src/HOL/TPTP/atp_export.ML

improved handling of induction rules in Sledgehammer

(*  Title:      HOL/ex/atp_export.ML
    Author:     Jasmin Blanchette, TU Muenchen
    Copyright   2011

Export Isabelle theories as first-order TPTP inferences, exploiting
Sledgehammer's translation.
*)

signature ATP_EXPORT =
sig
  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 -> string -> string -> unit
end;

structure ATP_Export : ATP_EXPORT =
struct

open ATP_Problem
open ATP_Translate
open ATP_Proof
open ATP_Systems

val fact_name_of = prefix fact_prefix o ascii_of

fun facts_of thy =
  Sledgehammer_Filter.all_facts (Proof_Context.init_global thy)
                                false(*FIXME works only for first-order*)
                                Symtab.empty true [] []
  |> filter (curry (op =) @{typ bool} o fastype_of
             o Object_Logic.atomize_term thy o prop_of o snd)

(* 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, NONE)) =
    Formula (ident, Lemma, phi, inference infers ident, NONE)
  | 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 problem =
  let
    val thy = Proof_Context.theory_of ctxt
    val prob_file = File.tmp_path (Path.explode "prob.tptp")
    val {exec, arguments, proof_delims, known_failures, ...} =
      get_atp thy spassN
    val _ = problem |> tptp_lines_for_atp_problem FOF
                    |> File.write_list prob_file
    val command =
      File.shell_path (Path.explode (getenv (fst exec) ^ "/" ^ snd exec)) ^
      " " ^ arguments ctxt false "" (seconds 1.0) (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 (Formula (ident, _, phi, _, _)) =
    exists (fn prefix => String.isPrefix prefix ident)
           likely_tautology_prefixes andalso
    is_none (run_some_atp ctxt
                 [(factsN, [Formula (ident, Conjecture, phi, NONE, NONE)])])
  | is_problem_line_tautology _ _ = false

structure String_Graph = Graph(type key = string val ord = string_ord);

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

fun generate_tptp_inference_file_for_theory ctxt thy type_enc file_name =
  let
    val format = FOF
    val type_enc = type_enc |> type_enc_from_string Sound
    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), prop_of th))
      |> prepare_atp_problem ctxt format Axiom Axiom type_enc true combinatorsN
                             false true [] @{prop False}
    val atp_problem =
      atp_problem
      |> map (apsnd (filter_out (is_problem_line_tautology ctxt)))
    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 |> add_inferences_to_problem infers
                  |> order_problem_facts name_ord
    val ss = tptp_lines_for_atp_problem FOF atp_problem
    val _ = app (File.append path) ss
  in () end

end;