src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Sun May 01 18:37:24 2011 +0200 (2011-05-01)
changeset 42539 f6ba908b8b27
parent 42538 9e3e45636459
child 42540 77d9915e6a11
permissions -rw-r--r--
generate typing for "hBOOL" in "Many_Typed" mode + tuning
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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 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 unmangled_const : string -> string * string fo_term list
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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 * (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 fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val type_decl_prefix = "type_"
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val class_rel_clause_prefix = "clrel_";
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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 is_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_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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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 <> is_base andalso
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  (member (op =) [@{const_name HOL.eq}, @{const_name Metis.fequal}] 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 = is_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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fun combformula_for_prop thy eq_as_iff =
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  let
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    fun do_term bs t ts =
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      combterm_from_term thy bs (Envir.eta_contract t)
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      |>> AAtom ||> union (op =) ts
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    fun do_quant bs q s T t' =
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      let val s = Name.variant (map fst bs) s in
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        do_formula ((s, T) :: bs) t'
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        #>> mk_aquant q [(`make_bound_var s, SOME (combtyp_from_typ T))]
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      end
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    and do_conn bs c t1 t2 =
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      do_formula bs t1 ##>> do_formula bs t2
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      #>> uncurry (mk_aconn c)
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    and do_formula bs t =
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      case t of
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        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
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      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
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        do_quant bs AForall s T t'
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      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
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        do_quant bs AExists s T t'
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      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
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      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
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      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
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      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
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        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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      | _ => do_term bs t
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  in do_formula [] end
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val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
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fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
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fun conceal_bounds Ts t =
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  subst_bounds (map (Free o apfst concealed_bound_name)
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                    (0 upto length Ts - 1 ~~ Ts), t)
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fun reveal_bounds Ts =
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  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
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                    (0 upto length Ts - 1 ~~ Ts))
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(* Removes the lambdas from an equation of the form "t = (%x. u)".
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   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
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fun extensionalize_term t =
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  let
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    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
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      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
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                                        Type (_, [_, res_T])]))
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                    $ t2 $ Abs (var_s, var_T, t')) =
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        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
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          let val var_t = Var ((var_s, j), var_T) in
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            Const (s, T' --> T' --> res_T)
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              $ betapply (t2, var_t) $ subst_bound (var_t, t')
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            |> aux (j + 1)
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          end
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        else
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          t
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      | aux _ t = t
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  in aux (maxidx_of_term t + 1) t end
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fun introduce_combinators_in_term ctxt kind t =
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  let val thy = Proof_Context.theory_of ctxt in
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    if Meson.is_fol_term thy t then
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      t
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    else
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      let
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        fun aux Ts t =
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          case t of
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            @{const Not} $ t1 => @{const Not} $ aux Ts t1
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          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
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            t0 $ Abs (s, T, aux (T :: Ts) t')
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          | (t0 as Const (@{const_name All}, _)) $ t1 =>
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            aux Ts (t0 $ eta_expand Ts t1 1)
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          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
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            t0 $ Abs (s, T, aux (T :: Ts) t')
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          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
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            aux Ts (t0 $ eta_expand Ts t1 1)
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          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
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          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
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          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
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          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
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              $ t1 $ t2 =>
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            t0 $ aux Ts t1 $ aux Ts t2
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          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
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                   t
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                 else
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                   t |> conceal_bounds Ts
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                     |> Envir.eta_contract
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                     |> cterm_of thy
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                     |> Meson_Clausify.introduce_combinators_in_cterm
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                     |> prop_of |> Logic.dest_equals |> snd
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                     |> reveal_bounds Ts
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        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
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      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
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      handle THM _ =>
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             (* A type variable of sort "{}" will make abstraction fail. *)
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             if kind = Conjecture then HOLogic.false_const
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             else HOLogic.true_const
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  end
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(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
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   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
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fun freeze_term t =
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  let
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    fun aux (t $ u) = aux t $ aux u
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      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
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      | aux (Var ((s, i), T)) =
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        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
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      | aux t = t
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  in t |> exists_subterm is_Var t ? aux end
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(* making fact and conjecture formulas *)
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fun make_formula ctxt eq_as_iff presimp name kind t =
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  let
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    val thy = Proof_Context.theory_of ctxt
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    val t = t |> Envir.beta_eta_contract
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              |> transform_elim_term
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              |> Object_Logic.atomize_term thy
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    val need_trueprop = (fastype_of t = HOLogic.boolT)
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    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
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              |> extensionalize_term
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              |> presimp ? presimplify_term thy
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              |> perhaps (try (HOLogic.dest_Trueprop))
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              |> introduce_combinators_in_term ctxt kind
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              |> kind <> Axiom ? freeze_term
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    val (combformula, ctypes_sorts) = combformula_for_prop thy eq_as_iff t []
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  in
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    {name = name, combformula = combformula, kind = kind,
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     ctypes_sorts = ctypes_sorts}
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  end
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fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, _), th) =
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  case (keep_trivial,
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        make_formula ctxt eq_as_iff presimp name Axiom (prop_of th)) of
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    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
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    NONE
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  | (_, formula) => SOME formula
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fun make_conjecture ctxt ts =
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  let val last = length ts - 1 in
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    map2 (fn j => make_formula ctxt true true (string_of_int j)
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                               (if j = last then Conjecture else Hypothesis))
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         (0 upto last) ts
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  end
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(** Helper facts **)
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fun fold_formula f (AQuant (_, _, phi)) = fold_formula f phi
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  | fold_formula f (AConn (_, phis)) = fold (fold_formula f) phis
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  | fold_formula f (AAtom tm) = f tm
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fun count_term (ATerm ((s, _), tms)) =
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  (if is_atp_variable s then I
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   else Symtab.map_entry s (Integer.add 1))
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  #> fold count_term tms
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fun count_formula x = fold_formula count_term x
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val init_counters =
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  metis_helpers |> map fst |> sort_distinct string_ord |> map (rpair 0)
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  |> Symtab.make
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fun get_helper_facts ctxt type_sys formulas =
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   316
  let
blanchet@42449
   317
    val no_dangerous_types = type_system_types_dangerous_types type_sys
blanchet@41140
   318
    val ct = init_counters |> fold count_formula formulas
blanchet@41140
   319
    fun is_used s = the (Symtab.lookup ct s) > 0
blanchet@41140
   320
    fun dub c needs_full_types (th, j) =
blanchet@41140
   321
      ((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""),
blanchet@41140
   322
        false), th)
blanchet@41990
   323
    fun make_facts eq_as_iff = map_filter (make_fact ctxt false eq_as_iff false)
blanchet@38282
   324
  in
blanchet@41145
   325
    (metis_helpers
blanchet@41145
   326
     |> filter (is_used o fst)
blanchet@41145
   327
     |> maps (fn (c, (needs_full_types, ths)) =>
blanchet@41145
   328
                 if needs_full_types andalso not no_dangerous_types then
blanchet@41145
   329
                   []
blanchet@41145
   330
                 else
blanchet@41145
   331
                   ths ~~ (1 upto length ths)
blanchet@41145
   332
                   |> map (dub c needs_full_types)
blanchet@41145
   333
                   |> make_facts (not needs_full_types)),
blanchet@41145
   334
     if type_sys = Tags false then
blanchet@41145
   335
       let
blanchet@41145
   336
         fun var s = ATerm (`I s, [])
blanchet@41145
   337
         fun tag tm = ATerm (`I type_tag_name, [var "X", tm])
blanchet@41145
   338
       in
blanchet@42538
   339
         [Formula (Fof, helper_prefix ^ ascii_of "ti_ti", Axiom,
blanchet@42527
   340
                   AAtom (ATerm (`I "equal",
blanchet@42527
   341
                                 [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42529
   342
                   |> close_formula_universally, NONE, NONE)]
blanchet@41145
   343
       end
blanchet@41145
   344
     else
blanchet@41145
   345
       [])
blanchet@38282
   346
  end
blanchet@38282
   347
blanchet@41990
   348
fun translate_atp_fact ctxt keep_trivial =
blanchet@41990
   349
  `(make_fact ctxt keep_trivial true true)
blanchet@39004
   350
blanchet@41134
   351
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
blanchet@38282
   352
  let
wenzelm@42361
   353
    val thy = Proof_Context.theory_of ctxt
blanchet@41091
   354
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@41091
   355
    val (facts, fact_names) =
blanchet@41091
   356
      rich_facts
blanchet@41091
   357
      |> map_filter (fn (NONE, _) => NONE
blanchet@41091
   358
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@41091
   359
      |> ListPair.unzip
blanchet@40204
   360
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@39005
   361
       boost an ATP's performance (for some reason). *)
blanchet@40204
   362
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@38282
   363
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42353
   364
    val all_ts = goal_t :: fact_ts
blanchet@42353
   365
    val subs = tfree_classes_of_terms all_ts
blanchet@42353
   366
    val supers = tvar_classes_of_terms all_ts
blanchet@42353
   367
    val tycons = type_consts_of_terms thy all_ts
blanchet@41313
   368
    val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
blanchet@41137
   369
    val (supers', arity_clauses) =
blanchet@41137
   370
      if type_sys = No_Types then ([], [])
blanchet@41137
   371
      else make_arity_clauses thy tycons supers
blanchet@38282
   372
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@38282
   373
  in
blanchet@41313
   374
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@38282
   375
  end
blanchet@38282
   376
blanchet@41138
   377
fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t])
blanchet@38282
   378
blanchet@38282
   379
fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
blanchet@38282
   380
  | fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
blanchet@38282
   381
  | fo_term_for_combtyp (CombType (name, tys)) =
blanchet@38282
   382
    ATerm (name, map fo_term_for_combtyp tys)
blanchet@38282
   383
blanchet@38282
   384
fun fo_literal_for_type_literal (TyLitVar (class, name)) =
blanchet@38282
   385
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   386
  | fo_literal_for_type_literal (TyLitFree (class, name)) =
blanchet@38282
   387
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   388
blanchet@38282
   389
fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@38282
   390
blanchet@41138
   391
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@41138
   392
   considered dangerous because their "exhaust" properties can easily lead to
blanchet@41138
   393
   unsound ATP proofs. The checks below are an (unsound) approximation of
blanchet@41138
   394
   finiteness. *)
blanchet@41138
   395
blanchet@41138
   396
fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true
blanchet@41138
   397
  | is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) =
blanchet@41138
   398
    is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us
blanchet@41138
   399
  | is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false
blanchet@41138
   400
and is_type_dangerous ctxt (Type (s, Ts)) =
blanchet@41138
   401
    is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts
blanchet@41140
   402
  | is_type_dangerous _ _ = false
blanchet@41138
   403
and is_type_constr_dangerous ctxt s =
wenzelm@42361
   404
  let val thy = Proof_Context.theory_of ctxt in
blanchet@41138
   405
    case Datatype_Data.get_info thy s of
blanchet@41138
   406
      SOME {descr, ...} =>
blanchet@41138
   407
      forall (fn (_, (_, _, constrs)) =>
blanchet@41138
   408
                 forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr
blanchet@41138
   409
    | NONE =>
blanchet@41138
   410
      case Typedef.get_info ctxt s of
blanchet@41138
   411
        ({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type
blanchet@41138
   412
      | [] => true
blanchet@41138
   413
  end
blanchet@41138
   414
blanchet@41138
   415
fun is_combtyp_dangerous ctxt (CombType ((s, _), tys)) =
blanchet@41138
   416
    (case strip_prefix_and_unascii type_const_prefix s of
blanchet@41138
   417
       SOME s' => forall (is_combtyp_dangerous ctxt) tys andalso
blanchet@41138
   418
                  is_type_constr_dangerous ctxt (invert_const s')
blanchet@41138
   419
     | NONE => false)
blanchet@41138
   420
  | is_combtyp_dangerous _ _ = false
blanchet@41138
   421
blanchet@41138
   422
fun should_tag_with_type ctxt (Tags full_types) ty =
blanchet@41138
   423
    full_types orelse is_combtyp_dangerous ctxt ty
blanchet@41138
   424
  | should_tag_with_type _ _ _ = false
blanchet@41138
   425
blanchet@41140
   426
val fname_table =
blanchet@41140
   427
  [("c_False", (0, ("c_fFalse", @{const_name Metis.fFalse}))),
blanchet@41140
   428
   ("c_True", (0, ("c_fTrue", @{const_name Metis.fTrue}))),
blanchet@41140
   429
   ("c_Not", (1, ("c_fNot", @{const_name Metis.fNot}))),
blanchet@41140
   430
   ("c_conj", (2, ("c_fconj", @{const_name Metis.fconj}))),
blanchet@41140
   431
   ("c_disj", (2, ("c_fdisj", @{const_name Metis.fdisj}))),
blanchet@41140
   432
   ("c_implies", (2, ("c_fimplies", @{const_name Metis.fimplies}))),
blanchet@41140
   433
   ("equal", (2, ("c_fequal", @{const_name Metis.fequal})))]
blanchet@41140
   434
blanchet@42227
   435
(* We are crossing our fingers that it doesn't clash with anything else. *)
blanchet@42227
   436
val mangled_type_sep = "\000"
blanchet@42227
   437
blanchet@42531
   438
fun mangled_combtyp_component f (CombTFree name) = f name
blanchet@42531
   439
  | mangled_combtyp_component f (CombTVar name) =
blanchet@42236
   440
    f name (* FIXME: shouldn't happen *)
blanchet@42236
   441
    (* raise Fail "impossible schematic type variable" *)
blanchet@42531
   442
  | mangled_combtyp_component f (CombType (name, tys)) =
blanchet@42531
   443
    "(" ^ commas (map (mangled_combtyp_component f) tys) ^ ")" ^ f name
blanchet@42531
   444
blanchet@42531
   445
fun mangled_combtyp ty =
blanchet@42531
   446
  (make_type (mangled_combtyp_component fst ty),
blanchet@42531
   447
   mangled_combtyp_component snd ty)
blanchet@42227
   448
blanchet@42227
   449
fun mangled_type_suffix f g tys =
blanchet@42531
   450
  fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42531
   451
            o mangled_combtyp_component f) tys ""
blanchet@42227
   452
blanchet@42534
   453
fun mangled_const_fst ty_args s = s ^ mangled_type_suffix fst ascii_of ty_args
blanchet@42534
   454
fun mangled_const_snd ty_args s' = s' ^ mangled_type_suffix snd I ty_args
blanchet@42534
   455
fun mangled_const ty_args (s, s') =
blanchet@42534
   456
  (mangled_const_fst ty_args s, mangled_const_snd ty_args s')
blanchet@42533
   457
blanchet@42227
   458
val parse_mangled_ident =
blanchet@42227
   459
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42227
   460
blanchet@42227
   461
fun parse_mangled_type x =
blanchet@42227
   462
  ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")"
blanchet@42227
   463
      -- parse_mangled_ident >> (ATerm o swap)
blanchet@42227
   464
   || parse_mangled_ident >> (ATerm o rpair [])) x
blanchet@42227
   465
and parse_mangled_types x =
blanchet@42227
   466
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42227
   467
blanchet@42227
   468
fun unmangled_type s =
blanchet@42227
   469
  s |> suffix ")" |> raw_explode
blanchet@42227
   470
    |> Scan.finite Symbol.stopper
blanchet@42227
   471
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42227
   472
                                                quote s)) parse_mangled_type))
blanchet@42227
   473
    |> fst
blanchet@42227
   474
blanchet@42227
   475
fun unmangled_const s =
blanchet@42227
   476
  let val ss = space_explode mangled_type_sep s in
blanchet@42227
   477
    (hd ss, map unmangled_type (tl ss))
blanchet@42227
   478
  end
blanchet@42227
   479
blanchet@42531
   480
fun pred_combtyp ty =
blanchet@42531
   481
  case combtyp_from_typ @{typ "unit => bool"} of
blanchet@42531
   482
    CombType (name, [_, bool_ty]) => CombType (name, [ty, bool_ty])
blanchet@42531
   483
  | _ => raise Fail "expected two-argument type constructor"
blanchet@42531
   484
blanchet@42534
   485
fun has_type_combatom ty tm =
blanchet@42534
   486
  CombApp (CombConst ((const_prefix ^ is_base, is_base), pred_combtyp ty, [ty]),
blanchet@42534
   487
           tm)
blanchet@42534
   488
  |> AAtom
blanchet@42534
   489
blanchet@42530
   490
fun formula_for_combformula ctxt type_sys =
blanchet@38282
   491
  let
blanchet@42530
   492
    fun do_term top_level u =
blanchet@38282
   493
      let
blanchet@38282
   494
        val (head, args) = strip_combterm_comb u
blanchet@38282
   495
        val (x, ty_args) =
blanchet@38282
   496
          case head of
blanchet@38282
   497
            CombConst (name as (s, s'), _, ty_args) =>
blanchet@41140
   498
            (case AList.lookup (op =) fname_table s of
blanchet@41140
   499
               SOME (n, fname) =>
blanchet@41150
   500
               (if top_level andalso length args = n then
blanchet@41150
   501
                  case s of
blanchet@41150
   502
                    "c_False" => ("$false", s')
blanchet@41150
   503
                  | "c_True" => ("$true", s')
blanchet@41150
   504
                  | _ => name
blanchet@41150
   505
                else
blanchet@41150
   506
                  fname, [])
blanchet@41140
   507
             | NONE =>
blanchet@41140
   508
               case strip_prefix_and_unascii const_prefix s of
blanchet@41140
   509
                 NONE => (name, ty_args)
blanchet@41140
   510
               | SOME s'' =>
blanchet@42227
   511
                 let val s'' = invert_const s'' in
blanchet@42524
   512
                   case type_arg_policy type_sys s'' of
blanchet@42227
   513
                     No_Type_Args => (name, [])
blanchet@42227
   514
                   | Explicit_Type_Args => (name, ty_args)
blanchet@42534
   515
                   | Mangled_Types => (mangled_const ty_args name, [])
blanchet@42227
   516
                 end)
blanchet@38282
   517
          | CombVar (name, _) => (name, [])
blanchet@38282
   518
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42530
   519
        val t = ATerm (x, map fo_term_for_combtyp ty_args @
blanchet@42530
   520
                          map (do_term false) args)
blanchet@41138
   521
        val ty = combtyp_of u
blanchet@42530
   522
      in
blanchet@42530
   523
        t |> (if should_tag_with_type ctxt type_sys ty then
blanchet@42530
   524
                tag_with_type (fo_term_for_combtyp ty)
blanchet@42530
   525
              else
blanchet@42530
   526
                I)
blanchet@42530
   527
      end
blanchet@42531
   528
    val do_bound_type =
blanchet@42531
   529
      if type_sys = Many_Typed then SOME o mangled_combtyp else K NONE
blanchet@42531
   530
    val do_out_of_bound_type =
blanchet@42531
   531
      if member (op =) [Args true, Mangled true] type_sys then
blanchet@42531
   532
        (fn (s, ty) =>
blanchet@42534
   533
            has_type_combatom ty (CombVar (s, ty))
blanchet@42534
   534
            |> formula_for_combformula ctxt type_sys |> SOME)
blanchet@42531
   535
      else
blanchet@42531
   536
        K NONE
blanchet@42530
   537
    fun do_formula (AQuant (q, xs, phi)) =
blanchet@42531
   538
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42531
   539
                                      | SOME ty => do_bound_type ty)),
blanchet@42534
   540
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42531
   541
                    (map_filter
blanchet@42531
   542
                         (fn (_, NONE) => NONE
blanchet@42531
   543
                           | (s, SOME ty) => do_out_of_bound_type (s, ty)) xs)
blanchet@42531
   544
                    (do_formula phi))
blanchet@42530
   545
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42530
   546
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42530
   547
  in do_formula end
blanchet@38282
   548
blanchet@41138
   549
fun formula_for_fact ctxt type_sys
blanchet@40204
   550
                     ({combformula, ctypes_sorts, ...} : translated_formula) =
blanchet@38282
   551
  mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
blanchet@42353
   552
                (atp_type_literals_for_types type_sys Axiom ctypes_sorts))
blanchet@42522
   553
           (formula_for_combformula ctxt type_sys
blanchet@42522
   554
                                    (close_combformula_universally combformula))
blanchet@38282
   555
blanchet@42538
   556
fun logic_for_type_sys Many_Typed = Tff
blanchet@42538
   557
  | logic_for_type_sys _ = Fof
blanchet@42538
   558
blanchet@42180
   559
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42180
   560
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42180
   561
   the remote provers might care. *)
blanchet@42180
   562
fun problem_line_for_fact ctxt prefix type_sys
blanchet@42180
   563
                          (j, formula as {name, kind, ...}) =
blanchet@42538
   564
  Formula (logic_for_type_sys type_sys,
blanchet@42538
   565
           prefix ^ string_of_int j ^ "_" ^ ascii_of name, kind,
blanchet@42538
   566
           formula_for_fact ctxt type_sys formula, NONE, NONE)
blanchet@38282
   567
blanchet@38282
   568
fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@38282
   569
                                                       superclass, ...}) =
blanchet@38282
   570
  let val ty_arg = ATerm (("T", "T"), []) in
blanchet@42538
   571
    Formula (Fof, class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42527
   572
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42529
   573
                               AAtom (ATerm (superclass, [ty_arg]))]),
blanchet@42529
   574
             NONE, NONE)
blanchet@38282
   575
  end
blanchet@38282
   576
blanchet@38282
   577
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
blanchet@38282
   578
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@38282
   579
  | fo_literal_for_arity_literal (TVarLit (c, sort)) =
blanchet@38282
   580
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@38282
   581
blanchet@38282
   582
fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@38282
   583
                                                ...}) =
blanchet@42538
   584
  Formula (Fof, arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42527
   585
           mk_ahorn (map (formula_for_fo_literal o apfst not
blanchet@42527
   586
                          o fo_literal_for_arity_literal) premLits)
blanchet@42527
   587
                    (formula_for_fo_literal
blanchet@42529
   588
                         (fo_literal_for_arity_literal conclLit)), NONE, NONE)
blanchet@38282
   589
blanchet@41138
   590
fun problem_line_for_conjecture ctxt type_sys
blanchet@40114
   591
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42538
   592
  Formula (logic_for_type_sys type_sys, conjecture_prefix ^ name, kind,
blanchet@42527
   593
           formula_for_combformula ctxt type_sys
blanchet@42527
   594
                                   (close_combformula_universally combformula),
blanchet@42529
   595
           NONE, NONE)
blanchet@38282
   596
blanchet@42353
   597
fun free_type_literals type_sys ({ctypes_sorts, ...} : translated_formula) =
blanchet@42353
   598
  ctypes_sorts |> atp_type_literals_for_types type_sys Conjecture
blanchet@41137
   599
               |> map fo_literal_for_type_literal
blanchet@38282
   600
blanchet@39975
   601
fun problem_line_for_free_type j lit =
blanchet@42538
   602
  Formula (Fof, tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42529
   603
           formula_for_fo_literal lit, NONE, NONE)
blanchet@42353
   604
fun problem_lines_for_free_types type_sys facts =
blanchet@38282
   605
  let
blanchet@42353
   606
    val litss = map (free_type_literals type_sys) facts
blanchet@38282
   607
    val lits = fold (union (op =)) litss []
blanchet@39975
   608
  in map2 problem_line_for_free_type (0 upto length lits - 1) lits end
blanchet@38282
   609
blanchet@38282
   610
(** "hBOOL" and "hAPP" **)
blanchet@38282
   611
blanchet@42520
   612
type sym_info = {min_arity: int, max_arity: int, fun_sym: bool}
blanchet@38282
   613
blanchet@42533
   614
fun consider_term_syms top_level (ATerm ((s, _), ts)) =
blanchet@39452
   615
  (if is_atp_variable s then
blanchet@38282
   616
     I
blanchet@38282
   617
   else
blanchet@38282
   618
     let val n = length ts in
blanchet@38282
   619
       Symtab.map_default
blanchet@42520
   620
           (s, {min_arity = n, max_arity = 0, fun_sym = false})
blanchet@42520
   621
           (fn {min_arity, max_arity, fun_sym} =>
blanchet@38282
   622
               {min_arity = Int.min (n, min_arity),
blanchet@38282
   623
                max_arity = Int.max (n, max_arity),
blanchet@42520
   624
                fun_sym = fun_sym orelse not top_level})
blanchet@38282
   625
     end)
blanchet@42533
   626
  #> fold (consider_term_syms (top_level andalso s = type_tag_name)) ts
blanchet@42533
   627
val consider_formula_syms = fold_formula (consider_term_syms true)
blanchet@38282
   628
blanchet@42533
   629
fun consider_problem_line_syms (Type_Decl _) = I
blanchet@42538
   630
  | consider_problem_line_syms (Formula (_, _, _, phi, _, _)) =
blanchet@42533
   631
    consider_formula_syms phi
blanchet@42533
   632
fun consider_problem_syms problem =
blanchet@42533
   633
  fold (fold consider_problem_line_syms o snd) problem
blanchet@38282
   634
blanchet@42539
   635
(* The "equal" entry is needed for helper facts if the problem otherwise does
blanchet@42539
   636
   not involve equality. *)
blanchet@42539
   637
val default_entries =
blanchet@42539
   638
  [("equal", {min_arity = 2, max_arity = 2, fun_sym = false})]
blanchet@41140
   639
blanchet@42520
   640
fun sym_table_for_problem explicit_apply problem =
blanchet@41140
   641
  if explicit_apply then
blanchet@41140
   642
    NONE
blanchet@41140
   643
  else
blanchet@42539
   644
    SOME (Symtab.empty |> fold Symtab.default default_entries
blanchet@42533
   645
                       |> consider_problem_syms problem)
blanchet@38282
   646
blanchet@41134
   647
fun min_arity_of thy type_sys NONE s =
blanchet@41138
   648
    (if s = "equal" orelse s = type_tag_name orelse
blanchet@38282
   649
        String.isPrefix type_const_prefix s orelse
blanchet@38282
   650
        String.isPrefix class_prefix s then
blanchet@38282
   651
       16383 (* large number *)
blanchet@38748
   652
     else case strip_prefix_and_unascii const_prefix s of
blanchet@42524
   653
       SOME s' => s' |> unmangled_const |> fst |> invert_const
blanchet@42524
   654
                     |> num_atp_type_args thy type_sys
blanchet@38282
   655
     | NONE => 0)
blanchet@42520
   656
  | min_arity_of _ _ (SOME sym_tab) s =
blanchet@42520
   657
    case Symtab.lookup sym_tab s of
blanchet@42520
   658
      SOME ({min_arity, ...} : sym_info) => min_arity
blanchet@38282
   659
    | NONE => 0
blanchet@38282
   660
blanchet@38282
   661
fun full_type_of (ATerm ((s, _), [ty, _])) =
blanchet@41138
   662
    if s = type_tag_name then SOME ty else NONE
blanchet@41138
   663
  | full_type_of _ = NONE
blanchet@38282
   664
blanchet@38282
   665
fun list_hAPP_rev _ t1 [] = t1
blanchet@38282
   666
  | list_hAPP_rev NONE t1 (t2 :: ts2) =
blanchet@42539
   667
    ATerm (`I explicit_app_name, [list_hAPP_rev NONE t1 ts2, t2])
blanchet@38282
   668
  | list_hAPP_rev (SOME ty) t1 (t2 :: ts2) =
blanchet@41138
   669
    case full_type_of t2 of
blanchet@41138
   670
      SOME ty2 =>
blanchet@41138
   671
      let val ty' = ATerm (`make_fixed_type_const @{type_name fun},
blanchet@41138
   672
                           [ty2, ty]) in
blanchet@42539
   673
        ATerm (`I explicit_app_name,
blanchet@41138
   674
               [tag_with_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2])
blanchet@41138
   675
      end
blanchet@41138
   676
    | NONE => list_hAPP_rev NONE t1 (t2 :: ts2)
blanchet@38282
   677
blanchet@42520
   678
fun repair_applications_in_term thy type_sys sym_tab =
blanchet@38282
   679
  let
blanchet@38282
   680
    fun aux opt_ty (ATerm (name as (s, _), ts)) =
blanchet@41138
   681
      if s = type_tag_name then
blanchet@38282
   682
        case ts of
blanchet@38282
   683
          [t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2])
blanchet@41138
   684
        | _ => raise Fail "malformed type tag"
blanchet@38282
   685
      else
blanchet@38282
   686
        let
blanchet@38282
   687
          val ts = map (aux NONE) ts
blanchet@42520
   688
          val (ts1, ts2) = chop (min_arity_of thy type_sys sym_tab s) ts
blanchet@38282
   689
        in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end
blanchet@38282
   690
  in aux NONE end
blanchet@38282
   691
blanchet@42539
   692
fun boolify t = ATerm (`I boolify_name, [t])
blanchet@38282
   693
blanchet@38282
   694
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   695
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   696
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   697
   arguments and is used as a predicate. *)
blanchet@42520
   698
fun is_pred_sym NONE s =
blanchet@38589
   699
    s = "equal" orelse s = "$false" orelse s = "$true" orelse
blanchet@38589
   700
    String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s
blanchet@42520
   701
  | is_pred_sym (SOME sym_tab) s =
blanchet@42520
   702
    case Symtab.lookup sym_tab s of
blanchet@42520
   703
      SOME {min_arity, max_arity, fun_sym} =>
blanchet@42520
   704
      not fun_sym andalso min_arity = max_arity
blanchet@38282
   705
    | NONE => false
blanchet@38282
   706
blanchet@42520
   707
fun repair_predicates_in_term pred_sym_tab (t as ATerm ((s, _), ts)) =
blanchet@41138
   708
  if s = type_tag_name then
blanchet@38282
   709
    case ts of
blanchet@38282
   710
      [_, t' as ATerm ((s', _), _)] =>
blanchet@42520
   711
      if is_pred_sym pred_sym_tab s' then t' else boolify t
blanchet@41138
   712
    | _ => raise Fail "malformed type tag"
blanchet@38282
   713
  else
blanchet@42520
   714
    t |> not (is_pred_sym pred_sym_tab s) ? boolify
blanchet@38282
   715
blanchet@42521
   716
fun repair_formula thy type_sys sym_tab =
blanchet@38282
   717
  let
blanchet@42520
   718
    val pred_sym_tab = case type_sys of Tags _ => NONE | _ => sym_tab
blanchet@38282
   719
    fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
blanchet@38282
   720
      | aux (AConn (c, phis)) = AConn (c, map aux phis)
blanchet@38282
   721
      | aux (AAtom tm) =
blanchet@42520
   722
        AAtom (tm |> repair_applications_in_term thy type_sys sym_tab
blanchet@42520
   723
                  |> repair_predicates_in_term pred_sym_tab)
blanchet@42522
   724
  in aux #> close_formula_universally end
blanchet@38282
   725
blanchet@42527
   726
fun repair_problem_line thy type_sys sym_tab
blanchet@42538
   727
        (Formula (logic, ident, kind, phi, source, useful_info)) =
blanchet@42538
   728
    Formula (logic, ident, kind, repair_formula thy type_sys sym_tab phi,
blanchet@42538
   729
             source, useful_info)
blanchet@42528
   730
  | repair_problem_line _ _ _ _ = raise Fail "unexpected non-formula"
blanchet@42521
   731
fun repair_problem thy = map o apsnd o map oo repair_problem_line thy
blanchet@38282
   732
blanchet@42534
   733
fun is_const_relevant type_sys sym_tab unmangled_s s =
blanchet@42534
   734
  not (String.isPrefix bound_var_prefix unmangled_s) andalso
blanchet@42534
   735
  unmangled_s <> "equal" andalso
blanchet@42534
   736
  (type_sys = Many_Typed orelse not (is_pred_sym sym_tab s))
blanchet@42533
   737
blanchet@42534
   738
fun consider_combterm_consts type_sys sym_tab tm =
blanchet@42533
   739
  let val (head, args) = strip_combterm_comb tm in
blanchet@42533
   740
    (case head of
blanchet@42533
   741
       CombConst ((s, s'), ty, ty_args) =>
blanchet@42533
   742
       (* FIXME: exploit type subsumption *)
blanchet@42534
   743
       is_const_relevant type_sys sym_tab s
blanchet@42534
   744
                         (s |> member (op =) [Many_Typed, Mangled true] type_sys
blanchet@42534
   745
                               ? mangled_const_fst ty_args)
blanchet@42534
   746
       ? Symtab.insert_list (op =) (s, (s', ty_args, ty))
blanchet@42533
   747
     | _ => I) (* FIXME: hAPP on var *)
blanchet@42534
   748
    #> fold (consider_combterm_consts type_sys sym_tab) args
blanchet@42533
   749
  end
blanchet@42533
   750
blanchet@42534
   751
fun consider_fact_consts type_sys sym_tab
blanchet@42534
   752
                         ({combformula, ...} : translated_formula) =
blanchet@42534
   753
  fold_formula (consider_combterm_consts type_sys sym_tab) combformula
blanchet@42533
   754
blanchet@42533
   755
fun const_table_for_facts type_sys sym_tab facts =
blanchet@42533
   756
  Symtab.empty |> member (op =) [Many_Typed, Args true, Mangled true] type_sys
blanchet@42534
   757
                  ? fold (consider_fact_consts type_sys sym_tab) facts
blanchet@42533
   758
blanchet@42534
   759
fun strip_and_map_combtyp f (ty as CombType ((s, _), tys)) =
blanchet@42533
   760
    (case (strip_prefix_and_unascii type_const_prefix s, tys) of
blanchet@42533
   761
       (SOME @{type_name fun}, [dom_ty, ran_ty]) =>
blanchet@42534
   762
       strip_and_map_combtyp f ran_ty |>> cons (f dom_ty)
blanchet@42534
   763
     | _ => ([], f ty))
blanchet@42534
   764
  | strip_and_map_combtyp f ty = ([], f ty)
blanchet@42533
   765
blanchet@42534
   766
fun type_decl_line_for_const_entry ctxt type_sys sym_tab s (s', ty_args, ty) =
blanchet@42534
   767
  if type_sys = Many_Typed then
blanchet@42534
   768
    let
blanchet@42534
   769
      val (arg_tys, res_ty) = strip_and_map_combtyp mangled_combtyp ty
blanchet@42534
   770
      val (s, s') = (s, s') |> mangled_const ty_args
blanchet@42534
   771
    in
blanchet@42534
   772
      Type_Decl (type_decl_prefix ^ ascii_of s, (s, s'), arg_tys,
blanchet@42534
   773
                 if is_pred_sym sym_tab s then `I tff_bool_type else res_ty)
blanchet@42534
   774
    end
blanchet@42534
   775
  else
blanchet@42533
   776
    let
blanchet@42534
   777
      val (arg_tys, res_ty) = strip_and_map_combtyp I ty
blanchet@42534
   778
      val bounds =
blanchet@42534
   779
        map (`I o make_bound_var o string_of_int) (1 upto length arg_tys)
blanchet@42534
   780
        ~~ map SOME arg_tys
blanchet@42534
   781
      val bound_tms =
blanchet@42534
   782
        map (fn (name, ty) => CombConst (name, the ty, [])) bounds
blanchet@42534
   783
    in
blanchet@42538
   784
      Formula (Fof, type_decl_prefix ^ ascii_of s, Axiom,
blanchet@42534
   785
               mk_aquant AForall bounds
blanchet@42534
   786
                         (has_type_combatom res_ty
blanchet@42534
   787
                              (fold (curry (CombApp o swap)) bound_tms
blanchet@42534
   788
                                    (CombConst ((s, s'), ty, ty_args))))
blanchet@42534
   789
               |> formula_for_combformula ctxt type_sys,
blanchet@42534
   790
               NONE, NONE)
blanchet@42534
   791
    end
blanchet@42534
   792
fun type_decl_lines_for_const ctxt type_sys sym_tab (s, xs) =
blanchet@42534
   793
  map (type_decl_line_for_const_entry ctxt type_sys sym_tab s) xs
blanchet@42533
   794
blanchet@42539
   795
fun add_extra_type_decl_lines Many_Typed =
blanchet@42539
   796
    cons (Type_Decl (type_decl_prefix ^ boolify_name, `I boolify_name,
blanchet@42539
   797
                     [mangled_combtyp (combtyp_from_typ @{typ bool})],
blanchet@42539
   798
                     `I tff_bool_type))
blanchet@42539
   799
  | add_extra_type_decl_lines _ = I
blanchet@42539
   800
blanchet@41157
   801
val factsN = "Relevant facts"
blanchet@41157
   802
val class_relsN = "Class relationships"
blanchet@41157
   803
val aritiesN = "Arity declarations"
blanchet@41157
   804
val helpersN = "Helper facts"
blanchet@42533
   805
val type_declsN = "Type declarations"
blanchet@41157
   806
val conjsN = "Conjectures"
blanchet@41313
   807
val free_typesN = "Type variables"
blanchet@41157
   808
blanchet@41157
   809
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
   810
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
   811
    if heading = needle then j
blanchet@41157
   812
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
   813
blanchet@42521
   814
fun prepare_atp_problem ctxt readable_names type_sys explicit_apply hyp_ts
blanchet@42521
   815
                        concl_t facts =
blanchet@38282
   816
  let
wenzelm@42361
   817
    val thy = Proof_Context.theory_of ctxt
blanchet@41313
   818
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
   819
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@42522
   820
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
   821
       Flotter hack. *)
blanchet@38282
   822
    val problem =
blanchet@42180
   823
      [(factsN, map (problem_line_for_fact ctxt fact_prefix type_sys)
blanchet@42180
   824
                    (0 upto length facts - 1 ~~ facts)),
blanchet@41157
   825
       (class_relsN, map problem_line_for_class_rel_clause class_rel_clauses),
blanchet@41157
   826
       (aritiesN, map problem_line_for_arity_clause arity_clauses),
blanchet@41157
   827
       (helpersN, []),
blanchet@42533
   828
       (type_declsN, []),
blanchet@41313
   829
       (conjsN, map (problem_line_for_conjecture ctxt type_sys) conjs),
blanchet@42353
   830
       (free_typesN, problem_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42520
   831
    val sym_tab = sym_table_for_problem explicit_apply problem
blanchet@42521
   832
    val problem = problem |> repair_problem thy type_sys sym_tab
blanchet@42521
   833
    val helper_facts =
blanchet@42538
   834
      problem |> maps (map_filter (fn Formula (_, _, _, phi, _, _) => SOME phi
blanchet@42528
   835
                                    | _ => NONE) o snd)
blanchet@42527
   836
              |> get_helper_facts ctxt type_sys
blanchet@42533
   837
    val const_tab = const_table_for_facts type_sys sym_tab (conjs @ facts)
blanchet@42533
   838
    val type_decl_lines =
blanchet@42534
   839
      Symtab.fold_rev (append o type_decl_lines_for_const ctxt type_sys sym_tab)
blanchet@42534
   840
                      const_tab []
blanchet@42539
   841
      |> add_extra_type_decl_lines type_sys
blanchet@41157
   842
    val helper_lines =
blanchet@42521
   843
      helper_facts
blanchet@42180
   844
      |>> map (pair 0
blanchet@42180
   845
               #> problem_line_for_fact ctxt helper_prefix type_sys
blanchet@42521
   846
               #> repair_problem_line thy type_sys sym_tab)
blanchet@41157
   847
      |> op @
blanchet@41140
   848
    val (problem, pool) =
blanchet@42533
   849
      problem |> fold (AList.update (op =))
blanchet@42533
   850
                      [(helpersN, helper_lines), (type_declsN, type_decl_lines)]
blanchet@41140
   851
              |> nice_atp_problem readable_names
blanchet@38282
   852
  in
blanchet@38282
   853
    (problem,
blanchet@38282
   854
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@41157
   855
     offset_of_heading_in_problem conjsN problem 0,
blanchet@41157
   856
     fact_names |> Vector.fromList)
blanchet@38282
   857
  end
blanchet@38282
   858
blanchet@41313
   859
(* FUDGE *)
blanchet@41313
   860
val conj_weight = 0.0
blanchet@41770
   861
val hyp_weight = 0.1
blanchet@41770
   862
val fact_min_weight = 0.2
blanchet@41313
   863
val fact_max_weight = 1.0
blanchet@41313
   864
blanchet@41313
   865
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
   866
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
   867
  #> fold (add_term_weights weight) tms
blanchet@42538
   868
fun add_problem_line_weights weight (Formula (_, _, _, phi, _, _)) =
blanchet@42528
   869
    fold_formula (add_term_weights weight) phi
blanchet@42528
   870
  | add_problem_line_weights _ _ = I
blanchet@41313
   871
blanchet@41313
   872
fun add_conjectures_weights [] = I
blanchet@41313
   873
  | add_conjectures_weights conjs =
blanchet@41313
   874
    let val (hyps, conj) = split_last conjs in
blanchet@41313
   875
      add_problem_line_weights conj_weight conj
blanchet@41313
   876
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
   877
    end
blanchet@41313
   878
blanchet@41313
   879
fun add_facts_weights facts =
blanchet@41313
   880
  let
blanchet@41313
   881
    val num_facts = length facts
blanchet@41313
   882
    fun weight_of j =
blanchet@41313
   883
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
   884
                        / Real.fromInt num_facts
blanchet@41313
   885
  in
blanchet@41313
   886
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
   887
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
   888
  end
blanchet@41313
   889
blanchet@41313
   890
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
   891
fun atp_problem_weights problem =
blanchet@41313
   892
  Symtab.empty
blanchet@41313
   893
  |> add_conjectures_weights (these (AList.lookup (op =) problem conjsN))
blanchet@41313
   894
  |> add_facts_weights (these (AList.lookup (op =) problem factsN))
blanchet@41313
   895
  |> Symtab.dest
blanchet@41726
   896
  |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@41313
   897
blanchet@38282
   898
end;