src/HOL/Tools/Sledgehammer/sledgehammer.ML

implemented 'max_proofs' mechanism

(*  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;