(*  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_literal = ATP_Translate.type_literal

   datatype isa_thm =

     Isa_Reflexive_or_Trivial |

     Isa_Raw of thm

   val metis_equal : string

   val metis_predicator : string

   val metis_app_op : string

   val metis_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) * (string * bool)) list

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

   val prepare_metis_problem :

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

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

 val metis_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), (metis_equal, false)),

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

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

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

    ((prefixed_type_tag_name, 2), (metis_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 Type_Infer.paramify_vars

                  else

                    t

                | t => t)

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

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

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

 datatype isa_thm =

   Isa_Reflexive_or_Trivial |

   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_name_from_atp s ary =

   AList.lookup (op =) metis_name_table (s, ary) |> the_default (s, false)

 fun metis_term_from_atp (ATerm (s, tms)) =

   if is_tptp_variable s then

     Metis_Term.Var s

   else

     let val (s, swap) = metis_name_from_atp s (length tms) in

       Metis_Term.Fn (s, tms |> map metis_term_from_atp |> swap ? rev)

     end

 fun metis_atom_from_atp (AAtom tm) =

     (case metis_term_from_atp 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 (AConn (ANot, [phi])) =

     (false, metis_atom_from_atp phi)

   | metis_literal_from_atp phi = (true, metis_atom_from_atp phi)

 fun metis_literals_from_atp (AConn (AOr, [phi1, phi2])) =

     uncurry (union (op =)) (pairself metis_literals_from_atp (phi1, phi2))

   | metis_literals_from_atp phi = [metis_literal_from_atp phi]

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

     let

       fun some isa =

         SOME (phi |> metis_literals_from_atp |> Metis_LiteralSet.fromList

                   |> Metis_Thm.axiom, isa)

     in

       if ident = type_tag_idempotence_helper_name orelse

          String.isPrefix lightweight_tags_sym_formula_prefix ident then

         Isa_Reflexive_or_Trivial |> some

       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 conjecture_prefix) ident of

         SOME s =>

         let val j = the (Int.fromString s) in

           if j = length clauses then NONE

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

         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_sys conj_clauses fact_clauses =

   let

     val type_sys = type_sys_from_string type_sys

     val clauses =

       conj_clauses @ fact_clauses

       |> (if polymorphism_of_type_sys type_sys = Polymorphic then

             I

           else

             map (pair 0)

             #> rpair ctxt

             #-> Monomorph.monomorph atp_schematic_consts_of

             #> fst #> maps (map (zero_var_indexes o snd)))

     val (old_skolems, props) =

       fold_rev (fn clause => fn (old_skolems, props) =>

                    clause |> prop_of |> Logic.strip_imp_concl

                           |> conceal_old_skolem_terms (length clauses)

                                                       old_skolems

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

            clauses ([], [])

 (*

 val _ = tracing ("PROPS:\n" ^ cat_lines (map (Syntax.string_of_term ctxt) props))

 *)

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

       prepare_atp_problem ctxt CNF Hypothesis Axiom type_sys false false props

                           @{prop False} []

 (*

 val _ = tracing ("ATP PROBLEM: " ^ cat_lines (tptp_lines_for_atp_problem CNF atp_problem))

 *)

     (* "rev" is for compatibility *)

     val axioms =

       atp_problem |> maps (map_filter (metis_axiom_from_atp clauses) o snd)

                   |> rev

   in (sym_tab, axioms, old_skolems) end

 end;