src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Sun May 01 18:37:24 2011 +0200 (2011-05-01)
changeset 42561 23ddc4e3d19c
parent 42560 7bb3796a4975
child 42562 f1d903f789b1
permissions -rw-r--r--
have properly type-instantiated helper facts (combinators and If)
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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 update_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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fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
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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 num_type_args thy s
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  else 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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val unmangled_const_name = space_explode mangled_type_sep #> hd
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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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   315
  let
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   316
    fun aux (t $ u) = aux t $ aux u
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   317
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
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   318
      | aux (Var ((s, i), T)) =
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   319
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
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   320
      | aux t = t
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   321
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   322
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   323
(* making fact and conjecture formulas *)
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   324
fun make_formula ctxt eq_as_iff presimp name kind t =
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   325
  let
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   326
    val thy = Proof_Context.theory_of ctxt
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   327
    val t = t |> Envir.beta_eta_contract
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   328
              |> transform_elim_term
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   329
              |> Object_Logic.atomize_term thy
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   330
    val need_trueprop = (fastype_of t = HOLogic.boolT)
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   331
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
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   332
              |> extensionalize_term
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   333
              |> presimp ? presimplify_term thy
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   334
              |> perhaps (try (HOLogic.dest_Trueprop))
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   335
              |> introduce_combinators_in_term ctxt kind
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   336
              |> kind <> Axiom ? freeze_term
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   337
    val (combformula, ctypes_sorts) =
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   338
      combformula_for_prop thy eq_as_iff t []
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   339
  in
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   340
    {name = name, combformula = combformula, kind = kind,
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   341
     ctypes_sorts = ctypes_sorts}
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   342
  end
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   343
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   344
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, _), t) =
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   345
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name Axiom t) of
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   346
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
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   347
    NONE
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   348
  | (_, formula) => SOME formula
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   349
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   350
fun make_conjecture ctxt ts =
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   351
  let val last = length ts - 1 in
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   352
    map2 (fn j => make_formula ctxt true true (string_of_int j)
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   353
                               (if j = last then Conjecture else Hypothesis))
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   354
         (0 upto last) ts
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   355
  end
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   356
blanchet@38282
   357
(** Helper facts **)
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   358
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   359
fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
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   360
  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
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   361
  | formula_map f (AAtom tm) = AAtom (f tm)
blanchet@42542
   362
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   363
fun formula_fold f (AQuant (_, _, phi)) = formula_fold f phi
blanchet@42542
   364
  | formula_fold f (AConn (_, phis)) = fold (formula_fold f) phis
blanchet@42542
   365
  | formula_fold f (AAtom tm) = f tm
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   366
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   367
fun ti_ti_helper_fact () =
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   368
  let
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   369
    fun var s = ATerm (`I s, [])
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   370
    fun tag tm = ATerm (`I type_tag_name, [var "X", tm])
blanchet@38282
   371
  in
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   372
    Formula (Fof, helper_prefix ^ ascii_of "ti_ti", Axiom,
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   373
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42561
   374
             |> close_formula_universally, NONE, NONE)
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   375
  end
blanchet@38282
   376
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   377
(* FIXME #### : abolish combtyp altogether *)
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   378
fun typ_from_combtyp (CombType ((s, _), tys)) =
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   379
    Type (s |> strip_prefix_and_unascii type_const_prefix |> the
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   380
            |> invert_const,
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   381
          map typ_from_combtyp tys)
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   382
  | typ_from_combtyp (CombTFree (s, _)) =
blanchet@42561
   383
    TFree (s |> strip_prefix_and_unascii tfree_prefix |> the, HOLogic.typeS)
blanchet@42561
   384
  | typ_from_combtyp (CombTVar (s, _)) =
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   385
    TVar ((s |> strip_prefix_and_unascii tvar_prefix |> the, 0), HOLogic.typeS)
blanchet@42561
   386
blanchet@42561
   387
fun helper_facts_for_typed_const ctxt type_sys s (_, _, ty) =
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   388
  case strip_prefix_and_unascii const_prefix s of
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   389
    SOME s'' =>
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   390
    let
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   391
      val thy = Proof_Context.theory_of ctxt
blanchet@42561
   392
      val unmangled_s = s'' |> unmangled_const_name
blanchet@42561
   393
      (* ### FIXME avoid duplicate names *)
blanchet@42561
   394
      fun dub_and_inst c needs_full_types (th, j) =
blanchet@42561
   395
        ((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""),
blanchet@42561
   396
          false),
blanchet@42561
   397
         th |> prop_of
blanchet@42561
   398
            |> specialize_type thy (invert_const unmangled_s,
blanchet@42561
   399
                                    typ_from_combtyp ty))
blanchet@42561
   400
      fun make_facts eq_as_iff =
blanchet@42561
   401
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42561
   402
    in
blanchet@42561
   403
      metis_helpers
blanchet@42561
   404
      |> maps (fn (metis_s, (needs_full_types, ths)) =>
blanchet@42561
   405
                  if metis_s <> unmangled_s orelse
blanchet@42561
   406
                     (needs_full_types andalso
blanchet@42561
   407
                      not (type_system_types_dangerous_types type_sys)) then
blanchet@42561
   408
                    []
blanchet@42561
   409
                  else
blanchet@42561
   410
                    ths ~~ (1 upto length ths)
blanchet@42561
   411
                    |> map (dub_and_inst s needs_full_types)
blanchet@42561
   412
                    |> make_facts (not needs_full_types))
blanchet@42561
   413
    end
blanchet@42561
   414
  | NONE => []
blanchet@42561
   415
fun helper_facts_for_const ctxt type_sys (s, xs) =
blanchet@42561
   416
  maps (helper_facts_for_typed_const ctxt type_sys s) xs
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   417
fun helper_facts ctxt type_sys typed_const_tab =
blanchet@42561
   418
  (Symtab.fold_rev (append o helper_facts_for_const ctxt type_sys)
blanchet@42561
   419
                   typed_const_tab [],
blanchet@42561
   420
   if type_sys = Tags false then [ti_ti_helper_fact ()] else [])
blanchet@42561
   421
blanchet@42544
   422
fun translate_atp_fact ctxt keep_trivial =
blanchet@42561
   423
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@39004
   424
blanchet@41134
   425
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
blanchet@38282
   426
  let
wenzelm@42361
   427
    val thy = Proof_Context.theory_of ctxt
blanchet@41091
   428
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@41091
   429
    val (facts, fact_names) =
blanchet@41091
   430
      rich_facts
blanchet@41091
   431
      |> map_filter (fn (NONE, _) => NONE
blanchet@41091
   432
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@41091
   433
      |> ListPair.unzip
blanchet@40204
   434
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@39005
   435
       boost an ATP's performance (for some reason). *)
blanchet@40204
   436
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@38282
   437
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42353
   438
    val all_ts = goal_t :: fact_ts
blanchet@42353
   439
    val subs = tfree_classes_of_terms all_ts
blanchet@42353
   440
    val supers = tvar_classes_of_terms all_ts
blanchet@42353
   441
    val tycons = type_consts_of_terms thy all_ts
blanchet@42544
   442
    val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
blanchet@41137
   443
    val (supers', arity_clauses) =
blanchet@41137
   444
      if type_sys = No_Types then ([], [])
blanchet@41137
   445
      else make_arity_clauses thy tycons supers
blanchet@38282
   446
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@38282
   447
  in
blanchet@41313
   448
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@38282
   449
  end
blanchet@38282
   450
blanchet@42561
   451
val proxy_table =
blanchet@42561
   452
  [("c_False", ("c_fFalse", @{const_name Metis.fFalse})),
blanchet@42561
   453
   ("c_True", ("c_fTrue", @{const_name Metis.fTrue})),
blanchet@42561
   454
   ("c_Not", ("c_fNot", @{const_name Metis.fNot})),
blanchet@42561
   455
   ("c_conj", ("c_fconj", @{const_name Metis.fconj})),
blanchet@42561
   456
   ("c_disj", ("c_fdisj", @{const_name Metis.fdisj})),
blanchet@42561
   457
   ("c_implies", ("c_fimplies", @{const_name Metis.fimplies})),
blanchet@42561
   458
   ("equal", ("c_fequal", @{const_name Metis.fequal}))]
blanchet@42561
   459
blanchet@42561
   460
fun repair_combterm_consts type_sys =
blanchet@42561
   461
  let
blanchet@42561
   462
    fun aux top_level (CombApp (tm1, tm2)) =
blanchet@42561
   463
        CombApp (aux top_level tm1, aux false tm2)
blanchet@42561
   464
      | aux top_level (CombConst (name as (s, _), ty, ty_args)) =
blanchet@42561
   465
        (case strip_prefix_and_unascii const_prefix s of
blanchet@42561
   466
           NONE => (name, ty_args)
blanchet@42561
   467
         | SOME s'' =>
blanchet@42561
   468
           let val s'' = invert_const s'' in
blanchet@42561
   469
             case type_arg_policy type_sys s'' of
blanchet@42561
   470
               No_Type_Args => (name, [])
blanchet@42561
   471
             | Mangled_Types => (mangled_const_name ty_args name, [])
blanchet@42561
   472
             | Explicit_Type_Args => (name, ty_args)
blanchet@42561
   473
           end)
blanchet@42561
   474
        |> (fn (name as (s, s'), ty_args) =>
blanchet@42561
   475
               case AList.lookup (op =) proxy_table s of
blanchet@42561
   476
                 SOME proxy_name =>
blanchet@42561
   477
                 if top_level then
blanchet@42561
   478
                   (case s of
blanchet@42561
   479
                      "c_False" => ("$false", s')
blanchet@42561
   480
                    | "c_True" => ("$true", s')
blanchet@42561
   481
                    | _ => name, [])
blanchet@42561
   482
                  else
blanchet@42561
   483
                    (proxy_name, ty_args)
blanchet@42561
   484
                | NONE => (name, ty_args))
blanchet@42561
   485
        |> (fn (name, ty_args) => CombConst (name, ty, ty_args))
blanchet@42561
   486
      | aux _ tm = tm
blanchet@42561
   487
  in aux true end
blanchet@42561
   488
blanchet@41138
   489
fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t])
blanchet@38282
   490
blanchet@38282
   491
fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
blanchet@38282
   492
  | fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
blanchet@38282
   493
  | fo_term_for_combtyp (CombType (name, tys)) =
blanchet@38282
   494
    ATerm (name, map fo_term_for_combtyp tys)
blanchet@38282
   495
blanchet@38282
   496
fun fo_literal_for_type_literal (TyLitVar (class, name)) =
blanchet@38282
   497
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   498
  | fo_literal_for_type_literal (TyLitFree (class, name)) =
blanchet@38282
   499
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   500
blanchet@38282
   501
fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@38282
   502
blanchet@41138
   503
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@41138
   504
   considered dangerous because their "exhaust" properties can easily lead to
blanchet@41138
   505
   unsound ATP proofs. The checks below are an (unsound) approximation of
blanchet@41138
   506
   finiteness. *)
blanchet@41138
   507
blanchet@41138
   508
fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true
blanchet@41138
   509
  | is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) =
blanchet@41138
   510
    is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us
blanchet@41138
   511
  | is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false
blanchet@41138
   512
and is_type_dangerous ctxt (Type (s, Ts)) =
blanchet@41138
   513
    is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts
blanchet@41140
   514
  | is_type_dangerous _ _ = false
blanchet@41138
   515
and is_type_constr_dangerous ctxt s =
wenzelm@42361
   516
  let val thy = Proof_Context.theory_of ctxt in
blanchet@41138
   517
    case Datatype_Data.get_info thy s of
blanchet@41138
   518
      SOME {descr, ...} =>
blanchet@41138
   519
      forall (fn (_, (_, _, constrs)) =>
blanchet@41138
   520
                 forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr
blanchet@41138
   521
    | NONE =>
blanchet@41138
   522
      case Typedef.get_info ctxt s of
blanchet@41138
   523
        ({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type
blanchet@41138
   524
      | [] => true
blanchet@41138
   525
  end
blanchet@41138
   526
blanchet@41138
   527
fun is_combtyp_dangerous ctxt (CombType ((s, _), tys)) =
blanchet@41138
   528
    (case strip_prefix_and_unascii type_const_prefix s of
blanchet@41138
   529
       SOME s' => forall (is_combtyp_dangerous ctxt) tys andalso
blanchet@41138
   530
                  is_type_constr_dangerous ctxt (invert_const s')
blanchet@41138
   531
     | NONE => false)
blanchet@41138
   532
  | is_combtyp_dangerous _ _ = false
blanchet@41138
   533
blanchet@41138
   534
fun should_tag_with_type ctxt (Tags full_types) ty =
blanchet@41138
   535
    full_types orelse is_combtyp_dangerous ctxt ty
blanchet@41138
   536
  | should_tag_with_type _ _ _ = false
blanchet@41138
   537
blanchet@42531
   538
fun pred_combtyp ty =
blanchet@42531
   539
  case combtyp_from_typ @{typ "unit => bool"} of
blanchet@42531
   540
    CombType (name, [_, bool_ty]) => CombType (name, [ty, bool_ty])
blanchet@42531
   541
  | _ => raise Fail "expected two-argument type constructor"
blanchet@42531
   542
blanchet@42542
   543
fun type_pred_combatom type_sys ty tm =
blanchet@42549
   544
  CombApp (CombConst (`make_fixed_const type_pred_base, pred_combtyp ty, [ty]),
blanchet@42549
   545
           tm)
blanchet@42542
   546
  |> repair_combterm_consts type_sys
blanchet@42534
   547
  |> AAtom
blanchet@42534
   548
blanchet@42530
   549
fun formula_for_combformula ctxt type_sys =
blanchet@38282
   550
  let
blanchet@42556
   551
    fun do_term top_level u =
blanchet@38282
   552
      let
blanchet@38282
   553
        val (head, args) = strip_combterm_comb u
blanchet@38282
   554
        val (x, ty_args) =
blanchet@38282
   555
          case head of
blanchet@42553
   556
            CombConst (name, _, ty_args) => (name, ty_args)
blanchet@38282
   557
          | CombVar (name, _) => (name, [])
blanchet@38282
   558
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42556
   559
        val t = ATerm (x, map fo_term_for_combtyp ty_args @
blanchet@42556
   560
                          map (do_term false) args)
blanchet@41138
   561
        val ty = combtyp_of u
blanchet@42530
   562
      in
blanchet@42556
   563
        t |> (if not top_level andalso
blanchet@42556
   564
                 should_tag_with_type ctxt type_sys ty then
blanchet@42530
   565
                tag_with_type (fo_term_for_combtyp ty)
blanchet@42530
   566
              else
blanchet@42530
   567
                I)
blanchet@42530
   568
      end
blanchet@42531
   569
    val do_bound_type =
blanchet@42531
   570
      if type_sys = Many_Typed then SOME o mangled_combtyp else K NONE
blanchet@42531
   571
    val do_out_of_bound_type =
blanchet@42548
   572
      if member (op =) [Mangled true, Args true] type_sys then
blanchet@42531
   573
        (fn (s, ty) =>
blanchet@42542
   574
            type_pred_combatom type_sys ty (CombVar (s, ty))
blanchet@42534
   575
            |> formula_for_combformula ctxt type_sys |> SOME)
blanchet@42531
   576
      else
blanchet@42531
   577
        K NONE
blanchet@42530
   578
    fun do_formula (AQuant (q, xs, phi)) =
blanchet@42531
   579
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42531
   580
                                      | SOME ty => do_bound_type ty)),
blanchet@42534
   581
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42531
   582
                    (map_filter
blanchet@42531
   583
                         (fn (_, NONE) => NONE
blanchet@42531
   584
                           | (s, SOME ty) => do_out_of_bound_type (s, ty)) xs)
blanchet@42531
   585
                    (do_formula phi))
blanchet@42530
   586
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42556
   587
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42530
   588
  in do_formula end
blanchet@38282
   589
blanchet@41138
   590
fun formula_for_fact ctxt type_sys
blanchet@40204
   591
                     ({combformula, ctypes_sorts, ...} : translated_formula) =
blanchet@38282
   592
  mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
blanchet@42353
   593
                (atp_type_literals_for_types type_sys Axiom ctypes_sorts))
blanchet@42522
   594
           (formula_for_combformula ctxt type_sys
blanchet@42522
   595
                                    (close_combformula_universally combformula))
blanchet@42542
   596
  |> close_formula_universally
blanchet@38282
   597
blanchet@42538
   598
fun logic_for_type_sys Many_Typed = Tff
blanchet@42538
   599
  | logic_for_type_sys _ = Fof
blanchet@42538
   600
blanchet@42180
   601
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42180
   602
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42180
   603
   the remote provers might care. *)
blanchet@42545
   604
fun formula_line_for_fact ctxt prefix type_sys
blanchet@42180
   605
                          (j, formula as {name, kind, ...}) =
blanchet@42538
   606
  Formula (logic_for_type_sys type_sys,
blanchet@42538
   607
           prefix ^ string_of_int j ^ "_" ^ ascii_of name, kind,
blanchet@42538
   608
           formula_for_fact ctxt type_sys formula, NONE, NONE)
blanchet@38282
   609
blanchet@42545
   610
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@38282
   611
                                                       superclass, ...}) =
blanchet@42542
   612
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42538
   613
    Formula (Fof, class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42527
   614
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42542
   615
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42542
   616
             |> close_formula_universally, NONE, NONE)
blanchet@38282
   617
  end
blanchet@38282
   618
blanchet@38282
   619
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
blanchet@38282
   620
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@38282
   621
  | fo_literal_for_arity_literal (TVarLit (c, sort)) =
blanchet@38282
   622
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@38282
   623
blanchet@42545
   624
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@38282
   625
                                                ...}) =
blanchet@42538
   626
  Formula (Fof, arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42527
   627
           mk_ahorn (map (formula_for_fo_literal o apfst not
blanchet@42527
   628
                          o fo_literal_for_arity_literal) premLits)
blanchet@42527
   629
                    (formula_for_fo_literal
blanchet@42542
   630
                         (fo_literal_for_arity_literal conclLit))
blanchet@42542
   631
           |> close_formula_universally, NONE, NONE)
blanchet@38282
   632
blanchet@42545
   633
fun formula_line_for_conjecture ctxt type_sys
blanchet@40114
   634
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42538
   635
  Formula (logic_for_type_sys type_sys, conjecture_prefix ^ name, kind,
blanchet@42527
   636
           formula_for_combformula ctxt type_sys
blanchet@42542
   637
                                   (close_combformula_universally combformula)
blanchet@42542
   638
           |> close_formula_universally, NONE, NONE)
blanchet@38282
   639
blanchet@42353
   640
fun free_type_literals type_sys ({ctypes_sorts, ...} : translated_formula) =
blanchet@42353
   641
  ctypes_sorts |> atp_type_literals_for_types type_sys Conjecture
blanchet@41137
   642
               |> map fo_literal_for_type_literal
blanchet@38282
   643
blanchet@42545
   644
fun formula_line_for_free_type j lit =
blanchet@42538
   645
  Formula (Fof, tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42529
   646
           formula_for_fo_literal lit, NONE, NONE)
blanchet@42545
   647
fun formula_lines_for_free_types type_sys facts =
blanchet@38282
   648
  let
blanchet@42353
   649
    val litss = map (free_type_literals type_sys) facts
blanchet@38282
   650
    val lits = fold (union (op =)) litss []
blanchet@42545
   651
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@38282
   652
blanchet@38282
   653
(** "hBOOL" and "hAPP" **)
blanchet@38282
   654
blanchet@42544
   655
type repair_info = {pred_sym: bool, min_arity: int, max_arity: int}
blanchet@38282
   656
blanchet@42560
   657
fun add_combterm_to_sym_table explicit_apply =
blanchet@42558
   658
  let
blanchet@42558
   659
    fun aux top_level tm =
blanchet@42558
   660
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   661
        (case head of
blanchet@42558
   662
           CombConst ((s, _), _, _) =>
blanchet@42558
   663
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   664
             I
blanchet@42558
   665
           else
blanchet@42558
   666
             let val arity = length args in
blanchet@42558
   667
               Symtab.map_default
blanchet@42558
   668
                   (s, {pred_sym = true,
blanchet@42558
   669
                        min_arity = if explicit_apply then 0 else arity,
blanchet@42558
   670
                        max_arity = 0})
blanchet@42558
   671
                   (fn {pred_sym, min_arity, max_arity} =>
blanchet@42558
   672
                       {pred_sym = pred_sym andalso top_level,
blanchet@42558
   673
                        min_arity = Int.min (arity, min_arity),
blanchet@42558
   674
                        max_arity = Int.max (arity, max_arity)})
blanchet@42558
   675
            end
blanchet@42558
   676
         | _ => I)
blanchet@42558
   677
        #> fold (aux false) args
blanchet@42558
   678
      end
blanchet@42558
   679
  in aux true end
blanchet@38282
   680
blanchet@42560
   681
val add_fact_to_sym_table = fact_lift o formula_fold o add_combterm_to_sym_table
blanchet@38282
   682
blanchet@42539
   683
(* The "equal" entry is needed for helper facts if the problem otherwise does
blanchet@42557
   684
   not involve equality. The "$false" and $"true" entries are needed to ensure
blanchet@42557
   685
   that no "hBOOL" is introduced for them. The "hBOOL" entry is needed to ensure
blanchet@42557
   686
   that no "hAPP"s are introduced for passing arguments to it. *)
blanchet@42557
   687
val default_sym_table_entries =
blanchet@42544
   688
  [("equal", {pred_sym = true, min_arity = 2, max_arity = 2}),
blanchet@42557
   689
   ("$false", {pred_sym = true, min_arity = 0, max_arity = 0}),
blanchet@42557
   690
   ("$true", {pred_sym = true, min_arity = 0, max_arity = 0}),
blanchet@42544
   691
   (make_fixed_const boolify_base,
blanchet@42545
   692
    {pred_sym = true, min_arity = 1, max_arity = 1})]
blanchet@41140
   693
blanchet@42544
   694
fun sym_table_for_facts explicit_apply facts =
blanchet@42558
   695
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42560
   696
               |> fold (add_fact_to_sym_table explicit_apply) facts
blanchet@38282
   697
blanchet@42558
   698
fun min_arity_of sym_tab s =
blanchet@42558
   699
  case Symtab.lookup sym_tab s of
blanchet@42558
   700
    SOME ({min_arity, ...} : repair_info) => min_arity
blanchet@42558
   701
  | NONE =>
blanchet@42558
   702
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   703
      SOME s =>
blanchet@42561
   704
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42547
   705
        if s = boolify_base then 1
blanchet@42547
   706
        else if s = explicit_app_base then 2
blanchet@42547
   707
        else if s = type_pred_base then 1
blanchet@42557
   708
        else 0
blanchet@42547
   709
      end
blanchet@42544
   710
    | NONE => 0
blanchet@38282
   711
blanchet@38282
   712
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   713
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   714
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   715
   arguments and is used as a predicate. *)
blanchet@42558
   716
fun is_pred_sym sym_tab s =
blanchet@42558
   717
  case Symtab.lookup sym_tab s of
blanchet@42558
   718
    SOME {pred_sym, min_arity, max_arity} =>
blanchet@42558
   719
    pred_sym andalso min_arity = max_arity
blanchet@42558
   720
  | NONE => false
blanchet@38282
   721
blanchet@42542
   722
val boolify_combconst =
blanchet@42544
   723
  CombConst (`make_fixed_const boolify_base,
blanchet@42544
   724
             combtyp_from_typ @{typ "bool => bool"}, [])
blanchet@42542
   725
fun boolify tm = CombApp (boolify_combconst, tm)
blanchet@42542
   726
blanchet@42544
   727
fun repair_pred_syms_in_combterm sym_tab tm =
blanchet@42542
   728
  case strip_combterm_comb tm of
blanchet@42542
   729
    (CombConst ((s, _), _, _), _) =>
blanchet@42544
   730
    if is_pred_sym sym_tab s then tm else boolify tm
blanchet@42542
   731
  | _ => boolify tm
blanchet@42542
   732
blanchet@42544
   733
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   734
blanchet@42544
   735
val fun_name = `make_fixed_type_const @{type_name fun}
blanchet@42544
   736
blanchet@42544
   737
fun explicit_app arg head =
blanchet@42544
   738
  let
blanchet@42544
   739
    val head_ty = combtyp_of head
blanchet@42544
   740
    val (arg_ty, res_ty) = dest_combfun head_ty
blanchet@42544
   741
    val explicit_app =
blanchet@42544
   742
      CombConst (`make_fixed_const explicit_app_base,
blanchet@42544
   743
                 CombType (fun_name, [head_ty, head_ty]), [arg_ty, res_ty])
blanchet@42544
   744
  in list_app explicit_app [head, arg] end
blanchet@42544
   745
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   746
blanchet@42557
   747
fun repair_apps_in_combterm sym_tab =
blanchet@42544
   748
  let
blanchet@42544
   749
    fun aux tm =
blanchet@42544
   750
      case strip_combterm_comb tm of
blanchet@42544
   751
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   752
        args |> map aux
blanchet@42557
   753
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   754
             |>> list_app head
blanchet@42544
   755
             |-> list_explicit_app
blanchet@42544
   756
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   757
  in aux end
blanchet@38282
   758
blanchet@42557
   759
fun repair_combterm type_sys sym_tab =
blanchet@42556
   760
  repair_pred_syms_in_combterm sym_tab
blanchet@42557
   761
  #> repair_apps_in_combterm sym_tab
blanchet@42544
   762
  #> repair_combterm_consts type_sys
blanchet@42557
   763
val repair_combformula = formula_map oo repair_combterm
blanchet@42558
   764
val repair_fact = update_combformula oo repair_combformula
blanchet@42544
   765
blanchet@42544
   766
fun is_const_relevant type_sys sym_tab s =
blanchet@42542
   767
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42544
   768
  (type_sys = Many_Typed orelse not (is_pred_sym sym_tab s))
blanchet@38282
   769
blanchet@42544
   770
fun consider_combterm_consts type_sys sym_tab tm =
blanchet@42533
   771
  let val (head, args) = strip_combterm_comb tm in
blanchet@42533
   772
    (case head of
blanchet@42533
   773
       CombConst ((s, s'), ty, ty_args) =>
blanchet@42533
   774
       (* FIXME: exploit type subsumption *)
blanchet@42544
   775
       is_const_relevant type_sys sym_tab s
blanchet@42534
   776
       ? Symtab.insert_list (op =) (s, (s', ty_args, ty))
blanchet@42544
   777
     | _ => I)
blanchet@42544
   778
    #> fold (consider_combterm_consts type_sys sym_tab) args
blanchet@42533
   779
  end
blanchet@42533
   780
blanchet@42558
   781
fun consider_fact_consts type_sys sym_tab =
blanchet@42558
   782
  fact_lift (formula_fold (consider_combterm_consts type_sys sym_tab))
blanchet@42533
   783
blanchet@42545
   784
(* FIXME: needed? *)
blanchet@42561
   785
fun typed_const_table_for_facts type_sys sym_tab facts =
blanchet@42548
   786
  Symtab.empty |> member (op =) [Many_Typed, Mangled true, Args true] type_sys
blanchet@42544
   787
                  ? fold (consider_fact_consts type_sys sym_tab) facts
blanchet@42533
   788
blanchet@42544
   789
fun strip_and_map_combtyp 0 f ty = ([], f ty)
blanchet@42544
   790
  | strip_and_map_combtyp n f (ty as CombType ((s, _), tys)) =
blanchet@42533
   791
    (case (strip_prefix_and_unascii type_const_prefix s, tys) of
blanchet@42533
   792
       (SOME @{type_name fun}, [dom_ty, ran_ty]) =>
blanchet@42544
   793
       strip_and_map_combtyp (n - 1) f ran_ty |>> cons (f dom_ty)
blanchet@42534
   794
     | _ => ([], f ty))
blanchet@42544
   795
  | strip_and_map_combtyp _ _ _ = raise Fail "unexpected non-function"
blanchet@42533
   796
blanchet@42546
   797
fun problem_line_for_typed_const ctxt type_sys sym_tab s j (s', ty_args, ty) =
blanchet@42557
   798
  let val arity = min_arity_of sym_tab s in
blanchet@42544
   799
    if type_sys = Many_Typed then
blanchet@42544
   800
      let
blanchet@42544
   801
        val (arg_tys, res_ty) = strip_and_map_combtyp arity mangled_combtyp ty
blanchet@42544
   802
        val (s, s') = (s, s') |> mangled_const_name ty_args
blanchet@42544
   803
      in
blanchet@42546
   804
        Decl (sym_decl_prefix ^ ascii_of s, (s, s'),
blanchet@42546
   805
              arg_tys,
blanchet@42561
   806
              (* ### FIXME: put that in typed_const_tab *)
blanchet@42544
   807
              if is_pred_sym sym_tab s then `I tff_bool_type else res_ty)
blanchet@42544
   808
      end
blanchet@42544
   809
    else
blanchet@42544
   810
      let
blanchet@42544
   811
        val (arg_tys, res_ty) = strip_and_map_combtyp arity I ty
blanchet@42544
   812
        val bounds =
blanchet@42544
   813
          map (`I o make_bound_var o string_of_int) (1 upto length arg_tys)
blanchet@42544
   814
          ~~ map SOME arg_tys
blanchet@42544
   815
        val bound_tms =
blanchet@42544
   816
          map (fn (name, ty) => CombConst (name, the ty, [])) bounds
blanchet@42546
   817
        val freshener =
blanchet@42546
   818
          case type_sys of Args _ => string_of_int j ^ "_" | _ => ""
blanchet@42544
   819
      in
blanchet@42546
   820
        Formula (Fof, sym_decl_prefix ^ freshener ^ "_" ^ ascii_of s, Axiom,
blanchet@42544
   821
                 CombConst ((s, s'), ty, ty_args)
blanchet@42544
   822
                 |> fold (curry (CombApp o swap)) bound_tms
blanchet@42544
   823
                 |> type_pred_combatom type_sys res_ty
blanchet@42544
   824
                 |> mk_aquant AForall bounds
blanchet@42544
   825
                 |> formula_for_combformula ctxt type_sys,
blanchet@42544
   826
                 NONE, NONE)
blanchet@42544
   827
      end
blanchet@42544
   828
  end
blanchet@42561
   829
fun problem_lines_for_sym_decl ctxt type_sys sym_tab (s, xs) =
blanchet@42546
   830
  map2 (problem_line_for_typed_const ctxt type_sys sym_tab s)
blanchet@42546
   831
       (0 upto length xs - 1) xs
blanchet@42561
   832
fun problem_lines_for_sym_decls ctxt type_sys repaired_sym_tab typed_const_tab =
blanchet@42561
   833
  Symtab.fold_rev
blanchet@42561
   834
      (append o problem_lines_for_sym_decl ctxt type_sys repaired_sym_tab)
blanchet@42561
   835
      typed_const_tab []
blanchet@42543
   836
blanchet@42543
   837
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
   838
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
   839
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
   840
    fold add_tff_types_in_formula phis
blanchet@42543
   841
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
   842
blanchet@42543
   843
fun add_tff_types_in_problem_line (Decl (_, _, arg_tys, res_ty)) =
blanchet@42543
   844
    union (op =) (res_ty :: arg_tys)
blanchet@42543
   845
  | add_tff_types_in_problem_line (Formula (_, _, _, phi, _, _)) =
blanchet@42543
   846
    add_tff_types_in_formula phi
blanchet@42543
   847
blanchet@42543
   848
fun tff_types_in_problem problem =
blanchet@42543
   849
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
   850
blanchet@42545
   851
fun decl_line_for_tff_type (s, s') =
blanchet@42543
   852
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tff_type_of_types)
blanchet@42543
   853
blanchet@42543
   854
val type_declsN = "Types"
blanchet@42544
   855
val sym_declsN = "Symbol types"
blanchet@41157
   856
val factsN = "Relevant facts"
blanchet@41157
   857
val class_relsN = "Class relationships"
blanchet@42543
   858
val aritiesN = "Arities"
blanchet@41157
   859
val helpersN = "Helper facts"
blanchet@41157
   860
val conjsN = "Conjectures"
blanchet@41313
   861
val free_typesN = "Type variables"
blanchet@41157
   862
blanchet@41157
   863
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
   864
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
   865
    if heading = needle then j
blanchet@41157
   866
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
   867
blanchet@42521
   868
fun prepare_atp_problem ctxt readable_names type_sys explicit_apply hyp_ts
blanchet@42521
   869
                        concl_t facts =
blanchet@38282
   870
  let
blanchet@41313
   871
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
   872
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@42544
   873
    val sym_tab = sym_table_for_facts explicit_apply (conjs @ facts)
blanchet@42561
   874
    val conjs = conjs |> map (repair_fact type_sys sym_tab)
blanchet@42561
   875
    val facts = facts |> map (repair_fact type_sys sym_tab)
blanchet@42561
   876
    val repaired_sym_tab = sym_table_for_facts false (conjs @ facts)
blanchet@42561
   877
    val typed_const_tab =
blanchet@42561
   878
      typed_const_table_for_facts type_sys repaired_sym_tab (conjs @ facts)
blanchet@42561
   879
    val sym_decl_lines =
blanchet@42561
   880
      problem_lines_for_sym_decls ctxt type_sys repaired_sym_tab typed_const_tab
blanchet@42561
   881
    val (helpers, raw_helper_lines) = helper_facts ctxt type_sys typed_const_tab
blanchet@42561
   882
    val helpers = helpers |> map (repair_fact type_sys sym_tab)
blanchet@42522
   883
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
   884
       Flotter hack. *)
blanchet@38282
   885
    val problem =
blanchet@42561
   886
      [(sym_declsN, sym_decl_lines),
blanchet@42545
   887
       (factsN, map (formula_line_for_fact ctxt fact_prefix type_sys)
blanchet@42180
   888
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
   889
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
   890
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42561
   891
       (helpersN, map (formula_line_for_fact ctxt helper_prefix type_sys)
blanchet@42561
   892
                      (0 upto length helpers - 1 ~~ helpers) @
blanchet@42561
   893
                  raw_helper_lines),
blanchet@42545
   894
       (conjsN, map (formula_line_for_conjecture ctxt type_sys) conjs),
blanchet@42545
   895
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
   896
    val problem =
blanchet@42561
   897
      problem
blanchet@42561
   898
      |> (if type_sys = Many_Typed then
blanchet@42561
   899
            cons (type_declsN,
blanchet@42561
   900
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42561
   901
          else
blanchet@42561
   902
            I)
blanchet@42561
   903
    val (problem, pool) = problem |> nice_atp_problem readable_names
blanchet@38282
   904
  in
blanchet@38282
   905
    (problem,
blanchet@38282
   906
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42541
   907
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
   908
     offset_of_heading_in_problem conjsN problem 0,
blanchet@41157
   909
     fact_names |> Vector.fromList)
blanchet@38282
   910
  end
blanchet@38282
   911
blanchet@41313
   912
(* FUDGE *)
blanchet@41313
   913
val conj_weight = 0.0
blanchet@41770
   914
val hyp_weight = 0.1
blanchet@41770
   915
val fact_min_weight = 0.2
blanchet@41313
   916
val fact_max_weight = 1.0
blanchet@41313
   917
blanchet@41313
   918
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
   919
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
   920
  #> fold (add_term_weights weight) tms
blanchet@42538
   921
fun add_problem_line_weights weight (Formula (_, _, _, phi, _, _)) =
blanchet@42542
   922
    formula_fold (add_term_weights weight) phi
blanchet@42528
   923
  | add_problem_line_weights _ _ = I
blanchet@41313
   924
blanchet@41313
   925
fun add_conjectures_weights [] = I
blanchet@41313
   926
  | add_conjectures_weights conjs =
blanchet@41313
   927
    let val (hyps, conj) = split_last conjs in
blanchet@41313
   928
      add_problem_line_weights conj_weight conj
blanchet@41313
   929
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
   930
    end
blanchet@41313
   931
blanchet@41313
   932
fun add_facts_weights facts =
blanchet@41313
   933
  let
blanchet@41313
   934
    val num_facts = length facts
blanchet@41313
   935
    fun weight_of j =
blanchet@41313
   936
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
   937
                        / Real.fromInt num_facts
blanchet@41313
   938
  in
blanchet@41313
   939
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
   940
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
   941
  end
blanchet@41313
   942
blanchet@41313
   943
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
   944
fun atp_problem_weights problem =
blanchet@41313
   945
  Symtab.empty
blanchet@41313
   946
  |> add_conjectures_weights (these (AList.lookup (op =) problem conjsN))
blanchet@41313
   947
  |> add_facts_weights (these (AList.lookup (op =) problem factsN))
blanchet@41313
   948
  |> Symtab.dest
blanchet@41726
   949
  |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@41313
   950
blanchet@38282
   951
end;