(*  Title:      HOL/TPTP/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

   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_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

                                 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 format 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 (case format of DFG _ => spassN | _ => eN)

     val _ = problem |> lines_for_atp_problem format |> 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 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, 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

 (* 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 <> 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 Axiom type_enc true combinatorsN

                              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

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

       |> order_problem_facts name_ord

     val ss = lines_for_atp_problem format atp_problem

     val _ = app (File.append path) ss

   in () end

 end;