(* Title: HOL/Tools/Sledgehammer/sledgehammer_provers.ML
Author: Fabian Immler, TU Muenchen
Author: Makarius
Author: Jasmin Blanchette, TU Muenchen
Generic prover abstraction for Sledgehammer.
*)
signature SLEDGEHAMMER_PROVERS =
sig
type failure = ATP_Proof.failure
type stature = ATP_Problem_Generate.stature
type type_enc = ATP_Problem_Generate.type_enc
type fact = Sledgehammer_Fact.fact
type reconstructor = Sledgehammer_Reconstruct.reconstructor
type play = Sledgehammer_Reconstruct.play
type minimize_command = Sledgehammer_Reconstruct.minimize_command
datatype mode = Auto_Try | Try | Normal | MaSh | Auto_Minimize | Minimize
type params =
{debug : bool,
verbose : bool,
overlord : bool,
blocking : bool,
provers : string list,
type_enc : string option,
strict : bool,
lam_trans : string option,
uncurried_aliases : bool option,
learn : bool,
fact_filter : string option,
max_facts : int option,
fact_thresholds : real * real,
max_mono_iters : int option,
max_new_mono_instances : int option,
isar_proofs : bool,
isar_compress : real,
slice : bool,
minimize : bool option,
timeout : Time.time option,
preplay_timeout : Time.time option,
expect : string}
type relevance_fudge =
{local_const_multiplier : real,
worse_irrel_freq : real,
higher_order_irrel_weight : real,
abs_rel_weight : real,
abs_irrel_weight : real,
skolem_irrel_weight : real,
theory_const_rel_weight : real,
theory_const_irrel_weight : real,
chained_const_irrel_weight : real,
intro_bonus : real,
elim_bonus : real,
simp_bonus : real,
local_bonus : real,
assum_bonus : real,
chained_bonus : real,
max_imperfect : real,
max_imperfect_exp : real,
threshold_divisor : real,
ridiculous_threshold : real}
type prover_problem =
{state : Proof.state,
goal : thm,
subgoal : int,
subgoal_count : int,
factss : (string * fact list) list}
type prover_result =
{outcome : failure option,
used_facts : (string * stature) list,
used_from : fact list,
run_time : Time.time,
preplay : play Lazy.lazy,
message : play -> string,
message_tail : string}
type prover =
params -> ((string * string list) list -> string -> minimize_command)
-> prover_problem -> prover_result
val dest_dir : string Config.T
val problem_prefix : string Config.T
val completish : bool Config.T
val atp_full_names : bool Config.T
val smt_triggers : bool Config.T
val smt_weights : bool Config.T
val smt_weight_min_facts : int Config.T
val smt_min_weight : int Config.T
val smt_max_weight : int Config.T
val smt_max_weight_index : int Config.T
val smt_weight_curve : (int -> int) Unsynchronized.ref
val smt_max_slices : int Config.T
val smt_slice_fact_frac : real Config.T
val smt_slice_time_frac : real Config.T
val smt_slice_min_secs : int Config.T
val SledgehammerN : string
val plain_metis : reconstructor
val select_smt_solver : string -> Proof.context -> Proof.context
val extract_reconstructor :
params -> reconstructor -> string * (string * string list) list
val is_reconstructor : string -> bool
val is_atp : theory -> string -> bool
val is_smt_prover : Proof.context -> string -> bool
val is_ho_atp: Proof.context -> string -> bool
val is_unit_equational_atp : Proof.context -> string -> bool
val is_prover_supported : Proof.context -> string -> bool
val is_prover_installed : Proof.context -> string -> bool
val default_max_facts_for_prover : Proof.context -> bool -> string -> int
val is_unit_equality : term -> bool
val is_appropriate_prop_for_prover : Proof.context -> string -> term -> bool
val is_built_in_const_for_prover :
Proof.context -> string -> string * typ -> term list -> bool * term list
val atp_relevance_fudge : relevance_fudge
val smt_relevance_fudge : relevance_fudge
val relevance_fudge_for_prover : Proof.context -> string -> relevance_fudge
val weight_smt_fact :
Proof.context -> int -> ((string * stature) * thm) * int
-> (string * stature) * (int option * thm)
val supported_provers : Proof.context -> unit
val kill_provers : unit -> unit
val running_provers : unit -> unit
val messages : int option -> unit
val is_fact_chained : (('a * stature) * 'b) -> bool
val filter_used_facts :
bool -> (''a * stature) list -> ((''a * stature) * 'b) list ->
((''a * stature) * 'b) list
val get_prover : Proof.context -> mode -> string -> prover
end;
structure Sledgehammer_Provers : SLEDGEHAMMER_PROVERS =
struct
open ATP_Util
open ATP_Problem
open ATP_Proof
open ATP_Systems
open ATP_Problem_Generate
open ATP_Proof_Reconstruct
open Metis_Tactic
open Sledgehammer_Util
open Sledgehammer_Fact
open Sledgehammer_Reconstruct
(** The Sledgehammer **)
datatype mode = Auto_Try | Try | Normal | MaSh | Auto_Minimize | Minimize
(* Identifier that distinguishes Sledgehammer from other tools that could use
"Async_Manager". *)
val SledgehammerN = "Sledgehammer"
val reconstructor_names = [metisN, smtN]
val plain_metis = Metis (hd partial_type_encs, combsN)
val is_reconstructor = member (op =) reconstructor_names
val is_atp = member (op =) o supported_atps
val select_smt_solver = Context.proof_map o SMT_Config.select_solver
fun is_smt_prover ctxt = member (op =) (SMT_Solver.available_solvers_of ctxt)
fun is_atp_for_format is_format ctxt name =
let val thy = Proof_Context.theory_of ctxt in
case try (get_atp thy) name of
SOME config =>
exists (fn (_, ((_, format, _, _, _), _)) => is_format format)
(#best_slices (config ()) ctxt)
| NONE => false
end
val is_unit_equational_atp = is_atp_for_format (curry (op =) CNF_UEQ)
val is_ho_atp = is_atp_for_format is_format_higher_order
fun is_prover_supported ctxt =
let val thy = Proof_Context.theory_of ctxt in
is_reconstructor orf is_atp thy orf is_smt_prover ctxt
end
fun is_prover_installed ctxt =
is_reconstructor orf is_smt_prover ctxt orf
is_atp_installed (Proof_Context.theory_of ctxt)
fun get_slices slice slices =
(0 upto length slices - 1) ~~ slices |> not slice ? (List.last #> single)
val reconstructor_default_max_facts = 20
fun default_max_facts_for_prover ctxt slice name =
let val thy = Proof_Context.theory_of ctxt in
if is_reconstructor name then
reconstructor_default_max_facts
else if is_atp thy name then
fold (Integer.max o fst o #1 o fst o snd o snd)
(get_slices slice (#best_slices (get_atp thy name ()) ctxt)) 0
else (* is_smt_prover ctxt name *)
SMT_Solver.default_max_relevant ctxt name
end
fun is_if (@{const_name If}, _) = true
| is_if _ = false
(* Beware of "if and only if" (which is translated as such) and "If" (which is
translated to conditional equations). *)
fun is_good_unit_equality T t u =
T <> @{typ bool} andalso not (exists (exists_Const is_if) [t, u])
fun is_unit_equality (@{const Trueprop} $ t) = is_unit_equality t
| is_unit_equality (Const (@{const_name all}, _) $ Abs (_, _, t)) =
is_unit_equality t
| is_unit_equality (Const (@{const_name All}, _) $ Abs (_, _, t)) =
is_unit_equality t
| is_unit_equality (Const (@{const_name "=="}, Type (_, [T, _])) $ t $ u) =
is_good_unit_equality T t u
| is_unit_equality (Const (@{const_name HOL.eq}, Type (_ , [T, _])) $ t $ u) =
is_good_unit_equality T t u
| is_unit_equality _ = false
fun is_appropriate_prop_for_prover ctxt name =
if is_unit_equational_atp ctxt name then is_unit_equality else K true
fun is_built_in_const_for_prover ctxt name =
if is_smt_prover ctxt name then
let val ctxt = ctxt |> select_smt_solver name in
fn x => fn ts =>
if SMT_Builtin.is_builtin_num_ext ctxt (list_comb (Const x, ts)) then
(true, [])
else if SMT_Builtin.is_builtin_fun_ext ctxt x ts then
(true, ts)
else
(false, ts)
end
else
fn (s, _) => fn ts => (member (op =) atp_irrelevant_consts s, ts)
(* FUDGE *)
val atp_relevance_fudge =
{local_const_multiplier = 1.5,
worse_irrel_freq = 100.0,
higher_order_irrel_weight = 1.05,
abs_rel_weight = 0.5,
abs_irrel_weight = 2.0,
skolem_irrel_weight = 0.05,
theory_const_rel_weight = 0.5,
theory_const_irrel_weight = 0.25,
chained_const_irrel_weight = 0.25,
intro_bonus = 0.15,
elim_bonus = 0.15,
simp_bonus = 0.15,
local_bonus = 0.55,
assum_bonus = 1.05,
chained_bonus = 1.5,
max_imperfect = 11.5,
max_imperfect_exp = 1.0,
threshold_divisor = 2.0,
ridiculous_threshold = 0.01}
(* FUDGE (FIXME) *)
val smt_relevance_fudge =
{local_const_multiplier = #local_const_multiplier atp_relevance_fudge,
worse_irrel_freq = #worse_irrel_freq atp_relevance_fudge,
higher_order_irrel_weight = #higher_order_irrel_weight atp_relevance_fudge,
abs_rel_weight = #abs_rel_weight atp_relevance_fudge,
abs_irrel_weight = #abs_irrel_weight atp_relevance_fudge,
skolem_irrel_weight = #skolem_irrel_weight atp_relevance_fudge,
theory_const_rel_weight = #theory_const_rel_weight atp_relevance_fudge,
theory_const_irrel_weight = #theory_const_irrel_weight atp_relevance_fudge,
chained_const_irrel_weight = #chained_const_irrel_weight atp_relevance_fudge,
intro_bonus = #intro_bonus atp_relevance_fudge,
elim_bonus = #elim_bonus atp_relevance_fudge,
simp_bonus = #simp_bonus atp_relevance_fudge,
local_bonus = #local_bonus atp_relevance_fudge,
assum_bonus = #assum_bonus atp_relevance_fudge,
chained_bonus = #chained_bonus atp_relevance_fudge,
max_imperfect = #max_imperfect atp_relevance_fudge,
max_imperfect_exp = #max_imperfect_exp atp_relevance_fudge,
threshold_divisor = #threshold_divisor atp_relevance_fudge,
ridiculous_threshold = #ridiculous_threshold atp_relevance_fudge}
fun relevance_fudge_for_prover ctxt name =
if is_smt_prover ctxt name then smt_relevance_fudge else atp_relevance_fudge
fun supported_provers ctxt =
let
val thy = Proof_Context.theory_of ctxt
val (remote_provers, local_provers) =
reconstructor_names @
sort_strings (supported_atps thy) @
sort_strings (SMT_Solver.available_solvers_of ctxt)
|> List.partition (String.isPrefix remote_prefix)
in
Output.urgent_message ("Supported provers: " ^
commas (local_provers @ remote_provers) ^ ".")
end
fun kill_provers () = Async_Manager.kill_threads SledgehammerN "prover"
fun running_provers () = Async_Manager.running_threads SledgehammerN "prover"
val messages = Async_Manager.thread_messages SledgehammerN "prover"
(** problems, results, ATPs, etc. **)
type params =
{debug : bool,
verbose : bool,
overlord : bool,
blocking : bool,
provers : string list,
type_enc : string option,
strict : bool,
lam_trans : string option,
uncurried_aliases : bool option,
learn : bool,
fact_filter : string option,
max_facts : int option,
fact_thresholds : real * real,
max_mono_iters : int option,
max_new_mono_instances : int option,
isar_proofs : bool,
isar_compress : real,
slice : bool,
minimize : bool option,
timeout : Time.time option,
preplay_timeout : Time.time option,
expect : string}
type relevance_fudge =
{local_const_multiplier : real,
worse_irrel_freq : real,
higher_order_irrel_weight : real,
abs_rel_weight : real,
abs_irrel_weight : real,
skolem_irrel_weight : real,
theory_const_rel_weight : real,
theory_const_irrel_weight : real,
chained_const_irrel_weight : real,
intro_bonus : real,
elim_bonus : real,
simp_bonus : real,
local_bonus : real,
assum_bonus : real,
chained_bonus : real,
max_imperfect : real,
max_imperfect_exp : real,
threshold_divisor : real,
ridiculous_threshold : real}
type prover_problem =
{state : Proof.state,
goal : thm,
subgoal : int,
subgoal_count : int,
factss : (string * fact list) list}
type prover_result =
{outcome : failure option,
used_facts : (string * stature) list,
used_from : fact list,
run_time : Time.time,
preplay : play Lazy.lazy,
message : play -> string,
message_tail : string}
type prover =
params -> ((string * string list) list -> string -> minimize_command)
-> prover_problem -> prover_result
(* configuration attributes *)
(* Empty string means create files in Isabelle's temporary files directory. *)
val dest_dir =
Attrib.setup_config_string @{binding sledgehammer_dest_dir} (K "")
val problem_prefix =
Attrib.setup_config_string @{binding sledgehammer_problem_prefix} (K "prob")
val completish =
Attrib.setup_config_bool @{binding sledgehammer_completish} (K false)
(* In addition to being easier to read, readable names are often much shorter,
especially if types are mangled in names. This makes a difference for some
provers (e.g., E). For these reason, short names are enabled by default. *)
val atp_full_names =
Attrib.setup_config_bool @{binding sledgehammer_atp_full_names} (K false)
val smt_triggers =
Attrib.setup_config_bool @{binding sledgehammer_smt_triggers} (K true)
val smt_weights =
Attrib.setup_config_bool @{binding sledgehammer_smt_weights} (K true)
val smt_weight_min_facts =
Attrib.setup_config_int @{binding sledgehammer_smt_weight_min_facts} (K 20)
(* FUDGE *)
val smt_min_weight =
Attrib.setup_config_int @{binding sledgehammer_smt_min_weight} (K 0)
val smt_max_weight =
Attrib.setup_config_int @{binding sledgehammer_smt_max_weight} (K 10)
val smt_max_weight_index =
Attrib.setup_config_int @{binding sledgehammer_smt_max_weight_index} (K 200)
val smt_weight_curve = Unsynchronized.ref (fn x : int => x * x)
fun smt_fact_weight ctxt j num_facts =
if Config.get ctxt smt_weights andalso
num_facts >= Config.get ctxt smt_weight_min_facts then
let
val min = Config.get ctxt smt_min_weight
val max = Config.get ctxt smt_max_weight
val max_index = Config.get ctxt smt_max_weight_index
val curve = !smt_weight_curve
in
SOME (max - (max - min + 1) * curve (Int.max (0, max_index - j - 1))
div curve max_index)
end
else
NONE
fun weight_smt_fact ctxt num_facts ((info, th), j) =
let val thy = Proof_Context.theory_of ctxt in
(info, (smt_fact_weight ctxt j num_facts, th |> Thm.transfer thy))
end
fun overlord_file_location_for_prover prover =
(getenv "ISABELLE_HOME_USER", "prob_" ^ prover)
fun proof_banner mode name =
case mode of
Auto_Try => "Auto Sledgehammer (" ^ quote name ^ ") found a proof"
| Try => "Sledgehammer (" ^ quote name ^ ") found a proof"
| _ => "Try this"
fun bunch_of_reconstructors needs_full_types lam_trans =
if needs_full_types then
[Metis (full_type_enc, lam_trans false),
Metis (really_full_type_enc, lam_trans false),
Metis (full_type_enc, lam_trans true),
Metis (really_full_type_enc, lam_trans true),
SMT]
else
[Metis (partial_type_enc, lam_trans false),
Metis (full_type_enc, lam_trans false),
Metis (no_typesN, lam_trans true),
Metis (really_full_type_enc, lam_trans true),
SMT]
fun extract_reconstructor ({type_enc, lam_trans, ...} : params)
(Metis (type_enc', lam_trans')) =
let
val override_params =
(if is_none type_enc andalso type_enc' = hd partial_type_encs then
[]
else
[("type_enc", [hd (unalias_type_enc type_enc')])]) @
(if is_none lam_trans andalso lam_trans' = metis_default_lam_trans then
[]
else
[("lam_trans", [lam_trans'])])
in (metisN, override_params) end
| extract_reconstructor _ SMT = (smtN, [])
(* based on "Mirabelle.can_apply" and generalized *)
fun timed_apply timeout tac state i =
let
val {context = ctxt, facts, goal} = Proof.goal state
val full_tac = Method.insert_tac facts i THEN tac ctxt i
in time_limit timeout (try (Seq.pull o full_tac)) goal end
fun tac_for_reconstructor (Metis (type_enc, lam_trans)) =
metis_tac [type_enc] lam_trans
| tac_for_reconstructor SMT = SMT_Solver.smt_tac
fun timed_reconstructor reconstr debug timeout ths =
(Config.put Metis_Tactic.verbose debug
#> Config.put SMT_Config.verbose debug
#> (fn ctxt => tac_for_reconstructor reconstr ctxt ths))
|> timed_apply timeout
fun is_fact_chained ((_, (sc, _)), _) = sc = Chained
fun filter_used_facts keep_chained used =
filter ((member (op =) used o fst) orf
(if keep_chained then is_fact_chained else K false))
fun play_one_line_proof mode debug verbose timeout pairs state i preferred
reconstrs =
let
fun get_preferred reconstrs =
if member (op =) reconstrs preferred then preferred
else List.last reconstrs
in
if timeout = SOME Time.zeroTime then
Trust_Playable (get_preferred reconstrs, NONE)
else
let
val _ =
if mode = Minimize then Output.urgent_message "Preplaying proof..."
else ()
val ths = pairs |> sort_wrt (fst o fst) |> map snd
fun play [] [] = Failed_to_Play (get_preferred reconstrs)
| play timed_outs [] =
Trust_Playable (get_preferred timed_outs, timeout)
| play timed_out (reconstr :: reconstrs) =
let
val _ =
if verbose then
"Trying \"" ^ string_for_reconstructor reconstr ^ "\"" ^
(case timeout of
SOME timeout => " for " ^ string_from_time timeout
| NONE => "") ^ "..."
|> Output.urgent_message
else
()
val timer = Timer.startRealTimer ()
in
case timed_reconstructor reconstr debug timeout ths state i of
SOME (SOME _) => Played (reconstr, Timer.checkRealTimer timer)
| _ => play timed_out reconstrs
end
handle TimeLimit.TimeOut => play (reconstr :: timed_out) reconstrs
in play [] reconstrs end
end
(* generic TPTP-based ATPs *)
(* Too general means, positive equality literal with a variable X as one
operand, when X does not occur properly in the other operand. This rules out
clearly inconsistent facts such as X = a | X = b, though it by no means
guarantees soundness. *)
fun get_facts_for_filter _ [(_, facts)] = facts
| get_facts_for_filter fact_filter factss =
case AList.lookup (op =) factss fact_filter of
SOME facts => facts
| NONE => snd (hd factss)
(* Unwanted equalities are those between a (bound or schematic) variable that
does not properly occur in the second operand. *)
val is_exhaustive_finite =
let
fun is_bad_equal (Var z) t =
not (exists_subterm (fn Var z' => z = z' | _ => false) t)
| is_bad_equal (Bound j) t = not (loose_bvar1 (t, j))
| is_bad_equal _ _ = false
fun do_equals t1 t2 = is_bad_equal t1 t2 orelse is_bad_equal t2 t1
fun do_formula pos t =
case (pos, t) of
(_, @{const Trueprop} $ t1) => do_formula pos t1
| (true, Const (@{const_name all}, _) $ Abs (_, _, t')) =>
do_formula pos t'
| (true, Const (@{const_name All}, _) $ Abs (_, _, t')) =>
do_formula pos t'
| (false, Const (@{const_name Ex}, _) $ Abs (_, _, t')) =>
do_formula pos t'
| (_, @{const "==>"} $ t1 $ t2) =>
do_formula (not pos) t1 andalso
(t2 = @{prop False} orelse do_formula pos t2)
| (_, @{const HOL.implies} $ t1 $ t2) =>
do_formula (not pos) t1 andalso
(t2 = @{const False} orelse do_formula pos t2)
| (_, @{const Not} $ t1) => do_formula (not pos) t1
| (true, @{const HOL.disj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
| (false, @{const HOL.conj} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
| (true, Const (@{const_name HOL.eq}, _) $ t1 $ t2) => do_equals t1 t2
| (true, Const (@{const_name "=="}, _) $ t1 $ t2) => do_equals t1 t2
| _ => false
in do_formula true end
fun has_bound_or_var_of_type pred =
exists_subterm (fn Var (_, T as Type _) => pred T
| Abs (_, T as Type _, _) => pred T
| _ => false)
(* Facts are forbidden to contain variables of these types. The typical reason
is that they lead to unsoundness. Note that "unit" satisfies numerous
equations like "?x = ()". The resulting clauses will have no type constraint,
yielding false proofs. Even "bool" leads to many unsound proofs, though only
for higher-order problems. *)
(* Facts containing variables of type "unit" or "bool" or of the form
"ALL x. x = A | x = B | x = C" are likely to lead to unsound proofs if types
are omitted. *)
fun is_dangerous_prop ctxt =
transform_elim_prop
#> (has_bound_or_var_of_type (is_type_surely_finite ctxt) orf
is_exhaustive_finite)
(* Important messages are important but not so important that users want to see
them each time. *)
val atp_important_message_keep_quotient = 25
fun choose_type_enc soundness best_type_enc format =
the_default best_type_enc
#> type_enc_from_string soundness
#> adjust_type_enc format
val metis_minimize_max_time = seconds 2.0
fun choose_minimize_command params minimize_command name preplay =
let
val (name, override_params) =
case preplay of
Played (reconstr, time) =>
if Time.<= (time, metis_minimize_max_time) then
extract_reconstructor params reconstr
else
(name, [])
| _ => (name, [])
in minimize_command override_params name end
fun repair_monomorph_context max_iters best_max_iters max_new_instances
best_max_new_instances =
Config.put Monomorph.max_rounds (max_iters |> the_default best_max_iters)
#> Config.put Monomorph.max_new_instances
(max_new_instances |> the_default best_max_new_instances)
#> Config.put Monomorph.keep_partial_instances false
fun suffix_for_mode Auto_Try = "_try"
| suffix_for_mode Try = "_try"
| suffix_for_mode Normal = ""
| suffix_for_mode MaSh = ""
| suffix_for_mode Auto_Minimize = "_min"
| suffix_for_mode Minimize = "_min"
(* Give the ATPs some slack before interrupting them the hard way. "z3_tptp" on
Linux appears to be the only ATP that does not honor its time limit. *)
val atp_timeout_slack = seconds 1.0
val mono_max_privileged_facts = 10
fun run_atp mode name
({exec, arguments, proof_delims, known_failures, prem_role, best_slices,
best_max_mono_iters, best_max_new_mono_instances, ...} : atp_config)
(params as {debug, verbose, overlord, type_enc, strict, lam_trans,
uncurried_aliases, fact_filter, max_facts, max_mono_iters,
max_new_mono_instances, isar_proofs, isar_compress,
slice, timeout, preplay_timeout, ...})
minimize_command
({state, goal, subgoal, subgoal_count, factss, ...} : prover_problem) =
let
val thy = Proof.theory_of state
val ctxt = Proof.context_of state
val atp_mode =
if Config.get ctxt completish then Sledgehammer_Completish
else Sledgehammer
val (_, hyp_ts, concl_t) = strip_subgoal ctxt goal subgoal
val (dest_dir, problem_prefix) =
if overlord then overlord_file_location_for_prover name
else (Config.get ctxt dest_dir, Config.get ctxt problem_prefix)
val problem_file_name =
Path.basic (problem_prefix ^ (if overlord then "" else serial_string ()) ^
suffix_for_mode mode ^ "_" ^ string_of_int subgoal)
val prob_path =
if dest_dir = "" then
File.tmp_path problem_file_name
else if File.exists (Path.explode dest_dir) then
Path.append (Path.explode dest_dir) problem_file_name
else
error ("No such directory: " ^ quote dest_dir ^ ".")
val command0 =
case find_first (fn var => getenv var <> "") (fst exec) of
SOME var =>
let
val pref = getenv var ^ "/"
val paths = map (Path.explode o prefix pref) (snd exec)
in
case find_first File.exists paths of
SOME path => path
| NONE => error ("Bad executable: " ^ Path.print (hd paths) ^ ".")
end
| NONE => error ("The environment variable " ^ quote (hd (fst exec)) ^
" is not set.")
fun split_time s =
let
val split = String.tokens (fn c => str c = "\n")
val (output, t) =
s |> split |> (try split_last #> the_default ([], "0"))
|>> cat_lines
fun as_num f = f >> (fst o read_int)
val num = as_num (Scan.many1 Symbol.is_ascii_digit)
val digit = Scan.one Symbol.is_ascii_digit
val num3 = as_num (digit ::: digit ::: (digit >> single))
val time = num --| Scan.$$ "." -- num3 >> (fn (a, b) => a * 1000 + b)
val as_time =
raw_explode #> Scan.read Symbol.stopper time #> the_default 0
in (output, as_time t |> Time.fromMilliseconds) end
fun run () =
let
(* If slicing is disabled, we expand the last slice to fill the entire
time available. *)
val actual_slices = get_slices slice (best_slices ctxt)
val num_actual_slices = length actual_slices
fun monomorphize_facts facts =
let
val ctxt =
ctxt
|> repair_monomorph_context max_mono_iters best_max_mono_iters
max_new_mono_instances best_max_new_mono_instances
(* pseudo-theorem involving the same constants as the subgoal *)
val subgoal_th =
Logic.list_implies (hyp_ts, concl_t) |> Skip_Proof.make_thm thy
val rths =
facts |> chop mono_max_privileged_facts
|>> map (pair 1 o snd)
||> map (pair 2 o snd)
|> op @
|> cons (0, subgoal_th)
in
Monomorph.monomorph atp_schematic_consts_of rths ctxt |> fst |> tl
|> curry ListPair.zip (map fst facts)
|> maps (fn (name, rths) =>
map (pair name o zero_var_indexes o snd) rths)
end
fun run_slice time_left (cache_key, cache_value)
(slice, (time_frac,
(key as ((best_max_facts, best_fact_filter), format,
best_type_enc, best_lam_trans,
best_uncurried_aliases),
extra))) =
let
val effective_fact_filter =
fact_filter |> the_default best_fact_filter
val facts = get_facts_for_filter effective_fact_filter factss
val num_facts =
length facts |> is_none max_facts ? Integer.min best_max_facts
val soundness = if strict then Strict else Non_Strict
val type_enc =
type_enc |> choose_type_enc soundness best_type_enc format
val sound = is_type_enc_sound type_enc
val real_ms = Real.fromInt o Time.toMilliseconds
val slice_timeout =
case time_left of
SOME time_left =>
((real_ms time_left
|> (if slice < num_actual_slices - 1 then
curry Real.min (time_frac * real_ms (the timeout))
else
I))
* 0.001)
|> seconds |> SOME
| NONE => NONE
val generous_slice_timeout =
if mode = MaSh then NONE
else Option.map (curry Time.+ atp_timeout_slack) slice_timeout
val _ =
if debug then
quote name ^ " slice #" ^ string_of_int (slice + 1) ^
" with " ^ string_of_int num_facts ^ " fact" ^
plural_s num_facts ^
(case slice_timeout of
SOME timeout => " for " ^ string_from_time timeout
| NONE => "") ^ "..."
|> Output.urgent_message
else
()
val readable_names = not (Config.get ctxt atp_full_names)
val lam_trans =
case lam_trans of
SOME s => s
| NONE => best_lam_trans
val uncurried_aliases =
case uncurried_aliases of
SOME b => b
| NONE => best_uncurried_aliases
val value as (atp_problem, _, fact_names, _, _) =
if cache_key = SOME key then
cache_value
else
facts
|> not sound
? filter_out (is_dangerous_prop ctxt o prop_of o snd)
|> take num_facts
|> not (is_type_enc_polymorphic type_enc) ? monomorphize_facts
|> map (apsnd prop_of)
|> prepare_atp_problem ctxt format prem_role type_enc atp_mode
lam_trans uncurried_aliases
readable_names true hyp_ts concl_t
fun sel_weights () = atp_problem_selection_weights atp_problem
fun ord_info () = atp_problem_term_order_info atp_problem
val ord = effective_term_order ctxt name
val full_proof = debug orelse isar_proofs
val args =
arguments ctxt full_proof extra
(slice_timeout |> the_default one_day)
(File.shell_path prob_path) (ord, ord_info, sel_weights)
val command =
"(exec 2>&1; " ^ File.shell_path command0 ^ " " ^ args ^ " " ^ ")"
|> enclose "TIMEFORMAT='%3R'; { time " " ; }"
val _ =
atp_problem
|> lines_for_atp_problem format ord ord_info
|> cons ("% " ^ command ^ "\n")
|> File.write_list prob_path
val ((output, run_time), used_from, (atp_proof, outcome)) =
time_limit generous_slice_timeout Isabelle_System.bash_output
command
|>> (if overlord then
prefix ("% " ^ command ^ "\n% " ^ timestamp () ^ "\n")
else
I)
|> fst |> split_time
|> (fn accum as (output, _) =>
(accum, facts,
extract_tstplike_proof_and_outcome verbose proof_delims
known_failures output
|>> atp_proof_from_tstplike_proof atp_problem
handle UNRECOGNIZED_ATP_PROOF () =>
([], SOME ProofIncomplete)))
handle TimeLimit.TimeOut =>
(("", the slice_timeout), [], ([], SOME TimedOut))
val outcome =
case outcome of
NONE =>
(case used_facts_in_unsound_atp_proof ctxt fact_names atp_proof
|> Option.map (sort string_ord) of
SOME facts =>
let
val failure =
UnsoundProof (is_type_enc_sound type_enc, facts)
in
if debug then (warning (string_for_failure failure); NONE)
else SOME failure
end
| NONE => NONE)
| _ => outcome
in
((SOME key, value), (output, run_time, facts, atp_proof, outcome))
end
val timer = Timer.startRealTimer ()
fun maybe_run_slice slice
(result as (cache, (_, run_time0, _, _, SOME _))) =
let
val time_left =
Option.map
(fn timeout => Time.- (timeout, Timer.checkRealTimer timer))
timeout
in
if time_left <> NONE andalso
Time.<= (the time_left, Time.zeroTime) then
result
else
run_slice time_left cache slice
|> (fn (cache, (output, run_time, used_from, atp_proof,
outcome)) =>
(cache, (output, Time.+ (run_time0, run_time), used_from,
atp_proof, outcome)))
end
| maybe_run_slice _ result = result
in
((NONE, ([], Symtab.empty, Vector.fromList [], [], Symtab.empty)),
("", Time.zeroTime, [], [], SOME InternalError))
|> fold maybe_run_slice actual_slices
end
(* If the problem file has not been exported, remove it; otherwise, export
the proof file too. *)
fun clean_up () =
if dest_dir = "" then (try File.rm prob_path; ()) else ()
fun export (_, (output, _, _, _, _)) =
if dest_dir = "" then ()
else File.write (Path.explode (Path.implode prob_path ^ "_proof")) output
val ((_, (_, pool, fact_names, _, sym_tab)),
(output, run_time, used_from, atp_proof, outcome)) =
with_cleanup clean_up run () |> tap export
val important_message =
if mode = Normal andalso
random_range 0 (atp_important_message_keep_quotient - 1) = 0 then
extract_important_message output
else
""
val (used_facts, preplay, message, message_tail) =
case outcome of
NONE =>
let
val used_facts = used_facts_in_atp_proof ctxt fact_names atp_proof
val needs_full_types = is_typed_helper_used_in_atp_proof atp_proof
val reconstrs =
bunch_of_reconstructors needs_full_types
(lam_trans_from_atp_proof atp_proof
o (fn desperate => if desperate then hide_lamsN
else metis_default_lam_trans))
in
(used_facts,
Lazy.lazy (fn () =>
let
val used_pairs =
used_from |> filter_used_facts false used_facts
in
play_one_line_proof mode debug verbose preplay_timeout
used_pairs state subgoal (hd reconstrs) reconstrs
end),
fn preplay =>
let
val _ =
if verbose then
Output.urgent_message "Generating proof text..."
else
()
val isar_params =
(debug, verbose, preplay_timeout, isar_compress,
pool, fact_names, sym_tab, atp_proof, goal)
val one_line_params =
(preplay, proof_banner mode name, used_facts,
choose_minimize_command params minimize_command name preplay,
subgoal, subgoal_count)
val num_chained = length (#facts (Proof.goal state))
in
proof_text ctxt isar_proofs isar_params num_chained
one_line_params
end,
(if verbose then
"\nATP real CPU time: " ^ string_from_time run_time ^ "."
else
"") ^
(if important_message <> "" then
"\n\nImportant message from Dr. Geoff Sutcliffe:\n" ^
important_message
else
""))
end
| SOME failure =>
([], Lazy.value (Failed_to_Play plain_metis),
fn _ => string_for_failure failure, "")
in
{outcome = outcome, used_facts = used_facts, used_from = used_from,
run_time = run_time, preplay = preplay, message = message,
message_tail = message_tail}
end
fun rotate_one (x :: xs) = xs @ [x]
(* "SMT_Failure.Abnormal_Termination" carries the solver's return code. Until
these are sorted out properly in the SMT module, we have to interpret these
ourselves. *)
val remote_smt_failures =
[(2, NoLibwwwPerl),
(22, CantConnect)]
val z3_failures =
[(101, OutOfResources),
(103, MalformedInput),
(110, MalformedInput),
(112, TimedOut)]
val unix_failures =
[(138, Crashed),
(139, Crashed)]
val smt_failures = remote_smt_failures @ z3_failures @ unix_failures
fun failure_from_smt_failure (SMT_Failure.Counterexample {is_real_cex, ...}) =
if is_real_cex then Unprovable else GaveUp
| failure_from_smt_failure SMT_Failure.Time_Out = TimedOut
| failure_from_smt_failure (SMT_Failure.Abnormal_Termination code) =
(case AList.lookup (op =) smt_failures code of
SOME failure => failure
| NONE => UnknownError ("Abnormal termination with exit code " ^
string_of_int code ^ "."))
| failure_from_smt_failure SMT_Failure.Out_Of_Memory = OutOfResources
| failure_from_smt_failure (SMT_Failure.Other_Failure msg) =
UnknownError msg
(* FUDGE *)
val smt_max_slices =
Attrib.setup_config_int @{binding sledgehammer_smt_max_slices} (K 8)
val smt_slice_fact_frac =
Attrib.setup_config_real @{binding sledgehammer_smt_slice_fact_frac}
(K 0.667)
val smt_slice_time_frac =
Attrib.setup_config_real @{binding sledgehammer_smt_slice_time_frac} (K 0.333)
val smt_slice_min_secs =
Attrib.setup_config_int @{binding sledgehammer_smt_slice_min_secs} (K 3)
fun smt_filter_loop name
({debug, verbose, overlord, max_mono_iters,
max_new_mono_instances, timeout, slice, ...} : params)
state goal i =
let
fun repair_context ctxt =
ctxt |> select_smt_solver name
|> Config.put SMT_Config.verbose debug
|> (if overlord then
Config.put SMT_Config.debug_files
(overlord_file_location_for_prover name
|> (fn (path, name) => path ^ "/" ^ name))
else
I)
|> Config.put SMT_Config.infer_triggers
(Config.get ctxt smt_triggers)
val ctxt = Proof.context_of state |> repair_context
val state = state |> Proof.map_context (K ctxt)
val max_slices = if slice then Config.get ctxt smt_max_slices else 1
fun do_slice timeout slice outcome0 time_so_far
(weighted_factss as (fact_filter, weighted_facts) :: _) =
let
val timer = Timer.startRealTimer ()
val state =
state |> Proof.map_context
(repair_monomorph_context max_mono_iters
default_max_mono_iters max_new_mono_instances
default_max_new_mono_instances)
val slice_timeout =
if slice < max_slices andalso timeout <> NONE then
let val ms = timeout |> the |> Time.toMilliseconds in
Int.min (ms,
Int.max (1000 * Config.get ctxt smt_slice_min_secs,
Real.ceil (Config.get ctxt smt_slice_time_frac
* Real.fromInt ms)))
|> Time.fromMilliseconds |> SOME
end
else
timeout
val num_facts = length weighted_facts
val _ =
if debug then
quote name ^ " slice " ^ string_of_int slice ^ " with " ^
string_of_int num_facts ^ " fact" ^ plural_s num_facts ^
(case slice_timeout of
SOME timeout => " for " ^ string_from_time timeout
| NONE => "") ^ "..."
|> Output.urgent_message
else
()
val birth = Timer.checkRealTimer timer
val _ =
if debug then Output.urgent_message "Invoking SMT solver..." else ()
val state_facts = these (try (#facts o Proof.goal) state)
val (outcome, used_facts) =
SMT_Solver.smt_filter_preprocess ctxt state_facts goal weighted_facts
i
|> SMT_Solver.smt_filter_apply (slice_timeout |> the_default one_day)
|> (fn {outcome, used_facts} => (outcome, used_facts))
handle exn => if Exn.is_interrupt exn then
reraise exn
else
(ML_Compiler.exn_message exn
|> SMT_Failure.Other_Failure |> SOME, [])
val death = Timer.checkRealTimer timer
val outcome0 = if is_none outcome0 then SOME outcome else outcome0
val time_so_far = Time.+ (time_so_far, Time.- (death, birth))
val too_many_facts_perhaps =
case outcome of
NONE => false
| SOME (SMT_Failure.Counterexample _) => false
| SOME SMT_Failure.Time_Out => slice_timeout <> timeout
| SOME (SMT_Failure.Abnormal_Termination _) => true (* kind of *)
| SOME SMT_Failure.Out_Of_Memory => true
| SOME (SMT_Failure.Other_Failure _) => true
val timeout =
Option.map
(fn timeout => Time.- (timeout, Timer.checkRealTimer timer))
timeout
in
if too_many_facts_perhaps andalso slice < max_slices andalso
num_facts > 0 andalso
(timeout = NONE orelse Time.> (the timeout, Time.zeroTime)) then
let
val new_num_facts =
Real.ceil (Config.get ctxt smt_slice_fact_frac
* Real.fromInt num_facts)
val weighted_factss as (new_fact_filter, _) :: _ =
weighted_factss
|> rotate_one
|> app_hd (apsnd (take new_num_facts))
val show_filter = fact_filter <> new_fact_filter
fun num_of_facts fact_filter num_facts =
string_of_int num_facts ^
(if show_filter then " " ^ quote fact_filter else "") ^
" fact" ^ plural_s num_facts
val _ =
if verbose andalso is_some outcome then
quote name ^ " invoked with " ^
num_of_facts fact_filter num_facts ^ ": " ^
string_for_failure (failure_from_smt_failure (the outcome)) ^
" Retrying with " ^ num_of_facts new_fact_filter new_num_facts ^
"..."
|> Output.urgent_message
else
()
in
do_slice timeout (slice + 1) outcome0 time_so_far weighted_factss
end
else
{outcome = if is_none outcome then NONE else the outcome0,
used_facts = used_facts, used_from = map (apsnd snd) weighted_facts,
run_time = time_so_far}
end
in do_slice timeout 1 NONE Time.zeroTime end
fun run_smt_solver mode name (params as {debug, verbose, preplay_timeout, ...})
minimize_command
({state, goal, subgoal, subgoal_count, factss, ...} : prover_problem) =
let
val ctxt = Proof.context_of state
fun weight_facts facts =
let val num_facts = length facts in
facts ~~ (0 upto num_facts - 1)
|> map (weight_smt_fact ctxt num_facts)
end
val weighted_factss = factss |> map (apsnd weight_facts)
val {outcome, used_facts = used_pairs, used_from, run_time} =
smt_filter_loop name params state goal subgoal weighted_factss
val used_facts = used_pairs |> map fst
val outcome = outcome |> Option.map failure_from_smt_failure
val (preplay, message, message_tail) =
case outcome of
NONE =>
(Lazy.lazy (fn () =>
play_one_line_proof mode debug verbose preplay_timeout used_pairs
state subgoal SMT
(bunch_of_reconstructors false (fn desperate =>
if desperate then liftingN else metis_default_lam_trans))),
fn preplay =>
let
val one_line_params =
(preplay, proof_banner mode name, used_facts,
choose_minimize_command params minimize_command name preplay,
subgoal, subgoal_count)
val num_chained = length (#facts (Proof.goal state))
in one_line_proof_text num_chained one_line_params end,
if verbose then
"\nSMT solver real CPU time: " ^ string_from_time run_time ^ "."
else
"")
| SOME failure =>
(Lazy.value (Failed_to_Play plain_metis),
fn _ => string_for_failure failure, "")
in
{outcome = outcome, used_facts = used_facts, used_from = used_from,
run_time = run_time, preplay = preplay, message = message,
message_tail = message_tail}
end
fun run_reconstructor mode name
(params as {debug, verbose, timeout, type_enc, lam_trans, ...})
minimize_command
({state, subgoal, subgoal_count, factss = (_, facts) :: _, ...}
: prover_problem) =
let
val reconstr =
if name = metisN then
Metis (type_enc |> the_default (hd partial_type_encs),
lam_trans |> the_default metis_default_lam_trans)
else if name = smtN then
SMT
else
raise Fail ("unknown reconstructor: " ^ quote name)
val used_facts = facts |> map fst
in
case play_one_line_proof (if mode = Minimize then Normal else mode) debug
verbose timeout facts state subgoal reconstr
[reconstr] of
play as Played (_, time) =>
{outcome = NONE, used_facts = used_facts, used_from = facts,
run_time = time, preplay = Lazy.value play,
message =
fn play =>
let
val (_, override_params) = extract_reconstructor params reconstr
val one_line_params =
(play, proof_banner mode name, used_facts,
minimize_command override_params name, subgoal,
subgoal_count)
val num_chained = length (#facts (Proof.goal state))
in one_line_proof_text num_chained one_line_params end,
message_tail = ""}
| play =>
let
val failure = case play of Failed_to_Play _ => GaveUp | _ => TimedOut
in
{outcome = SOME failure, used_facts = [], used_from = [],
run_time = Time.zeroTime, preplay = Lazy.value play,
message = fn _ => string_for_failure failure, message_tail = ""}
end
end
fun get_prover ctxt mode name =
let val thy = Proof_Context.theory_of ctxt in
if is_reconstructor name then run_reconstructor mode name
else if is_atp thy name then run_atp mode name (get_atp thy name ())
else if is_smt_prover ctxt name then run_smt_solver mode name
else error ("No such prover: " ^ name ^ ".")
end
end;