(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_filter_mash.ML

    Author:     Jasmin Blanchette, TU Muenchen

Sledgehammer's machine-learning-based relevance filter (MaSh).

*)

signature SLEDGEHAMMER_FILTER_MASH =

sig

  type status = ATP_Problem_Generate.status

  type stature = ATP_Problem_Generate.stature

  type fact = Sledgehammer_Fact.fact

  type fact_override = Sledgehammer_Fact.fact_override

  type params = Sledgehammer_Provers.params

  type relevance_fudge = Sledgehammer_Provers.relevance_fudge

  type prover_result = Sledgehammer_Provers.prover_result

  val escape_meta : string -> string

  val escape_metas : string list -> string

  val all_non_tautological_facts_of :

    theory -> status Termtab.table -> fact list

  val theory_ord : theory * theory -> order

  val thm_ord : thm * thm -> order

  val thy_facts_from_thms : ('a * thm) list -> string list Symtab.table

  val has_thy : theory -> thm -> bool

  val parent_facts : theory -> string list Symtab.table -> string list

  val features_of : theory -> status -> term list -> string list

  val isabelle_dependencies_of : string list -> thm -> string list

  val goal_of_thm : theory -> thm -> thm

  val run_prover : Proof.context -> params -> fact list -> thm -> prover_result

  val generate_accessibility : Proof.context -> theory -> bool -> string -> unit

  val generate_features : Proof.context -> theory -> bool -> string -> unit

  val generate_isa_dependencies :

    Proof.context -> theory -> bool -> string -> unit

  val generate_atp_dependencies :

    Proof.context -> params -> theory -> bool -> string -> unit

  val mash_RESET : unit -> unit

  val mash_ADD : string -> string list -> string list -> string list -> unit

  val mash_DEL : string list -> string list -> unit

  val mash_SUGGEST : string list -> string list -> string list

  val mash_reset : unit -> unit

  val mash_can_suggest_facts : unit -> bool

  val mash_suggest_facts :

    Proof.context -> params -> string -> int -> term list -> term -> fact list

    -> fact list * fact list

  val mash_can_learn_thy : theory -> bool

  val mash_learn_thy : theory -> real -> unit

  val mash_learn_proof : theory -> term -> thm list -> unit

  val relevant_facts :

    Proof.context -> params -> string -> int -> fact_override -> term list

    -> term -> fact list -> fact list

end;

structure Sledgehammer_Filter_MaSh : SLEDGEHAMMER_FILTER_MASH =

struct

open ATP_Util

open ATP_Problem_Generate

open Sledgehammer_Util

open Sledgehammer_Fact

open Sledgehammer_Filter_Iter

open Sledgehammer_Provers

val mash_dir = "mash"

val model_file = "model"

val state_file = "state"

fun mk_path file =

  getenv "ISABELLE_HOME_USER" ^ "/" ^ mash_dir ^ "/" ^ file

  |> Path.explode

val fresh_fact_prefix = Long_Name.separator

(*** Isabelle helpers ***)

fun escape_meta_char c =

  if Char.isAlphaNum c orelse c = #"_" orelse c = #"." orelse c = #"(" orelse

     c = #")" orelse c = #"," then

    String.str c

  else

    (* fixed width, in case more digits follow *)

    "\\" ^ stringN_of_int 3 (Char.ord c)

val escape_meta = String.translate escape_meta_char

val escape_metas = map escape_meta #> space_implode " "

val thy_feature_prefix = "y_"

val thy_feature_name_of = prefix thy_feature_prefix

val const_name_of = prefix const_prefix

val type_name_of = prefix type_const_prefix

val class_name_of = prefix class_prefix

local

fun has_bool @{typ bool} = true

  | has_bool (Type (_, Ts)) = exists has_bool Ts

  | has_bool _ = false

fun has_fun (Type (@{type_name fun}, _)) = true

  | has_fun (Type (_, Ts)) = exists has_fun Ts

  | has_fun _ = false

val is_conn = member (op =)

  [@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},

   @{const_name HOL.implies}, @{const_name Not},

   @{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex},

   @{const_name HOL.eq}]

val has_bool_arg_const =

  exists_Const (fn (c, T) =>

                   not (is_conn c) andalso exists has_bool (binder_types T))

fun higher_inst_const thy (c, T) =

  case binder_types T of

    [] => false

  | Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts

val binders = [@{const_name All}, @{const_name Ex}]

in

fun is_fo_term thy t =

  let

    val t =

      t |> Envir.beta_eta_contract

        |> transform_elim_prop

        |> Object_Logic.atomize_term thy

  in

    Term.is_first_order binders t andalso

    not (exists_subterm (fn Var (_, T) => has_bool T orelse has_fun T

                          | _ => false) t orelse

         has_bool_arg_const t orelse exists_Const (higher_inst_const thy) t)

  end

end

fun interesting_terms_types_and_classes term_max_depth type_max_depth ts =

  let

    val bad_types = [@{type_name prop}, @{type_name bool}, @{type_name fun}]

    val bad_consts = atp_widely_irrelevant_consts

    fun do_add_type (Type (s, Ts)) =

        (not (member (op =) bad_types s) ? insert (op =) (type_name_of s))

        #> fold do_add_type Ts

      | do_add_type (TFree (_, S)) = union (op =) (map class_name_of S)

      | do_add_type (TVar (_, S)) = union (op =) (map class_name_of S)

    fun add_type T = type_max_depth >= 0 ? do_add_type T

    fun mk_app s args =

      if member (op <>) args "" then s ^ "(" ^ space_implode "," args ^ ")"

      else s

    fun patternify ~1 _ = ""

      | patternify depth t =

        case strip_comb t of

          (Const (s, _), args) =>

          mk_app (const_name_of s) (map (patternify (depth - 1)) args)

        | _ => ""

    fun add_term_patterns ~1 _ = I

      | add_term_patterns depth t =

        insert (op =) (patternify depth t)

        #> add_term_patterns (depth - 1) t

    val add_term = add_term_patterns term_max_depth

    fun add_patterns t =

      let val (head, args) = strip_comb t in

        (case head of

           Const (s, T) =>

           not (member (op =) bad_consts s) ? (add_term t #> add_type T)

         | Free (_, T) => add_type T

         | Var (_, T) => add_type T

         | Abs (_, T, body) => add_type T #> add_patterns body

         | _ => I)

        #> fold add_patterns args

      end

  in [] |> fold add_patterns ts |> sort string_ord end

fun is_likely_tautology th =

  null (interesting_terms_types_and_classes 0 ~1 [prop_of th]) andalso

  not (Thm.eq_thm_prop (@{thm ext}, th))

fun is_too_meta thy th =

  fastype_of (Object_Logic.atomize_term thy (prop_of th)) <> @{typ bool}

fun all_non_tautological_facts_of thy css_table =

  all_facts_of thy css_table

  |> filter_out ((is_likely_tautology orf is_too_meta thy) o snd)

fun theory_ord p =

  if Theory.eq_thy p then EQUAL

  else if Theory.subthy p then LESS

  else if Theory.subthy (swap p) then GREATER

  else EQUAL

val thm_ord = theory_ord o pairself theory_of_thm

(* ### FIXME: optimize *)

fun thy_facts_from_thms ths =

  ths |> map (snd #> `(theory_of_thm #> Context.theory_name))

      |> AList.group (op =)

      |> sort (int_ord o pairself (length o Theory.ancestors_of o theory_of_thm

                                   o hd o snd))

      |> map (apsnd (sort (rev_order o thm_ord) #> map Thm.get_name_hint))

      |> Symtab.make

fun has_thy thy th =

  Context.theory_name thy = Context.theory_name (theory_of_thm th)

fun parent_facts thy thy_facts =

  let

    fun add_last thy =

      case Symtab.lookup thy_facts (Context.theory_name thy) of

        SOME (last_fact :: _) => insert (op =) last_fact

      | _ => add_parent thy

    and add_parent thy = fold add_last (Theory.parents_of thy)

  in add_parent thy [] end

fun is_exists (s, _) = (s = @{const_name Ex} orelse s = @{const_name Ex1})

val term_max_depth = 1

val type_max_depth = 1

(* TODO: Generate type classes for types? *)

fun features_of thy status ts =

  thy_feature_name_of (Context.theory_name thy) ::

  interesting_terms_types_and_classes term_max_depth type_max_depth ts

  |> exists (not o is_lambda_free) ts ? cons "lambdas"

  |> exists (exists_Const is_exists) ts ? cons "skolems"

  |> exists (not o is_fo_term thy) ts ? cons "ho"

  |> (case status of

        General => I

      | Induction => cons "induction"

      | Intro => cons "intro"

      | Inductive => cons "inductive"

      | Elim => cons "elim"

      | Simp => cons "simp"

      | Def => cons "def")

fun isabelle_dependencies_of all_facts =

  thms_in_proof (SOME all_facts) #> sort string_ord

val freezeT = Type.legacy_freeze_type

fun freeze (t $ u) = freeze t $ freeze u

  | freeze (Abs (s, T, t)) = Abs (s, freezeT T, freeze t)

  | freeze (Var ((s, _), T)) = Free (s, freezeT T)

  | freeze (Const (s, T)) = Const (s, freezeT T)

  | freeze (Free (s, T)) = Free (s, freezeT T)

  | freeze t = t

fun goal_of_thm thy = prop_of #> freeze #> cterm_of thy #> Goal.init

fun run_prover ctxt (params as {provers, ...}) facts goal =

  let

    val problem =

      {state = Proof.init ctxt, goal = goal, subgoal = 1, subgoal_count = 1,

       facts = facts |> map (apfst (apfst (fn name => name ())))

                     |> map Sledgehammer_Provers.Untranslated_Fact}

    val prover =

      Sledgehammer_Minimize.get_minimizing_prover ctxt

          Sledgehammer_Provers.Normal (hd provers)

  in prover params (K (K (K ""))) problem end

(* ###

fun compute_accessibility thy thy_facts =

  let

    fun add_facts (f :: fs) prevs = (f, prevs) :: add_facts fs [th]

    fun add_thy facts =

      let

        val thy = theory_of_thm (hd facts)

        val parents = parent_facts thy_facts thy

      in add_thms facts parents end

  in fold (add_thy o snd) thy_facts end

*)

fun accessibility_of thy thy_facts =

  case Symtab.lookup thy_facts (Context.theory_name thy) of

    SOME (fact :: _) => [fact]

  | _ => parent_facts thy thy_facts

fun theory_of_fact thy fact =

  Context.this_theory thy (hd (Long_Name.explode fact))

fun generate_accessibility ctxt thy include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    fun do_fact fact prevs =

      let

        val s = escape_meta fact ^ ": " ^ escape_metas prevs ^ "\n"

        val _ = File.append path s

      in [fact] end

    val thy_facts =

      all_non_tautological_facts_of thy Termtab.empty

      |> not include_thy ? filter_out (has_thy thy o snd)

      |> thy_facts_from_thms

    fun do_thy facts =

      let

        val thy = theory_of_fact thy (hd facts)

        val parents = parent_facts thy thy_facts

      in fold do_fact facts parents; () end

  in Symtab.fold (fn (_, facts) => K (do_thy facts)) thy_facts () end

fun generate_features ctxt thy include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val css_table = clasimpset_rule_table_of ctxt

    val facts =

      all_non_tautological_facts_of thy css_table

      |> not include_thy ? filter_out (has_thy thy o snd)

    fun do_fact ((_, (_, status)), th) =

      let

        val name = Thm.get_name_hint th

        val feats = features_of (theory_of_thm th) status [prop_of th]

        val s = escape_meta name ^ ": " ^ escape_metas feats ^ "\n"

      in File.append path s end

  in List.app do_fact facts end

fun generate_isa_dependencies ctxt thy include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val ths =

      all_non_tautological_facts_of thy Termtab.empty

      |> not include_thy ? filter_out (has_thy thy o snd)

      |> map snd

    val all_names = ths |> map Thm.get_name_hint

    fun do_thm th =

      let

        val name = Thm.get_name_hint th

        val deps = isabelle_dependencies_of all_names th

        val s = escape_meta name ^ ": " ^ escape_metas deps ^ "\n"

      in File.append path s end

  in List.app do_thm ths end

fun generate_atp_dependencies ctxt (params as {provers, max_facts, ...}) thy

                              include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val facts =

      all_non_tautological_facts_of thy Termtab.empty

      |> not include_thy ? filter_out (has_thy thy o snd)

    val ths = facts |> map snd

    val all_names = ths |> map Thm.get_name_hint

    fun is_dep dep (_, th) = Thm.get_name_hint th = dep

    fun add_isa_dep facts dep accum =

      if exists (is_dep dep) accum then

        accum

      else case find_first (is_dep dep) facts of

        SOME ((name, status), th) => accum @ [((name, status), th)]

      | NONE => accum (* shouldn't happen *)

    fun fix_name ((_, stature), th) =

      ((fn () => th |> Thm.get_name_hint, stature), th)

    fun do_thm th =

      let

        val name = Thm.get_name_hint th

        val goal = goal_of_thm thy th

        val (_, hyp_ts, concl_t) = ATP_Util.strip_subgoal ctxt goal 1

        val deps =

          case isabelle_dependencies_of all_names th of

            [] => []

          | isa_dep as [_] => isa_dep (* can hardly beat that *)

          | isa_deps =>

            let

              val facts =

                facts |> filter (fn (_, th') => thm_ord (th', th) = LESS)

              val facts =

                facts |> iterative_relevant_facts ctxt params (hd provers)

                             (the max_facts) NONE hyp_ts concl_t

                      |> fold (add_isa_dep facts) isa_deps

                      |> map fix_name

            in

              case run_prover ctxt params facts goal of

                {outcome = NONE, used_facts, ...} =>

                used_facts |> map fst |> sort string_ord

              | _ => isa_deps

            end

        val s = escape_meta name ^ ": " ^ escape_metas deps ^ "\n"

      in File.append path s end

  in List.app do_thm ths end

(*** Low-level communication with MaSh ***)

fun mash_RESET () = (warning "MaSh RESET"; File.rm (mk_path model_file))

fun mash_ADD fact access feats deps =

  warning ("MaSh ADD " ^ fact ^ ": " ^ escape_metas access ^ "; " ^

           escape_metas feats ^ "; " ^ escape_metas deps)

fun mash_DEL facts feats =

  warning ("MaSh DEL " ^ escape_metas facts ^ "; " ^ escape_metas feats)

fun mash_SUGGEST access feats =

  (warning ("MaSh SUGGEST " ^ escape_metas access ^ "; " ^ escape_metas feats);

   [])

(*** High-level communication with MaSh ***)

type mash_state =

  {fresh : int,

   completed_thys : unit Symtab.table,

   thy_facts : string list Symtab.table}

val mash_zero =

  {fresh = 0,

   completed_thys = Symtab.empty,

   thy_facts = Symtab.empty}

local

fun mash_load (state as (true, _)) = state

  | mash_load _ =

    let

      val path = mk_path state_file

      val _ = Isabelle_System.mkdir (path |> Path.dir)

    in

      (true,

       case try File.read_lines path of

         SOME (fresh_line :: comp_line :: facts_lines) =>

         let

           fun comp_thys_of_line comp_line =

             Symtab.make (comp_line |> space_explode " " |> map (rpair ()))

           fun add_facts_line line =

             case space_explode " " line of

               thy :: facts => Symtab.update_new (thy, facts)

             | _ => I (* shouldn't happen *)

         in

           {fresh = Int.fromString fresh_line |> the_default 0,

            completed_thys = comp_thys_of_line comp_line,

            thy_facts = fold add_facts_line facts_lines Symtab.empty}

         end

       | _ => mash_zero)

    end

fun mash_save ({fresh, completed_thys, thy_facts} : mash_state) =

  let

    val path = mk_path state_file

    val comp_line = (completed_thys |> Symtab.keys |> escape_metas) ^ "\n"

    fun fact_line_for (thy, facts) = escape_metas (thy :: facts) ^ "\n"

  in

    File.write path (string_of_int fresh ^ "\n" ^ comp_line);

    Symtab.fold (fn thy_fact => fn () =>

                    File.append path (fact_line_for thy_fact)) thy_facts

  end

val global_state =

  Synchronized.var "Sledgehammer_Filter_MaSh.global_state" (false, mash_zero)

in

fun mash_change f =

  Synchronized.change global_state (mash_load ##> (f #> tap mash_save))

fun mash_peek f = Synchronized.change global_state (mash_load ##> tap f)

fun mash_value () = Synchronized.change_result global_state (mash_load #> `snd)

fun mash_reset () =

  Synchronized.change global_state (fn _ =>

      (mash_RESET (); File.rm (mk_path state_file); (true, mash_zero)))

end

fun mash_can_suggest_facts () =

  not (Symtab.is_empty (#thy_facts (mash_value ())))

fun mash_suggest_facts ctxt params prover max_facts hyp_ts concl_t facts =

  let

    val thy = Proof_Context.theory_of ctxt

    val access = accessibility_of thy (#thy_facts (mash_value ()))

    val feats = features_of thy General (concl_t :: hyp_ts)

    val suggs = mash_SUGGEST access feats

  in (facts, []) end

fun mash_can_learn_thy thy =

  not (Symtab.defined (#completed_thys (mash_value ()))

                      (Context.theory_name thy))

fun mash_learn_thy thy timeout = ()

(* ### *)

fun mash_learn_proof thy t ths =

  mash_change (fn {fresh, completed_thys, thy_facts} =>

    let

      val fact = fresh_fact_prefix ^ string_of_int fresh

      val access = accessibility_of thy thy_facts

      val feats = features_of thy General [t]

      val deps = ths |> map Thm.get_name_hint

    in

      mash_ADD fact access feats deps;

      {fresh = fresh + 1, completed_thys = completed_thys,

       thy_facts = thy_facts}

    end)

fun relevant_facts ctxt params prover max_facts

        ({add, only, ...} : fact_override) hyp_ts concl_t facts =

  if only then

    facts

  else if max_facts <= 0 then

    []

  else

    let

      val add_ths = Attrib.eval_thms ctxt add

      fun prepend_facts ths accepts =

        ((facts |> filter (member Thm.eq_thm_prop ths o snd)) @

         (accepts |> filter_out (member Thm.eq_thm_prop ths o snd)))

        |> take max_facts

      val iter_facts =

        iterative_relevant_facts ctxt params prover max_facts NONE hyp_ts

                                 concl_t facts

      val (mash_facts, mash_rejected) =

        mash_suggest_facts ctxt params prover max_facts hyp_ts concl_t facts

      val mesh_facts = iter_facts (* ### *)

    in

      mesh_facts

      |> not (null add_ths) ? prepend_facts add_ths

    end

end;