src/HOL/Tools/Sledgehammer/sledgehammer_prover_atp.ML

improved lin.arith. for terms involving division

(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_prover_atp.ML
    Author:     Fabian Immler, TU Muenchen
    Author:     Makarius
    Author:     Jasmin Blanchette, TU Muenchen

ATPs as Sledgehammer provers.
*)

signature SLEDGEHAMMER_PROVER_ATP =
sig
  type mode = Sledgehammer_Prover.mode
  type prover = Sledgehammer_Prover.prover

  val atp_dest_dir : string Config.T
  val atp_problem_prefix : string Config.T
  val atp_completish : bool Config.T
  val atp_full_names : bool Config.T

  val is_ho_atp : Proof.context -> string -> bool

  val run_atp : mode -> string -> prover
end;

structure Sledgehammer_Prover_ATP : SLEDGEHAMMER_PROVER_ATP =
struct

open ATP_Util
open ATP_Problem
open ATP_Proof
open ATP_Problem_Generate
open ATP_Proof_Reconstruct
open ATP_Systems
open Sledgehammer_Util
open Sledgehammer_Proof_Methods
open Sledgehammer_Isar
open Sledgehammer_Prover

(* Empty string means create files in Isabelle's temporary files directory. *)
val atp_dest_dir = Attrib.setup_config_string @{binding sledgehammer_atp_dest_dir} (K "")
val atp_problem_prefix =
  Attrib.setup_config_string @{binding sledgehammer_atp_problem_prefix} (K "prob")
val atp_completish = Attrib.setup_config_bool @{binding sledgehammer_atp_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)

fun is_atp_of_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_ho_atp = is_atp_of_format is_format_higher_order

fun choose_type_enc strictness best_type_enc format =
  the_default best_type_enc
  #> type_enc_of_string strictness
  #> adjust_type_enc format

fun has_bound_or_var_of_type pred =
  exists_subterm (fn Var (_, T as Type _) => pred T
                   | Abs (_, T as Type _, _) => pred T
                   | _ => false)

(* 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

(* Facts containing variables of finite types such as "unit" or "bool" or of the form
   "ALL x. x = A | x = B | x = C" are likely to lead to untypable proofs for unsound type
   encodings. *)
fun is_dangerous_prop ctxt =
  transform_elim_prop
  #> (has_bound_or_var_of_type (is_type_surely_finite ctxt) orf is_exhaustive_finite)

fun get_slices slice slices =
  (0 upto length slices - 1) ~~ slices |> not slice ? (List.last #> single)

fun get_facts_of_filter _ [(_, facts)] = facts
  | get_facts_of_filter fact_filter factss =
    (case AList.lookup (op =) factss fact_filter of
      SOME facts => facts
    | NONE => snd (hd factss))

(* For low values of "max_facts", this fudge value ensures that most slices are invoked with a
   nontrivial amount of facts. *)
val max_fact_factor_fudge = 5

val mono_max_privileged_facts = 10

fun suffix_of_mode Auto_Try = "_try"
  | suffix_of_mode Try = "_try"
  | suffix_of_mode Normal = ""
  | suffix_of_mode MaSh = ""
  | suffix_of_mode Auto_Minimize = "_min"
  | suffix_of_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

(* Important messages are important but not so important that users want to see
   them each time. *)
val atp_important_message_keep_quotient = 25

fun run_atp mode name
    (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, compress_isar,
       try0_isar, smt_proofs, slice, minimize, timeout, preplay_timeout, ...})
    minimize_command
    ({comment, state, goal, subgoal, subgoal_count, factss, ...} : prover_problem) =
  let
    val thy = Proof.theory_of state
    val ctxt = Proof.context_of state

    val {exec, arguments, proof_delims, known_failures, prem_role, best_slices, best_max_mono_iters,
      best_max_new_mono_instances, ...} = get_atp thy name ()

    val atp_mode = if Config.get ctxt atp_completish then Sledgehammer_Completish else Sledgehammer
    val (_, hyp_ts, concl_t) = strip_subgoal goal subgoal ctxt
    val (dest_dir, problem_prefix) =
      if overlord then overlord_file_location_of_prover name
      else (Config.get ctxt atp_dest_dir, Config.get ctxt atp_problem_prefix)
    val problem_file_name =
      Path.basic (problem_prefix ^ (if overlord then "" else serial_string ()) ^
                  suffix_of_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 exec = exec ()
    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 (List.last (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
        val num = Scan.many1 Symbol.is_ascii_digit >> (fst o read_int)
        val digit = Scan.one Symbol.is_ascii_digit
        val num3 = digit ::: digit ::: (digit >> single) >> (fst o read_int)
        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 all_slices = best_slices ctxt
        val actual_slices = get_slices slice all_slices

        fun max_facts_of_slices (slices : (real * (slice_spec * string)) list) =
          fold (Integer.max o fst o #1 o fst o snd) slices 0

        val num_actual_slices = length actual_slices
        val max_fact_factor =
          Real.fromInt (case max_facts of NONE => max_facts_of_slices all_slices | SOME max => max)
          / Real.fromInt (max_facts_of_slices (map snd 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 ctxt rths
            |> 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_of_filter effective_fact_filter factss
            val num_facts =
              Real.ceil (max_fact_factor * Real.fromInt best_max_facts) + max_fact_factor_fudge
              |> Integer.min (length facts)
            val strictness = if strict then Strict else Non_Strict
            val type_enc = type_enc |> choose_type_enc strictness best_type_enc format
            val sound = is_type_enc_sound type_enc
            val real_ms = Real.fromInt o Time.toMilliseconds
            val slice_timeout =
              (real_ms time_left
               |> (if slice < num_actual_slices - 1 then
                     curry Real.min (time_frac * real_ms timeout)
                   else
                     I))
              * 0.001
              |> seconds
            val generous_slice_timeout =
              if mode = MaSh then one_day else Time.+ (slice_timeout, atp_timeout_slack)
            val _ =
              if debug then
                quote name ^ " slice #" ^ string_of_int (slice + 1) ^
                " with " ^ string_of_int num_facts ^ " fact" ^
                plural_s num_facts ^ " for " ^ string_of_time slice_timeout ^ "..."
                |> Output.urgent_message
              else
                ()
            val readable_names = not (Config.get ctxt atp_full_names)
            val lam_trans = lam_trans |> the_default best_lam_trans
            val uncurried_aliases = uncurried_aliases |> the_default 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 = isar_proofs |> the_default (mode = Minimize)
            val args =
              arguments ctxt full_proof extra slice_timeout (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_of_atp_problem format ord ord_info
              |> cons ("% " ^ command ^ "\n" ^ (if comment = "" then "" else "% " ^ comment ^ "\n"))
              |> File.write_list prob_path
            val ((output, run_time), (atp_proof, outcome)) =
              TimeLimit.timeLimit 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,
                      extract_tstplike_proof_and_outcome verbose proof_delims known_failures output
                      |>> atp_proof_of_tstplike_proof atp_problem
                      handle UNRECOGNIZED_ATP_PROOF () => ([], SOME ProofIncomplete)))
              handle TimeLimit.TimeOut => (("", 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_of_atp_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 = Time.- (timeout, Timer.checkRealTimer timer) in
              if Time.<= (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, lifted, 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 meths =
            bunch_of_proof_methods (smt_proofs <> SOME false) needs_full_types
              (if atp_proof_prefers_lifting atp_proof then liftingN else hide_lamsN)
        in
          (used_facts,
           Lazy.lazy (fn () =>
             let val used_pairs = used_from |> filter_used_facts false used_facts in
               play_one_line_proof mode verbose preplay_timeout used_pairs state subgoal (hd meths)
                 meths
             end),
           fn preplay =>
              let
                val _ = if verbose then Output.urgent_message "Generating proof text..." else ()
                fun isar_params () =
                  let
                    val metis_type_enc =
                      if is_typed_helper_used_in_atp_proof atp_proof then SOME full_typesN else NONE
                    val metis_lam_trans =
                      if atp_proof_prefers_lifting atp_proof then SOME liftingN else NONE
                    val atp_proof =
                      atp_proof
                      |> termify_atp_proof ctxt pool lifted sym_tab
                      |> introduce_spass_skolem
                      |> factify_atp_proof fact_names hyp_ts concl_t
                  in
                    (verbose, (metis_type_enc, metis_lam_trans), preplay_timeout, compress_isar,
                     try0_isar, minimize <> SOME false, atp_proof, goal)
                  end
                val one_line_params =
                  (preplay, proof_banner mode name, used_facts,
                   choose_minimize_command thy params minimize_command name preplay, subgoal,
                   subgoal_count)
                val num_chained = length (#facts (Proof.goal state))
              in
                proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained one_line_params
              end,
           (if verbose then "\nATP real CPU time: " ^ string_of_time run_time ^ "." else "") ^
           (if important_message <> "" then
              "\n\nImportant message from Dr. Geoff Sutcliffe:\n" ^ important_message
            else
              ""))
        end
      | SOME failure =>
        ([], Lazy.value (Metis_Method (NONE, NONE), Play_Failed),
         fn _ => string_of_atp_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

end;