(*  Title:      HOL/Tools/Metis/metis_translate.ML

    Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA

    Author:     Kong W. Susanto, Cambridge University Computer Laboratory

    Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory

    Author:     Jasmin Blanchette, TU Muenchen

Translation of HOL to FOL for Metis.

*)

signature METIS_TRANSLATE =

sig

  type type_enc = ATP_Translate.type_enc

  datatype isa_thm =

    Isa_Reflexive_or_Trivial |

    Isa_Lambda_Lifted |

    Isa_Raw of thm

  val metis_equal : string

  val metis_predicator : string

  val metis_app_op : string

  val metis_systematic_type_tag : string

  val metis_ad_hoc_type_tag : string

  val metis_generated_var_prefix : string

  val trace : bool Config.T

  val verbose : bool Config.T

  val trace_msg : Proof.context -> (unit -> string) -> unit

  val verbose_warning : Proof.context -> string -> unit

  val metis_name_table : ((string * int) * ((type_enc -> string) * bool)) list

  val reveal_old_skolem_terms : (string * term) list -> term -> term

  val reveal_lambda_lifted : (string * term) list -> term -> term

  val prepare_metis_problem :

    Proof.context -> type_enc -> string -> thm list -> thm list

    -> int Symtab.table * (Metis_Thm.thm * isa_thm) list

       * ((string * term) list * (string * term) list)

end

structure Metis_Translate : METIS_TRANSLATE =

struct

open ATP_Problem

open ATP_Translate

val metis_equal = "="

val metis_predicator = "{}"

val metis_app_op = Metis_Name.toString Metis_Term.appName

val metis_systematic_type_tag =

  Metis_Name.toString Metis_Term.hasTypeFunctionName

val metis_ad_hoc_type_tag = "**"

val metis_generated_var_prefix = "_"

val trace = Attrib.setup_config_bool @{binding metis_trace} (K false)

val verbose = Attrib.setup_config_bool @{binding metis_verbose} (K true)

fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()

fun verbose_warning ctxt msg =

  if Config.get ctxt verbose then warning ("Metis: " ^ msg) else ()

val metis_name_table =

  [((tptp_equal, 2), (K metis_equal, false)),

   ((tptp_old_equal, 2), (K metis_equal, false)),

   ((prefixed_predicator_name, 1), (K metis_predicator, false)),

   ((prefixed_app_op_name, 2), (K metis_app_op, false)),

   ((prefixed_type_tag_name, 2),

    (fn type_enc =>

        if level_of_type_enc type_enc = All_Types then metis_systematic_type_tag

        else metis_ad_hoc_type_tag, true))]

fun old_skolem_const_name i j num_T_args =

  old_skolem_const_prefix ^ Long_Name.separator ^

  (space_implode Long_Name.separator (map string_of_int [i, j, num_T_args]))

fun conceal_old_skolem_terms i old_skolems t =

  if exists_Const (curry (op =) @{const_name Meson.skolem} o fst) t then

    let

      fun aux old_skolems

             (t as (Const (@{const_name Meson.skolem}, Type (_, [_, T])) $ _)) =

          let

            val (old_skolems, s) =

              if i = ~1 then

                (old_skolems, @{const_name undefined})

              else case AList.find (op aconv) old_skolems t of

                s :: _ => (old_skolems, s)

              | [] =>

                let

                  val s = old_skolem_const_name i (length old_skolems)

                                                (length (Term.add_tvarsT T []))

                in ((s, t) :: old_skolems, s) end

          in (old_skolems, Const (s, T)) end

        | aux old_skolems (t1 $ t2) =

          let

            val (old_skolems, t1) = aux old_skolems t1

            val (old_skolems, t2) = aux old_skolems t2

          in (old_skolems, t1 $ t2) end

        | aux old_skolems (Abs (s, T, t')) =

          let val (old_skolems, t') = aux old_skolems t' in

            (old_skolems, Abs (s, T, t'))

          end

        | aux old_skolems t = (old_skolems, t)

    in aux old_skolems t end

  else

    (old_skolems, t)

fun reveal_old_skolem_terms old_skolems =

  map_aterms (fn t as Const (s, _) =>

                 if String.isPrefix old_skolem_const_prefix s then

                   AList.lookup (op =) old_skolems s |> the

                   |> map_types (map_type_tvar (K dummyT))

                 else

                   t

               | t => t)

fun reveal_lambda_lifted lambdas =

  map_aterms (fn t as Const (s, _) =>

                 if String.isPrefix lam_lifted_prefix s then

                   case AList.lookup (op =) lambdas s of

                     SOME t =>

                     Const (@{const_name Metis.lambda}, dummyT)

                     $ map_types (map_type_tvar (K dummyT))

                                 (reveal_lambda_lifted lambdas t)

                   | NONE => t

                 else

                   t

               | t => t)

(* ------------------------------------------------------------------------- *)

(* Logic maps manage the interface between HOL and first-order logic.        *)

(* ------------------------------------------------------------------------- *)

datatype isa_thm =

  Isa_Reflexive_or_Trivial |

  Isa_Lambda_Lifted |

  Isa_Raw of thm

val proxy_defs = map (fst o snd o snd) proxy_table

val prepare_helper =

  Meson.make_meta_clause #> rewrite_rule (map safe_mk_meta_eq proxy_defs)

fun metis_term_from_atp type_enc (ATerm (s, tms)) =

  if is_tptp_variable s then

    Metis_Term.Var (Metis_Name.fromString s)

  else

    (case AList.lookup (op =) metis_name_table (s, length tms) of

       SOME (f, swap) => (f type_enc, swap)

     | NONE => (s, false))

    |> (fn (s, swap) =>

           Metis_Term.Fn (Metis_Name.fromString s,

                          tms |> map (metis_term_from_atp type_enc)

                              |> swap ? rev))

fun metis_atom_from_atp type_enc (AAtom tm) =

    (case metis_term_from_atp type_enc tm of

       Metis_Term.Fn x => x

     | _ => raise Fail "non CNF -- expected function")

  | metis_atom_from_atp _ _ = raise Fail "not CNF -- expected atom"

fun metis_literal_from_atp type_enc (AConn (ANot, [phi])) =

    (false, metis_atom_from_atp type_enc phi)

  | metis_literal_from_atp type_enc phi =

    (true, metis_atom_from_atp type_enc phi)

fun metis_literals_from_atp type_enc (AConn (AOr, phis)) =

    maps (metis_literals_from_atp type_enc) phis

  | metis_literals_from_atp type_enc phi = [metis_literal_from_atp type_enc phi]

fun metis_axiom_from_atp type_enc clauses (Formula (ident, _, phi, _, _)) =

    let

      fun some isa =

        SOME (phi |> metis_literals_from_atp type_enc

                  |> Metis_LiteralSet.fromList

                  |> Metis_Thm.axiom, isa)

    in

      if ident = type_tag_idempotence_helper_name orelse

         String.isPrefix tags_sym_formula_prefix ident then

        Isa_Reflexive_or_Trivial |> some

      else if String.isPrefix conjecture_prefix ident then

        NONE

      else if String.isPrefix helper_prefix ident then

        case (String.isSuffix typed_helper_suffix ident,

              space_explode "_" ident) of

          (needs_fairly_sound, _ :: const :: j :: _) =>

          nth ((const, needs_fairly_sound)

               |> AList.lookup (op =) helper_table |> the)

              (the (Int.fromString j) - 1)

          |> prepare_helper

          |> Isa_Raw |> some

        | _ => raise Fail ("malformed helper identifier " ^ quote ident)

      else case try (unprefix fact_prefix) ident of

        SOME s =>

        let val s = s |> space_explode "_" |> tl |> space_implode "_"

          in

          case Int.fromString s of

            SOME j =>

            Meson.make_meta_clause (snd (nth clauses j)) |> Isa_Raw |> some

          | NONE =>

            if String.isPrefix lam_fact_prefix (unascii_of s) then

              Isa_Lambda_Lifted |> some

            else

              raise Fail ("malformed fact identifier " ^ quote ident)

        end

      | NONE => TrueI |> Isa_Raw |> some

    end

  | metis_axiom_from_atp _ _ _ = raise Fail "not CNF -- expected formula"

(* Function to generate metis clauses, including comb and type clauses *)

fun prepare_metis_problem ctxt type_enc lam_trans conj_clauses fact_clauses =

  let

    val (conj_clauses, fact_clauses) =

      if polymorphism_of_type_enc type_enc = Polymorphic then

        (conj_clauses, fact_clauses)

      else

        conj_clauses @ fact_clauses

        |> map (pair 0)

        |> rpair (ctxt |> Config.put Monomorph.keep_partial_instances false)

        |-> Monomorph.monomorph atp_schematic_consts_of

        |> fst |> chop (length conj_clauses)

        |> pairself (maps (map (zero_var_indexes o snd)))

    val num_conjs = length conj_clauses

    val clauses =

      map2 (fn j => pair (Int.toString j, Local))

           (0 upto num_conjs - 1) conj_clauses @

      (* "General" below isn't quite correct; the fact could be local. *)

      map2 (fn j => pair (Int.toString (num_conjs + j), General))

           (0 upto length fact_clauses - 1) fact_clauses

    val (old_skolems, props) =

      fold_rev (fn (name, th) => fn (old_skolems, props) =>

                   th |> prop_of |> Logic.strip_imp_concl

                      |> conceal_old_skolem_terms (length clauses) old_skolems

                      ||> (fn prop => (name, prop) :: props))

               clauses ([], [])

    (*

    val _ =

      tracing ("PROPS:\n" ^

               cat_lines (map (Syntax.string_of_term ctxt o snd) props))

    *)

    val lam_trans = if lam_trans = combinatorsN then no_lamsN else lam_trans

    val (atp_problem, _, _, lifted, sym_tab) =

      prepare_atp_problem ctxt CNF Hypothesis Axiom type_enc false lam_trans

                          false false [] @{prop False} props

    (*

    val _ = tracing ("ATP PROBLEM: " ^

                     cat_lines (lines_for_atp_problem CNF atp_problem))

    *)

    (* "rev" is for compatibility with existing proof scripts. *)

    val axioms =

      atp_problem

      |> maps (map_filter (metis_axiom_from_atp type_enc clauses) o snd) |> rev

  in (sym_tab, axioms, (lifted, old_skolems)) end

end;