(*  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 params = Sledgehammer_Provers.params

  type relevance_override = Sledgehammer_Fact.relevance_override

  type relevance_fudge = Sledgehammer_Provers.relevance_fudge

  type prover_result = Sledgehammer_Provers.prover_result

  val fact_name_of : string -> string

  val all_non_tautological_facts_of :

    theory -> (((unit -> string) * stature) * thm) list

  val theory_ord : theory * theory -> order

  val thm_ord : thm * thm -> order

  val thms_by_thy : ('a * thm) list -> (string * thm list) list

  val has_thy : theory -> thm -> bool

  val parent_thms : (string * thm list) list -> theory -> string list

  val features_of : theory -> status * thm -> string list

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

  val goal_of_thm : theory -> thm -> thm

  val iter_facts :

    Proof.context -> params -> int -> thm

    -> (((unit -> string) * stature) * thm) list

    -> ((string * stature) * thm) list

  val run_prover :

    Proof.context -> params -> ((string * stature) * thm) list -> thm

    -> prover_result

  val generate_accessibility : theory -> bool -> string -> unit

  val generate_features : theory -> bool -> string -> unit

  val generate_isa_dependencies : theory -> bool -> string -> unit

  val generate_atp_dependencies :

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

  val reset : unit -> unit

  val can_suggest_facts : unit -> bool

(* ###  val suggest_facts : ... *)

  val can_learn_thy : theory -> bool

  val learn_thy : theory -> real -> unit

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

  val relevant_facts :

    Proof.context -> params -> string -> int -> relevance_override -> thm list

    -> term list -> term -> (((unit -> string) * stature) * thm) list

    -> ((string * stature) * thm) 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

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

fun mash_reset () =

  tracing "MaSh RESET"

fun mash_add fact (access, feats, deps) =

  tracing ("MaSh ADD " ^ fact ^ ": " ^ space_implode " " access ^ "; " ^

           space_implode " " feats ^ "; " ^ space_implode " " deps)

fun mash_del fact =

  tracing ("MaSh DEL " ^ fact)

fun mash_suggest fact (access, feats) =

  tracing ("MaSh SUGGEST " ^ fact ^ ": " ^ space_implode " " access ^ "; " ^

           space_implode " " feats)

(*** Isabelle helpers ***)

val fact_name_of = prefix fact_prefix o ascii_of

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 thy_prefix = "y_"

val fact_name_of = escape_meta

val thy_name_of = prefix thy_prefix o escape_meta

val const_name_of = prefix const_prefix o escape_meta

val type_name_of = prefix type_const_prefix o escape_meta

val class_name_of = prefix class_prefix o escape_meta

val thy_name_of_thm = theory_of_thm #> Context.theory_name

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 t =

  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 [] |> add_patterns t |> 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 =

  all_facts_of thy

  |> 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

fun thms_by_thy ths =

  ths |> map (snd #> `thy_name_of_thm)

      |> AList.group (op =)

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

                                   o hd o snd))

      |> map (apsnd (sort thm_ord))

fun has_thy thy th = (Context.theory_name thy = thy_name_of_thm th)

fun parent_thms thy_ths thy =

  Theory.parents_of thy

  |> map Context.theory_name

  |> map_filter (AList.lookup (op =) thy_ths)

  |> map List.last

  |> map (fact_name_of o Thm.get_name_hint)

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

val max_depth = 1

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

fun features_of thy (status, th) =

  let val t = Thm.prop_of th in

    thy_name_of (thy_name_of_thm th) ::

    interesting_terms_types_and_classes max_depth max_depth t

    |> not (has_no_lambdas t) ? cons "lambdas"

    |> exists_Const is_exists t ? cons "skolems"

    |> not (is_fo_term thy t) ? 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")

  end

fun isabelle_dependencies_of all_facts =

  thms_in_proof (SOME all_facts)

  #> map fact_name_of #> 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 iter_facts ctxt (params as {provers, ...}) max_relevant goal =

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

    iterative_relevant_facts ctxt params (hd provers) max_relevant NONE

                             no_relevance_override [] hyp_ts concl_t

  end

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 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 generate_accessibility thy include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    fun do_thm th prevs =

      let

        val s = th ^ ": " ^ space_implode " " prevs ^ "\n"

        val _ = File.append path s

      in [th] end

    val thy_ths =

      all_non_tautological_facts_of thy

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

      |> thms_by_thy

    fun do_thy ths =

      let

        val thy = theory_of_thm (hd ths)

        val parents = parent_thms thy_ths thy

        val ths = ths |> map (fact_name_of o Thm.get_name_hint)

      in fold do_thm ths parents; () end

  in List.app (do_thy o snd) thy_ths end

fun generate_features thy include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val facts =

      all_non_tautological_facts_of thy

      |> 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 thy (status, th)

        val s = fact_name_of name ^ ": " ^ space_implode " " feats ^ "\n"

      in File.append path s end

  in List.app do_fact facts end

fun generate_isa_dependencies thy include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val ths =

      all_non_tautological_facts_of thy

      |> 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 = fact_name_of name ^ ": " ^ space_implode " " deps ^ "\n"

      in File.append path s end

  in List.app do_thm ths end

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

                              include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val facts =

      all_non_tautological_facts_of thy

      |> 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) = fact_name_of (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) =

      ((th |> Thm.get_name_hint |> fact_name_of, stature), th)

    fun do_thm th =

      let

        val name = Thm.get_name_hint th

        val goal = goal_of_thm thy th

        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 |> iter_facts ctxt params (the max_relevant) goal

                      |> 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 = fact_name_of name ^ ": " ^ space_implode " " deps ^ "\n"

      in File.append path s end

  in List.app do_thm ths end

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

fun reset () =

  ()

fun can_suggest_facts () =

  true

fun can_learn_thy thy =

  true

fun learn_thy thy timeout =

  ()

fun learn_proof thy t thms =

  ()

fun relevant_facts ctxt params prover max_relevant

                   (override as {add, only, ...}) chained_ths hyp_ts concl_t

                   facts =

  if only then

    facts |> map (apfst (apfst (fn f => f ()))) (* ###*)

  else if max_relevant <= 0 then

    []

  else

    let

      val add_ths = Attrib.eval_thms ctxt add

      fun prepend_facts ths facts =

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

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

        |> take max_relevant

    in

      iterative_relevant_facts ctxt params prover max_relevant NONE override

                               chained_ths hyp_ts concl_t facts

      |> not (null add_ths) ? prepend_facts add_ths

    end

end;