src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Sun May 01 18:37:24 2011 +0200 (2011-05-01)
changeset 42543 f9d402d144d4
parent 42542 024920b65ce2
child 42544 75cb06eee990
permissions -rw-r--r--
declare TFF types so that SNARK can be used with types
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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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    Tags of bool |
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    Args of bool |
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    Mangled 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_name : string
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  val explicit_app_name : 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 -> type_system -> 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_name = "hBOOL"
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val explicit_app_name = "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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  Tags of bool |
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  Args of bool |
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  Mangled 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 (Tags 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 (Mangled 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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   | Tags full_types => full_types
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   | Args _ => false
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   | Mangled _ => false
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   | No_Types => true)
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datatype type_arg_policy = No_Type_Args | Explicit_Type_Args | Mangled_Types
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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 repair_combterm_consts type_sys =
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  let
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    fun aux (CombApp tmp) = CombApp (pairself aux tmp)
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      | aux (CombConst (name as (s, _), ty, ty_args)) =
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        (case strip_prefix_and_unascii const_prefix s of
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           NONE => (name, ty_args)
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         | SOME s'' =>
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           let val s'' = invert_const s'' in
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             case type_arg_policy type_sys s'' of
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               No_Type_Args => (name, [])
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             | Explicit_Type_Args => (name, ty_args)
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             | Mangled_Types => (mangled_const_name ty_args name, [])
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           end)
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        |> (fn (name, ty_args) => CombConst (name, ty, ty_args))
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      | aux tm = tm
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  in aux end
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fun combformula_for_prop thy type_sys 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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      |>> repair_combterm_consts type_sys
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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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   317
                     |> prop_of |> Logic.dest_equals |> snd
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   318
                     |> reveal_bounds Ts
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   319
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
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   320
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
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   321
      handle THM _ =>
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   322
             (* A type variable of sort "{}" will make abstraction fail. *)
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   323
             if kind = Conjecture then HOLogic.false_const
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   324
             else HOLogic.true_const
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   325
  end
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   326
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   327
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
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   328
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
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   329
fun freeze_term t =
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   330
  let
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   331
    fun aux (t $ u) = aux t $ aux u
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   332
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
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   333
      | aux (Var ((s, i), T)) =
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   334
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
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   335
      | aux t = t
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   336
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   337
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   338
(* making fact and conjecture formulas *)
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   339
fun make_formula ctxt type_sys eq_as_iff presimp name kind t =
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   340
  let
wenzelm@42361
   341
    val thy = Proof_Context.theory_of ctxt
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   342
    val t = t |> Envir.beta_eta_contract
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   343
              |> transform_elim_term
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   344
              |> Object_Logic.atomize_term thy
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   345
    val need_trueprop = (fastype_of t = HOLogic.boolT)
blanchet@38652
   346
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@38282
   347
              |> extensionalize_term
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   348
              |> presimp ? presimplify_term thy
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   349
              |> perhaps (try (HOLogic.dest_Trueprop))
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   350
              |> introduce_combinators_in_term ctxt kind
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   351
              |> kind <> Axiom ? freeze_term
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   352
    val (combformula, ctypes_sorts) =
blanchet@42542
   353
      combformula_for_prop thy type_sys eq_as_iff t []
blanchet@38282
   354
  in
blanchet@38752
   355
    {name = name, combformula = combformula, kind = kind,
blanchet@38752
   356
     ctypes_sorts = ctypes_sorts}
blanchet@38282
   357
  end
blanchet@38282
   358
blanchet@42542
   359
fun make_fact ctxt type_sys keep_trivial eq_as_iff presimp ((name, _), th) =
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   360
  case (keep_trivial,
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   361
        make_formula ctxt type_sys eq_as_iff presimp name Axiom (prop_of th)) of
blanchet@41990
   362
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   363
    NONE
blanchet@41990
   364
  | (_, formula) => SOME formula
blanchet@42542
   365
fun make_conjecture ctxt type_sys ts =
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   366
  let val last = length ts - 1 in
blanchet@42542
   367
    map2 (fn j => make_formula ctxt type_sys true true (string_of_int j)
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   368
                               (if j = last then Conjecture else Hypothesis))
blanchet@38613
   369
         (0 upto last) ts
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   370
  end
blanchet@38282
   371
blanchet@38282
   372
(** Helper facts **)
blanchet@38282
   373
blanchet@42542
   374
fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
blanchet@42542
   375
  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
blanchet@42542
   376
  | formula_map f (AAtom tm) = AAtom (f tm)
blanchet@42542
   377
blanchet@42542
   378
fun formula_fold f (AQuant (_, _, phi)) = formula_fold f phi
blanchet@42542
   379
  | formula_fold f (AConn (_, phis)) = fold (formula_fold f) phis
blanchet@42542
   380
  | formula_fold f (AAtom tm) = f tm
blanchet@41313
   381
blanchet@41140
   382
fun count_term (ATerm ((s, _), tms)) =
blanchet@42542
   383
  (if is_atp_variable s then I else Symtab.map_entry s (Integer.add 1))
blanchet@41140
   384
  #> fold count_term tms
blanchet@42542
   385
fun count_formula x = formula_fold count_term x
blanchet@38282
   386
blanchet@38282
   387
val init_counters =
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   388
  metis_helpers |> map fst |> sort_distinct string_ord |> map (rpair 0)
blanchet@41140
   389
  |> Symtab.make
blanchet@38282
   390
blanchet@42542
   391
(* ### FIXME: do this on repaired combterms *)
blanchet@42521
   392
fun get_helper_facts ctxt type_sys formulas =
blanchet@38282
   393
  let
blanchet@42449
   394
    val no_dangerous_types = type_system_types_dangerous_types type_sys
blanchet@41140
   395
    val ct = init_counters |> fold count_formula formulas
blanchet@41140
   396
    fun is_used s = the (Symtab.lookup ct s) > 0
blanchet@41140
   397
    fun dub c needs_full_types (th, j) =
blanchet@41140
   398
      ((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""),
blanchet@41140
   399
        false), th)
blanchet@42542
   400
    fun make_facts eq_as_iff =
blanchet@42542
   401
      map_filter (make_fact ctxt type_sys false eq_as_iff false)
blanchet@38282
   402
  in
blanchet@41145
   403
    (metis_helpers
blanchet@41145
   404
     |> filter (is_used o fst)
blanchet@41145
   405
     |> maps (fn (c, (needs_full_types, ths)) =>
blanchet@41145
   406
                 if needs_full_types andalso not no_dangerous_types then
blanchet@41145
   407
                   []
blanchet@41145
   408
                 else
blanchet@41145
   409
                   ths ~~ (1 upto length ths)
blanchet@41145
   410
                   |> map (dub c needs_full_types)
blanchet@41145
   411
                   |> make_facts (not needs_full_types)),
blanchet@41145
   412
     if type_sys = Tags false then
blanchet@41145
   413
       let
blanchet@41145
   414
         fun var s = ATerm (`I s, [])
blanchet@41145
   415
         fun tag tm = ATerm (`I type_tag_name, [var "X", tm])
blanchet@41145
   416
       in
blanchet@42538
   417
         [Formula (Fof, helper_prefix ^ ascii_of "ti_ti", Axiom,
blanchet@42527
   418
                   AAtom (ATerm (`I "equal",
blanchet@42527
   419
                                 [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42529
   420
                   |> close_formula_universally, NONE, NONE)]
blanchet@41145
   421
       end
blanchet@41145
   422
     else
blanchet@41145
   423
       [])
blanchet@38282
   424
  end
blanchet@38282
   425
blanchet@42542
   426
fun translate_atp_fact ctxt type_sys keep_trivial =
blanchet@42542
   427
  `(make_fact ctxt type_sys keep_trivial true true)
blanchet@39004
   428
blanchet@41134
   429
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
blanchet@38282
   430
  let
wenzelm@42361
   431
    val thy = Proof_Context.theory_of ctxt
blanchet@41091
   432
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@41091
   433
    val (facts, fact_names) =
blanchet@41091
   434
      rich_facts
blanchet@41091
   435
      |> map_filter (fn (NONE, _) => NONE
blanchet@41091
   436
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@41091
   437
      |> ListPair.unzip
blanchet@40204
   438
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@39005
   439
       boost an ATP's performance (for some reason). *)
blanchet@40204
   440
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@38282
   441
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42353
   442
    val all_ts = goal_t :: fact_ts
blanchet@42353
   443
    val subs = tfree_classes_of_terms all_ts
blanchet@42353
   444
    val supers = tvar_classes_of_terms all_ts
blanchet@42353
   445
    val tycons = type_consts_of_terms thy all_ts
blanchet@42542
   446
    val conjs = make_conjecture ctxt type_sys (hyp_ts @ [concl_t])
blanchet@41137
   447
    val (supers', arity_clauses) =
blanchet@41137
   448
      if type_sys = No_Types then ([], [])
blanchet@41137
   449
      else make_arity_clauses thy tycons supers
blanchet@38282
   450
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@38282
   451
  in
blanchet@41313
   452
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@38282
   453
  end
blanchet@38282
   454
blanchet@41138
   455
fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t])
blanchet@38282
   456
blanchet@38282
   457
fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
blanchet@38282
   458
  | fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
blanchet@38282
   459
  | fo_term_for_combtyp (CombType (name, tys)) =
blanchet@38282
   460
    ATerm (name, map fo_term_for_combtyp tys)
blanchet@38282
   461
blanchet@38282
   462
fun fo_literal_for_type_literal (TyLitVar (class, name)) =
blanchet@38282
   463
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   464
  | fo_literal_for_type_literal (TyLitFree (class, name)) =
blanchet@38282
   465
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   466
blanchet@38282
   467
fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@38282
   468
blanchet@41138
   469
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@41138
   470
   considered dangerous because their "exhaust" properties can easily lead to
blanchet@41138
   471
   unsound ATP proofs. The checks below are an (unsound) approximation of
blanchet@41138
   472
   finiteness. *)
blanchet@41138
   473
blanchet@41138
   474
fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true
blanchet@41138
   475
  | is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) =
blanchet@41138
   476
    is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us
blanchet@41138
   477
  | is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false
blanchet@41138
   478
and is_type_dangerous ctxt (Type (s, Ts)) =
blanchet@41138
   479
    is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts
blanchet@41140
   480
  | is_type_dangerous _ _ = false
blanchet@41138
   481
and is_type_constr_dangerous ctxt s =
wenzelm@42361
   482
  let val thy = Proof_Context.theory_of ctxt in
blanchet@41138
   483
    case Datatype_Data.get_info thy s of
blanchet@41138
   484
      SOME {descr, ...} =>
blanchet@41138
   485
      forall (fn (_, (_, _, constrs)) =>
blanchet@41138
   486
                 forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr
blanchet@41138
   487
    | NONE =>
blanchet@41138
   488
      case Typedef.get_info ctxt s of
blanchet@41138
   489
        ({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type
blanchet@41138
   490
      | [] => true
blanchet@41138
   491
  end
blanchet@41138
   492
blanchet@41138
   493
fun is_combtyp_dangerous ctxt (CombType ((s, _), tys)) =
blanchet@41138
   494
    (case strip_prefix_and_unascii type_const_prefix s of
blanchet@41138
   495
       SOME s' => forall (is_combtyp_dangerous ctxt) tys andalso
blanchet@41138
   496
                  is_type_constr_dangerous ctxt (invert_const s')
blanchet@41138
   497
     | NONE => false)
blanchet@41138
   498
  | is_combtyp_dangerous _ _ = false
blanchet@41138
   499
blanchet@41138
   500
fun should_tag_with_type ctxt (Tags full_types) ty =
blanchet@41138
   501
    full_types orelse is_combtyp_dangerous ctxt ty
blanchet@41138
   502
  | should_tag_with_type _ _ _ = false
blanchet@41138
   503
blanchet@41140
   504
val fname_table =
blanchet@41140
   505
  [("c_False", (0, ("c_fFalse", @{const_name Metis.fFalse}))),
blanchet@41140
   506
   ("c_True", (0, ("c_fTrue", @{const_name Metis.fTrue}))),
blanchet@41140
   507
   ("c_Not", (1, ("c_fNot", @{const_name Metis.fNot}))),
blanchet@41140
   508
   ("c_conj", (2, ("c_fconj", @{const_name Metis.fconj}))),
blanchet@41140
   509
   ("c_disj", (2, ("c_fdisj", @{const_name Metis.fdisj}))),
blanchet@41140
   510
   ("c_implies", (2, ("c_fimplies", @{const_name Metis.fimplies}))),
blanchet@41140
   511
   ("equal", (2, ("c_fequal", @{const_name Metis.fequal})))]
blanchet@41140
   512
blanchet@42531
   513
fun pred_combtyp ty =
blanchet@42531
   514
  case combtyp_from_typ @{typ "unit => bool"} of
blanchet@42531
   515
    CombType (name, [_, bool_ty]) => CombType (name, [ty, bool_ty])
blanchet@42531
   516
  | _ => raise Fail "expected two-argument type constructor"
blanchet@42531
   517
blanchet@42542
   518
fun type_pred_combatom type_sys ty tm =
blanchet@42542
   519
  CombApp (CombConst ((const_prefix ^ type_pred_base, type_pred_base),
blanchet@42542
   520
                      pred_combtyp ty, [ty]), tm)
blanchet@42542
   521
  |> repair_combterm_consts type_sys
blanchet@42534
   522
  |> AAtom
blanchet@42534
   523
blanchet@42530
   524
fun formula_for_combformula ctxt type_sys =
blanchet@38282
   525
  let
blanchet@42530
   526
    fun do_term top_level u =
blanchet@38282
   527
      let
blanchet@38282
   528
        val (head, args) = strip_combterm_comb u
blanchet@38282
   529
        val (x, ty_args) =
blanchet@38282
   530
          case head of
blanchet@38282
   531
            CombConst (name as (s, s'), _, ty_args) =>
blanchet@41140
   532
            (case AList.lookup (op =) fname_table s of
blanchet@41140
   533
               SOME (n, fname) =>
blanchet@42542
   534
(*### FIXME: do earlier? *)
blanchet@41150
   535
               (if top_level andalso length args = n then
blanchet@41150
   536
                  case s of
blanchet@41150
   537
                    "c_False" => ("$false", s')
blanchet@41150
   538
                  | "c_True" => ("$true", s')
blanchet@41150
   539
                  | _ => name
blanchet@41150
   540
                else
blanchet@41150
   541
                  fname, [])
blanchet@42542
   542
             | NONE => (name, ty_args))
blanchet@38282
   543
          | CombVar (name, _) => (name, [])
blanchet@38282
   544
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42530
   545
        val t = ATerm (x, map fo_term_for_combtyp ty_args @
blanchet@42530
   546
                          map (do_term false) 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@42531
   557
      if member (op =) [Args true, Mangled 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@42530
   572
      | do_formula (AAtom tm) = AAtom (do_term true 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@42180
   589
fun problem_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@38282
   595
fun problem_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@38282
   609
fun problem_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@41138
   618
fun problem_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@39975
   629
fun problem_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@42353
   632
fun problem_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@39975
   636
  in map2 problem_line_for_free_type (0 upto length lits - 1) lits end
blanchet@38282
   637
blanchet@38282
   638
(** "hBOOL" and "hAPP" **)
blanchet@38282
   639
blanchet@42542
   640
type hrepair_info = {min_arity: int, max_arity: int, pred_sym: bool}
blanchet@38282
   641
blanchet@42542
   642
fun consider_combterm_for_hrepair 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@42542
   651
               (s, {min_arity = n, max_arity = 0, pred_sym = true})
blanchet@42542
   652
               (fn {min_arity, max_arity, pred_sym} =>
blanchet@42542
   653
                   {min_arity = Int.min (n, min_arity),
blanchet@42542
   654
                    max_arity = Int.max (n, max_arity),
blanchet@42542
   655
                    pred_sym = pred_sym andalso top_level})
blanchet@42542
   656
        end
blanchet@42542
   657
     | _ => I)
blanchet@42542
   658
    #> fold (consider_combterm_for_hrepair false) args
blanchet@42542
   659
  end
blanchet@38282
   660
blanchet@42542
   661
fun consider_fact_for_hrepair ({combformula, ...} : translated_formula) =
blanchet@42542
   662
  formula_fold (consider_combterm_for_hrepair true) combformula
blanchet@38282
   663
blanchet@42539
   664
(* The "equal" entry is needed for helper facts if the problem otherwise does
blanchet@42539
   665
   not involve equality. *)
blanchet@42539
   666
val default_entries =
blanchet@42542
   667
  [("equal", {min_arity = 2, max_arity = 2, pred_sym = true}),
blanchet@42542
   668
   (boolify_name, {min_arity = 1, max_arity = 1, pred_sym = true})]
blanchet@41140
   669
blanchet@42542
   670
fun hrepair_table_for_facts explicit_apply facts =
blanchet@41140
   671
  if explicit_apply then
blanchet@41140
   672
    NONE
blanchet@41140
   673
  else
blanchet@42539
   674
    SOME (Symtab.empty |> fold Symtab.default default_entries
blanchet@42542
   675
                       |> fold consider_fact_for_hrepair facts)
blanchet@38282
   676
blanchet@41134
   677
fun min_arity_of thy type_sys NONE s =
blanchet@41138
   678
    (if s = "equal" orelse s = type_tag_name orelse
blanchet@38282
   679
        String.isPrefix type_const_prefix s orelse
blanchet@38282
   680
        String.isPrefix class_prefix s then
blanchet@38282
   681
       16383 (* large number *)
blanchet@38748
   682
     else case strip_prefix_and_unascii const_prefix s of
blanchet@42524
   683
       SOME s' => s' |> unmangled_const |> fst |> invert_const
blanchet@42524
   684
                     |> num_atp_type_args thy type_sys
blanchet@38282
   685
     | NONE => 0)
blanchet@42542
   686
  | min_arity_of _ _ (SOME hrepairs) s =
blanchet@42542
   687
    case Symtab.lookup hrepairs s of
blanchet@42542
   688
      SOME ({min_arity, ...} : hrepair_info) => min_arity
blanchet@38282
   689
    | NONE => 0
blanchet@38282
   690
blanchet@38282
   691
fun full_type_of (ATerm ((s, _), [ty, _])) =
blanchet@41138
   692
    if s = type_tag_name then SOME ty else NONE
blanchet@41138
   693
  | full_type_of _ = NONE
blanchet@38282
   694
blanchet@38282
   695
fun list_hAPP_rev _ t1 [] = t1
blanchet@38282
   696
  | list_hAPP_rev NONE t1 (t2 :: ts2) =
blanchet@42539
   697
    ATerm (`I explicit_app_name, [list_hAPP_rev NONE t1 ts2, t2])
blanchet@38282
   698
  | list_hAPP_rev (SOME ty) t1 (t2 :: ts2) =
blanchet@41138
   699
    case full_type_of t2 of
blanchet@41138
   700
      SOME ty2 =>
blanchet@41138
   701
      let val ty' = ATerm (`make_fixed_type_const @{type_name fun},
blanchet@41138
   702
                           [ty2, ty]) in
blanchet@42539
   703
        ATerm (`I explicit_app_name,
blanchet@41138
   704
               [tag_with_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2])
blanchet@41138
   705
      end
blanchet@41138
   706
    | NONE => list_hAPP_rev NONE t1 (t2 :: ts2)
blanchet@38282
   707
blanchet@42542
   708
fun hrepair_applications_in_term thy type_sys hrepairs =
blanchet@38282
   709
  let
blanchet@38282
   710
    fun aux opt_ty (ATerm (name as (s, _), ts)) =
blanchet@41138
   711
      if s = type_tag_name then
blanchet@38282
   712
        case ts of
blanchet@38282
   713
          [t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2])
blanchet@41138
   714
        | _ => raise Fail "malformed type tag"
blanchet@38282
   715
      else
blanchet@38282
   716
        let
blanchet@38282
   717
          val ts = map (aux NONE) ts
blanchet@42542
   718
          val (ts1, ts2) = chop (min_arity_of thy type_sys hrepairs s) ts
blanchet@38282
   719
        in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end
blanchet@38282
   720
  in aux NONE end
blanchet@38282
   721
blanchet@38282
   722
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   723
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   724
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   725
   arguments and is used as a predicate. *)
blanchet@42520
   726
fun is_pred_sym NONE s =
blanchet@38589
   727
    s = "equal" orelse s = "$false" orelse s = "$true" orelse
blanchet@38589
   728
    String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s
blanchet@42542
   729
  | is_pred_sym (SOME hrepairs) s =
blanchet@42542
   730
    case Symtab.lookup hrepairs s of
blanchet@42542
   731
      SOME {min_arity, max_arity, pred_sym} =>
blanchet@42542
   732
      pred_sym andalso min_arity = max_arity
blanchet@38282
   733
    | NONE => false
blanchet@38282
   734
blanchet@42542
   735
val boolify_combconst =
blanchet@42542
   736
  CombConst (`I boolify_name, combtyp_from_typ @{typ "bool => bool"}, [])
blanchet@42542
   737
fun boolify tm = CombApp (boolify_combconst, tm)
blanchet@42542
   738
blanchet@42542
   739
fun hrepair_pred_syms_in_combterm hrepairs tm =
blanchet@42542
   740
  case strip_combterm_comb tm of
blanchet@42542
   741
    (CombConst ((s, _), _, _), _) =>
blanchet@42542
   742
    if is_pred_sym hrepairs s then tm else boolify tm
blanchet@42542
   743
  | _ => boolify tm
blanchet@42542
   744
blanchet@42542
   745
fun hrepair_apps_in_combterm hrepairs tm = tm
blanchet@38282
   746
blanchet@42542
   747
fun hrepair_combterm type_sys hrepairs =
blanchet@42542
   748
  (case type_sys of Tags _ => I | _ => hrepair_pred_syms_in_combterm hrepairs)
blanchet@42542
   749
  #> hrepair_apps_in_combterm hrepairs
blanchet@42542
   750
val hrepair_combformula = formula_map oo hrepair_combterm
blanchet@42542
   751
val hrepair_fact = map_combformula oo hrepair_combformula
blanchet@38282
   752
blanchet@42542
   753
fun is_const_relevant type_sys hrepairs s =
blanchet@42542
   754
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42542
   755
  (type_sys = Many_Typed orelse not (is_pred_sym hrepairs s))
blanchet@38282
   756
blanchet@42542
   757
fun consider_combterm_consts type_sys hrepairs tm =
blanchet@42533
   758
  let val (head, args) = strip_combterm_comb tm in
blanchet@42533
   759
    (case head of
blanchet@42533
   760
       CombConst ((s, s'), ty, ty_args) =>
blanchet@42533
   761
       (* FIXME: exploit type subsumption *)
blanchet@42542
   762
       is_const_relevant type_sys hrepairs s
blanchet@42534
   763
       ? Symtab.insert_list (op =) (s, (s', ty_args, ty))
blanchet@42533
   764
     | _ => I) (* FIXME: hAPP on var *)
blanchet@42542
   765
    #> fold (consider_combterm_consts type_sys hrepairs) args
blanchet@42533
   766
  end
blanchet@42533
   767
blanchet@42542
   768
fun consider_fact_consts type_sys hrepairs
blanchet@42534
   769
                         ({combformula, ...} : translated_formula) =
blanchet@42542
   770
  formula_fold (consider_combterm_consts type_sys hrepairs) combformula
blanchet@42533
   771
blanchet@42542
   772
fun const_table_for_facts type_sys hrepairs facts =
blanchet@42533
   773
  Symtab.empty |> member (op =) [Many_Typed, Args true, Mangled true] type_sys
blanchet@42542
   774
                  ? fold (consider_fact_consts type_sys hrepairs) facts
blanchet@42533
   775
blanchet@42534
   776
fun strip_and_map_combtyp f (ty as CombType ((s, _), tys)) =
blanchet@42533
   777
    (case (strip_prefix_and_unascii type_const_prefix s, tys) of
blanchet@42533
   778
       (SOME @{type_name fun}, [dom_ty, ran_ty]) =>
blanchet@42534
   779
       strip_and_map_combtyp f ran_ty |>> cons (f dom_ty)
blanchet@42534
   780
     | _ => ([], f ty))
blanchet@42534
   781
  | strip_and_map_combtyp f ty = ([], f ty)
blanchet@42533
   782
blanchet@42543
   783
fun sym_decl_line_for_const_entry ctxt type_sys hrepairs s (s', ty_args, ty) =
blanchet@42534
   784
  if type_sys = Many_Typed then
blanchet@42534
   785
    let
blanchet@42534
   786
      val (arg_tys, res_ty) = strip_and_map_combtyp mangled_combtyp ty
blanchet@42542
   787
      val (s, s') = (s, s') |> mangled_const_name ty_args
blanchet@42534
   788
    in
blanchet@42543
   789
      Decl (sym_decl_prefix ^ ascii_of s, (s, s'), arg_tys,
blanchet@42543
   790
            if is_pred_sym hrepairs s then `I tff_bool_type else res_ty)
blanchet@42534
   791
    end
blanchet@42534
   792
  else
blanchet@42533
   793
    let
blanchet@42534
   794
      val (arg_tys, res_ty) = strip_and_map_combtyp I ty
blanchet@42534
   795
      val bounds =
blanchet@42534
   796
        map (`I o make_bound_var o string_of_int) (1 upto length arg_tys)
blanchet@42534
   797
        ~~ map SOME arg_tys
blanchet@42534
   798
      val bound_tms =
blanchet@42534
   799
        map (fn (name, ty) => CombConst (name, the ty, [])) bounds
blanchet@42534
   800
    in
blanchet@42543
   801
      Formula (Fof, sym_decl_prefix ^ ascii_of s, Axiom,
blanchet@42542
   802
               CombConst ((s, s'), ty, ty_args)
blanchet@42542
   803
               |> fold (curry (CombApp o swap)) bound_tms
blanchet@42542
   804
               |> type_pred_combatom type_sys res_ty
blanchet@42542
   805
               |> mk_aquant AForall bounds
blanchet@42534
   806
               |> formula_for_combformula ctxt type_sys,
blanchet@42534
   807
               NONE, NONE)
blanchet@42534
   808
    end
blanchet@42543
   809
fun sym_decl_lines_for_const ctxt type_sys hrepairs (s, xs) =
blanchet@42543
   810
  map (sym_decl_line_for_const_entry ctxt type_sys hrepairs s) xs
blanchet@42543
   811
blanchet@42543
   812
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
   813
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
   814
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
   815
    fold add_tff_types_in_formula phis
blanchet@42543
   816
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
   817
blanchet@42543
   818
fun add_tff_types_in_problem_line (Decl (_, _, arg_tys, res_ty)) =
blanchet@42543
   819
    union (op =) (res_ty :: arg_tys)
blanchet@42543
   820
  | add_tff_types_in_problem_line (Formula (_, _, _, phi, _, _)) =
blanchet@42543
   821
    add_tff_types_in_formula phi
blanchet@42543
   822
blanchet@42543
   823
fun tff_types_in_problem problem =
blanchet@42543
   824
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
   825
blanchet@42543
   826
fun problem_line_for_tff_type (s, s') =
blanchet@42543
   827
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tff_type_of_types)
blanchet@42543
   828
blanchet@42543
   829
val type_declsN = "Types"
blanchet@42543
   830
val sym_declsN = "Symbols"
blanchet@41157
   831
val factsN = "Relevant facts"
blanchet@41157
   832
val class_relsN = "Class relationships"
blanchet@42543
   833
val aritiesN = "Arities"
blanchet@41157
   834
val helpersN = "Helper facts"
blanchet@41157
   835
val conjsN = "Conjectures"
blanchet@41313
   836
val free_typesN = "Type variables"
blanchet@41157
   837
blanchet@41157
   838
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
   839
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
   840
    if heading = needle then j
blanchet@41157
   841
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
   842
blanchet@42521
   843
fun prepare_atp_problem ctxt readable_names type_sys explicit_apply hyp_ts
blanchet@42521
   844
                        concl_t facts =
blanchet@38282
   845
  let
blanchet@41313
   846
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
   847
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@42542
   848
    val hrepairs = hrepair_table_for_facts explicit_apply (conjs @ facts)
blanchet@42542
   849
    val conjs = map (hrepair_fact type_sys hrepairs) conjs
blanchet@42542
   850
    val facts = map (hrepair_fact type_sys hrepairs) facts
blanchet@42522
   851
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
   852
       Flotter hack. *)
blanchet@38282
   853
    val problem =
blanchet@42541
   854
      [(type_declsN, []),
blanchet@42543
   855
       (sym_declsN, []),
blanchet@42541
   856
       (factsN, map (problem_line_for_fact ctxt fact_prefix type_sys)
blanchet@42180
   857
                    (0 upto length facts - 1 ~~ facts)),
blanchet@41157
   858
       (class_relsN, map problem_line_for_class_rel_clause class_rel_clauses),
blanchet@41157
   859
       (aritiesN, map problem_line_for_arity_clause arity_clauses),
blanchet@41157
   860
       (helpersN, []),
blanchet@41313
   861
       (conjsN, map (problem_line_for_conjecture ctxt type_sys) conjs),
blanchet@42353
   862
       (free_typesN, problem_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42521
   863
    val helper_facts =
blanchet@42538
   864
      problem |> maps (map_filter (fn Formula (_, _, _, phi, _, _) => SOME phi
blanchet@42528
   865
                                    | _ => NONE) o snd)
blanchet@42527
   866
              |> get_helper_facts ctxt type_sys
blanchet@42542
   867
              |>> map (hrepair_fact type_sys hrepairs)
blanchet@42542
   868
    val const_tab = const_table_for_facts type_sys hrepairs (conjs @ facts)
blanchet@42543
   869
    val sym_decl_lines =
blanchet@42543
   870
      Symtab.fold_rev (append o sym_decl_lines_for_const ctxt type_sys hrepairs)
blanchet@42534
   871
                      const_tab []
blanchet@41157
   872
    val helper_lines =
blanchet@42521
   873
      helper_facts
blanchet@42542
   874
      |>> map (pair 0 #> problem_line_for_fact ctxt helper_prefix type_sys)
blanchet@41157
   875
      |> op @
blanchet@42543
   876
    val problem =
blanchet@42533
   877
      problem |> fold (AList.update (op =))
blanchet@42543
   878
                      [(sym_declsN, sym_decl_lines),
blanchet@42543
   879
                       (helpersN, helper_lines)]
blanchet@42543
   880
    val type_decl_lines =
blanchet@42543
   881
      if type_sys = Many_Typed then
blanchet@42543
   882
        problem |> tff_types_in_problem |> map problem_line_for_tff_type
blanchet@42543
   883
      else
blanchet@42543
   884
        []
blanchet@42543
   885
    val (problem, pool) =
blanchet@42543
   886
      problem |> AList.update (op =) (type_declsN, type_decl_lines)
blanchet@41140
   887
              |> nice_atp_problem readable_names
blanchet@38282
   888
  in
blanchet@38282
   889
    (problem,
blanchet@38282
   890
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42541
   891
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
   892
     offset_of_heading_in_problem conjsN problem 0,
blanchet@41157
   893
     fact_names |> Vector.fromList)
blanchet@38282
   894
  end
blanchet@38282
   895
blanchet@41313
   896
(* FUDGE *)
blanchet@41313
   897
val conj_weight = 0.0
blanchet@41770
   898
val hyp_weight = 0.1
blanchet@41770
   899
val fact_min_weight = 0.2
blanchet@41313
   900
val fact_max_weight = 1.0
blanchet@41313
   901
blanchet@41313
   902
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
   903
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
   904
  #> fold (add_term_weights weight) tms
blanchet@42538
   905
fun add_problem_line_weights weight (Formula (_, _, _, phi, _, _)) =
blanchet@42542
   906
    formula_fold (add_term_weights weight) phi
blanchet@42528
   907
  | add_problem_line_weights _ _ = I
blanchet@41313
   908
blanchet@41313
   909
fun add_conjectures_weights [] = I
blanchet@41313
   910
  | add_conjectures_weights conjs =
blanchet@41313
   911
    let val (hyps, conj) = split_last conjs in
blanchet@41313
   912
      add_problem_line_weights conj_weight conj
blanchet@41313
   913
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
   914
    end
blanchet@41313
   915
blanchet@41313
   916
fun add_facts_weights facts =
blanchet@41313
   917
  let
blanchet@41313
   918
    val num_facts = length facts
blanchet@41313
   919
    fun weight_of j =
blanchet@41313
   920
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
   921
                        / Real.fromInt num_facts
blanchet@41313
   922
  in
blanchet@41313
   923
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
   924
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
   925
  end
blanchet@41313
   926
blanchet@41313
   927
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
   928
fun atp_problem_weights problem =
blanchet@41313
   929
  Symtab.empty
blanchet@41313
   930
  |> add_conjectures_weights (these (AList.lookup (op =) problem conjsN))
blanchet@41313
   931
  |> add_facts_weights (these (AList.lookup (op =) problem factsN))
blanchet@41313
   932
  |> Symtab.dest
blanchet@41726
   933
  |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@41313
   934
blanchet@38282
   935
end;