(* Title: HOL/Tools/Sledgehammer/sledgehammer.ML
Author: Fabian Immler, TU Muenchen
Author: Makarius
Author: Jasmin Blanchette, TU Muenchen
Sledgehammer's heart.
*)
signature SLEDGEHAMMER =
sig
type stature = ATP_Problem_Generate.stature
type fact = Sledgehammer_Fact.fact
type fact_override = Sledgehammer_Fact.fact_override
type proof_method = Sledgehammer_Proof_Methods.proof_method
type play_outcome = Sledgehammer_Proof_Methods.play_outcome
type mode = Sledgehammer_Prover.mode
type params = Sledgehammer_Prover.params
type induction_rules = Sledgehammer_Prover.induction_rules
type prover_problem = Sledgehammer_Prover.prover_problem
type prover_result = Sledgehammer_Prover.prover_result
datatype sledgehammer_outcome =
SH_Some of prover_result
| SH_Unknown
| SH_Timeout
| SH_None
val short_string_of_sledgehammer_outcome : sledgehammer_outcome -> string
val play_one_line_proof : bool -> Time.time -> (string * stature) list -> Proof.state -> int ->
proof_method * proof_method list list -> (string * stature) list * (proof_method * play_outcome)
val string_of_factss : (string * fact list) list -> string
val run_sledgehammer : params -> mode -> (string -> unit) option -> int -> fact_override ->
Proof.state -> bool * (sledgehammer_outcome * string)
end;
structure Sledgehammer : SLEDGEHAMMER =
struct
open ATP_Util
open ATP_Problem
open ATP_Proof
open ATP_Problem_Generate
open Sledgehammer_Util
open Sledgehammer_Fact
open Sledgehammer_Proof_Methods
open Sledgehammer_Isar_Proof
open Sledgehammer_Isar_Preplay
open Sledgehammer_Isar_Minimize
open Sledgehammer_ATP_Systems
open Sledgehammer_Prover
open Sledgehammer_Prover_ATP
open Sledgehammer_Prover_Minimize
open Sledgehammer_MaSh
datatype sledgehammer_outcome =
SH_Some of prover_result
| SH_Unknown
| SH_Timeout
| SH_None
fun short_string_of_sledgehammer_outcome (SH_Some _) = "some"
| short_string_of_sledgehammer_outcome SH_Unknown = "unknown"
| short_string_of_sledgehammer_outcome SH_Timeout = "timeout"
| short_string_of_sledgehammer_outcome SH_None = "none"
fun alternative f (SOME x) (SOME y) = SOME (f (x, y))
| alternative _ (x as SOME _) NONE = x
| alternative _ NONE (y as SOME _) = y
| alternative _ NONE NONE = NONE
fun max_outcome outcomes =
let
val result = find_first (fn (SH_Some _, _) => true | _ => false) outcomes
val unknown = find_first (fn (SH_Unknown, _) => true | _ => false) outcomes
val timeout = find_first (fn (SH_Timeout, _) => true | _ => false) outcomes
val none = find_first (fn (SH_None, _) => true | _ => false) outcomes
in
result
|> alternative snd unknown
|> alternative snd timeout
|> alternative snd none
|> the_default (SH_Unknown, "")
end
fun play_one_line_proof minimize timeout used_facts state i (preferred_meth, methss) =
(if timeout = Time.zeroTime then
(used_facts, (preferred_meth, Play_Timed_Out Time.zeroTime))
else
let
val ctxt = Proof.context_of state
val fact_names = used_facts |> filter_out (fn (_, (sc, _)) => sc = Chained) |> map fst
val {facts = chained, goal, ...} = Proof.goal state
val goal_t = Logic.get_goal (Thm.prop_of goal) i
fun try_methss [] [] = (used_facts, (preferred_meth, Play_Timed_Out Time.zeroTime))
| try_methss ress [] =
(used_facts,
(case AList.lookup (op =) ress preferred_meth of
SOME play => (preferred_meth, play)
| NONE => hd (sort (play_outcome_ord o apply2 snd) (rev ress))))
| try_methss ress (meths :: methss) =
let
fun mk_step fact_names meths =
Prove {
qualifiers = [],
obtains = [],
label = ("", 0),
goal = goal_t,
subproofs = [],
facts = ([], fact_names),
proof_methods = meths,
comment = ""}
in
(case preplay_isar_step ctxt chained timeout [] (mk_step fact_names meths) of
(res as (meth, Played time)) :: _ =>
if not minimize then
(used_facts, res)
else
let
val (time', used_names') =
minimized_isar_step ctxt chained time (mk_step fact_names [meth])
||> (facts_of_isar_step #> snd)
val used_facts' = filter (member (op =) used_names' o fst) used_facts
in
(used_facts', (meth, Played time'))
end
| ress' => try_methss (ress' @ ress) methss)
end
in
try_methss [] methss
end)
|> (fn (used_facts, (meth, play)) =>
(used_facts |> filter_out (fn (_, (sc, _)) => sc = Chained), (meth, play)))
fun launch_prover (params as {verbose, spy, ...}) mode learn
(problem as {state, subgoal, factss, ...} : prover_problem) slice name =
let
val ctxt = Proof.context_of state
val _ = spying spy (fn () => (state, subgoal, name, "Launched"))
fun print_used_facts used_facts used_from =
tag_list 1 used_from
|> map (fn (j, fact) => fact |> apsnd (K j))
|> filter_used_facts false used_facts
|> map (fn ((name, _), j) => name ^ "@" ^ string_of_int j)
|> commas
|> prefix ("Facts in " ^ name ^ " proof: ")
|> writeln
fun spying_str_of_res ({outcome = NONE, used_facts, used_from, ...} : prover_result) =
let
val num_used_facts = length used_facts
fun find_indices facts =
tag_list 1 facts
|> map (fn (j, fact) => fact |> apsnd (K j))
|> filter_used_facts false used_facts
|> distinct (eq_fst (op =))
|> map (prefix "@" o string_of_int o snd)
fun filter_info (fact_filter, facts) =
let
val indices = find_indices facts
(* "Int.max" is there for robustness -- it shouldn't be necessary *)
val unknowns = replicate (Int.max (0, num_used_facts - length indices)) "?"
in
(commas (indices @ unknowns), fact_filter)
end
val filter_infos =
map filter_info (("actual", used_from) :: factss)
|> AList.group (op =)
|> map (fn (indices, fact_filters) => commas fact_filters ^ ": " ^ indices)
in
"Success: Found proof with " ^ string_of_int num_used_facts ^ " fact" ^
plural_s num_used_facts ^
(if num_used_facts = 0 then "" else ": " ^ commas filter_infos)
end
| spying_str_of_res {outcome = SOME failure, ...} =
"Failure: " ^ string_of_atp_failure failure
in
get_minimizing_prover ctxt mode learn name params problem slice
|> verbose ? tap (fn {outcome = NONE, used_facts as _ :: _, used_from, ...} =>
print_used_facts used_facts used_from
| _ => ())
|> spy ? tap (fn res => spying spy (fn () => (state, subgoal, name, spying_str_of_res res)))
end
fun preplay_prover_result ({ minimize, preplay_timeout, ...} : params) state subgoal
(result as {outcome, used_facts, preferred_methss, message, ...} : prover_result) =
let
val output =
if outcome = SOME ATP_Proof.TimedOut then
SH_Timeout
else if is_some outcome then
SH_None
else
SH_Some result
fun output_message () = message (fn () =>
play_one_line_proof minimize preplay_timeout used_facts state subgoal preferred_methss)
in
(output, output_message)
end
fun check_expected_outcome ctxt prover_name expect outcome =
let
val outcome_code = short_string_of_sledgehammer_outcome outcome
in
(* The "expect" argument is deliberately ignored if the prover is missing so that
"Metis_Examples" can be processed on any machine. *)
if expect = "" orelse outcome_code = expect orelse
not (is_prover_installed ctxt prover_name) then
()
else
error ("Unexpected outcome: " ^ quote outcome_code)
end
fun launch_prover_and_preplay (params as {debug, timeout, expect, ...}) mode writeln_result learn
(problem as {state, subgoal, ...}) slice prover_name =
let
val ctxt = Proof.context_of state
val hard_timeout = Time.scale 5.0 timeout
fun really_go () =
launch_prover params mode learn problem slice prover_name
|> preplay_prover_result params state subgoal
fun go () =
if debug then
really_go ()
else
(really_go ()
handle
ERROR msg => (SH_Unknown, fn () => "Error: " ^ msg ^ "\n")
| exn =>
if Exn.is_interrupt exn then Exn.reraise exn
else (SH_Unknown, fn () => "Internal error:\n" ^ Runtime.exn_message exn ^ "\n"))
val (outcome, message) = Timeout.apply hard_timeout go ()
val () = check_expected_outcome ctxt prover_name expect outcome
val message = message ()
val () =
(case outcome of
SH_Some _ =>
the_default writeln writeln_result (prover_name ^ ": " ^ message)
| _ => ())
in
(outcome, message)
end
fun string_of_facts facts =
"Including " ^ string_of_int (length facts) ^ " relevant fact" ^ plural_s (length facts) ^ ": " ^
(facts |> map (fst o fst) |> space_implode " ")
fun string_of_factss factss =
if forall (null o snd) factss then
"Found no relevant facts"
else
cat_lines (map (fn (filter, facts) =>
(if filter = "" then "" else filter ^ ": ") ^ string_of_facts facts) factss)
val default_slice_schedule =
(* FUDGE (based on Seventeen evaluation) *)
[cvc4N, zipperpositionN, vampireN, veritN, eN, cvc4N, zipperpositionN, cvc4N, vampireN, cvc4N,
cvc4N, vampireN, cvc4N, eN, iproverN, zipperpositionN, vampireN, eN, vampireN, zipperpositionN,
z3N, cvc4N, vampireN, iproverN, vampireN, zipperpositionN, z3N, z3N, cvc4N, cvc4N]
fun schedule_of_provers provers num_slices =
let
val num_default_slices = length default_slice_schedule
val unknown_provers = filter_out (member (op =) default_slice_schedule) provers
fun round_robin _ [] = []
| round_robin 0 _ = []
| round_robin n (prover :: provers) = prover :: round_robin (n - 1) (provers @ [prover])
in
if num_slices <= num_default_slices then
take num_slices default_slice_schedule
else
default_slice_schedule @ round_robin (num_slices - num_default_slices) unknown_provers
end
fun prover_slices_of_schedule ctxt schedule =
let
fun triplicate_slices original =
let
val shift =
map (apfst (apsnd (fn fact_filter =>
if fact_filter = mashN then mepoN
else if fact_filter = mepoN then meshN
else mashN)))
val shifted_once = shift original
val shifted_twice = shift shifted_once
in
original @ shifted_once @ shifted_twice
end
val provers = distinct (op =) schedule
val prover_slices =
map (fn prover => (prover, triplicate_slices (get_slices ctxt prover))) provers
fun translate _ [] = []
| translate prover_slices (prover :: schedule) =
(case AList.lookup (op =) prover_slices prover of
SOME (slice :: slices) =>
let val prover_slices' = AList.update (op =) (prover, slices) prover_slices in
(prover, slice) :: translate prover_slices' schedule
end
| _ => translate prover_slices schedule)
in
translate prover_slices schedule
end
fun run_sledgehammer (params as {verbose, spy, provers, induction_rules, max_facts, max_proofs,
slices, ...})
mode writeln_result i (fact_override as {only, ...}) state =
if null provers then
error "No prover is set"
else
(case subgoal_count state of
0 => (error "No subgoal!"; (false, (SH_None, "")))
| n =>
let
val _ = Proof.assert_backward state
val print = if mode = Normal andalso is_none writeln_result then writeln else K ()
val found_proofs = Synchronized.var "found_proofs" 0
fun found_proof prover_name =
if mode = Normal then
(Synchronized.change found_proofs (fn n => n + 1);
(writeln_result |> the_default writeln) (prover_name ^ " found a proof..."))
else
()
val ctxt = Proof.context_of state
val inst_inducts = induction_rules = SOME Instantiate
val {facts = chained_thms, goal, ...} = Proof.goal state
val (_, hyp_ts, concl_t) = strip_subgoal goal i ctxt
val _ =
(case find_first (not o is_prover_supported ctxt) provers of
SOME name => error ("No such prover: " ^ name)
| NONE => ())
val _ = print "Sledgehammering..."
val _ = spying spy (fn () => (state, i, "***", "Starting " ^ str_of_mode mode ^ " mode"))
val ({elapsed, ...}, all_facts) = Timing.timing
(nearly_all_facts_of_context ctxt inst_inducts fact_override chained_thms hyp_ts) concl_t
val _ = spying spy (fn () => (state, i, "All",
"Extracting " ^ string_of_int (length all_facts) ^ " facts from background theory in " ^
string_of_int (Time.toMilliseconds elapsed) ^ " ms"))
val spying_str_of_factss =
commas o map (fn (filter, facts) => filter ^ ": " ^ string_of_int (length facts))
fun get_factss provers =
let
val max_max_facts =
(case max_facts of
SOME n => n
| NONE =>
fold (fn prover =>
fold (fn ((n, _), _) => Integer.max n) (get_slices ctxt prover))
provers 0)
val ({elapsed, ...}, factss) = Timing.timing
(relevant_facts ctxt params (hd provers) max_max_facts fact_override hyp_ts concl_t)
all_facts
val induction_rules = the_default (if only then Include else Exclude) induction_rules
val factss = map (apsnd (maybe_filter_out_induction_rules induction_rules)) factss
val () = spying spy (fn () => (state, i, "All",
"Filtering facts in " ^ string_of_int (Time.toMilliseconds elapsed) ^
" ms (MaSh algorithm: " ^ str_of_mash_algorithm (the_mash_algorithm ()) ^ ")"));
val () = if verbose then print (string_of_factss factss) else ()
val () = spying spy (fn () =>
(state, i, "All", "Selected facts: " ^ spying_str_of_factss factss))
in
factss
end
fun launch_provers () =
let
val problem =
{comment = "", state = state, goal = goal, subgoal = i, subgoal_count = n,
factss = get_factss provers, found_proof = found_proof}
val learn = mash_learn_proof ctxt params (Thm.prop_of goal)
val launch = launch_prover_and_preplay params mode writeln_result learn
val schedule =
if mode = Auto_Try then
provers
else
schedule_of_provers provers slices
val prover_slices = prover_slices_of_schedule ctxt schedule
in
if mode = Auto_Try then
(SH_Unknown, "")
|> fold (fn (prover, slice) =>
fn accum as (SH_Some _, _) => accum
| _ => launch problem slice prover)
prover_slices
else
(learn chained_thms;
Par_List.map (fn (prover, slice) =>
if Synchronized.value found_proofs < max_proofs then
launch problem slice prover
else
(SH_Unknown, ""))
prover_slices
|> max_outcome)
end
in
(launch_provers ()
handle Timeout.TIMEOUT _ => (SH_Timeout, ""))
|> `(fn (outcome, _) =>
(case outcome of
SH_Some _ => (print "QED"; true)
| _ => (print "Sorry"; false)))
end)
end;