(*  Title:      HOL/TPTP/atp_theory_export.ML

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2011

Export Isabelle theories as first-order TPTP inferences, exploiting

Sledgehammer's translation.

*)

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_tptp_graph_file_for_theory :

    Proof.context -> 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

val fact_name_of = prefix fact_prefix o ascii_of

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 (curry (op =) @{typ bool} o fastype_of

               o Object_Logic.atomize_term thy o prop_of o snd)

  end

(* 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 all_names 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

                    (is_some all_names andalso

                     not (member (op =) (the all_names) 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 thm =

  let

    fun collect (s, _, _) = if s <> "" then insert (op =) s else I

    val names =

      [] |> fold_body_thms (Thm.get_name_hint thm) all_names collect

                           [Thm.proof_body_of thm]

         |> map fact_name_of

  in names end

fun interesting_const_names ctxt =

  let val thy = Proof_Context.theory_of ctxt in

    Sledgehammer_Filter.const_names_in_fact thy

        (Sledgehammer_Provers.is_built_in_const_for_prover ctxt eN)

  end

fun generate_tptp_graph_file_for_theory ctxt thy file_name =

  let

    val path = file_name |> Path.explode

    val _ = File.write path ""

    val axioms = Theory.all_axioms_of thy |> map fst

    fun do_thm thm =

      let

        val name = Thm.get_name_hint thm

        val s =

          "[" ^ Thm.legacy_get_kind thm ^ "] " ^

          (if member (op =) axioms name then "A" else "T") ^ " " ^

          prefix fact_prefix (ascii_of name) ^ ": " ^

          commas (theorems_mentioned_in_proof_term NONE thm) ^ "; " ^

          commas (map (prefix const_prefix o ascii_of)

                      (interesting_const_names ctxt (Thm.prop_of thm))) ^ " \n"

      in File.append path s end

    val thms = facts_of thy |> map snd

    val _ = map do_thm thms

  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 (Decl (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 = if format = DFG then spassN else 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 command =

      File.shell_path (Path.explode (getenv (hd (fst exec)) ^ "/" ^ snd exec)) ^

      " " ^ 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 likely_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)

           likely_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 = polymorphism_of_type_enc type_enc <> Raw_Polymorphic

    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 all_names = facts |> map (Thm.get_name_hint o snd)

    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

      |> (format <> DFG ? 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;