src/HOL/Tools/Metis/metis_translate.ML
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(*  Title:      HOL/Tools/Metis/metis_translate.ML
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    Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
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    Author:     Kong W. Susanto, Cambridge University Computer Laboratory
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    Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory
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    Author:     Jasmin Blanchette, TU Muenchen
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Translation of HOL to FOL for Metis.
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*)
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signature METIS_TRANSLATE =
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sig
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  type type_literal = ATP_Translate.type_literal
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  datatype mode = FO | HO | FT | New
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  type metis_problem =
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    {axioms: (Metis_Thm.thm * thm) list,
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     tfrees: type_literal list,
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     old_skolems: (string * term) list}
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  val metis_generated_var_prefix : string
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  val new_skolem_const_prefix : string
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  val num_type_args: theory -> string -> int
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  val new_skolem_var_name_from_const : string -> string
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  val reveal_old_skolem_terms : (string * term) list -> term -> term
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  val string_of_mode : mode -> string
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  val prepare_metis_problem :
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    mode -> Proof.context -> bool -> thm list -> thm list list
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    -> mode * metis_problem
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end
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structure Metis_Translate : METIS_TRANSLATE =
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struct
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open ATP_Translate
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val metis_generated_var_prefix = "_"
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(* The number of type arguments of a constant, zero if it's monomorphic. For
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   (instances of) Skolem pseudoconstants, this information is encoded in the
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   constant name. *)
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fun num_type_args thy s =
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  if String.isPrefix skolem_const_prefix s then
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    s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
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  else
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    (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
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fun new_skolem_var_name_from_const s =
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  let val ss = s |> space_explode Long_Name.separator in
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    nth ss (length ss - 2)
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  end
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fun predicate_of thy ((@{const Not} $ P), pos) = predicate_of thy (P, not pos)
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  | predicate_of thy (t, pos) =
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    (combterm_from_term thy [] (Envir.eta_contract t), pos)
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fun literals_of_term1 args thy (@{const Trueprop} $ P) =
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    literals_of_term1 args thy P
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  | literals_of_term1 args thy (@{const HOL.disj} $ P $ Q) =
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    literals_of_term1 (literals_of_term1 args thy P) thy Q
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  | literals_of_term1 (lits, ts) thy P =
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    let val ((pred, ts'), pol) = predicate_of thy (P, true) in
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      ((pol, pred) :: lits, union (op =) ts ts')
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    end
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val literals_of_term = literals_of_term1 ([], [])
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fun old_skolem_const_name i j num_T_args =
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  old_skolem_const_prefix ^ Long_Name.separator ^
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  (space_implode Long_Name.separator (map string_of_int [i, j, num_T_args]))
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fun conceal_old_skolem_terms i old_skolems t =
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  if exists_Const (curry (op =) @{const_name Meson.skolem} o fst) t then
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    let
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      fun aux old_skolems
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             (t as (Const (@{const_name Meson.skolem}, Type (_, [_, T])) $ _)) =
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          let
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            val (old_skolems, s) =
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              if i = ~1 then
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                (old_skolems, @{const_name undefined})
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              else case AList.find (op aconv) old_skolems t of
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                s :: _ => (old_skolems, s)
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              | [] =>
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                let
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                  val s = old_skolem_const_name i (length old_skolems)
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                                                (length (Term.add_tvarsT T []))
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                in ((s, t) :: old_skolems, s) end
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          in (old_skolems, Const (s, T)) end
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        | aux old_skolems (t1 $ t2) =
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          let
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            val (old_skolems, t1) = aux old_skolems t1
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            val (old_skolems, t2) = aux old_skolems t2
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          in (old_skolems, t1 $ t2) end
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        | aux old_skolems (Abs (s, T, t')) =
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          let val (old_skolems, t') = aux old_skolems t' in
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            (old_skolems, Abs (s, T, t'))
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          end
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        | aux old_skolems t = (old_skolems, t)
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    in aux old_skolems t end
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  else
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    (old_skolems, t)
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fun reveal_old_skolem_terms old_skolems =
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  map_aterms (fn t as Const (s, _) =>
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                 if String.isPrefix old_skolem_const_prefix s then
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                   AList.lookup (op =) old_skolems s |> the
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                   |> map_types Type_Infer.paramify_vars
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                 else
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                   t
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               | t => t)
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(* ------------------------------------------------------------------------- *)
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(* HOL to FOL  (Isabelle to Metis)                                           *)
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(* ------------------------------------------------------------------------- *)
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(* first-order, higher-order, fully-typed, new *)
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datatype mode = FO | HO | FT | New
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fun string_of_mode FO = "FO"
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  | string_of_mode HO = "HO"
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  | string_of_mode FT = "FT"
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  | string_of_mode New = "New"
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fun fn_isa_to_met_sublevel "equal" = "c_fequal"
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  | fn_isa_to_met_sublevel "c_False" = "c_fFalse"
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  | fn_isa_to_met_sublevel "c_True" = "c_fTrue"
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  | fn_isa_to_met_sublevel "c_Not" = "c_fNot"
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  | fn_isa_to_met_sublevel "c_conj" = "c_fconj"
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  | fn_isa_to_met_sublevel "c_disj" = "c_fdisj"
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  | fn_isa_to_met_sublevel "c_implies" = "c_fimplies"
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  | fn_isa_to_met_sublevel x = x
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fun fn_isa_to_met_toplevel "equal" = "="
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  | fn_isa_to_met_toplevel x = x
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fun metis_lit b c args = (b, (c, args));
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fun metis_term_from_typ (Type (s, Ts)) =
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    Metis_Term.Fn (make_fixed_type_const s, map metis_term_from_typ Ts)
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  | metis_term_from_typ (TFree (s, _)) =
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    Metis_Term.Fn (make_fixed_type_var s, [])
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  | metis_term_from_typ (TVar (x, _)) =
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    Metis_Term.Var (make_schematic_type_var x)
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(*These two functions insert type literals before the real literals. That is the
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  opposite order from TPTP linkup, but maybe OK.*)
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fun hol_term_to_fol_FO tm =
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  case strip_combterm_comb tm of
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      (CombConst ((c, _), _, Ts), tms) =>
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        let val tyargs = map metis_term_from_typ Ts
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            val args = map hol_term_to_fol_FO tms
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        in Metis_Term.Fn (c, tyargs @ args) end
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    | (CombVar ((v, _), _), []) => Metis_Term.Var v
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    | _ => raise Fail "non-first-order combterm"
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fun hol_term_to_fol_HO (CombConst ((a, _), _, Ts)) =
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      Metis_Term.Fn (fn_isa_to_met_sublevel a, map metis_term_from_typ Ts)
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  | hol_term_to_fol_HO (CombVar ((s, _), _)) = Metis_Term.Var s
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  | hol_term_to_fol_HO (CombApp (tm1, tm2)) =
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       Metis_Term.Fn (".", map hol_term_to_fol_HO [tm1, tm2]);
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(*The fully-typed translation, to avoid type errors*)
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fun tag_with_type tm T =
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  Metis_Term.Fn (type_tag_name, [tm, metis_term_from_typ T])
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fun hol_term_to_fol_FT (CombVar ((s, _), ty)) =
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    tag_with_type (Metis_Term.Var s) ty
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  | hol_term_to_fol_FT (CombConst ((a, _), ty, _)) =
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    tag_with_type (Metis_Term.Fn (fn_isa_to_met_sublevel a, [])) ty
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  | hol_term_to_fol_FT (tm as CombApp (tm1,tm2)) =
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    tag_with_type (Metis_Term.Fn (".", map hol_term_to_fol_FT [tm1, tm2]))
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                  (combtyp_of tm)
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fun hol_literal_to_fol FO (pos, tm) =
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      let
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        val (CombConst((p, _), _, Ts), tms) = strip_combterm_comb tm
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        val tylits = if p = "equal" then [] else map metis_term_from_typ Ts
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        val lits = map hol_term_to_fol_FO tms
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      in metis_lit pos (fn_isa_to_met_toplevel p) (tylits @ lits) end
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  | hol_literal_to_fol HO (pos, tm) =
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     (case strip_combterm_comb tm of
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          (CombConst(("equal", _), _, _), tms) =>
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            metis_lit pos "=" (map hol_term_to_fol_HO tms)
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        | _ => metis_lit pos "{}" [hol_term_to_fol_HO tm])   (*hBOOL*)
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  | hol_literal_to_fol FT (pos, tm) =
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     (case strip_combterm_comb tm of
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          (CombConst(("equal", _), _, _), tms) =>
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            metis_lit pos "=" (map hol_term_to_fol_FT tms)
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        | _ => metis_lit pos "{}" [hol_term_to_fol_FT tm])   (*hBOOL*);
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fun literals_of_hol_term thy mode t =
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  let val (lits, types_sorts) = literals_of_term thy t in
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    (map (hol_literal_to_fol mode) lits, types_sorts)
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  end
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(*Sign should be "true" for conjecture type constraints, "false" for type lits in clauses.*)
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fun metis_of_type_literals pos (TyLitVar ((s, _), (s', _))) =
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    metis_lit pos s [Metis_Term.Var s']
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  | metis_of_type_literals pos (TyLitFree ((s, _), (s', _))) =
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    metis_lit pos s [Metis_Term.Fn (s',[])]
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fun has_default_sort _ (TVar _) = false
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  | has_default_sort ctxt (TFree (x, s)) =
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    (s = the_default [] (Variable.def_sort ctxt (x, ~1)));
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fun metis_of_tfree tf =
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  Metis_Thm.axiom (Metis_LiteralSet.singleton (metis_of_type_literals true tf));
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fun hol_thm_to_fol is_conjecture ctxt type_lits mode j old_skolems th =
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  let
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    val thy = Proof_Context.theory_of ctxt
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    val (old_skolems, (mlits, types_sorts)) =
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     th |> prop_of |> Logic.strip_imp_concl
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        |> conceal_old_skolem_terms j old_skolems
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        ||> (HOLogic.dest_Trueprop #> literals_of_hol_term thy mode)
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  in
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    if is_conjecture then
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      (Metis_Thm.axiom (Metis_LiteralSet.fromList mlits),
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       raw_type_literals_for_types types_sorts, old_skolems)
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    else
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      let
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        val tylits = types_sorts |> filter_out (has_default_sort ctxt)
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                                 |> raw_type_literals_for_types
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        val mtylits =
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          if type_lits then map (metis_of_type_literals false) tylits else []
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      in
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        (Metis_Thm.axiom (Metis_LiteralSet.fromList(mtylits @ mlits)), [],
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         old_skolems)
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      end
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  end;
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(* ------------------------------------------------------------------------- *)
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(* Logic maps manage the interface between HOL and first-order logic.        *)
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(* ------------------------------------------------------------------------- *)
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type metis_problem =
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  {axioms: (Metis_Thm.thm * thm) list,
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   tfrees: type_literal list,
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   old_skolems: (string * term) list}
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fun is_quasi_fol_clause thy =
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  Meson.is_fol_term thy o snd o conceal_old_skolem_terms ~1 [] o prop_of
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(*Extract TFree constraints from context to include as conjecture clauses*)
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fun init_tfrees ctxt =
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  let fun add ((a,i),s) Ts = if i = ~1 then TFree(a,s) :: Ts else Ts in
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    Vartab.fold add (#2 (Variable.constraints_of ctxt)) []
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    |> raw_type_literals_for_types
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  end;
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(*Insert non-logical axioms corresponding to all accumulated TFrees*)
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fun add_tfrees {axioms, tfrees, old_skolems} : metis_problem =
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     {axioms = map (rpair TrueI o metis_of_tfree) (distinct (op =) tfrees) @
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               axioms,
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      tfrees = tfrees, old_skolems = old_skolems}
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(*transform isabelle type / arity clause to metis clause *)
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fun add_type_thm [] lmap = lmap
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  | add_type_thm ((ith, mth) :: cls) {axioms, tfrees, old_skolems} =
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      add_type_thm cls {axioms = (mth, ith) :: axioms, tfrees = tfrees,
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                        old_skolems = old_skolems}
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fun const_in_metis c (pred, tm_list) =
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  let
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    fun in_mterm (Metis_Term.Var _) = false
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      | in_mterm (Metis_Term.Fn (nm, tm_list)) =
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        c = nm orelse exists in_mterm tm_list
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  in c = pred orelse exists in_mterm tm_list end
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(* ARITY CLAUSE *)
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fun m_arity_cls (TConsLit ((c, _), (t, _), args)) =
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    metis_lit true c [Metis_Term.Fn(t, map (Metis_Term.Var o fst) args)]
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  | m_arity_cls (TVarLit ((c, _), (s, _))) =
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    metis_lit false c [Metis_Term.Var s]
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(*TrueI is returned as the Isabelle counterpart because there isn't any.*)
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fun arity_cls ({prem_lits, concl_lits, ...} : arity_clause) =
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  (TrueI,
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   Metis_Thm.axiom (Metis_LiteralSet.fromList
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                        (map m_arity_cls (concl_lits :: prem_lits))));
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(* CLASSREL CLAUSE *)
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fun m_class_rel_cls (subclass, _) (superclass, _) =
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  [metis_lit false subclass [Metis_Term.Var "T"], metis_lit true superclass [Metis_Term.Var "T"]];
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fun class_rel_cls ({subclass, superclass, ...} : class_rel_clause) =
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  (TrueI, Metis_Thm.axiom (Metis_LiteralSet.fromList (m_class_rel_cls subclass superclass)));
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fun type_ext thy tms =
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  let val subs = tfree_classes_of_terms tms
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      val supers = tvar_classes_of_terms tms
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      val tycons = type_consts_of_terms thy tms
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      val (supers', arity_clauses) = make_arity_clauses thy tycons supers
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      val class_rel_clauses = make_class_rel_clauses thy subs supers'
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  in  map class_rel_cls class_rel_clauses @ map arity_cls arity_clauses
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  end;
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(* Function to generate metis clauses, including comb and type clauses *)
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fun prepare_metis_problem New ctxt type_lits cls thss =
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    error "Not implemented yet"
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  | prepare_metis_problem mode ctxt type_lits cls thss =
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    let
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      val thy = Proof_Context.theory_of ctxt
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      (* The modes FO and FT are sticky. HO can be downgraded to FO. *)
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      val mode =
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        if mode = HO andalso
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           forall (forall (is_quasi_fol_clause thy)) (cls :: thss) then
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          FO
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        else
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          mode
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      (*transform isabelle clause to metis clause *)
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      fun add_thm is_conjecture (isa_ith, metis_ith)
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                  {axioms, tfrees, old_skolems} : metis_problem =
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        let
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          val (mth, tfree_lits, old_skolems) =
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            hol_thm_to_fol is_conjecture ctxt type_lits mode (length axioms)
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                           old_skolems metis_ith
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        in
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           {axioms = (mth, isa_ith) :: axioms,
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            tfrees = union (op =) tfree_lits tfrees, old_skolems = old_skolems}
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        end;
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      val lmap = {axioms = [], tfrees = init_tfrees ctxt, old_skolems = []}
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                 |> fold (add_thm true o `Meson.make_meta_clause) cls
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                 |> add_tfrees
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                 |> fold (fold (add_thm false o `Meson.make_meta_clause)) thss
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      val clause_lists = map (Metis_Thm.clause o #1) (#axioms lmap)
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      fun is_used c =
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        exists (Metis_LiteralSet.exists (const_in_metis c o #2)) clause_lists
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      val lmap =
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        if mode = FO then
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          lmap
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        else
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          let
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            val fdefs = @{thms fFalse_def fTrue_def fNot_def fconj_def fdisj_def
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                               fimplies_def fequal_def}
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            val prepare_helper =
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              zero_var_indexes
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              #> `(Meson.make_meta_clause
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                   #> rewrite_rule (map safe_mk_meta_eq fdefs))
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            val helper_ths =
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              helper_table
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              |> filter (is_used o prefix const_prefix o fst)
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              |> maps (fn (_, (needs_full_types, thms)) =>
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                          if needs_full_types andalso mode <> FT then []
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                          else map prepare_helper thms)
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          in lmap |> fold (add_thm false) helper_ths end
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    in
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      (mode,
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       add_type_thm (type_ext thy (maps (map prop_of) (cls :: thss))) lmap)
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    end
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end;