(*  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 locality = Sledgehammer_Filter.locality

  type relevance_fudge = Sledgehammer_Filter.relevance_fudge

  type translated_formula = Sledgehammer_ATP_Translate.translated_formula

  type minimize_command = Sledgehammer_ATP_Reconstruct.minimize_command

  type params =

    {blocking: bool,

     debug: bool,

     verbose: bool,

     overlord: bool,

     provers: string list,

     full_types: bool,

     explicit_apply: bool,

     relevance_thresholds: real * real,

     max_relevant: int option,

     isar_proof: bool,

     isar_shrink_factor: int,

     timeout: Time.time,

     expect: string}

  datatype fact =

    Untranslated of (string * locality) * thm |

    Translated of term * ((string * locality) * translated_formula) option

  type prover_problem =

    {state: Proof.state,

     goal: thm,

     subgoal: int,

     subgoal_count: int,

     facts: fact list}

  type prover_result =

    {outcome: failure option,

     used_facts: (string * locality) list,

     run_time_in_msecs: int option,

     message: string}

  type prover = params -> minimize_command -> prover_problem -> prover_result

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

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

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

  val default_max_relevant_for_prover : Proof.context -> string -> int

  val is_built_in_const_for_prover :

    Proof.context -> string -> string * typ -> term list -> bool

  val atp_relevance_fudge : relevance_fudge

  val smt_relevance_fudge : relevance_fudge

  val relevance_fudge_for_prover : Proof.context -> string -> relevance_fudge

  val dest_dir : string Config.T

  val problem_prefix : string Config.T

  val measure_run_time : bool Config.T

  val available_provers : Proof.context -> unit

  val kill_provers : unit -> unit

  val running_provers : unit -> unit

  val messages : int option -> unit

  val get_prover : Proof.context -> bool -> string -> prover

  val run_prover :

    params -> bool -> (string -> minimize_command) -> bool -> prover_problem

    -> string -> bool * Proof.state

  val setup : theory -> theory

end;

structure Sledgehammer_Provers : SLEDGEHAMMER_PROVERS =

struct

open ATP_Problem

open ATP_Proof

open ATP_Systems

open Metis_Translate

open Sledgehammer_Util

open Sledgehammer_Filter

open Sledgehammer_ATP_Translate

open Sledgehammer_ATP_Reconstruct

(** The Sledgehammer **)

(* Identifier to distinguish Sledgehammer from other tools using

   "Async_Manager". *)

val das_Tool = "Sledgehammer"

fun is_smt_prover ctxt name =

  let val smts = SMT_Solver.available_solvers_of ctxt in

    case try (unprefix remote_prefix) name of

      SOME suffix => member (op =) smts suffix andalso

                     SMT_Solver.is_remotely_available ctxt suffix

    | NONE => member (op =) smts name

  end

fun is_prover_available ctxt name =

  let val thy = ProofContext.theory_of ctxt in

    is_smt_prover ctxt name orelse member (op =) (available_atps thy) name

  end

fun is_prover_installed ctxt name =

  let val thy = ProofContext.theory_of ctxt in

    if is_smt_prover ctxt name then

      String.isPrefix remote_prefix name orelse

      SMT_Solver.is_locally_installed ctxt name

    else

      is_atp_installed thy name

  end

fun available_smt_solvers ctxt =

  let val smts = SMT_Solver.available_solvers_of ctxt in

    smts @ map (prefix remote_prefix)

               (filter (SMT_Solver.is_remotely_available ctxt) smts)

  end

fun default_max_relevant_for_prover ctxt name =

  let val thy = ProofContext.theory_of ctxt in

    if is_smt_prover ctxt name then

      SMT_Solver.default_max_relevant ctxt

          (perhaps (try (unprefix remote_prefix)) name)

    else

      #default_max_relevant (get_atp thy name)

  end

(* These are typically simplified away by "Meson.presimplify". Equality is

   handled specially via "fequal". *)

val atp_irrelevant_consts =

  [@{const_name False}, @{const_name True}, @{const_name If}, @{const_name Let},

   @{const_name HOL.eq}]

fun is_built_in_const_for_prover ctxt name (s, T) args =

  if is_smt_prover ctxt name then SMT_Builtin.is_builtin_ext ctxt (s, T) args

  else member (op =) atp_irrelevant_consts s

(* FUDGE *)

val atp_relevance_fudge =

  {worse_irrel_freq = 100.0,

   higher_order_irrel_weight = 1.05,

   abs_rel_weight = 0.5,

   abs_irrel_weight = 2.0,

   skolem_irrel_weight = 0.75,

   theory_const_rel_weight = 0.5,

   theory_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 = 0.1}

(* FUDGE (FIXME) *)

val smt_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,

   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 available_provers ctxt =

  let

    val thy = ProofContext.theory_of ctxt

    val (remote_provers, local_provers) =

      sort_strings (available_atps thy) @

      sort_strings (available_smt_solvers ctxt)

      |> List.partition (String.isPrefix remote_prefix)

  in

    Output.urgent_message ("Available provers: " ^

                           commas (local_provers @ remote_provers) ^ ".")

  end

fun kill_provers () = Async_Manager.kill_threads das_Tool "provers"

fun running_provers () = Async_Manager.running_threads das_Tool "provers"

val messages = Async_Manager.thread_messages das_Tool "prover"

(** problems, results, ATPs, etc. **)

type params =

  {blocking: bool,

   debug: bool,

   verbose: bool,

   overlord: bool,

   provers: string list,

   full_types: bool,

   explicit_apply: bool,

   relevance_thresholds: real * real,

   max_relevant: int option,

   isar_proof: bool,

   isar_shrink_factor: int,

   timeout: Time.time,

   expect: string}

datatype fact =

  Untranslated of (string * locality) * thm |

  Translated of term * ((string * locality) * translated_formula) option

type prover_problem =

  {state: Proof.state,

   goal: thm,

   subgoal: int,

   subgoal_count: int,

   facts: fact list}

type prover_result =

  {outcome: failure option,

   message: string,

   used_facts: (string * locality) list,

   run_time_in_msecs: int option}

type prover = params -> minimize_command -> prover_problem -> prover_result

(* configuration attributes *)

val (dest_dir, dest_dir_setup) =

  Attrib.config_string "sledgehammer_dest_dir" (K "")

  (* Empty string means create files in Isabelle's temporary files directory. *)

val (problem_prefix, problem_prefix_setup) =

  Attrib.config_string "sledgehammer_problem_prefix" (K "prob")

val (measure_run_time, measure_run_time_setup) =

  Attrib.config_bool "sledgehammer_measure_run_time" (K false)

fun with_path cleanup after f path =

  Exn.capture f path

  |> tap (fn _ => cleanup path)

  |> Exn.release

  |> tap (after path)

fun prover_description ctxt ({blocking, verbose, ...} : params) name num_facts i

                       n goal =

  quote name ^

  (if verbose then

     " with " ^ string_of_int num_facts ^ " fact" ^ plural_s num_facts

   else

     "") ^

  " on " ^ (if n = 1 then "goal" else "subgoal " ^ string_of_int i) ^ ":" ^

  (if blocking then

     ""

   else

     "\n" ^ Syntax.string_of_term ctxt (Thm.term_of (Thm.cprem_of goal i)))

fun proof_banner auto =

  if auto then "Auto Sledgehammer found a proof" else "Try this command"

(* generic TPTP-based ATPs *)

fun dest_Untranslated (Untranslated p) = p

  | dest_Untranslated (Translated _) = raise Fail "dest_Untranslated"

fun translated_fact ctxt (Untranslated p) = translate_fact ctxt p

  | translated_fact _ (Translated p) = p

fun int_opt_add (SOME m) (SOME n) = SOME (m + n)

  | int_opt_add _ _ = NONE

(* Important messages are important but not so important that users want to see

   them each time. *)

val important_message_keep_factor = 0.1

fun run_atp auto atp_name

        {exec, required_execs, arguments, has_incomplete_mode, proof_delims,

         known_failures, explicit_forall, use_conjecture_for_hypotheses, ...}

        ({debug, verbose, overlord, full_types, explicit_apply, isar_proof,

          isar_shrink_factor, timeout, ...} : params)

        minimize_command ({state, goal, subgoal, facts, ...} : prover_problem) =

  let

    val ctxt = Proof.context_of state

    val (_, hyp_ts, concl_t) = strip_subgoal goal subgoal

    val facts =

      facts |> map (translated_fact ctxt)

    val dest_dir = if overlord then getenv "ISABELLE_HOME_USER"

                   else Config.get ctxt dest_dir

    val problem_prefix = Config.get ctxt problem_prefix

    val problem_file_name =

      Path.basic ((if overlord then "prob_" ^ atp_name

                   else problem_prefix ^ serial_string ())

                  ^ "_" ^ string_of_int subgoal)

    val problem_path_name =

      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 measure_run_time = verbose orelse Config.get ctxt measure_run_time

    val command = Path.explode (getenv (fst exec) ^ "/" ^ snd exec)

    (* write out problem file and call ATP *)

    fun command_line complete timeout probfile =

      let

        val core = File.shell_path command ^ " " ^ arguments complete timeout ^

                   " " ^ File.shell_path probfile

      in

        (if measure_run_time then "TIMEFORMAT='%3R'; { time " ^ core ^ " ; }"

         else "exec " ^ core) ^ " 2>&1"

      end

    fun split_time s =

      let

        val split = String.tokens (fn c => str c = "\n");

        val (output, t) = s |> split |> split_last |> apfst 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 = Scan.read Symbol.stopper time o raw_explode

      in (output, as_time t) end;

    fun run_on probfile =

      case filter (curry (op =) "" o getenv o fst) (exec :: required_execs) of

        (home_var, _) :: _ =>

        error ("The environment variable " ^ quote home_var ^ " is not set.")

      | [] =>

        if File.exists command then

          let

            fun run complete timeout =

              let

                val command = command_line complete timeout probfile

                val ((output, msecs), res_code) =

                  bash_output command

                  |>> (if overlord then

                         prefix ("% " ^ command ^ "\n% " ^ timestamp () ^ "\n")

                       else

                         I)

                  |>> (if measure_run_time then split_time else rpair NONE)

                val (tstplike_proof, outcome) =

                  extract_tstplike_proof_and_outcome complete res_code

                      proof_delims known_failures output

              in (output, msecs, tstplike_proof, outcome) end

            val readable_names = debug andalso overlord

            val (atp_problem, pool, conjecture_offset, fact_names) =

              prepare_atp_problem ctxt readable_names explicit_forall full_types

                                  explicit_apply hyp_ts concl_t facts

            val ss = tptp_strings_for_atp_problem use_conjecture_for_hypotheses

                                                  atp_problem

            val _ = File.write_list probfile ss

            val conjecture_shape =

              conjecture_offset + 1 upto conjecture_offset + length hyp_ts + 1

              |> map single

            val run_twice = has_incomplete_mode andalso not auto

            val timer = Timer.startRealTimer ()

            val result =

              run false (if run_twice then

                           Time.fromMilliseconds

                                         (2 * Time.toMilliseconds timeout div 3)

                         else

                           timeout)

              |> run_twice

                 ? (fn (_, msecs0, _, SOME _) =>

                       run true (Time.- (timeout, Timer.checkRealTimer timer))

                       |> (fn (output, msecs, tstplike_proof, outcome) =>

                              (output, int_opt_add msecs0 msecs, tstplike_proof,

                               outcome))

                     | result => result)

          in ((pool, conjecture_shape, fact_names), result) end

        else

          error ("Bad executable: " ^ Path.implode command ^ ".")

    (* If the problem file has not been exported, remove it; otherwise, export

       the proof file too. *)

    fun cleanup probfile =

      if dest_dir = "" then try File.rm probfile else NONE

    fun export probfile (_, (output, _, _, _)) =

      if dest_dir = "" then

        ()

      else

        File.write (Path.explode (Path.implode probfile ^ "_proof")) output

    val ((pool, conjecture_shape, fact_names),

         (output, msecs, tstplike_proof, outcome)) =

      with_path cleanup export run_on problem_path_name

    val (conjecture_shape, fact_names) =

      repair_conjecture_shape_and_fact_names output conjecture_shape fact_names

    val important_message =

      if not auto andalso random () <= important_message_keep_factor then

        extract_important_message output

      else

        ""

    val (message, used_facts) =

      case outcome of

        NONE =>

        proof_text isar_proof

            (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)

            (proof_banner auto, full_types, minimize_command, tstplike_proof,

             fact_names, goal, subgoal)

        |>> (fn message =>

                message ^

                (if verbose then

                   "\nATP real CPU time: " ^

                   string_from_time (Time.fromMilliseconds (the msecs)) ^ "."

                 else

                   "") ^

                (if important_message <> "" then

                   "\n\nImportant message from Dr. Geoff Sutcliffe:\n" ^

                   important_message

                 else

                   ""))

      | SOME failure => (string_for_failure "ATP" failure, [])

  in

    {outcome = outcome, message = message, used_facts = used_facts,

     run_time_in_msecs = msecs}

  end

(* "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 =

  [(22, CantConnect),

   (127, NoPerl),

   (2, NoLibwwwPerl)]

val z3_failures =

  [(103, MalformedInput),

   (110, MalformedInput)]

val unix_failures =

  [(139, Crashed)]

val smt_failures = remote_smt_failures @ z3_failures @ unix_failures

fun failure_from_smt_failure (SMT_Failure.Counterexample _) = Unprovable

  | 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)

  | failure_from_smt_failure SMT_Failure.Out_Of_Memory = OutOfResources

  | failure_from_smt_failure _ = UnknownError

(* FUDGE *)

val smt_max_iter = 8

val smt_iter_fact_divisor = 2

val smt_iter_min_msecs = 5000

val smt_iter_timeout_divisor = 2

val smt_monomorph_limit = 4

fun smt_filter_loop ({verbose, timeout, ...} : params) remote state i =

  let

    val ctxt = Proof.context_of state

    fun iter timeout iter_num outcome0 msecs_so_far facts =

      let

        val timer = Timer.startRealTimer ()

        val ms = timeout |> Time.toMilliseconds

        val iter_timeout =

          if iter_num < smt_max_iter then

            Int.min (ms, Int.max (smt_iter_min_msecs,

                                  ms div smt_iter_timeout_divisor))

            |> Time.fromMilliseconds

          else

            timeout

        val num_facts = length facts

        val _ =

          if verbose then

            "SMT iteration with " ^ string_of_int num_facts ^ " fact" ^

            plural_s num_facts ^ " for " ^ string_from_time iter_timeout ^ "..."

            |> Output.urgent_message

          else

            ()

        val {outcome, used_facts, run_time_in_msecs} =

          SMT_Solver.smt_filter remote iter_timeout state facts i

        val _ =

          if verbose andalso is_some outcome then

            "SMT outcome: " ^ SMT_Failure.string_of_failure ctxt (the outcome)

            |> Output.urgent_message

          else

            ()

        val outcome0 = if is_none outcome0 then SOME outcome else outcome0

        val msecs_so_far = int_opt_add run_time_in_msecs msecs_so_far

        val too_many_facts_perhaps =

          case outcome of

            NONE => false

          | SOME (SMT_Failure.Counterexample _) => false

          | SOME SMT_Failure.Time_Out => iter_timeout <> timeout

          | SOME (SMT_Failure.Abnormal_Termination code) =>

            (if verbose then

               "The SMT solver invoked with " ^ string_of_int num_facts ^

               " fact" ^ plural_s num_facts ^ " terminated abnormally with \

               \exit code " ^ string_of_int code ^ "."

               |> warning

             else

               ();

             true (* kind of *))

          | SOME SMT_Failure.Out_Of_Memory => true

          | SOME _ => true

        val timeout = Time.- (timeout, Timer.checkRealTimer timer)

      in

        if too_many_facts_perhaps andalso iter_num < smt_max_iter andalso

           num_facts > 0 andalso Time.> (timeout, Time.zeroTime) then

          let val facts = take (num_facts div smt_iter_fact_divisor) facts in

            iter timeout (iter_num + 1) outcome0 msecs_so_far facts

          end

        else

          {outcome = if is_none outcome then NONE else the outcome0,

           used_facts = used_facts, run_time_in_msecs = msecs_so_far}

      end

  in iter timeout 1 NONE (SOME 0) end

(* taken from "Mirabelle" and generalized *)

fun can_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

    case try (TimeLimit.timeLimit timeout (Seq.pull o full_tac)) goal of

      SOME (SOME _) => true

    | _ => false

  end

val smt_metis_timeout = seconds 0.5

fun can_apply_metis debug state i ths =

  can_apply smt_metis_timeout

            (Config.put Metis_Tactics.verbose debug

             #> (fn ctxt => Metis_Tactics.metis_tac ctxt ths)) state i

fun run_smt_solver auto name (params as {debug, ...}) minimize_command

        ({state, subgoal, subgoal_count, facts, ...} : prover_problem) =

  let

    val (remote, suffix) =

      case try (unprefix remote_prefix) name of

        SOME suffix => (true, suffix)

      | NONE => (false, name)

    val repair_context =

      Context.proof_map (SMT_Config.select_solver suffix)

      #> Config.put SMT_Config.verbose debug

      #> Config.put SMT_Config.monomorph_limit smt_monomorph_limit

    val state = state |> Proof.map_context repair_context

    val thy = Proof.theory_of state

    val get_fact = Option.map (apsnd (Thm.transfer thy)) o try dest_Untranslated

    val facts = facts |> map_filter get_fact

    val {outcome, used_facts, run_time_in_msecs} =

      smt_filter_loop params remote state subgoal facts

    val (chained_lemmas, other_lemmas) = split_used_facts (map fst used_facts)

    val outcome = outcome |> Option.map failure_from_smt_failure

    val message =

      case outcome of

        NONE =>

        let

          val method =

            if can_apply_metis debug state subgoal (map snd used_facts) then

              "metis"

            else

              "smt"

        in

          try_command_line (proof_banner auto)

                           (apply_on_subgoal subgoal subgoal_count ^

                            command_call method (map fst other_lemmas)) ^

          minimize_line minimize_command

                        (map fst (other_lemmas @ chained_lemmas))

        end

      | SOME failure => string_for_failure "SMT solver" failure

  in

    {outcome = outcome, used_facts = map fst used_facts,

     run_time_in_msecs = run_time_in_msecs, message = message}

  end

fun get_prover ctxt auto name =

  let val thy = ProofContext.theory_of ctxt in

    if is_smt_prover ctxt name then

      run_smt_solver auto name

    else if member (op =) (available_atps thy) name then

      run_atp auto name (get_atp thy name)

    else

      error ("No such prover: " ^ name ^ ".")

  end

fun run_prover (params as {blocking, debug, max_relevant, timeout, expect, ...})

               auto minimize_command only

               {state, goal, subgoal, subgoal_count, facts} name =

  let

    val ctxt = Proof.context_of state

    val birth_time = Time.now ()

    val death_time = Time.+ (birth_time, timeout)

    val max_relevant =

      the_default (default_max_relevant_for_prover ctxt name) max_relevant

    val num_facts = length facts |> not only ? Integer.min max_relevant

    val desc =

      prover_description ctxt params name num_facts subgoal subgoal_count goal

    val prover = get_prover ctxt auto name

    val problem =

      {state = state, goal = goal, subgoal = subgoal,

       subgoal_count = subgoal_count, facts = take num_facts facts}

    fun go () =

      let

        fun really_go () =

          prover params (minimize_command name) problem

          |> (fn {outcome, message, ...} =>

                 (if is_some outcome then "none" else "some", message))

        val (outcome_code, message) =

          if debug then

            really_go ()

          else

            (really_go ()

             handle ERROR message => ("unknown", "Error: " ^ message ^ "\n")

                  | exn =>

                    if Exn.is_interrupt exn then

                      reraise exn

                    else

                      ("unknown", "Internal error:\n" ^

                                  ML_Compiler.exn_message exn ^ "\n"))

        val _ =

          if expect = "" orelse outcome_code = expect then

            ()

          else if blocking then

            error ("Unexpected outcome: " ^ quote outcome_code ^ ".")

          else

            warning ("Unexpected outcome: " ^ quote outcome_code ^ ".");

      in (outcome_code = "some", message) end

  in

    if auto then

      let val (success, message) = TimeLimit.timeLimit timeout go () in

        (success, state |> success ? Proof.goal_message (fn () =>

             Pretty.chunks [Pretty.str "", Pretty.mark Markup.hilite

                 (Pretty.str message)]))

      end

    else if blocking then

      let val (success, message) = TimeLimit.timeLimit timeout go () in

        List.app Output.urgent_message

                 (Async_Manager.break_into_chunks [desc ^ "\n" ^ message]);

        (success, state)

      end

    else

      (Async_Manager.launch das_Tool birth_time death_time desc (snd o go);

       (false, state))

  end

val setup =

  dest_dir_setup

  #> problem_prefix_setup

  #> measure_run_time_setup

end;