src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Sun May 01 18:37:24 2011 +0200 (2011-05-01)
changeset 42553 d9963b253ffa
parent 42551 cd99d6d3027a
child 42556 f65e5f0341b8
permissions -rw-r--r--
fix handling of proxies after recent drastic changes to the type encodings
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
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    Author:     Fabian Immler, TU Muenchen
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    Author:     Makarius
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    Author:     Jasmin Blanchette, TU Muenchen
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Translation of HOL to FOL for Sledgehammer.
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*)
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signature SLEDGEHAMMER_ATP_TRANSLATE =
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sig
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  type 'a fo_term = 'a ATP_Problem.fo_term
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  type 'a problem = 'a ATP_Problem.problem
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  type translated_formula
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  datatype type_system =
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    Many_Typed |
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    Mangled of bool |
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    Args of bool |
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    Tags of bool |
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    No_Types
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  val fact_prefix : string
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  val conjecture_prefix : string
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  val boolify_base : string
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  val explicit_app_base : string
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  val type_pred_base : string
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  val type_prefix : string
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  val is_type_system_sound : type_system -> bool
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  val type_system_types_dangerous_types : type_system -> bool
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  val num_atp_type_args : theory -> type_system -> string -> int
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  val unmangled_const : string -> string * string fo_term list
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  val translate_atp_fact :
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    Proof.context -> bool -> (string * 'a) * thm
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    -> translated_formula option * ((string * 'a) * thm)
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  val prepare_atp_problem :
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    Proof.context -> bool -> type_system -> bool -> term list -> term
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    -> (translated_formula option * ((string * 'a) * thm)) list
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    -> string problem * string Symtab.table * int * int
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       * (string * 'a) list vector
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  val atp_problem_weights : string problem -> (string * real) list
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end;
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structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
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struct
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open ATP_Problem
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open Metis_Translate
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open Sledgehammer_Util
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val type_decl_prefix = "type_"
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val sym_decl_prefix = "sym_"
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val fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val class_rel_clause_prefix = "crel_";
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val arity_clause_prefix = "arity_"
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val tfree_prefix = "tfree_"
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val boolify_base = "hBOOL"
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val explicit_app_base = "hAPP"
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val type_pred_base = "is"
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val type_prefix = "ty_"
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fun make_type ty = type_prefix ^ ascii_of ty
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(* official TPTP TFF syntax *)
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val tff_type_of_types = "$tType"
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val tff_bool_type = "$o"
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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type translated_formula =
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  {name: string,
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   kind: formula_kind,
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   combformula: (name, combtyp, combterm) formula,
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   ctypes_sorts: typ list}
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fun map_combformula f
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        ({name, kind, combformula, ctypes_sorts} : translated_formula) =
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  {name = name, kind = kind, combformula = f combformula,
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   ctypes_sorts = ctypes_sorts} : translated_formula
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datatype type_system =
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  Many_Typed |
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  Mangled of bool |
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  Args of bool |
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  Tags of bool |
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  No_Types
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fun is_type_system_sound Many_Typed = true
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  | is_type_system_sound (Mangled full_types) = full_types
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  | is_type_system_sound (Args full_types) = full_types
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  | is_type_system_sound (Tags full_types) = full_types
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  | is_type_system_sound No_Types = false
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fun type_system_types_dangerous_types (Tags _) = true
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  | type_system_types_dangerous_types type_sys = is_type_system_sound type_sys
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fun dont_need_type_args type_sys s =
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  s <> type_pred_base andalso
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  (member (op =) [@{const_name HOL.eq}] s orelse
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   case type_sys of
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     Many_Typed => false
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   | Mangled _ => false
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   | Args _ => s = explicit_app_base
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   | Tags full_types => full_types orelse s = explicit_app_base
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   | No_Types => true)
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datatype type_arg_policy = No_Type_Args | Mangled_Types | Explicit_Type_Args
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fun type_arg_policy type_sys s =
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  if dont_need_type_args type_sys s then
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    No_Type_Args
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  else
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    case type_sys of
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      Many_Typed => Mangled_Types
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    | Mangled _ => Mangled_Types
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    | _ => Explicit_Type_Args
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fun num_atp_type_args thy type_sys s =
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  if type_arg_policy type_sys s = Explicit_Type_Args then
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    if s = type_pred_base then 1 else num_type_args thy s
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  else
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    0
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fun atp_type_literals_for_types type_sys kind Ts =
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  if type_sys = No_Types then
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    []
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  else
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    Ts |> type_literals_for_types
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       |> filter (fn TyLitVar _ => kind <> Conjecture
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                   | TyLitFree _ => kind = Conjecture)
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fun mk_anot phi = AConn (ANot, [phi])
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
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fun mk_aconns c phis =
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  let val (phis', phi') = split_last phis in
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    fold_rev (mk_aconn c) phis' phi'
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  end
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fun mk_ahorn [] phi = phi
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  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
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fun mk_aquant _ [] phi = phi
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  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
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    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
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  | mk_aquant q xs phi = AQuant (q, xs, phi)
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fun close_universally atom_vars phi =
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  let
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    fun formula_vars bounds (AQuant (_, xs, phi)) =
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        formula_vars (map fst xs @ bounds) phi
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      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
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      | formula_vars bounds (AAtom tm) =
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        union (op =) (atom_vars tm []
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                      |> filter_out (member (op =) bounds o fst))
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  in mk_aquant AForall (formula_vars [] phi []) phi end
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fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
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  | combterm_vars (CombConst _) = I
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  | combterm_vars (CombVar (name, ty)) = insert (op =) (name, SOME ty)
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val close_combformula_universally = close_universally combterm_vars
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fun term_vars (ATerm (name as (s, _), tms)) =
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  is_atp_variable s ? insert (op =) (name, NONE)
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  #> fold term_vars tms
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val close_formula_universally = close_universally term_vars
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(* We are crossing our fingers that it doesn't clash with anything else. *)
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val mangled_type_sep = "\000"
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fun mangled_combtyp_component f (CombTFree name) = f name
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  | mangled_combtyp_component f (CombTVar name) =
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    f name (* FIXME: shouldn't happen *)
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    (* raise Fail "impossible schematic type variable" *)
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  | mangled_combtyp_component f (CombType (name, tys)) =
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    f name ^ "(" ^ commas (map (mangled_combtyp_component f) tys) ^ ")"
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fun mangled_combtyp ty =
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  (make_type (mangled_combtyp_component fst ty),
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   mangled_combtyp_component snd ty)
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fun mangled_type_suffix f g tys =
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  fold_rev (curry (op ^) o g o prefix mangled_type_sep
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            o mangled_combtyp_component f) tys ""
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fun mangled_const_name_fst ty_args s =
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  s ^ mangled_type_suffix fst ascii_of ty_args
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fun mangled_const_name_snd ty_args s' = s' ^ mangled_type_suffix snd I ty_args
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fun mangled_const_name ty_args (s, s') =
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  (mangled_const_name_fst ty_args s, mangled_const_name_snd ty_args s')
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val parse_mangled_ident =
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  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
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fun parse_mangled_type x =
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  (parse_mangled_ident
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   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
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                    [] >> ATerm) x
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and parse_mangled_types x =
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  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
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fun unmangled_type s =
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  s |> suffix ")" |> raw_explode
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    |> Scan.finite Symbol.stopper
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           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
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                                                quote s)) parse_mangled_type))
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    |> fst
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fun unmangled_const s =
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  let val ss = space_explode mangled_type_sep s in
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    (hd ss, map unmangled_type (tl ss))
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  end
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fun combformula_for_prop thy eq_as_iff =
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  let
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    fun do_term bs t ts =
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      combterm_from_term thy bs (Envir.eta_contract t)
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      |>> AAtom ||> union (op =) ts
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    fun do_quant bs q s T t' =
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      let val s = Name.variant (map fst bs) s in
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        do_formula ((s, T) :: bs) t'
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        #>> mk_aquant q [(`make_bound_var s, SOME (combtyp_from_typ T))]
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      end
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    and do_conn bs c t1 t2 =
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      do_formula bs t1 ##>> do_formula bs t2
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      #>> uncurry (mk_aconn c)
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    and do_formula bs t =
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      case t of
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        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
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      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
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        do_quant bs AForall s T t'
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      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
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        do_quant bs AExists s T t'
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      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
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      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
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      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
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      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
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        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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      | _ => do_term bs t
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  in do_formula [] end
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val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
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fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
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fun conceal_bounds Ts t =
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  subst_bounds (map (Free o apfst concealed_bound_name)
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                    (0 upto length Ts - 1 ~~ Ts), t)
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fun reveal_bounds Ts =
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  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
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                    (0 upto length Ts - 1 ~~ Ts))
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(* Removes the lambdas from an equation of the form "t = (%x. u)".
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   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
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fun extensionalize_term t =
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  let
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    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
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      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
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                                        Type (_, [_, res_T])]))
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                    $ t2 $ Abs (var_s, var_T, t')) =
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        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
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          let val var_t = Var ((var_s, j), var_T) in
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            Const (s, T' --> T' --> res_T)
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              $ betapply (t2, var_t) $ subst_bound (var_t, t')
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            |> aux (j + 1)
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          end
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        else
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          t
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      | aux _ t = t
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  in aux (maxidx_of_term t + 1) t end
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fun introduce_combinators_in_term ctxt kind t =
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  let val thy = Proof_Context.theory_of ctxt in
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    if Meson.is_fol_term thy t then
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      t
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    else
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      let
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        fun aux Ts t =
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          case t of
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            @{const Not} $ t1 => @{const Not} $ aux Ts t1
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          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
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            t0 $ Abs (s, T, aux (T :: Ts) t')
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          | (t0 as Const (@{const_name All}, _)) $ t1 =>
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            aux Ts (t0 $ eta_expand Ts t1 1)
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          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
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            t0 $ Abs (s, T, aux (T :: Ts) t')
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          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
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            aux Ts (t0 $ eta_expand Ts t1 1)
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          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
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          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
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          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
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          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
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              $ t1 $ t2 =>
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            t0 $ aux Ts t1 $ aux Ts t2
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          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
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                   t
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                 else
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                   t |> conceal_bounds Ts
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                     |> Envir.eta_contract
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                     |> cterm_of thy
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                     |> Meson_Clausify.introduce_combinators_in_cterm
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                     |> prop_of |> Logic.dest_equals |> snd
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                     |> reveal_bounds Ts
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        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
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      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
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      handle THM _ =>
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             (* A type variable of sort "{}" will make abstraction fail. *)
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             if kind = Conjecture then HOLogic.false_const
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             else HOLogic.true_const
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  end
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(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
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   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
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fun freeze_term t =
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  let
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    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   316
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   317
      | aux (Var ((s, i), T)) =
blanchet@38282
   318
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   319
      | aux t = t
blanchet@38282
   320
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   321
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   322
(* making fact and conjecture formulas *)
blanchet@42544
   323
fun make_formula ctxt eq_as_iff presimp name kind t =
blanchet@38282
   324
  let
wenzelm@42361
   325
    val thy = Proof_Context.theory_of ctxt
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   326
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   327
              |> transform_elim_term
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   328
              |> Object_Logic.atomize_term thy
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   329
    val need_trueprop = (fastype_of t = HOLogic.boolT)
blanchet@38652
   330
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@38282
   331
              |> extensionalize_term
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   332
              |> presimp ? presimplify_term thy
blanchet@38282
   333
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   334
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   335
              |> kind <> Axiom ? freeze_term
blanchet@42542
   336
    val (combformula, ctypes_sorts) =
blanchet@42544
   337
      combformula_for_prop thy eq_as_iff t []
blanchet@38282
   338
  in
blanchet@38752
   339
    {name = name, combformula = combformula, kind = kind,
blanchet@38752
   340
     ctypes_sorts = ctypes_sorts}
blanchet@38282
   341
  end
blanchet@38282
   342
blanchet@42544
   343
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, _), th) =
blanchet@41990
   344
  case (keep_trivial,
blanchet@42544
   345
        make_formula ctxt eq_as_iff presimp name Axiom (prop_of th)) of
blanchet@41990
   346
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   347
    NONE
blanchet@41990
   348
  | (_, formula) => SOME formula
blanchet@42544
   349
fun make_conjecture ctxt ts =
blanchet@38613
   350
  let val last = length ts - 1 in
blanchet@42544
   351
    map2 (fn j => make_formula ctxt true true (string_of_int j)
blanchet@38613
   352
                               (if j = last then Conjecture else Hypothesis))
blanchet@38613
   353
         (0 upto last) ts
blanchet@38613
   354
  end
blanchet@38282
   355
blanchet@38282
   356
(** Helper facts **)
blanchet@38282
   357
blanchet@42542
   358
fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
blanchet@42542
   359
  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
blanchet@42542
   360
  | formula_map f (AAtom tm) = AAtom (f tm)
blanchet@42542
   361
blanchet@42542
   362
fun formula_fold f (AQuant (_, _, phi)) = formula_fold f phi
blanchet@42542
   363
  | formula_fold f (AConn (_, phis)) = fold (formula_fold f) phis
blanchet@42542
   364
  | formula_fold f (AAtom tm) = f tm
blanchet@41313
   365
blanchet@41140
   366
fun count_term (ATerm ((s, _), tms)) =
blanchet@42542
   367
  (if is_atp_variable s then I else Symtab.map_entry s (Integer.add 1))
blanchet@41140
   368
  #> fold count_term tms
blanchet@42542
   369
fun count_formula x = formula_fold count_term x
blanchet@38282
   370
blanchet@38282
   371
val init_counters =
blanchet@41140
   372
  metis_helpers |> map fst |> sort_distinct string_ord |> map (rpair 0)
blanchet@41140
   373
  |> Symtab.make
blanchet@38282
   374
blanchet@42542
   375
(* ### FIXME: do this on repaired combterms *)
blanchet@42521
   376
fun get_helper_facts ctxt type_sys formulas =
blanchet@38282
   377
  let
blanchet@42449
   378
    val no_dangerous_types = type_system_types_dangerous_types type_sys
blanchet@41140
   379
    val ct = init_counters |> fold count_formula formulas
blanchet@41140
   380
    fun is_used s = the (Symtab.lookup ct s) > 0
blanchet@41140
   381
    fun dub c needs_full_types (th, j) =
blanchet@41140
   382
      ((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""),
blanchet@41140
   383
        false), th)
blanchet@42544
   384
    fun make_facts eq_as_iff = map_filter (make_fact ctxt false eq_as_iff false)
blanchet@38282
   385
  in
blanchet@41145
   386
    (metis_helpers
blanchet@41145
   387
     |> filter (is_used o fst)
blanchet@41145
   388
     |> maps (fn (c, (needs_full_types, ths)) =>
blanchet@41145
   389
                 if needs_full_types andalso not no_dangerous_types then
blanchet@41145
   390
                   []
blanchet@41145
   391
                 else
blanchet@41145
   392
                   ths ~~ (1 upto length ths)
blanchet@41145
   393
                   |> map (dub c needs_full_types)
blanchet@41145
   394
                   |> make_facts (not needs_full_types)),
blanchet@41145
   395
     if type_sys = Tags false then
blanchet@41145
   396
       let
blanchet@41145
   397
         fun var s = ATerm (`I s, [])
blanchet@41145
   398
         fun tag tm = ATerm (`I type_tag_name, [var "X", tm])
blanchet@41145
   399
       in
blanchet@42538
   400
         [Formula (Fof, helper_prefix ^ ascii_of "ti_ti", Axiom,
blanchet@42527
   401
                   AAtom (ATerm (`I "equal",
blanchet@42527
   402
                                 [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42529
   403
                   |> close_formula_universally, NONE, NONE)]
blanchet@41145
   404
       end
blanchet@41145
   405
     else
blanchet@41145
   406
       [])
blanchet@38282
   407
  end
blanchet@38282
   408
blanchet@42544
   409
fun translate_atp_fact ctxt keep_trivial =
blanchet@42544
   410
  `(make_fact ctxt keep_trivial true true)
blanchet@39004
   411
blanchet@41134
   412
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
blanchet@38282
   413
  let
wenzelm@42361
   414
    val thy = Proof_Context.theory_of ctxt
blanchet@41091
   415
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@41091
   416
    val (facts, fact_names) =
blanchet@41091
   417
      rich_facts
blanchet@41091
   418
      |> map_filter (fn (NONE, _) => NONE
blanchet@41091
   419
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@41091
   420
      |> ListPair.unzip
blanchet@40204
   421
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@39005
   422
       boost an ATP's performance (for some reason). *)
blanchet@40204
   423
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@38282
   424
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42353
   425
    val all_ts = goal_t :: fact_ts
blanchet@42353
   426
    val subs = tfree_classes_of_terms all_ts
blanchet@42353
   427
    val supers = tvar_classes_of_terms all_ts
blanchet@42353
   428
    val tycons = type_consts_of_terms thy all_ts
blanchet@42544
   429
    val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
blanchet@41137
   430
    val (supers', arity_clauses) =
blanchet@41137
   431
      if type_sys = No_Types then ([], [])
blanchet@41137
   432
      else make_arity_clauses thy tycons supers
blanchet@38282
   433
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@38282
   434
  in
blanchet@41313
   435
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@38282
   436
  end
blanchet@38282
   437
blanchet@41138
   438
fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t])
blanchet@38282
   439
blanchet@38282
   440
fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
blanchet@38282
   441
  | fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
blanchet@38282
   442
  | fo_term_for_combtyp (CombType (name, tys)) =
blanchet@38282
   443
    ATerm (name, map fo_term_for_combtyp tys)
blanchet@38282
   444
blanchet@38282
   445
fun fo_literal_for_type_literal (TyLitVar (class, name)) =
blanchet@38282
   446
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   447
  | fo_literal_for_type_literal (TyLitFree (class, name)) =
blanchet@38282
   448
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   449
blanchet@38282
   450
fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@38282
   451
blanchet@41138
   452
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@41138
   453
   considered dangerous because their "exhaust" properties can easily lead to
blanchet@41138
   454
   unsound ATP proofs. The checks below are an (unsound) approximation of
blanchet@41138
   455
   finiteness. *)
blanchet@41138
   456
blanchet@41138
   457
fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true
blanchet@41138
   458
  | is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) =
blanchet@41138
   459
    is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us
blanchet@41138
   460
  | is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false
blanchet@41138
   461
and is_type_dangerous ctxt (Type (s, Ts)) =
blanchet@41138
   462
    is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts
blanchet@41140
   463
  | is_type_dangerous _ _ = false
blanchet@41138
   464
and is_type_constr_dangerous ctxt s =
wenzelm@42361
   465
  let val thy = Proof_Context.theory_of ctxt in
blanchet@41138
   466
    case Datatype_Data.get_info thy s of
blanchet@41138
   467
      SOME {descr, ...} =>
blanchet@41138
   468
      forall (fn (_, (_, _, constrs)) =>
blanchet@41138
   469
                 forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr
blanchet@41138
   470
    | NONE =>
blanchet@41138
   471
      case Typedef.get_info ctxt s of
blanchet@41138
   472
        ({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type
blanchet@41138
   473
      | [] => true
blanchet@41138
   474
  end
blanchet@41138
   475
blanchet@41138
   476
fun is_combtyp_dangerous ctxt (CombType ((s, _), tys)) =
blanchet@41138
   477
    (case strip_prefix_and_unascii type_const_prefix s of
blanchet@41138
   478
       SOME s' => forall (is_combtyp_dangerous ctxt) tys andalso
blanchet@41138
   479
                  is_type_constr_dangerous ctxt (invert_const s')
blanchet@41138
   480
     | NONE => false)
blanchet@41138
   481
  | is_combtyp_dangerous _ _ = false
blanchet@41138
   482
blanchet@41138
   483
fun should_tag_with_type ctxt (Tags full_types) ty =
blanchet@41138
   484
    full_types orelse is_combtyp_dangerous ctxt ty
blanchet@41138
   485
  | should_tag_with_type _ _ _ = false
blanchet@41138
   486
blanchet@42553
   487
val proxy_table =
blanchet@42553
   488
  [("c_False", ("c_fFalse", @{const_name Metis.fFalse})),
blanchet@42553
   489
   ("c_True", ("c_fTrue", @{const_name Metis.fTrue})),
blanchet@42553
   490
   ("c_Not", ("c_fNot", @{const_name Metis.fNot})),
blanchet@42553
   491
   ("c_conj", ("c_fconj", @{const_name Metis.fconj})),
blanchet@42553
   492
   ("c_disj", ("c_fdisj", @{const_name Metis.fdisj})),
blanchet@42553
   493
   ("c_implies", ("c_fimplies", @{const_name Metis.fimplies})),
blanchet@42553
   494
   ("equal", ("c_fequal", @{const_name Metis.fequal}))]
blanchet@41140
   495
blanchet@42544
   496
fun repair_combterm_consts type_sys =
blanchet@42544
   497
  let
blanchet@42553
   498
    fun aux top_level (CombApp (tm1, tm2)) =
blanchet@42553
   499
        CombApp (aux top_level tm1, aux false tm2)
blanchet@42553
   500
      | aux top_level (CombConst (name as (s, _), ty, ty_args)) =
blanchet@42544
   501
        (case strip_prefix_and_unascii const_prefix s of
blanchet@42544
   502
           NONE => (name, ty_args)
blanchet@42544
   503
         | SOME s'' =>
blanchet@42544
   504
           let val s'' = invert_const s'' in
blanchet@42544
   505
             case type_arg_policy type_sys s'' of
blanchet@42544
   506
               No_Type_Args => (name, [])
blanchet@42548
   507
             | Mangled_Types => (mangled_const_name ty_args name, [])
blanchet@42544
   508
             | Explicit_Type_Args => (name, ty_args)
blanchet@42544
   509
           end)
blanchet@42553
   510
        |> (fn (name as (s, s'), ty_args) =>
blanchet@42553
   511
               case AList.lookup (op =) proxy_table s of
blanchet@42553
   512
                 SOME proxy_name =>
blanchet@42553
   513
                 if top_level then
blanchet@42553
   514
                   (case s of
blanchet@42553
   515
                      "c_False" => ("$false", s')
blanchet@42553
   516
                    | "c_True" => ("$true", s')
blanchet@42553
   517
                    | _ => name, [])
blanchet@42553
   518
                  else
blanchet@42553
   519
                    (proxy_name, ty_args)
blanchet@42553
   520
                | NONE => (name, ty_args))
blanchet@42544
   521
        |> (fn (name, ty_args) => CombConst (name, ty, ty_args))
blanchet@42553
   522
      | aux _ tm = tm
blanchet@42553
   523
  in aux true end
blanchet@42544
   524
blanchet@42531
   525
fun pred_combtyp ty =
blanchet@42531
   526
  case combtyp_from_typ @{typ "unit => bool"} of
blanchet@42531
   527
    CombType (name, [_, bool_ty]) => CombType (name, [ty, bool_ty])
blanchet@42531
   528
  | _ => raise Fail "expected two-argument type constructor"
blanchet@42531
   529
blanchet@42542
   530
fun type_pred_combatom type_sys ty tm =
blanchet@42549
   531
  CombApp (CombConst (`make_fixed_const type_pred_base, pred_combtyp ty, [ty]),
blanchet@42549
   532
           tm)
blanchet@42542
   533
  |> repair_combterm_consts type_sys
blanchet@42534
   534
  |> AAtom
blanchet@42534
   535
blanchet@42530
   536
fun formula_for_combformula ctxt type_sys =
blanchet@38282
   537
  let
blanchet@42553
   538
    fun do_term u =
blanchet@38282
   539
      let
blanchet@38282
   540
        val (head, args) = strip_combterm_comb u
blanchet@38282
   541
        val (x, ty_args) =
blanchet@38282
   542
          case head of
blanchet@42553
   543
            CombConst (name, _, ty_args) => (name, ty_args)
blanchet@38282
   544
          | CombVar (name, _) => (name, [])
blanchet@38282
   545
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42553
   546
        val t = ATerm (x, map fo_term_for_combtyp ty_args @ map do_term args)
blanchet@41138
   547
        val ty = combtyp_of u
blanchet@42530
   548
      in
blanchet@42530
   549
        t |> (if should_tag_with_type ctxt type_sys ty then
blanchet@42530
   550
                tag_with_type (fo_term_for_combtyp ty)
blanchet@42530
   551
              else
blanchet@42530
   552
                I)
blanchet@42530
   553
      end
blanchet@42531
   554
    val do_bound_type =
blanchet@42531
   555
      if type_sys = Many_Typed then SOME o mangled_combtyp else K NONE
blanchet@42531
   556
    val do_out_of_bound_type =
blanchet@42548
   557
      if member (op =) [Mangled true, Args true] type_sys then
blanchet@42531
   558
        (fn (s, ty) =>
blanchet@42542
   559
            type_pred_combatom type_sys ty (CombVar (s, ty))
blanchet@42534
   560
            |> formula_for_combformula ctxt type_sys |> SOME)
blanchet@42531
   561
      else
blanchet@42531
   562
        K NONE
blanchet@42530
   563
    fun do_formula (AQuant (q, xs, phi)) =
blanchet@42531
   564
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42531
   565
                                      | SOME ty => do_bound_type ty)),
blanchet@42534
   566
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42531
   567
                    (map_filter
blanchet@42531
   568
                         (fn (_, NONE) => NONE
blanchet@42531
   569
                           | (s, SOME ty) => do_out_of_bound_type (s, ty)) xs)
blanchet@42531
   570
                    (do_formula phi))
blanchet@42530
   571
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42553
   572
      | do_formula (AAtom tm) = AAtom (do_term tm)
blanchet@42530
   573
  in do_formula end
blanchet@38282
   574
blanchet@41138
   575
fun formula_for_fact ctxt type_sys
blanchet@40204
   576
                     ({combformula, ctypes_sorts, ...} : translated_formula) =
blanchet@38282
   577
  mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
blanchet@42353
   578
                (atp_type_literals_for_types type_sys Axiom ctypes_sorts))
blanchet@42522
   579
           (formula_for_combformula ctxt type_sys
blanchet@42522
   580
                                    (close_combformula_universally combformula))
blanchet@42542
   581
  |> close_formula_universally
blanchet@38282
   582
blanchet@42538
   583
fun logic_for_type_sys Many_Typed = Tff
blanchet@42538
   584
  | logic_for_type_sys _ = Fof
blanchet@42538
   585
blanchet@42180
   586
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42180
   587
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42180
   588
   the remote provers might care. *)
blanchet@42545
   589
fun formula_line_for_fact ctxt prefix type_sys
blanchet@42180
   590
                          (j, formula as {name, kind, ...}) =
blanchet@42538
   591
  Formula (logic_for_type_sys type_sys,
blanchet@42538
   592
           prefix ^ string_of_int j ^ "_" ^ ascii_of name, kind,
blanchet@42538
   593
           formula_for_fact ctxt type_sys formula, NONE, NONE)
blanchet@38282
   594
blanchet@42545
   595
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@38282
   596
                                                       superclass, ...}) =
blanchet@42542
   597
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42538
   598
    Formula (Fof, class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42527
   599
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42542
   600
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42542
   601
             |> close_formula_universally, NONE, NONE)
blanchet@38282
   602
  end
blanchet@38282
   603
blanchet@38282
   604
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
blanchet@38282
   605
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@38282
   606
  | fo_literal_for_arity_literal (TVarLit (c, sort)) =
blanchet@38282
   607
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@38282
   608
blanchet@42545
   609
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@38282
   610
                                                ...}) =
blanchet@42538
   611
  Formula (Fof, arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42527
   612
           mk_ahorn (map (formula_for_fo_literal o apfst not
blanchet@42527
   613
                          o fo_literal_for_arity_literal) premLits)
blanchet@42527
   614
                    (formula_for_fo_literal
blanchet@42542
   615
                         (fo_literal_for_arity_literal conclLit))
blanchet@42542
   616
           |> close_formula_universally, NONE, NONE)
blanchet@38282
   617
blanchet@42545
   618
fun formula_line_for_conjecture ctxt type_sys
blanchet@40114
   619
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42538
   620
  Formula (logic_for_type_sys type_sys, conjecture_prefix ^ name, kind,
blanchet@42527
   621
           formula_for_combformula ctxt type_sys
blanchet@42542
   622
                                   (close_combformula_universally combformula)
blanchet@42542
   623
           |> close_formula_universally, NONE, NONE)
blanchet@38282
   624
blanchet@42353
   625
fun free_type_literals type_sys ({ctypes_sorts, ...} : translated_formula) =
blanchet@42353
   626
  ctypes_sorts |> atp_type_literals_for_types type_sys Conjecture
blanchet@41137
   627
               |> map fo_literal_for_type_literal
blanchet@38282
   628
blanchet@42545
   629
fun formula_line_for_free_type j lit =
blanchet@42538
   630
  Formula (Fof, tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42529
   631
           formula_for_fo_literal lit, NONE, NONE)
blanchet@42545
   632
fun formula_lines_for_free_types type_sys facts =
blanchet@38282
   633
  let
blanchet@42353
   634
    val litss = map (free_type_literals type_sys) facts
blanchet@38282
   635
    val lits = fold (union (op =)) litss []
blanchet@42545
   636
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@38282
   637
blanchet@38282
   638
(** "hBOOL" and "hAPP" **)
blanchet@38282
   639
blanchet@42544
   640
type repair_info = {pred_sym: bool, min_arity: int, max_arity: int}
blanchet@38282
   641
blanchet@42544
   642
fun consider_combterm_for_repair top_level tm =
blanchet@42542
   643
  let val (head, args) = strip_combterm_comb tm in
blanchet@42542
   644
    (case head of
blanchet@42542
   645
       CombConst ((s, _), _, _) =>
blanchet@42542
   646
       if String.isPrefix bound_var_prefix s then
blanchet@42542
   647
         I
blanchet@42542
   648
       else
blanchet@42542
   649
         let val n = length args in
blanchet@42542
   650
           Symtab.map_default
blanchet@42544
   651
               (s, {pred_sym = true, min_arity = n, max_arity = 0})
blanchet@42544
   652
               (fn {pred_sym, min_arity, max_arity} =>
blanchet@42544
   653
                   {pred_sym = pred_sym andalso top_level,
blanchet@42544
   654
                    min_arity = Int.min (n, min_arity),
blanchet@42544
   655
                    max_arity = Int.max (n, max_arity)})
blanchet@42542
   656
        end
blanchet@42542
   657
     | _ => I)
blanchet@42544
   658
    #> fold (consider_combterm_for_repair false) args
blanchet@42542
   659
  end
blanchet@38282
   660
blanchet@42544
   661
fun consider_fact_for_repair ({combformula, ...} : translated_formula) =
blanchet@42544
   662
  formula_fold (consider_combterm_for_repair true) combformula
blanchet@38282
   663
blanchet@42539
   664
(* The "equal" entry is needed for helper facts if the problem otherwise does
blanchet@42545
   665
   not involve equality. The "hBOOL" entry is needed to ensure that no "hAPP"s
blanchet@42545
   666
   are introduced for passing arguments to it. *)
blanchet@42539
   667
val default_entries =
blanchet@42544
   668
  [("equal", {pred_sym = true, min_arity = 2, max_arity = 2}),
blanchet@42544
   669
   (make_fixed_const boolify_base,
blanchet@42545
   670
    {pred_sym = true, min_arity = 1, max_arity = 1})]
blanchet@41140
   671
blanchet@42544
   672
fun sym_table_for_facts explicit_apply facts =
blanchet@41140
   673
  if explicit_apply then
blanchet@41140
   674
    NONE
blanchet@41140
   675
  else
blanchet@42539
   676
    SOME (Symtab.empty |> fold Symtab.default default_entries
blanchet@42544
   677
                       |> fold consider_fact_for_repair facts)
blanchet@38282
   678
blanchet@42544
   679
fun min_arity_of _ _ (SOME sym_tab) s =
blanchet@42544
   680
    (case Symtab.lookup sym_tab s of
blanchet@42544
   681
       SOME ({min_arity, ...} : repair_info) => min_arity
blanchet@42544
   682
     | NONE => 0)
blanchet@42544
   683
  | min_arity_of thy type_sys NONE s =
blanchet@42544
   684
    if s = "equal" orelse s = type_tag_name orelse
blanchet@42544
   685
       String.isPrefix type_const_prefix s orelse
blanchet@42544
   686
       String.isPrefix class_prefix s then
blanchet@42544
   687
      16383 (* large number *)
blanchet@42544
   688
    else case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   689
      SOME s =>
blanchet@42547
   690
      let val s = s |> unmangled_const |> fst |> invert_const in
blanchet@42547
   691
        if s = boolify_base then 1
blanchet@42547
   692
        else if s = explicit_app_base then 2
blanchet@42547
   693
        else if s = type_pred_base then 1
blanchet@42547
   694
        else num_atp_type_args thy type_sys s
blanchet@42547
   695
      end
blanchet@42544
   696
    | NONE => 0
blanchet@38282
   697
blanchet@38282
   698
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   699
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   700
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   701
   arguments and is used as a predicate. *)
blanchet@42520
   702
fun is_pred_sym NONE s =
blanchet@38589
   703
    s = "equal" orelse s = "$false" orelse s = "$true" orelse
blanchet@38589
   704
    String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s
blanchet@42544
   705
  | is_pred_sym (SOME sym_tab) s =
blanchet@42544
   706
    case Symtab.lookup sym_tab s of
blanchet@42544
   707
      SOME {pred_sym, min_arity, max_arity} =>
blanchet@42542
   708
      pred_sym andalso min_arity = max_arity
blanchet@38282
   709
    | NONE => false
blanchet@38282
   710
blanchet@42542
   711
val boolify_combconst =
blanchet@42544
   712
  CombConst (`make_fixed_const boolify_base,
blanchet@42544
   713
             combtyp_from_typ @{typ "bool => bool"}, [])
blanchet@42542
   714
fun boolify tm = CombApp (boolify_combconst, tm)
blanchet@42542
   715
blanchet@42544
   716
fun repair_pred_syms_in_combterm sym_tab tm =
blanchet@42542
   717
  case strip_combterm_comb tm of
blanchet@42542
   718
    (CombConst ((s, _), _, _), _) =>
blanchet@42544
   719
    if is_pred_sym sym_tab s then tm else boolify tm
blanchet@42542
   720
  | _ => boolify tm
blanchet@42542
   721
blanchet@42544
   722
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   723
blanchet@42544
   724
val fun_name = `make_fixed_type_const @{type_name fun}
blanchet@42544
   725
blanchet@42544
   726
fun explicit_app arg head =
blanchet@42544
   727
  let
blanchet@42544
   728
    val head_ty = combtyp_of head
blanchet@42544
   729
    val (arg_ty, res_ty) = dest_combfun head_ty
blanchet@42544
   730
    val explicit_app =
blanchet@42544
   731
      CombConst (`make_fixed_const explicit_app_base,
blanchet@42544
   732
                 CombType (fun_name, [head_ty, head_ty]), [arg_ty, res_ty])
blanchet@42544
   733
  in list_app explicit_app [head, arg] end
blanchet@42544
   734
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   735
blanchet@42544
   736
fun repair_apps_in_combterm thy type_sys sym_tab =
blanchet@42544
   737
  let
blanchet@42544
   738
    fun aux tm =
blanchet@42544
   739
      case strip_combterm_comb tm of
blanchet@42544
   740
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   741
        args |> map aux
blanchet@42544
   742
             |> chop (min_arity_of thy type_sys sym_tab s)
blanchet@42544
   743
             |>> list_app head
blanchet@42544
   744
             |-> list_explicit_app
blanchet@42544
   745
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   746
  in aux end
blanchet@38282
   747
blanchet@42544
   748
fun repair_combterm thy type_sys sym_tab =
blanchet@42544
   749
  (case type_sys of Tags _ => I | _ => repair_pred_syms_in_combterm sym_tab)
blanchet@42544
   750
  #> repair_apps_in_combterm thy type_sys sym_tab
blanchet@42544
   751
  #> repair_combterm_consts type_sys
blanchet@42544
   752
val repair_combformula = formula_map ooo repair_combterm
blanchet@42544
   753
val repair_fact = map_combformula ooo repair_combformula
blanchet@42544
   754
blanchet@42544
   755
fun is_const_relevant type_sys sym_tab s =
blanchet@42542
   756
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42544
   757
  (type_sys = Many_Typed orelse not (is_pred_sym sym_tab s))
blanchet@38282
   758
blanchet@42544
   759
fun consider_combterm_consts type_sys sym_tab tm =
blanchet@42533
   760
  let val (head, args) = strip_combterm_comb tm in
blanchet@42533
   761
    (case head of
blanchet@42533
   762
       CombConst ((s, s'), ty, ty_args) =>
blanchet@42533
   763
       (* FIXME: exploit type subsumption *)
blanchet@42544
   764
       is_const_relevant type_sys sym_tab s
blanchet@42534
   765
       ? Symtab.insert_list (op =) (s, (s', ty_args, ty))
blanchet@42544
   766
     | _ => I)
blanchet@42544
   767
    #> fold (consider_combterm_consts type_sys sym_tab) args
blanchet@42533
   768
  end
blanchet@42533
   769
blanchet@42544
   770
fun consider_fact_consts type_sys sym_tab
blanchet@42534
   771
                         ({combformula, ...} : translated_formula) =
blanchet@42544
   772
  formula_fold (consider_combterm_consts type_sys sym_tab) combformula
blanchet@42533
   773
blanchet@42545
   774
(* FIXME: needed? *)
blanchet@42544
   775
fun const_table_for_facts type_sys sym_tab facts =
blanchet@42548
   776
  Symtab.empty |> member (op =) [Many_Typed, Mangled true, Args true] type_sys
blanchet@42544
   777
                  ? fold (consider_fact_consts type_sys sym_tab) facts
blanchet@42533
   778
blanchet@42544
   779
fun strip_and_map_combtyp 0 f ty = ([], f ty)
blanchet@42544
   780
  | strip_and_map_combtyp n f (ty as CombType ((s, _), tys)) =
blanchet@42533
   781
    (case (strip_prefix_and_unascii type_const_prefix s, tys) of
blanchet@42533
   782
       (SOME @{type_name fun}, [dom_ty, ran_ty]) =>
blanchet@42544
   783
       strip_and_map_combtyp (n - 1) f ran_ty |>> cons (f dom_ty)
blanchet@42534
   784
     | _ => ([], f ty))
blanchet@42544
   785
  | strip_and_map_combtyp _ _ _ = raise Fail "unexpected non-function"
blanchet@42533
   786
blanchet@42546
   787
fun problem_line_for_typed_const ctxt type_sys sym_tab s j (s', ty_args, ty) =
blanchet@42544
   788
  let
blanchet@42544
   789
    val thy = Proof_Context.theory_of ctxt
blanchet@42544
   790
    val arity = min_arity_of thy type_sys sym_tab s
blanchet@42544
   791
  in
blanchet@42544
   792
    if type_sys = Many_Typed then
blanchet@42544
   793
      let
blanchet@42544
   794
        val (arg_tys, res_ty) = strip_and_map_combtyp arity mangled_combtyp ty
blanchet@42544
   795
        val (s, s') = (s, s') |> mangled_const_name ty_args
blanchet@42544
   796
      in
blanchet@42546
   797
        Decl (sym_decl_prefix ^ ascii_of s, (s, s'),
blanchet@42546
   798
              arg_tys,
blanchet@42544
   799
              if is_pred_sym sym_tab s then `I tff_bool_type else res_ty)
blanchet@42544
   800
      end
blanchet@42544
   801
    else
blanchet@42544
   802
      let
blanchet@42544
   803
        val (arg_tys, res_ty) = strip_and_map_combtyp arity I ty
blanchet@42544
   804
        val bounds =
blanchet@42544
   805
          map (`I o make_bound_var o string_of_int) (1 upto length arg_tys)
blanchet@42544
   806
          ~~ map SOME arg_tys
blanchet@42544
   807
        val bound_tms =
blanchet@42544
   808
          map (fn (name, ty) => CombConst (name, the ty, [])) bounds
blanchet@42546
   809
        val freshener =
blanchet@42546
   810
          case type_sys of Args _ => string_of_int j ^ "_" | _ => ""
blanchet@42544
   811
      in
blanchet@42546
   812
        Formula (Fof, sym_decl_prefix ^ freshener ^ "_" ^ ascii_of s, Axiom,
blanchet@42544
   813
                 CombConst ((s, s'), ty, ty_args)
blanchet@42544
   814
                 |> fold (curry (CombApp o swap)) bound_tms
blanchet@42544
   815
                 |> type_pred_combatom type_sys res_ty
blanchet@42544
   816
                 |> mk_aquant AForall bounds
blanchet@42544
   817
                 |> formula_for_combformula ctxt type_sys,
blanchet@42544
   818
                 NONE, NONE)
blanchet@42544
   819
      end
blanchet@42544
   820
  end
blanchet@42545
   821
fun problem_lines_for_const ctxt type_sys sym_tab (s, xs) =
blanchet@42546
   822
  map2 (problem_line_for_typed_const ctxt type_sys sym_tab s)
blanchet@42546
   823
       (0 upto length xs - 1) xs
blanchet@42543
   824
blanchet@42543
   825
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
   826
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
   827
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
   828
    fold add_tff_types_in_formula phis
blanchet@42543
   829
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
   830
blanchet@42543
   831
fun add_tff_types_in_problem_line (Decl (_, _, arg_tys, res_ty)) =
blanchet@42543
   832
    union (op =) (res_ty :: arg_tys)
blanchet@42543
   833
  | add_tff_types_in_problem_line (Formula (_, _, _, phi, _, _)) =
blanchet@42543
   834
    add_tff_types_in_formula phi
blanchet@42543
   835
blanchet@42543
   836
fun tff_types_in_problem problem =
blanchet@42543
   837
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
   838
blanchet@42545
   839
fun decl_line_for_tff_type (s, s') =
blanchet@42543
   840
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tff_type_of_types)
blanchet@42543
   841
blanchet@42543
   842
val type_declsN = "Types"
blanchet@42544
   843
val sym_declsN = "Symbol types"
blanchet@41157
   844
val factsN = "Relevant facts"
blanchet@41157
   845
val class_relsN = "Class relationships"
blanchet@42543
   846
val aritiesN = "Arities"
blanchet@41157
   847
val helpersN = "Helper facts"
blanchet@41157
   848
val conjsN = "Conjectures"
blanchet@41313
   849
val free_typesN = "Type variables"
blanchet@41157
   850
blanchet@41157
   851
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
   852
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
   853
    if heading = needle then j
blanchet@41157
   854
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
   855
blanchet@42521
   856
fun prepare_atp_problem ctxt readable_names type_sys explicit_apply hyp_ts
blanchet@42521
   857
                        concl_t facts =
blanchet@38282
   858
  let
blanchet@42544
   859
    val thy = Proof_Context.theory_of ctxt
blanchet@41313
   860
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
   861
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@42544
   862
    val sym_tab = sym_table_for_facts explicit_apply (conjs @ facts)
blanchet@42544
   863
    val conjs = map (repair_fact thy type_sys sym_tab) conjs
blanchet@42544
   864
    val facts = map (repair_fact thy type_sys sym_tab) facts
blanchet@42544
   865
    val sym_tab = sym_table_for_facts explicit_apply (conjs @ facts)
blanchet@42522
   866
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
   867
       Flotter hack. *)
blanchet@38282
   868
    val problem =
blanchet@42541
   869
      [(type_declsN, []),
blanchet@42543
   870
       (sym_declsN, []),
blanchet@42545
   871
       (factsN, map (formula_line_for_fact ctxt fact_prefix type_sys)
blanchet@42180
   872
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
   873
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
   874
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@41157
   875
       (helpersN, []),
blanchet@42545
   876
       (conjsN, map (formula_line_for_conjecture ctxt type_sys) conjs),
blanchet@42545
   877
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42521
   878
    val helper_facts =
blanchet@42538
   879
      problem |> maps (map_filter (fn Formula (_, _, _, phi, _, _) => SOME phi
blanchet@42528
   880
                                    | _ => NONE) o snd)
blanchet@42527
   881
              |> get_helper_facts ctxt type_sys
blanchet@42544
   882
              |>> map (repair_fact thy type_sys sym_tab)
blanchet@42544
   883
    val const_tab = const_table_for_facts type_sys sym_tab (conjs @ facts)
blanchet@42543
   884
    val sym_decl_lines =
blanchet@42545
   885
      Symtab.fold_rev (append o problem_lines_for_const ctxt type_sys sym_tab)
blanchet@42534
   886
                      const_tab []
blanchet@41157
   887
    val helper_lines =
blanchet@42521
   888
      helper_facts
blanchet@42545
   889
      |>> map (pair 0 #> formula_line_for_fact ctxt helper_prefix type_sys)
blanchet@41157
   890
      |> op @
blanchet@42543
   891
    val problem =
blanchet@42533
   892
      problem |> fold (AList.update (op =))
blanchet@42543
   893
                      [(sym_declsN, sym_decl_lines),
blanchet@42543
   894
                       (helpersN, helper_lines)]
blanchet@42543
   895
    val type_decl_lines =
blanchet@42543
   896
      if type_sys = Many_Typed then
blanchet@42545
   897
        problem |> tff_types_in_problem |> map decl_line_for_tff_type
blanchet@42543
   898
      else
blanchet@42543
   899
        []
blanchet@42543
   900
    val (problem, pool) =
blanchet@42543
   901
      problem |> AList.update (op =) (type_declsN, type_decl_lines)
blanchet@41140
   902
              |> nice_atp_problem readable_names
blanchet@38282
   903
  in
blanchet@38282
   904
    (problem,
blanchet@38282
   905
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42541
   906
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
   907
     offset_of_heading_in_problem conjsN problem 0,
blanchet@41157
   908
     fact_names |> Vector.fromList)
blanchet@38282
   909
  end
blanchet@38282
   910
blanchet@41313
   911
(* FUDGE *)
blanchet@41313
   912
val conj_weight = 0.0
blanchet@41770
   913
val hyp_weight = 0.1
blanchet@41770
   914
val fact_min_weight = 0.2
blanchet@41313
   915
val fact_max_weight = 1.0
blanchet@41313
   916
blanchet@41313
   917
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
   918
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
   919
  #> fold (add_term_weights weight) tms
blanchet@42538
   920
fun add_problem_line_weights weight (Formula (_, _, _, phi, _, _)) =
blanchet@42542
   921
    formula_fold (add_term_weights weight) phi
blanchet@42528
   922
  | add_problem_line_weights _ _ = I
blanchet@41313
   923
blanchet@41313
   924
fun add_conjectures_weights [] = I
blanchet@41313
   925
  | add_conjectures_weights conjs =
blanchet@41313
   926
    let val (hyps, conj) = split_last conjs in
blanchet@41313
   927
      add_problem_line_weights conj_weight conj
blanchet@41313
   928
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
   929
    end
blanchet@41313
   930
blanchet@41313
   931
fun add_facts_weights facts =
blanchet@41313
   932
  let
blanchet@41313
   933
    val num_facts = length facts
blanchet@41313
   934
    fun weight_of j =
blanchet@41313
   935
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
   936
                        / Real.fromInt num_facts
blanchet@41313
   937
  in
blanchet@41313
   938
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
   939
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
   940
  end
blanchet@41313
   941
blanchet@41313
   942
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
   943
fun atp_problem_weights problem =
blanchet@41313
   944
  Symtab.empty
blanchet@41313
   945
  |> add_conjectures_weights (these (AList.lookup (op =) problem conjsN))
blanchet@41313
   946
  |> add_facts_weights (these (AList.lookup (op =) problem factsN))
blanchet@41313
   947
  |> Symtab.dest
blanchet@41726
   948
  |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@41313
   949
blanchet@38282
   950
end;