relevance_fudge = Sledgehammer_Provers.relevance_fudge
type prover_result = Sledgehammer_Provers.prover_result
val trace : bool Config.T
val meshN : string
val iterN : string
val mashN : string
val fact_filters : string list
val escape_meta : string -> string
val escape_metas : string list -> string
val unescape_meta : string -> string
val unescape_metas : string -> string list
val extract_query : string -> string * string list
val suggested_facts : string list -> fact list -> fact list
val mesh_facts : int -> (fact list * int option) list -> fact list
val is_likely_tautology : Proof.context -> string -> thm -> bool
val is_too_meta : thm -> bool
val theory_ord : theory * theory -> order
val thm_ord : thm * thm -> order
val features_of :
Proof.context -> string -> theory -> status -> term list -> string list
val isabelle_dependencies_of : unit Symtab.table -> thm -> string list
val goal_of_thm : theory -> thm -> thm
val run_prover :
Proof.context -> params -> string -> fact list -> thm -> prover_result
val mash_RESET : Proof.context -> unit
val mash_INIT :
Proof.context -> bool
-> (string * string list * string list * string list) list -> unit
val mash_ADD :
Proof.context -> bool
-> (string * string list * string list * string list) list -> unit
val mash_QUERY :
Proof.context -> bool -> int -> string list * string list -> string list
val mash_reset : Proof.context -> unit
val mash_could_suggest_facts : unit -> bool
val mash_can_suggest_facts : unit -> bool
val mash_suggest_facts :
Proof.context -> params -> string -> int -> term list -> term -> fact list
-> fact list
val mash_learn_thy : Proof.context -> params -> theory -> Time.time -> unit
val mash_learn_proof :
Proof.context -> params -> term -> thm list -> fact list -> unit
val relevant_facts :
Proof.context -> params -> string -> int -> fact_override -> term list
-> term -> fact list -> fact list
end;
structure Sledgehammer_Filter_MaSh : SLEDGEHAMMER_FILTER_MASH =
struct
open ATP_Util
open ATP_Problem_Generate
open Sledgehammer_Util
open Sledgehammer_Fact
open Sledgehammer_Filter_Iter
open Sledgehammer_Provers
open Sledgehammer_Minimize
val trace =
Attrib.setup_config_bool @{binding sledgehammer_filter_mash_trace} (K false)
fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()
val meshN = "mesh"
val iterN = "iter"
val mashN = "mash"
val fact_filters = [meshN, iterN, mashN]
fun mash_home () = getenv "MASH_HOME"
fun mash_state_dir () =
getenv "ISABELLE_HOME_USER" ^ "/mash"
|> tap (Isabelle_System.mkdir o Path.explode)
fun mash_state_path () = mash_state_dir () ^ "/state" |> Path.explode
(*** Isabelle helpers ***)
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 escape_meta = String.translate meta_char
val escape_metas = map escape_meta #> space_implode " "
val unescape_meta = String.explode #> unmeta_chars []
val unescape_metas =
space_explode " " #> filter_out (curry (op =) "") #> map unescape_meta
fun extract_query line =
case space_explode ":" line of
[goal_name, suggs] => (unescape_meta goal_name, unescape_metas suggs)
| _ => ("", [])
fun find_suggested facts sugg =
find_first (fn (_, th) => Thm.get_name_hint th = sugg) facts
fun suggested_facts suggs facts = map_filter (find_suggested facts) suggs
fun sum_avg n xs =
fold (Integer.add o Integer.mult n) xs 0 div (length xs)
fun mesh_facts max_facts [(facts, _)] = facts |> take max_facts
| mesh_facts max_facts mess =
let
val n = length mess
val fact_eq = Thm.eq_thm o pairself snd
fun score_in fact (facts, def) =
case find_index (curry fact_eq fact) facts of
~1 => def
| j => SOME j
fun score_of fact = mess |> map_filter (score_in fact) |> sum_avg n
val facts = fold (union fact_eq o take max_facts o fst) mess []
in
facts |> map (`score_of) |> sort (int_ord o pairself fst) |> map snd
|> take max_facts
end
val thy_feature_prefix = "y_"
val thy_feature_name_of = prefix thy_feature_prefix
val const_name_of = prefix const_prefix
val type_name_of = prefix type_const_prefix
val class_name_of = prefix class_prefix
local
fun has_bool @{typ bool} = true
| has_bool (Type (_, Ts)) = exists has_bool Ts
| has_bool _ = false
fun has_fun (Type (@{type_name fun}, _)) = true
| has_fun (Type (_, Ts)) = exists has_fun Ts
| has_fun _ = false
val is_conn = member (op =)
[@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},
@{const_name HOL.implies}, @{const_name Not},
@{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex},
@{const_name HOL.eq}]
val has_bool_arg_const =
exists_Const (fn (c, T) =>
not (is_conn c) andalso exists has_bool (binder_types T))
fun higher_inst_const thy (s, T) =
case binder_types T of
[] => false
| Ts => length (binder_types (Sign.the_const_type thy s)) <> length Ts
handle TYPE _ => false
val binders = [@{const_name All}, @{const_name Ex}]
in
fun is_fo_term thy t =
let
val t =
t |> Envir.beta_eta_contract
|> transform_elim_prop
|> Object_Logic.atomize_term thy
in
Term.is_first_order binders t andalso
not (exists_subterm (fn Var (_, T) => has_bool T orelse has_fun T
| _ => false) t orelse
has_bool_arg_const t orelse exists_Const (higher_inst_const thy) t)
end
end
fun interesting_terms_types_and_classes ctxt prover term_max_depth
type_max_depth ts =
let
val bad_types = [@{type_name prop}, @{type_name bool}, @{type_name fun}]
fun is_bad_const (x as (s, _)) args =
member (op =) atp_logical_consts s orelse
fst (is_built_in_const_for_prover ctxt prover x args)
fun add_classes @{sort type} = I
| add_classes S = union (op =) (map class_name_of S)
fun do_add_type (Type (s, Ts)) =
(not (member (op =) bad_types s) ? insert (op =) (type_name_of s))
#> fold do_add_type Ts
| do_add_type (TFree (_, S)) = add_classes S
| do_add_type (TVar (_, S)) = add_classes S
fun add_type T = type_max_depth >= 0 ? do_add_type T
fun mk_app s args =
if member (op <>) args "" then s ^ "(" ^ space_implode "," args ^ ")"
else s
fun patternify ~1 _ = ""
| patternify depth t =
case strip_comb t of
(Const (s, _), args) =>
mk_app (const_name_of s) (map (patternify (depth - 1)) args)
| _ => ""
fun add_term_patterns ~1 _ = I
| add_term_patterns depth t =
insert (op =) (patternify depth t)
#> add_term_patterns (depth - 1) t
val add_term = add_term_patterns term_max_depth
fun add_patterns t =
let val (head, args) = strip_comb t in
(case head of
Const (x as (_, T)) =>
not (is_bad_const x args) ? (add_term t #> add_type T)
| Free (_, T) => add_type T
| Var (_, T) => add_type T
| Abs (_, T, body) => add_type T #> add_patterns body
| _ => I)
#> fold add_patterns args
end
in [] |> fold add_patterns ts |> sort string_ord end
fun is_likely_tautology ctxt prover th =
null (interesting_terms_types_and_classes ctxt prover 0 ~1 [prop_of th])
andalso not (Thm.eq_thm_prop (@{thm ext}, th))
(* ### FIXME: optimize *)
fun is_too_meta th =
fastype_of (Object_Logic.atomize_term (theory_of_thm th) (prop_of th))
<> @{typ bool}
fun theory_ord p =
if Theory.eq_thy p then
EQUAL
else if Theory.subthy p then
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
val thm_ord = theory_ord o pairself theory_of_thm
fun is_exists (s, _) = (s = @{const_name Ex} orelse s = @{const_name Ex1})
val term_max_depth = 1
val type_max_depth = 1
(* TODO: Generate type classes for types? *)
fun features_of ctxt prover thy status ts =
thy_feature_name_of (Context.theory_name thy) ::
interesting_terms_types_and_classes ctxt prover term_max_depth type_max_depth
ts
|> exists (not o is_lambda_free) ts ? cons "lambdas"
|> exists (exists_Const is_exists) ts ? cons "skolems"
|> exists (not o is_fo_term thy) ts ? cons "ho"
|> (case status of
General => I
| Induction => cons "induction"
| Intro => cons "intro"
| Inductive => cons "inductive"
| Elim => cons "elim"
| Simp => cons "simp"
| Def => cons "def")
fun isabelle_dependencies_of all_facts =
thms_in_proof (SOME all_facts) #> sort string_ord
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 ctxt params prover facts goal =
let
val problem =
{state = Proof.init ctxt, goal = goal, subgoal = 1, subgoal_count = 1,
facts = facts |> map (apfst (apfst (fn name => name ())))
|> map Untranslated_Fact}
val prover = get_minimizing_prover ctxt Normal prover
in prover params (K (K (K ""))) problem end
(*** Low-level communication with MaSh ***)
fun write_file write file =
let val path = Path.explode file in
File.write path ""; write (File.append path)
end
fun mash_info overlord =
if overlord then (getenv "ISABELLE_HOME_USER", "")
else (getenv "ISABELLE_TMP", serial_string ())
fun run_mash ctxt (temp_dir, serial) core =
let
val log_file = temp_dir ^ "/mash_log" ^ serial
val err_file = temp_dir ^ "/mash_err" ^ serial
val command =
mash_home () ^ "/mash.py --quiet --outputDir " ^ mash_state_dir () ^
" --log " ^ log_file ^ " " ^ core ^ " 2>&1 > " ^ err_file
in
trace_msg ctxt (fn () => "Running " ^ command);
write_file (K ()) log_file;
write_file (K ()) err_file;
Isabelle_System.bash command; ()
end
fun run_mash_init ctxt overlord write_access write_feats write_deps =
let
val info as (temp_dir, serial) = mash_info overlord
val in_dir = temp_dir ^ "/mash_init" ^ serial
|> tap (Isabelle_System.mkdir o Path.explode)
in
write_file write_access (in_dir ^ "/mash_accessibility");
write_file write_feats (in_dir ^ "/mash_features");
write_file write_deps (in_dir ^ "/mash_dependencies");
run_mash ctxt info ("--init --inputDir " ^ in_dir)
end
fun run_mash_commands ctxt overlord save max_suggs write_cmds read_suggs =
let
val info as (temp_dir, serial) = mash_info overlord
val sugg_file = temp_dir ^ "/mash_suggs" ^ serial
val cmd_file = temp_dir ^ "/mash_commands" ^ serial
in
write_file (K ()) sugg_file;
write_file write_cmds cmd_file;
run_mash ctxt info
("--inputFile " ^ cmd_file ^ " --predictions " ^ sugg_file ^
" --numberOfPredictions " ^ string_of_int max_suggs ^
(if save then " --saveModel" else ""));
read_suggs (fn () => File.read_lines (Path.explode sugg_file))
end
fun str_of_update (name, parents, feats, deps) =
"! " ^ escape_meta name ^ ": " ^ escape_metas parents ^ "; " ^
escape_metas feats ^ "; " ^ escape_metas deps ^ "\n"
fun str_of_query (parents, feats) =
"? " ^ escape_metas parents ^ "; " ^ escape_metas feats
fun init_str_of_update get (upd as (name, _, _, _)) =
escape_meta name ^ ": " ^ escape_metas (get upd) ^ "\n"
fun mash_RESET ctxt =
let val path = mash_state_dir () |> Path.explode in
trace_msg ctxt (K "MaSh RESET");
File.fold_dir (fn file => fn () =>
File.rm (Path.append path (Path.basic file)))
path ()
end
fun mash_INIT ctxt _ [] = mash_RESET ctxt
| mash_INIT ctxt overlord upds =
(trace_msg ctxt (fn () => "MaSh INIT " ^
elide_string 1000 (space_implode " " (map #1 upds)));
run_mash_init ctxt overlord
(fn append => List.app (append o init_str_of_update #2) upds)
(fn append => List.app (append o init_str_of_update #3) upds)
(fn append => List.app (append o init_str_of_update #4) upds))
fun mash_ADD _ _ [] = ()
| mash_ADD ctxt overlord upds =
(trace_msg ctxt (fn () => "MaSh ADD " ^
elide_string 1000 (space_implode " " (map #1 upds)));
run_mash_commands ctxt overlord true 0
(fn append => List.app (append o str_of_update) upds) (K ()))
fun mash_QUERY ctxt overlord max_suggs (query as (_, feats)) =
(trace_msg ctxt (fn () => "MaSh QUERY " ^ space_implode " " feats);
run_mash_commands ctxt overlord false max_suggs
(fn append => append (str_of_query query))
(fn suggs => snd (extract_query (List.last (suggs ()))))
handle List.Empty => [])
(*** High-level communication with MaSh ***)
type mash_state =
{thys : bool Symtab.table,
fact_graph : unit Graph.T}
val empty_state = {thys = Symtab.empty, fact_graph = Graph.empty}
local
fun mash_load (state as (true, _)) = state
| mash_load _ =
let val path = mash_state_path () in
(true,
case try File.read_lines path of
SOME (comp_thys :: incomp_thys :: fact_lines) =>
let
fun add_thy comp thy = Symtab.update (thy, comp)
fun add_fact_line line =
case extract_query line of
("", _) => I (* shouldn't happen *)
| (name, parents) =>
Graph.default_node (name, ())
#> fold (fn par => Graph.add_edge (par, name)) parents
val thys =
Symtab.empty |> fold (add_thy true) (unescape_metas comp_thys)
|> fold (add_thy false) (unescape_metas incomp_thys)
val fact_graph = Graph.empty |> fold add_fact_line fact_lines
in {thys = thys, fact_graph = fact_graph} end
| _ => empty_state)
end
fun mash_save ({thys, fact_graph, ...} : mash_state) =
let
val path = mash_state_path ()
val thys = Symtab.dest thys
val line_for_thys = escape_metas o AList.find (op =) thys
fun fact_line_for name parents =
escape_meta name ^ ": " ^ escape_metas parents
val append_fact = File.append path o suffix "\n" oo fact_line_for
in
File.write path (line_for_thys true ^ "\n" ^ line_for_thys false ^ "\n");
Graph.fold (fn (name, ((), (parents, _))) => fn () =>
append_fact name (Graph.Keys.dest parents))
fact_graph ()
end
val global_state =
Synchronized.var "Sledgehammer_Filter_MaSh.global_state" (false, empty_state)
in
fun mash_map f =
Synchronized.change global_state (mash_load ##> (f #> tap mash_save))
fun mash_get () = Synchronized.change_result global_state (mash_load #> `snd)
fun mash_reset ctxt =
Synchronized.change global_state (fn _ =>
(mash_RESET ctxt; File.write (mash_state_path ()) "";
(true, empty_state)))
end
fun mash_could_suggest_facts () = mash_home () <> ""
fun mash_can_suggest_facts () = not (Graph.is_empty (#fact_graph (mash_get ())))
fun parents_wrt_facts facts fact_graph =
let
val graph_facts = Symtab.make (map (rpair ()) (Graph.keys fact_graph))
val facts =
[] |> fold (cons o Thm.get_name_hint o snd) facts
|> filter (Symtab.defined graph_facts)
|> Graph.all_preds fact_graph
val facts = Symtab.empty |> fold (fn name => Symtab.update (name, ())) facts
in fact_graph |> Graph.restrict (Symtab.defined facts) |> Graph.maximals end
(* Generate more suggestions than requested, because some might be thrown out
later for various reasons and "meshing" gives better results with some
slack. *)
fun max_suggs_of max_facts = max_facts + Int.min (200, max_facts)
fun mash_suggest_facts ctxt ({overlord, ...} : params) prover max_facts hyp_ts
concl_t facts =
let
val thy = Proof_Context.theory_of ctxt
val fact_graph = #fact_graph (mash_get ())
val _ = warning (PolyML.makestring (length (fact_graph |> Graph.keys), length (fact_graph |> Graph.maximals),
length (fact_graph |> Graph.minimals))) (*###*)
val parents = parents_wrt_facts facts fact_graph
val feats = features_of ctxt prover thy General (concl_t :: hyp_ts)
val suggs =
mash_QUERY ctxt overlord (max_suggs_of max_facts) (parents, feats)
in suggested_facts suggs facts end
fun add_thys_for thy =
let fun add comp thy = Symtab.update (Context.theory_name thy, comp) in
add false thy #> fold (add true) (Theory.ancestors_of thy)
end
fun update_fact_graph ctxt (name, parents, feats, deps) (upds, graph) =
let
fun maybe_add_from from (accum as (parents, graph)) =
(from :: parents, Graph.add_edge_acyclic (from, name) graph)
handle Graph.CYCLES _ =>
(trace_msg ctxt (fn () =>
"Cycle between " ^ quote from ^ " and " ^ quote name); accum)
| Graph.UNDEF _ =>
(trace_msg ctxt (fn () => "Unknown node " ^ quote from); accum)
val graph = graph |> Graph.new_node (name, ())
val (parents, graph) = ([], graph) |> fold maybe_add_from parents
val (deps, graph) = ([], graph) |> fold maybe_add_from deps
in ((name, parents, feats, deps) :: upds, graph) end
val pass1_learn_timeout_factor = 0.5
val pass2_learn_timeout_factor = 10.0
(* The timeout is understood in a very slack fashion. *)
fun mash_learn_thy ctxt ({provers, verbose, overlord, ...} : params) thy
timeout =
let
val timer = Timer.startRealTimer ()
val prover = hd provers
fun timed_out frac =
Time.> (Timer.checkRealTimer timer, time_mult frac timeout)
val css_table = clasimpset_rule_table_of ctxt
val facts = all_facts_of thy css_table
val {fact_graph, ...} = mash_get ()
fun is_old (_, th) = can (Graph.get_node fact_graph) (Thm.get_name_hint th)
val new_facts = facts |> filter_out is_old |> sort (thm_ord o pairself snd)
in
if null new_facts then
()
else
let
val n = length new_facts
val _ =
if verbose then
"MaShing " ^ string_of_int n ^ " fact" ^ plural_s n ^
" (advisory timeout: " ^ string_from_time timeout ^ ")..."
|> Output.urgent_message
else
()
val ths = facts |> map snd
val all_names =
ths |> filter_out (is_likely_tautology ctxt prover orf is_too_meta)
|> map (rpair () o Thm.get_name_hint)
|> Symtab.make
fun do_fact _ (accum as (_, true)) = accum
| do_fact ((_, (_, status)), th) ((parents, upds), false) =
let
val name = Thm.get_name_hint th
val feats = features_of ctxt prover thy status [prop_of th]
val deps = isabelle_dependencies_of all_names th
val upd = (name, parents, feats, deps)
in (([name], upd :: upds), timed_out pass1_learn_timeout_factor) end
val parents = parents_wrt_facts facts fact_graph
val ((_, upds), _) =
((parents, []), false) |> fold do_fact new_facts |>> apsnd rev
val n = length upds
fun trans {thys, fact_graph} =
let
val mash_INIT_or_ADD =
if Graph.is_empty fact_graph then mash_INIT else mash_ADD
val (upds, fact_graph) =
([], fact_graph) |> fold (update_fact_graph ctxt) upds
in
(mash_INIT_or_ADD ctxt overlord (rev upds);
{thys = thys |> add_thys_for thy,
fact_graph = fact_graph})
end
in
TimeLimit.timeLimit (time_mult pass2_learn_timeout_factor timeout)
mash_map trans
handle TimeLimit.TimeOut =>
(if verbose then
"MaSh timed out trying to learn " ^ string_of_int n ^
" fact" ^ plural_s n ^ " in " ^
string_from_time (Timer.checkRealTimer timer) ^ "."
|> Output.urgent_message
else
());
(if verbose then
"MaSh learned " ^ string_of_int n ^ " fact" ^ plural_s n ^ " in " ^
string_from_time (Timer.checkRealTimer timer) ^ "."
|> Output.urgent_message
else
())
end
end
fun mash_learn_proof ctxt ({provers, overlord, ...} : params) t used_ths facts =
let
val thy = Proof_Context.theory_of ctxt
val prover = hd provers
val name = ATP_Util.timestamp () ^ serial_string () (* fresh enough *)
val feats = features_of ctxt prover thy General [t]
val deps = used_ths |> map Thm.get_name_hint
in
mash_map (fn {thys, fact_graph} =>
let
val parents = parents_wrt_facts facts fact_graph
val upds = [(name, parents, feats, deps)]
val (upds, fact_graph) =
([], fact_graph) |> fold (update_fact_graph ctxt) upds
in
mash_ADD ctxt overlord upds;
{thys = thys, fact_graph = fact_graph}
end)
end
(* The threshold should be large enough so that MaSh doesn't kick in for Auto
Sledgehammer and Try. *)
val min_secs_for_learning = 15
val short_learn_timeout_factor = 0.2
val long_learn_timeout_factor = 4.0
fun relevant_facts ctxt (params as {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
facts
else if max_facts <= 0 then
[]
else
let
val thy = Proof_Context.theory_of ctxt
fun maybe_learn can_suggest =
if Time.toSeconds timeout >= min_secs_for_learning then
if Multithreading.enabled () then
let
val factor =
if can_suggest then short_learn_timeout_factor
else long_learn_timeout_factor
in
Future.fork (fn () => mash_learn_thy ctxt params thy
(time_mult factor timeout)); ()
end
else
mash_learn_thy ctxt params thy
(time_mult short_learn_timeout_factor timeout)
else
()
val fact_filter =
case fact_filter of
SOME ff =>
(if ff <> iterN then maybe_learn (mash_can_suggest_facts ()) else ();
ff)
| NONE =>
if mash_can_suggest_facts () then (maybe_learn true; meshN)
else if mash_could_suggest_facts () then (maybe_learn false; iterN)
else iterN
val add_ths = Attrib.eval_thms ctxt add
fun prepend_facts ths accepts =
((facts |> filter (member Thm.eq_thm_prop ths o snd)) @
(accepts |> filter_out (member Thm.eq_thm_prop ths o snd)))
|> take max_facts
fun iter () =
iterative_relevant_facts ctxt params prover max_facts NONE hyp_ts
concl_t facts
|> (fn facts => (facts, SOME (length facts)))
fun mash () =
(mash_suggest_facts ctxt params prover max_facts hyp_ts concl_t facts,
NONE)
val mess =
[] |> (if fact_filter <> mashN then cons (iter ()) else I)
|> (if fact_filter <> iterN then cons (mash ()) else I)
in
mesh_facts max_facts mess
|> not (null add_ths) ? prepend_facts add_ths
end
end;