(*  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_lam_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_lam_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_lam_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"

 fun eliminate_lam_wrappers (Const (@{const_name Metis.lambda}, _) $ t) =

     eliminate_lam_wrappers t

   | eliminate_lam_wrappers (t $ u) =

     eliminate_lam_wrappers t $ eliminate_lam_wrappers u

   | eliminate_lam_wrappers (Abs (s, T, t)) =

     Abs (s, T, eliminate_lam_wrappers t)

   | eliminate_lam_wrappers t = t

 (* 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

                       ||> lam_trans = lam_liftingN ? eliminate_lam_wrappers

                       ||> (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;