(*  Title:      HOL/TPTP/atp_theory_export.ML

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2011

Export Isabelle theories as MaSh (Machine-learning for Sledgehammer) or as

first-order TPTP inferences.

*)

signature ATP_THEORY_EXPORT =

sig

  type atp_format = ATP_Problem.atp_format

  val theorems_mentioned_in_proof_term :

    string list option -> thm -> string list

  val generate_mash_accessibility_file_for_theory :

    theory -> bool -> string -> unit

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

  val generate_mash_dependency_file_for_theory :

    theory -> bool -> string -> unit

  val generate_mash_problem_file_for_theory : theory -> string -> unit

  val generate_tptp_inference_file_for_theory :

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

end;

structure ATP_Theory_Export (* ### : ATP_THEORY_EXPORT *) =

struct

open ATP_Problem

open ATP_Proof

open ATP_Problem_Generate

open ATP_Systems

open ATP_Util

fun stringN_of_int 0 _ = ""

  | stringN_of_int k n =

    stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)

fun escape_meta_char c =

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

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

    String.str c

  else if c = #"'" then

    "~"

  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

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

(* FIXME: Similar yet different code in "mirabelle.ML". The code here has a few

   fixes that seem to be missing over there; or maybe the two code portions are

   not doing the same? *)

fun fold_body_thms thm_name f =

  let

    fun app n (PBody {thms, ...}) =

      thms |> fold (fn (_, (name, prop, body)) => fn x =>

        let

          val body' = Future.join body

          val n' =

            n + (if name = "" orelse

                    (* uncommon case where the proved theorem occurs twice

                       (e.g., "Transitive_Closure.trancl_into_trancl") *)

                    (n = 1 andalso name = thm_name) then

                   0

                 else

                   1)

          val x' = x |> n' <= 1 ? app n' body'

        in (x' |> n = 1 ? f (name, prop, body')) end)

  in fold (app 0) end

fun theorems_mentioned_in_proof_term all_names th =

  let

    val is_name_ok =

      case all_names of

        SOME names => member (op =) names

      | NONE => (fn s => s <> "" andalso not (String.isPrefix "Pure." s))

    fun collect (s, _, _) = is_name_ok s ? insert (op =) s

    val names =

      [] |> fold_body_thms (Thm.get_name_hint th) collect [Thm.proof_body_of th]

         |> map fact_name_of

  in names 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

    val add_classes =

      subtract (op =) @{sort type} #> map class_name_of #> union (op =)

    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)) = add_classes S

      | do_add_type (TVar (_, S)) = add_classes 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 facts_of thy =

  let val ctxt = Proof_Context.init_global thy in

    Sledgehammer_Filter.all_facts ctxt false Symtab.empty true [] []

        (Sledgehammer_Filter.clasimpset_rule_table_of ctxt)

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

    |> rev

  end

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 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)

val thms_by_thy =

  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 generate_mash_accessibility_file_for_theory 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 =

      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)

        val _ = fold do_thm ths parents

      in () end

    val _ = List.app (do_thy o snd) thy_ths

  in () end

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}]

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

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

val max_depth = 1

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 generate_mash_feature_file_for_theory thy include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val facts = 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

    val _ = List.app do_fact facts

  in () end

val dependencies_of = theorems_mentioned_in_proof_term o SOME

fun generate_mash_dependency_file_for_theory thy include_thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val ths =

      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 = dependencies_of all_names th

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

      in File.append path s end

    val _ = List.app do_thm ths

  in () end

fun generate_mash_problem_file_for_theory thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val facts = facts_of thy

    val (new_facts, old_facts) =

      facts |> List.partition (has_thy thy o snd)

            |>> sort (thm_ord o pairself snd)

    val ths = facts |> map snd

    val all_names = ths |> map Thm.get_name_hint

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

      let

        val name = Thm.get_name_hint th

        val feats = features_of thy (status, th)

        val deps = dependencies_of all_names th

        val kind = Thm.legacy_get_kind th

        val name = fact_name_of name

        val core =

          name ^ ": " ^ space_implode " " prevs ^ "; " ^ space_implode " " feats

        val query = if kind <> "" then "? " ^ core ^ "\n" else ""

        val update = "! " ^ core ^ "; " ^ space_implode " " deps ^ "\n"

        val _ = File.append path (query ^ update)

      in [name] end

    val thy_ths = old_facts |> thms_by_thy

    val parents = parent_thms thy_ths thy

    val _ = fold do_fact new_facts parents

  in () end

fun inference_term [] = NONE

  | inference_term ss =

    ATerm (("inference", []),

           [ATerm (("isabelle", []), []),

            ATerm ((tptp_empty_list, []), []),

            ATerm ((tptp_empty_list, []),

            map (fn s => ATerm ((s, []), [])) ss)])

    |> SOME

fun inference infers ident =

  these (AList.lookup (op =) infers ident) |> inference_term

fun add_inferences_to_problem_line infers

                                   (Formula (ident, Axiom, phi, NONE, tms)) =

    Formula (ident, Lemma, phi, inference infers ident, tms)

  | add_inferences_to_problem_line _ line = line

fun add_inferences_to_problem infers =

  map (apsnd (map (add_inferences_to_problem_line infers)))

fun ident_of_problem_line (Class_Decl (ident, _, _)) = ident

  | ident_of_problem_line (Type_Decl (ident, _, _)) = ident

  | ident_of_problem_line (Sym_Decl (ident, _, _)) = ident

  | ident_of_problem_line (Class_Memb (ident, _, _, _)) = ident

  | ident_of_problem_line (Formula (ident, _, _, _, _)) = ident

fun run_some_atp ctxt format problem =

  let

    val thy = Proof_Context.theory_of ctxt

    val prob_file = File.tmp_path (Path.explode "prob")

    val atp = case format of DFG _ => spassN | _ => eN

    val {exec, arguments, proof_delims, known_failures, ...} =

      get_atp thy atp ()

    val ord = effective_term_order ctxt atp

    val _ = problem |> lines_for_atp_problem format ord (K [])

                    |> File.write_list prob_file

    val path = getenv (List.last (fst exec)) ^ "/" ^ snd exec

    val command =

      File.shell_path (Path.explode path) ^

      " " ^ arguments ctxt false "" (seconds 1.0) (ord, K [], K []) ^ " " ^

      File.shell_path prob_file

  in

    TimeLimit.timeLimit (seconds 0.3) Isabelle_System.bash_output command

    |> fst

    |> extract_tstplike_proof_and_outcome false true proof_delims known_failures

    |> snd

  end

  handle TimeLimit.TimeOut => SOME TimedOut

val tautology_prefixes =

  [@{theory HOL}, @{theory Meson}, @{theory ATP}, @{theory Metis}]

  |> map (fact_name_of o Context.theory_name)

fun is_problem_line_tautology ctxt format (Formula (ident, _, phi, _, _)) =

    exists (fn prefix => String.isPrefix prefix ident)

           tautology_prefixes andalso

    is_none (run_some_atp ctxt format

                 [(factsN, [Formula (ident, Conjecture, phi, NONE, [])])])

  | is_problem_line_tautology _ _ _ = false

fun order_facts ord = sort (ord o pairself ident_of_problem_line)

fun order_problem_facts _ [] = []

  | order_problem_facts ord ((heading, lines) :: problem) =

    if heading = factsN then (heading, order_facts ord lines) :: problem

    else (heading, lines) :: order_problem_facts ord problem

(* A fairly random selection of types used for monomorphizing. *)

val ground_types =

  [@{typ nat}, HOLogic.intT, HOLogic.realT, @{typ "nat => bool"}, @{typ bool},

   @{typ unit}]

fun ground_type_for_tvar _ [] tvar =

    raise TYPE ("ground_type_for_sorts", [TVar tvar], [])

  | ground_type_for_tvar thy (T :: Ts) tvar =

    if can (Sign.typ_match thy (TVar tvar, T)) Vartab.empty then T

    else ground_type_for_tvar thy Ts tvar

fun monomorphize_term ctxt t =

  let val thy = Proof_Context.theory_of ctxt in

    t |> map_types (map_type_tvar (ground_type_for_tvar thy ground_types))

    handle TYPE _ => @{prop True}

  end

fun generate_tptp_inference_file_for_theory ctxt thy format type_enc file_name =

  let

    val type_enc = type_enc |> type_enc_from_string Strict

                            |> adjust_type_enc format

    val mono = not (is_type_enc_polymorphic type_enc)

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val facts = facts_of thy

    val atp_problem =

      facts

      |> map (fn ((_, loc), th) =>

                 ((Thm.get_name_hint th, loc),

                   th |> prop_of |> mono ? monomorphize_term ctxt))

      |> prepare_atp_problem ctxt format Axiom type_enc Exporter combsN false

                             false true [] @{prop False}

      |> #1

    val atp_problem =

      atp_problem

      |> map (apsnd (filter_out (is_problem_line_tautology ctxt format)))

    val ths = facts |> map snd

    val all_names = ths |> map Thm.get_name_hint

    val infers =

      facts |> map (fn (_, th) =>

                       (fact_name_of (Thm.get_name_hint th),

                        theorems_mentioned_in_proof_term (SOME all_names) th))

    val all_atp_problem_names =

      atp_problem |> maps (map ident_of_problem_line o snd)

    val infers =

      infers |> filter (member (op =) all_atp_problem_names o fst)

             |> map (apsnd (filter (member (op =) all_atp_problem_names)))

    val ordered_names =

      String_Graph.empty

      |> fold (String_Graph.new_node o rpair ()) all_atp_problem_names

      |> fold (fn (to, froms) =>

                  fold (fn from => String_Graph.add_edge (from, to)) froms)

              infers

      |> String_Graph.topological_order

    val order_tab =

      Symtab.empty

      |> fold (Symtab.insert (op =))

              (ordered_names ~~ (1 upto length ordered_names))

    val name_ord = int_ord o pairself (the o Symtab.lookup order_tab)

    val atp_problem =

      atp_problem

      |> (case format of DFG _ => I | _ => add_inferences_to_problem infers)

      |> order_problem_facts name_ord

    val ord = effective_term_order ctxt eN (* dummy *)

    val ss = lines_for_atp_problem format ord (K []) atp_problem

    val _ = app (File.append path) ss

  in () end

end;