src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Wed May 04 23:26:20 2011 +0200 (2011-05-04)
changeset 42687 8a4682bf70ed
parent 42685 7a5116bd63b7
child 42688 097a61baeca9
permissions -rw-r--r--
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 locality = Sledgehammer_Filter.locality
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  datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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  datatype type_level =
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    All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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  datatype type_system =
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    Simple of type_level |
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    Preds of polymorphism * type_level |
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    Tags of polymorphism * type_level
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  type translated_formula
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  val readable_names : bool Config.T
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  val fact_prefix : string
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  val conjecture_prefix : string
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  val predicator_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 tff_type_prefix : string
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  val type_sys_from_string : string -> type_system
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  val polymorphism_of_type_sys : type_system -> polymorphism
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  val level_of_type_sys : type_system -> type_level
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  val is_type_sys_virtually_sound : type_system -> bool
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  val is_type_sys_fairly_sound : 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 * locality) * thm
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    -> translated_formula option * ((string * locality) * thm)
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  val prepare_atp_problem :
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    Proof.context -> 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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open Sledgehammer_Filter
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(* experimental *)
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val generate_useful_info = false
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(* Readable names are often much shorter, especially if types are mangled in
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   names. Also, the logic for generating legal SNARK sort names is only
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   implemented for readable names. Finally, readable names are, well, more
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   readable. For these reason, they are enabled by default. *)
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val readable_names =
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  Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
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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 predicator_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 tff_type_prefix = "ty_"
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fun make_tff_type s = tff_type_prefix ^ ascii_of s
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(* official TPTP syntax *)
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val tptp_tff_type_of_types = "$tType"
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val tptp_tff_bool_type = "$o"
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val tptp_false = "$false"
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val tptp_true = "$true"
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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datatype type_level =
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  All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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datatype type_system =
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  Simple of type_level |
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  Preds of polymorphism * type_level |
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  Tags of polymorphism * type_level
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fun type_sys_from_string s =
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  (case try (unprefix "mangled_") s of
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     SOME s => (Mangled_Monomorphic, s)
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   | NONE =>
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     case try (unprefix "mono_") s of
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       SOME s => (Monomorphic, s)
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     | NONE => (Polymorphic, s))
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  ||> (fn s =>
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          case try (unsuffix " ?") s of
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            SOME s => (Nonmonotonic_Types, s)
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          | NONE =>
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            case try (unsuffix " !") s of
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              SOME s => (Finite_Types, s)
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            | NONE => (All_Types, s))
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  |> (fn (polymorphism, (level, core)) =>
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         case (core, (polymorphism, level)) of
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           ("simple", (Polymorphic (* naja *), level)) => Simple level
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         | ("preds", extra) => Preds extra
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         | ("tags", extra) => Tags extra
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         | ("args", (_, All_Types (* naja *))) =>
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           Preds (polymorphism, Const_Arg_Types)
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         | ("erased", (Polymorphic, All_Types (* naja *))) =>
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           Preds (polymorphism, No_Types)
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         | _ => error ("Unknown type system: " ^ quote s ^ "."))
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fun polymorphism_of_type_sys (Simple _) = Mangled_Monomorphic
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  | polymorphism_of_type_sys (Preds (poly, _)) = poly
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  | polymorphism_of_type_sys (Tags (poly, _)) = poly
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fun level_of_type_sys (Simple level) = level
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  | level_of_type_sys (Preds (_, level)) = level
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  | level_of_type_sys (Tags (_, level)) = level
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fun is_type_level_virtually_sound level =
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  level = All_Types orelse level = Nonmonotonic_Types
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val is_type_sys_virtually_sound =
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  is_type_level_virtually_sound o level_of_type_sys
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fun is_type_level_fairly_sound level =
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  is_type_level_virtually_sound level orelse level = Finite_Types
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val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
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fun is_type_level_partial level =
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  level = Nonmonotonic_Types orelse level = Finite_Types
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fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
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  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
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  | formula_map f (AAtom tm) = AAtom (f tm)
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fun formula_fold pos f =
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  let
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    fun aux pos (AQuant (_, _, phi)) = aux pos phi
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      | aux pos (AConn (ANot, [phi])) = aux (Option.map not pos) phi
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      | aux pos (AConn (AImplies, [phi1, phi2])) =
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        aux (Option.map not pos) phi1 #> aux pos phi2
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      | aux pos (AConn (AAnd, phis)) = fold (aux pos) phis
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      | aux pos (AConn (AOr, phis)) = fold (aux pos) phis
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      | aux _ (AConn (_, phis)) = fold (aux NONE) phis
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      | aux pos (AAtom tm) = f pos tm
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  in aux (SOME pos) end
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type translated_formula =
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  {name: string,
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   locality: locality,
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   kind: formula_kind,
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   combformula: (name, typ, combterm) formula,
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   atomic_types: typ list}
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fun update_combformula f ({name, locality, kind, combformula, atomic_types}
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                          : translated_formula) =
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  {name = name, locality = locality, kind = kind, combformula = f combformula,
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   atomic_types = atomic_types} : translated_formula
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fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
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val boring_consts = [explicit_app_base, @{const_name Metis.fequal}]
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fun should_omit_type_args type_sys s =
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  s <> type_pred_base andalso s <> type_tag_name andalso
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  (s = @{const_name HOL.eq} orelse level_of_type_sys type_sys = No_Types orelse
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   (case type_sys of
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      Tags (_, All_Types) => true
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    | _ => polymorphism_of_type_sys type_sys <> Mangled_Monomorphic andalso
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           member (op =) boring_consts s))
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datatype type_arg_policy = No_Type_Args | Explicit_Type_Args | Mangled_Type_Args
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fun general_type_arg_policy type_sys =
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  if level_of_type_sys type_sys = No_Types then
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    No_Type_Args
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  else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
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    Mangled_Type_Args
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  else
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    Explicit_Type_Args
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fun type_arg_policy type_sys s =
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  if should_omit_type_args type_sys s then No_Type_Args
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  else general_type_arg_policy type_sys
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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 level_of_type_sys 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_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, T)) = insert (op =) (name, SOME T)
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fun close_combformula_universally phi = close_universally combterm_vars phi
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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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fun close_formula_universally phi = close_universally term_vars phi
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fun fo_term_from_typ (Type (s, Ts)) =
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    ATerm (`make_fixed_type_const s, map fo_term_from_typ Ts)
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  | fo_term_from_typ (TFree (s, _)) =
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    ATerm (`make_fixed_type_var s, [])
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  | fo_term_from_typ (TVar ((x as (s, _)), _)) =
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    ATerm ((make_schematic_type_var x, s), [])
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(* This shouldn't clash with anything else. *)
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val mangled_type_sep = "\000"
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fun generic_mangled_type_name f (ATerm (name, [])) = f name
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  | generic_mangled_type_name f (ATerm (name, tys)) =
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    f name ^ "(" ^ commas (map (generic_mangled_type_name f) tys) ^ ")"
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val mangled_type_name =
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  fo_term_from_typ
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  #> (fn ty => (make_tff_type (generic_mangled_type_name fst ty),
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                generic_mangled_type_name snd ty))
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fun generic_mangled_type_suffix f g Ts =
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  fold_rev (curry (op ^) o g o prefix mangled_type_sep
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            o generic_mangled_type_name f) Ts ""
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fun mangled_const_name T_args (s, s') =
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  let val ty_args = map fo_term_from_typ T_args in
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    (s ^ generic_mangled_type_suffix fst ascii_of ty_args,
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     s' ^ generic_mangled_type_suffix snd I ty_args)
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  end
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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 introduce_proxies tm =
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  let
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    fun aux top_level (CombApp (tm1, tm2)) =
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        CombApp (aux top_level tm1, aux false tm2)
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      | aux top_level (CombConst (name as (s, s'), T, T_args)) =
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        (case proxify_const s of
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           SOME proxy_base =>
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           if top_level then
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             (case s of
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                "c_False" => (tptp_false, s')
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              | "c_True" => (tptp_true, s')
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              | _ => name, [])
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           else
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             (proxy_base |>> prefix const_prefix, T_args)
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          | NONE => (name, T_args))
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        |> (fn (name, T_args) => CombConst (name, T, T_args))
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      | aux _ tm = tm
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  in aux true tm end
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fun combformula_from_prop thy eq_as_iff =
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  let
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    fun do_term bs t atomic_types =
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      combterm_from_term thy bs (Envir.eta_contract t)
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      |>> (introduce_proxies #> AAtom)
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   320
      ||> union (op =) atomic_types
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   321
    fun do_quant bs q s T t' =
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   322
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   323
        do_formula ((s, T) :: bs) t'
blanchet@42562
   324
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   325
      end
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   326
    and do_conn bs c t1 t2 =
blanchet@38282
   327
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   328
      #>> uncurry (mk_aconn c)
blanchet@38282
   329
    and do_formula bs t =
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   330
      case t of
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   331
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
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   332
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   333
        do_quant bs AForall s T t'
blanchet@38282
   334
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   335
        do_quant bs AExists s T t'
haftmann@38795
   336
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   337
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   338
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   339
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
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   340
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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   341
      | _ => do_term bs t
blanchet@38282
   342
  in do_formula [] end
blanchet@38282
   343
blanchet@38618
   344
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
blanchet@38282
   345
wenzelm@41491
   346
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   347
fun conceal_bounds Ts t =
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   348
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   349
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   350
fun reveal_bounds Ts =
blanchet@38282
   351
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   352
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   353
blanchet@38608
   354
(* Removes the lambdas from an equation of the form "t = (%x. u)".
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   355
   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
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   356
fun extensionalize_term t =
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   357
  let
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   358
    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
blanchet@38608
   359
      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
blanchet@38608
   360
                                        Type (_, [_, res_T])]))
blanchet@38608
   361
                    $ t2 $ Abs (var_s, var_T, t')) =
haftmann@38864
   362
        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
blanchet@38608
   363
          let val var_t = Var ((var_s, j), var_T) in
blanchet@38608
   364
            Const (s, T' --> T' --> res_T)
blanchet@38608
   365
              $ betapply (t2, var_t) $ subst_bound (var_t, t')
blanchet@38608
   366
            |> aux (j + 1)
blanchet@38608
   367
          end
blanchet@38608
   368
        else
blanchet@38608
   369
          t
blanchet@38608
   370
      | aux _ t = t
blanchet@38608
   371
  in aux (maxidx_of_term t + 1) t end
blanchet@38608
   372
blanchet@38282
   373
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   374
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   375
    if Meson.is_fol_term thy t then
blanchet@38491
   376
      t
blanchet@38491
   377
    else
blanchet@38491
   378
      let
blanchet@38491
   379
        fun aux Ts t =
blanchet@38491
   380
          case t of
blanchet@38491
   381
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   382
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   383
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   384
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   385
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   386
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   387
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   388
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   389
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   390
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   391
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   392
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   393
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   394
              $ t1 $ t2 =>
blanchet@38491
   395
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   396
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   397
                   t
blanchet@38491
   398
                 else
blanchet@38491
   399
                   t |> conceal_bounds Ts
blanchet@38491
   400
                     |> Envir.eta_contract
blanchet@38491
   401
                     |> cterm_of thy
blanchet@39890
   402
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   403
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   404
                     |> reveal_bounds Ts
blanchet@39370
   405
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   406
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   407
      handle THM _ =>
blanchet@38491
   408
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   409
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   410
             else HOLogic.true_const
blanchet@38491
   411
  end
blanchet@38282
   412
blanchet@38282
   413
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   414
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   415
fun freeze_term t =
blanchet@38282
   416
  let
blanchet@38282
   417
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   418
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   419
      | aux (Var ((s, i), T)) =
blanchet@38282
   420
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   421
      | aux t = t
blanchet@38282
   422
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   423
blanchet@40204
   424
(* making fact and conjecture formulas *)
blanchet@42640
   425
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   426
  let
wenzelm@42361
   427
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   428
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   429
              |> transform_elim_term
blanchet@41211
   430
              |> Object_Logic.atomize_term thy
blanchet@42563
   431
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   432
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@38282
   433
              |> extensionalize_term
blanchet@38282
   434
              |> presimp ? presimplify_term thy
blanchet@38282
   435
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   436
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   437
              |> kind <> Axiom ? freeze_term
blanchet@42562
   438
    val (combformula, atomic_types) =
blanchet@42562
   439
      combformula_from_prop thy eq_as_iff t []
blanchet@38282
   440
  in
blanchet@42640
   441
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   442
     atomic_types = atomic_types}
blanchet@38282
   443
  end
blanchet@38282
   444
blanchet@42640
   445
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   446
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   447
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   448
    NONE
blanchet@41990
   449
  | (_, formula) => SOME formula
blanchet@42561
   450
blanchet@42544
   451
fun make_conjecture ctxt ts =
blanchet@38613
   452
  let val last = length ts - 1 in
blanchet@42640
   453
    map2 (fn j => make_formula ctxt true true (string_of_int j) Chained
blanchet@38613
   454
                               (if j = last then Conjecture else Hypothesis))
blanchet@38613
   455
         (0 upto last) ts
blanchet@38613
   456
  end
blanchet@38282
   457
blanchet@42682
   458
(** Finite and infinite type inference **)
blanchet@42682
   459
blanchet@42682
   460
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   461
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   462
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   463
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   464
blanchet@42682
   465
fun datatype_constrs thy (T as Type (s, Ts)) =
blanchet@42682
   466
    (case Datatype.get_info thy s of
blanchet@42682
   467
       SOME {index, descr, ...} =>
blanchet@42682
   468
       let val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the in
blanchet@42682
   469
         map (apsnd (fn Us => map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
blanchet@42682
   470
             constrs
blanchet@42682
   471
       end
blanchet@42682
   472
     | NONE => [])
blanchet@42682
   473
  | datatype_constrs _ _ = []
blanchet@42682
   474
blanchet@42682
   475
(* Similar to "Nitpick_HOL.bounded_exact_card_of_type".
blanchet@42682
   476
   0 means infinite type, 1 means singleton type (e.g., "unit"), and 2 means
blanchet@42682
   477
   cardinality 2 or more. The specified default cardinality is returned if the
blanchet@42682
   478
   cardinality of the type can't be determined. *)
blanchet@42682
   479
fun tiny_card_of_type ctxt default_card T =
blanchet@42682
   480
  let
blanchet@42682
   481
    val max = 2 (* 1 would be too small for the "fun" case *)
blanchet@42682
   482
    fun aux avoid T =
blanchet@42682
   483
      (if member (op =) avoid T then
blanchet@42682
   484
         0
blanchet@42682
   485
       else case T of
blanchet@42682
   486
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@42682
   487
         (case (aux avoid T1, aux avoid T2) of
blanchet@42682
   488
            (_, 1) => 1
blanchet@42682
   489
          | (0, _) => 0
blanchet@42682
   490
          | (_, 0) => 0
blanchet@42682
   491
          | (k1, k2) =>
blanchet@42682
   492
            if k1 >= max orelse k2 >= max then max
blanchet@42682
   493
            else Int.min (max, Integer.pow k2 k1))
blanchet@42682
   494
       | @{typ int} => 0
blanchet@42682
   495
       | @{typ bool} => 2 (* optimization *)
blanchet@42682
   496
       | Type _ =>
blanchet@42682
   497
         let val thy = Proof_Context.theory_of ctxt in
blanchet@42682
   498
           case datatype_constrs thy T of
blanchet@42682
   499
             [] => default_card
blanchet@42682
   500
           | constrs =>
blanchet@42682
   501
             let
blanchet@42682
   502
               val constr_cards =
blanchet@42682
   503
                 map (Integer.prod o map (aux (T :: avoid)) o binder_types
blanchet@42682
   504
                      o snd) constrs
blanchet@42682
   505
             in
blanchet@42682
   506
               if exists (curry (op =) 0) constr_cards then 0
blanchet@42682
   507
               else Int.min (max, Integer.sum constr_cards)
blanchet@42682
   508
             end
blanchet@42682
   509
         end
blanchet@42682
   510
       | _ => default_card)
blanchet@42682
   511
  in Int.min (max, aux [] T) end
blanchet@42682
   512
blanchet@42682
   513
fun is_type_surely_finite ctxt T = tiny_card_of_type ctxt 0 T <> 0
blanchet@42682
   514
fun is_type_surely_infinite ctxt T = tiny_card_of_type ctxt 1 T = 0
blanchet@42682
   515
blanchet@42682
   516
fun should_encode_type _ _ All_Types _ = true
blanchet@42682
   517
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   518
  | should_encode_type _ nonmono_Ts Nonmonotonic_Types T =
blanchet@42682
   519
    exists (curry Type.raw_instance T) nonmono_Ts
blanchet@42682
   520
  | should_encode_type _ _ _ _ = false
blanchet@42682
   521
blanchet@42682
   522
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level)) T =
blanchet@42682
   523
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   524
  | should_predicate_on_type _ _ _ _ = false
blanchet@42682
   525
blanchet@42682
   526
fun should_tag_with_type ctxt nonmono_Ts (Tags (_, level)) T =
blanchet@42682
   527
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   528
  | should_tag_with_type _ _ _ _ = false
blanchet@42682
   529
blanchet@42682
   530
val homo_infinite_T = @{typ ind} (* any infinite type *)
blanchet@42682
   531
blanchet@42682
   532
fun homogenized_type ctxt nonmono_Ts level T =
blanchet@42682
   533
  if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
blanchet@42682
   534
blanchet@42573
   535
(** "hBOOL" and "hAPP" **)
blanchet@41313
   536
blanchet@42574
   537
type sym_info =
blanchet@42563
   538
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   539
blanchet@42574
   540
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   541
  let
blanchet@42558
   542
    fun aux top_level tm =
blanchet@42558
   543
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   544
        (case head of
blanchet@42563
   545
           CombConst ((s, _), T, _) =>
blanchet@42558
   546
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   547
             I
blanchet@42558
   548
           else
blanchet@42563
   549
             let val ary = length args in
blanchet@42558
   550
               Symtab.map_default
blanchet@42558
   551
                   (s, {pred_sym = true,
blanchet@42563
   552
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   553
                        max_ary = 0, typ = SOME T})
blanchet@42563
   554
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   555
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   556
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   557
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   558
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   559
            end
blanchet@42558
   560
         | _ => I)
blanchet@42558
   561
        #> fold (aux false) args
blanchet@42558
   562
      end
blanchet@42558
   563
  in aux true end
blanchet@42674
   564
fun add_fact_syms_to_table explicit_apply =
blanchet@42680
   565
  fact_lift (formula_fold true (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   566
blanchet@42675
   567
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   568
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   569
   (make_fixed_const predicator_base,
blanchet@42563
   570
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   571
  ([tptp_false, tptp_true]
blanchet@42563
   572
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   573
blanchet@42544
   574
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   575
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   576
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   577
blanchet@42558
   578
fun min_arity_of sym_tab s =
blanchet@42558
   579
  case Symtab.lookup sym_tab s of
blanchet@42574
   580
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   581
  | NONE =>
blanchet@42558
   582
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   583
      SOME s =>
blanchet@42570
   584
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   585
        if s = predicator_base then 1
blanchet@42547
   586
        else if s = explicit_app_base then 2
blanchet@42547
   587
        else if s = type_pred_base then 1
blanchet@42557
   588
        else 0
blanchet@42547
   589
      end
blanchet@42544
   590
    | NONE => 0
blanchet@38282
   591
blanchet@38282
   592
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   593
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   594
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   595
   arguments and is used as a predicate. *)
blanchet@42558
   596
fun is_pred_sym sym_tab s =
blanchet@42558
   597
  case Symtab.lookup sym_tab s of
blanchet@42574
   598
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   599
    pred_sym andalso min_ary = max_ary
blanchet@42558
   600
  | NONE => false
blanchet@38282
   601
blanchet@42568
   602
val predicator_combconst =
blanchet@42568
   603
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   604
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   605
blanchet@42568
   606
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   607
  case strip_combterm_comb tm of
blanchet@42542
   608
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   609
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   610
  | _ => predicator tm
blanchet@42542
   611
blanchet@42544
   612
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   613
blanchet@42544
   614
fun explicit_app arg head =
blanchet@42544
   615
  let
blanchet@42562
   616
    val head_T = combtyp_of head
blanchet@42562
   617
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   618
    val explicit_app =
blanchet@42562
   619
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42562
   620
                 [arg_T, res_T])
blanchet@42544
   621
  in list_app explicit_app [head, arg] end
blanchet@42544
   622
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   623
blanchet@42565
   624
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   625
  let
blanchet@42544
   626
    fun aux tm =
blanchet@42544
   627
      case strip_combterm_comb tm of
blanchet@42544
   628
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   629
        args |> map aux
blanchet@42557
   630
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   631
             |>> list_app head
blanchet@42544
   632
             |-> list_explicit_app
blanchet@42544
   633
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   634
  in aux end
blanchet@38282
   635
blanchet@42682
   636
fun impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42573
   637
  let
blanchet@42573
   638
    fun aux (CombApp tmp) = CombApp (pairself aux tmp)
blanchet@42574
   639
      | aux (CombConst (name as (s, _), T, T_args)) =
blanchet@42682
   640
        let
blanchet@42682
   641
          val level = level_of_type_sys type_sys
blanchet@42682
   642
          val (T, T_args) =
blanchet@42682
   643
            (* avoid needless identical homogenized versions of "hAPP" *)
blanchet@42682
   644
            if s = const_prefix ^ explicit_app_base then
blanchet@42682
   645
              T_args |> map (homogenized_type ctxt nonmono_Ts level)
blanchet@42682
   646
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42682
   647
                                    (T --> T, Ts)
blanchet@42682
   648
                                  end)
blanchet@42682
   649
            else
blanchet@42682
   650
              (T, T_args)
blanchet@42682
   651
        in
blanchet@42682
   652
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42682
   653
             NONE => (name, T_args)
blanchet@42682
   654
           | SOME s'' =>
blanchet@42682
   655
             let val s'' = invert_const s'' in
blanchet@42682
   656
               case type_arg_policy type_sys s'' of
blanchet@42682
   657
                 No_Type_Args => (name, [])
blanchet@42682
   658
               | Explicit_Type_Args => (name, T_args)
blanchet@42682
   659
               | Mangled_Type_Args => (mangled_const_name T_args name, [])
blanchet@42682
   660
             end)
blanchet@42682
   661
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42682
   662
        end
blanchet@42573
   663
      | aux tm = tm
blanchet@42573
   664
  in aux end
blanchet@42573
   665
blanchet@42682
   666
fun repair_combterm ctxt nonmono_Ts type_sys sym_tab =
blanchet@42565
   667
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   668
  #> introduce_predicators_in_combterm sym_tab
blanchet@42682
   669
  #> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42682
   670
fun repair_fact ctxt nonmono_Ts type_sys sym_tab =
blanchet@42682
   671
  update_combformula (formula_map
blanchet@42682
   672
      (repair_combterm ctxt nonmono_Ts type_sys sym_tab))
blanchet@42573
   673
blanchet@42573
   674
(** Helper facts **)
blanchet@42573
   675
blanchet@42573
   676
fun ti_ti_helper_fact () =
blanchet@42573
   677
  let
blanchet@42573
   678
    fun var s = ATerm (`I s, [])
blanchet@42589
   679
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   680
  in
blanchet@42612
   681
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   682
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42573
   683
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   684
  end
blanchet@42573
   685
blanchet@42574
   686
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   687
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   688
    SOME mangled_s =>
blanchet@42573
   689
    let
blanchet@42573
   690
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   691
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42579
   692
      fun dub_and_inst c needs_some_types (th, j) =
blanchet@42579
   693
        ((c ^ "_" ^ string_of_int j ^ (if needs_some_types then "T" else ""),
blanchet@42640
   694
          Chained),
blanchet@42573
   695
         let val t = th |> prop_of in
blanchet@42589
   696
           t |> (general_type_arg_policy type_sys = Mangled_Type_Args andalso
blanchet@42573
   697
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   698
                ? (case typ of
blanchet@42573
   699
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   700
                   | NONE => I)
blanchet@42573
   701
         end)
blanchet@42573
   702
      fun make_facts eq_as_iff =
blanchet@42573
   703
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42589
   704
      val has_some_types = is_type_sys_fairly_sound type_sys
blanchet@42573
   705
    in
blanchet@42573
   706
      metis_helpers
blanchet@42579
   707
      |> maps (fn (metis_s, (needs_some_types, ths)) =>
blanchet@42573
   708
                  if metis_s <> unmangled_s orelse
blanchet@42589
   709
                     (needs_some_types andalso not has_some_types) then
blanchet@42573
   710
                    []
blanchet@42573
   711
                  else
blanchet@42573
   712
                    ths ~~ (1 upto length ths)
blanchet@42579
   713
                    |> map (dub_and_inst mangled_s needs_some_types)
blanchet@42579
   714
                    |> make_facts (not needs_some_types))
blanchet@42573
   715
    end
blanchet@42573
   716
  | NONE => []
blanchet@42573
   717
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   718
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   719
blanchet@42573
   720
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   721
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   722
blanchet@42573
   723
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   724
  let
blanchet@42573
   725
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   726
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   727
    val (facts, fact_names) =
blanchet@42573
   728
      rich_facts
blanchet@42573
   729
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   730
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   731
      |> ListPair.unzip
blanchet@42573
   732
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   733
       boost an ATP's performance (for some reason). *)
blanchet@42573
   734
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   735
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   736
    val all_ts = goal_t :: fact_ts
blanchet@42573
   737
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   738
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   739
    val tycons = type_consts_of_terms thy all_ts
blanchet@42573
   740
    val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
blanchet@42573
   741
    val (supers', arity_clauses) =
blanchet@42589
   742
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   743
      else make_arity_clauses thy tycons supers
blanchet@42573
   744
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   745
  in
blanchet@42573
   746
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   747
  end
blanchet@42573
   748
blanchet@42573
   749
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   750
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   751
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   752
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   753
blanchet@42573
   754
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   755
blanchet@42682
   756
fun type_pred_combatom ctxt nonmono_Ts type_sys T tm =
blanchet@42573
   757
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T]),
blanchet@42573
   758
           tm)
blanchet@42682
   759
  |> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42573
   760
  |> AAtom
blanchet@42573
   761
blanchet@42680
   762
fun formula_from_combformula ctxt nonmono_Ts type_sys =
blanchet@42573
   763
  let
blanchet@42589
   764
    fun tag_with_type type_sys T tm =
blanchet@42589
   765
      CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42682
   766
      |> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42589
   767
      |> do_term true
blanchet@42589
   768
      |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42589
   769
    and do_term top_level u =
blanchet@42573
   770
      let
blanchet@42573
   771
        val (head, args) = strip_combterm_comb u
blanchet@42574
   772
        val (x, T_args) =
blanchet@42573
   773
          case head of
blanchet@42574
   774
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42573
   775
          | CombVar (name, _) => (name, [])
blanchet@42573
   776
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42574
   777
        val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42573
   778
                          map (do_term false) args)
blanchet@42574
   779
        val T = combtyp_of u
blanchet@42573
   780
      in
blanchet@42680
   781
        t |> (if not top_level andalso
blanchet@42680
   782
                should_tag_with_type ctxt nonmono_Ts type_sys T then
blanchet@42589
   783
                tag_with_type type_sys T
blanchet@42573
   784
              else
blanchet@42573
   785
                I)
blanchet@42573
   786
      end
blanchet@42573
   787
    val do_bound_type =
blanchet@42682
   788
      case type_sys of
blanchet@42684
   789
        Simple level =>
blanchet@42682
   790
        SOME o mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42682
   791
      | _ => K NONE
blanchet@42573
   792
    fun do_out_of_bound_type (s, T) =
blanchet@42680
   793
      if should_predicate_on_type ctxt nonmono_Ts type_sys T then
blanchet@42682
   794
        type_pred_combatom ctxt nonmono_Ts type_sys T (CombVar (s, T))
blanchet@42573
   795
        |> do_formula |> SOME
blanchet@42573
   796
      else
blanchet@42573
   797
        NONE
blanchet@42573
   798
    and do_formula (AQuant (q, xs, phi)) =
blanchet@42573
   799
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42574
   800
                                      | SOME T => do_bound_type T)),
blanchet@42573
   801
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42573
   802
                    (map_filter
blanchet@42573
   803
                         (fn (_, NONE) => NONE
blanchet@42574
   804
                           | (s, SOME T) => do_out_of_bound_type (s, T)) xs)
blanchet@42573
   805
                    (do_formula phi))
blanchet@42573
   806
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42573
   807
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42573
   808
  in do_formula end
blanchet@42573
   809
blanchet@42680
   810
fun formula_for_fact ctxt nonmono_Ts type_sys
blanchet@42573
   811
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42573
   812
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42573
   813
                (atp_type_literals_for_types type_sys Axiom atomic_types))
blanchet@42680
   814
           (formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42573
   815
                (close_combformula_universally combformula))
blanchet@42573
   816
  |> close_formula_universally
blanchet@42573
   817
blanchet@42640
   818
fun useful_isabelle_info s = SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42640
   819
blanchet@42573
   820
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   821
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   822
   the remote provers might care. *)
blanchet@42680
   823
fun formula_line_for_fact ctxt prefix nonmono_Ts type_sys
blanchet@42640
   824
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   825
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   826
                     else string_of_int j ^ "_") ^
blanchet@42647
   827
           ascii_of name,
blanchet@42680
   828
           kind, formula_for_fact ctxt nonmono_Ts type_sys formula, NONE,
blanchet@42640
   829
           if generate_useful_info then
blanchet@42640
   830
             case locality of
blanchet@42640
   831
               Intro => useful_isabelle_info "intro"
blanchet@42640
   832
             | Elim => useful_isabelle_info "elim"
blanchet@42640
   833
             | Simp => useful_isabelle_info "simp"
blanchet@42640
   834
             | _ => NONE
blanchet@42640
   835
           else
blanchet@42640
   836
             NONE)
blanchet@42573
   837
blanchet@42573
   838
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@42573
   839
                                                       superclass, ...}) =
blanchet@42573
   840
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   841
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   842
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   843
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42573
   844
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   845
  end
blanchet@42573
   846
blanchet@42573
   847
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   848
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   849
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   850
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   851
blanchet@42573
   852
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@42573
   853
                                                ...}) =
blanchet@42577
   854
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   855
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42573
   856
                          o fo_literal_from_arity_literal) premLits)
blanchet@42573
   857
                    (formula_from_fo_literal
blanchet@42573
   858
                         (fo_literal_from_arity_literal conclLit))
blanchet@42573
   859
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   860
blanchet@42680
   861
fun formula_line_for_conjecture ctxt nonmono_Ts type_sys
blanchet@42573
   862
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   863
  Formula (conjecture_prefix ^ name, kind,
blanchet@42680
   864
           formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42573
   865
                                    (close_combformula_universally combformula)
blanchet@42573
   866
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   867
blanchet@42573
   868
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   869
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   870
               |> map fo_literal_from_type_literal
blanchet@42573
   871
blanchet@42573
   872
fun formula_line_for_free_type j lit =
blanchet@42577
   873
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   874
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   875
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   876
  let
blanchet@42573
   877
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   878
    val lits = fold (union (op =)) litss []
blanchet@42573
   879
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   880
blanchet@42573
   881
(** Symbol declarations **)
blanchet@42544
   882
blanchet@42677
   883
fun insert_type get_T x xs =
blanchet@42677
   884
  let val T = get_T x in
blanchet@42677
   885
    if exists (curry Type.raw_instance T o get_T) xs then xs
blanchet@42677
   886
    else x :: filter_out ((fn T' => Type.raw_instance (T', T)) o get_T) xs
blanchet@42677
   887
  end
blanchet@42677
   888
blanchet@42574
   889
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   890
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42645
   891
  not (String.isPrefix "$" s) andalso
blanchet@42684
   892
  ((case type_sys of Simple _ => true | _ => false) orelse not pred_sym)
blanchet@38282
   893
blanchet@42574
   894
fun add_combterm_syms_to_decl_table type_sys repaired_sym_tab =
blanchet@42574
   895
  let
blanchet@42677
   896
    fun declare_sym decl decls =
blanchet@42579
   897
      case type_sys of
blanchet@42677
   898
        Preds (Polymorphic, All_Types) => insert_type #3 decl decls
blanchet@42579
   899
      | _ => insert (op =) decl decls
blanchet@42576
   900
    fun do_term tm =
blanchet@42574
   901
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   902
        (case head of
blanchet@42574
   903
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   904
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   905
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   906
               Symtab.map_default (s, [])
blanchet@42576
   907
                   (declare_sym (s', T_args, T, pred_sym, length args))
blanchet@42574
   908
             else
blanchet@42574
   909
               I
blanchet@42574
   910
           end
blanchet@42574
   911
         | _ => I)
blanchet@42576
   912
        #> fold do_term args
blanchet@42574
   913
      end
blanchet@42576
   914
  in do_term end
blanchet@42574
   915
fun add_fact_syms_to_decl_table type_sys repaired_sym_tab =
blanchet@42680
   916
  fact_lift (formula_fold true
blanchet@42677
   917
      (K (add_combterm_syms_to_decl_table type_sys repaired_sym_tab)))
blanchet@42574
   918
fun sym_decl_table_for_facts type_sys repaired_sym_tab facts =
blanchet@42589
   919
  Symtab.empty |> is_type_sys_fairly_sound type_sys
blanchet@42574
   920
                  ? fold (add_fact_syms_to_decl_table type_sys repaired_sym_tab)
blanchet@42574
   921
                         facts
blanchet@42533
   922
blanchet@42677
   923
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42677
   924
    String.isPrefix bound_var_prefix s
blanchet@42677
   925
  | is_var_or_bound_var (CombVar _) = true
blanchet@42677
   926
  | is_var_or_bound_var _ = false
blanchet@42677
   927
blanchet@42685
   928
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
   929
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42680
   930
fun add_combterm_nonmonotonic_types _ (SOME false) _ = I
blanchet@42680
   931
  | add_combterm_nonmonotonic_types ctxt _
blanchet@42680
   932
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
   933
                  tm2)) =
blanchet@42680
   934
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42680
   935
     not (is_type_surely_infinite ctxt T)) ? insert_type I T
blanchet@42680
   936
  | add_combterm_nonmonotonic_types _ _ _ = I
blanchet@42680
   937
fun add_fact_nonmonotonic_types ctxt ({kind, combformula, ...}
blanchet@42680
   938
                                      : translated_formula) =
blanchet@42680
   939
  formula_fold (kind <> Conjecture) (add_combterm_nonmonotonic_types ctxt)
blanchet@42680
   940
               combformula
blanchet@42680
   941
fun add_nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42680
   942
  level_of_type_sys type_sys = Nonmonotonic_Types
blanchet@42682
   943
  ? (insert_type I @{typ bool} (* in case helper "True_or_False" is included *)
blanchet@42682
   944
     #> fold (add_fact_nonmonotonic_types ctxt) facts)
blanchet@42677
   945
blanchet@42574
   946
fun n_ary_strip_type 0 T = ([], T)
blanchet@42574
   947
  | n_ary_strip_type n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42574
   948
    n_ary_strip_type (n - 1) ran_T |>> cons dom_T
blanchet@42574
   949
  | n_ary_strip_type _ _ = raise Fail "unexpected non-function"
blanchet@42533
   950
blanchet@42579
   951
fun result_type_of_decl (_, _, T, _, ary) = n_ary_strip_type ary T |> snd
blanchet@42579
   952
blanchet@42682
   953
fun decl_line_for_sym s (s', _, T, pred_sym, ary) =
blanchet@42579
   954
  let val (arg_Ts, res_T) = n_ary_strip_type ary T in
blanchet@42612
   955
    Decl (sym_decl_prefix ^ s, (s, s'), map mangled_type_name arg_Ts,
blanchet@42579
   956
          if pred_sym then `I tptp_tff_bool_type else mangled_type_name res_T)
blanchet@42579
   957
  end
blanchet@42579
   958
blanchet@42592
   959
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
   960
blanchet@42680
   961
fun formula_line_for_sym_decl ctxt nonmono_Ts type_sys n s j
blanchet@42680
   962
                              (s', T_args, T, _, ary) =
blanchet@42579
   963
  let
blanchet@42579
   964
    val (arg_Ts, res_T) = n_ary_strip_type ary T
blanchet@42579
   965
    val bound_names =
blanchet@42579
   966
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42579
   967
    val bound_tms =
blanchet@42579
   968
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
   969
    val bound_Ts =
blanchet@42592
   970
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
   971
                             else NONE)
blanchet@42579
   972
  in
blanchet@42612
   973
    Formula (sym_decl_prefix ^ s ^
blanchet@42612
   974
             (if n > 1 then "_" ^ string_of_int j else ""), Axiom,
blanchet@42579
   975
             CombConst ((s, s'), T, T_args)
blanchet@42579
   976
             |> fold (curry (CombApp o swap)) bound_tms
blanchet@42682
   977
             |> type_pred_combatom ctxt nonmono_Ts type_sys res_T
blanchet@42579
   978
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42680
   979
             |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42586
   980
             |> close_formula_universally,
blanchet@42579
   981
             NONE, NONE)
blanchet@42579
   982
  end
blanchet@42579
   983
blanchet@42680
   984
fun problem_lines_for_sym_decls ctxt nonmono_Ts type_sys (s, decls) =
blanchet@42682
   985
  case type_sys of
blanchet@42684
   986
    Simple _ => map (decl_line_for_sym s) decls
blanchet@42682
   987
  | _ =>
blanchet@42574
   988
    let
blanchet@42579
   989
      val decls =
blanchet@42579
   990
        case decls of
blanchet@42579
   991
          decl :: (decls' as _ :: _) =>
blanchet@42592
   992
          let val T = result_type_of_decl decl in
blanchet@42592
   993
            if forall ((fn T' => Type.raw_instance (T', T))
blanchet@42592
   994
                       o result_type_of_decl) decls' then
blanchet@42592
   995
              [decl]
blanchet@42592
   996
            else
blanchet@42592
   997
              decls
blanchet@42592
   998
          end
blanchet@42579
   999
        | _ => decls
blanchet@42579
  1000
      val n = length decls
blanchet@42579
  1001
      val decls =
blanchet@42680
  1002
        decls |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42579
  1003
                         o result_type_of_decl)
blanchet@42574
  1004
    in
blanchet@42680
  1005
      map2 (formula_line_for_sym_decl ctxt nonmono_Ts type_sys n s)
blanchet@42579
  1006
           (0 upto length decls - 1) decls
blanchet@42574
  1007
    end
blanchet@42579
  1008
blanchet@42680
  1009
fun problem_lines_for_sym_decl_table ctxt nonmono_Ts type_sys sym_decl_tab =
blanchet@42680
  1010
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt nonmono_Ts
blanchet@42680
  1011
                                                        type_sys)
blanchet@42574
  1012
                  sym_decl_tab []
blanchet@42543
  1013
blanchet@42543
  1014
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
  1015
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
  1016
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
  1017
    fold add_tff_types_in_formula phis
blanchet@42543
  1018
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
  1019
blanchet@42562
  1020
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
  1021
    union (op =) (res_T :: arg_Ts)
blanchet@42577
  1022
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
  1023
    add_tff_types_in_formula phi
blanchet@42543
  1024
blanchet@42543
  1025
fun tff_types_in_problem problem =
blanchet@42543
  1026
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
  1027
blanchet@42545
  1028
fun decl_line_for_tff_type (s, s') =
blanchet@42568
  1029
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
  1030
blanchet@42543
  1031
val type_declsN = "Types"
blanchet@42544
  1032
val sym_declsN = "Symbol types"
blanchet@41157
  1033
val factsN = "Relevant facts"
blanchet@41157
  1034
val class_relsN = "Class relationships"
blanchet@42543
  1035
val aritiesN = "Arities"
blanchet@41157
  1036
val helpersN = "Helper facts"
blanchet@41157
  1037
val conjsN = "Conjectures"
blanchet@41313
  1038
val free_typesN = "Type variables"
blanchet@41157
  1039
blanchet@41157
  1040
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
  1041
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
  1042
    if heading = needle then j
blanchet@41157
  1043
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
  1044
blanchet@42568
  1045
fun prepare_atp_problem ctxt type_sys explicit_apply hyp_ts concl_t facts =
blanchet@38282
  1046
  let
blanchet@41313
  1047
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
  1048
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@42563
  1049
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42682
  1050
    val nonmono_Ts =
blanchet@42682
  1051
      [] |> fold (add_nonmonotonic_types_for_facts ctxt type_sys) [facts, conjs]
blanchet@42682
  1052
    val repair = repair_fact ctxt nonmono_Ts type_sys sym_tab
blanchet@42682
  1053
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1054
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1055
    val helpers =
blanchet@42682
  1056
      repaired_sym_tab |> helper_facts_for_sym_table ctxt type_sys |> map repair
blanchet@42680
  1057
    val sym_decl_lines =
blanchet@42680
  1058
      conjs @ facts
blanchet@42680
  1059
      |> sym_decl_table_for_facts type_sys repaired_sym_tab
blanchet@42680
  1060
      |> problem_lines_for_sym_decl_table ctxt nonmono_Ts type_sys
blanchet@42522
  1061
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1062
       Flotter hack. *)
blanchet@38282
  1063
    val problem =
blanchet@42561
  1064
      [(sym_declsN, sym_decl_lines),
blanchet@42680
  1065
       (factsN, map (formula_line_for_fact ctxt fact_prefix nonmono_Ts type_sys)
blanchet@42180
  1066
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1067
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1068
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42680
  1069
       (helpersN, map (formula_line_for_fact ctxt helper_prefix nonmono_Ts
blanchet@42680
  1070
                                             type_sys)
blanchet@42563
  1071
                      (0 upto length helpers - 1 ~~ helpers)
blanchet@42579
  1072
                  |> (case type_sys of
blanchet@42589
  1073
                        Tags (Polymorphic, level) =>
blanchet@42687
  1074
                        is_type_level_partial level
blanchet@42589
  1075
                        ? cons (ti_ti_helper_fact ())
blanchet@42579
  1076
                      | _ => I)),
blanchet@42680
  1077
       (conjsN, map (formula_line_for_conjecture ctxt nonmono_Ts type_sys)
blanchet@42680
  1078
                    conjs),
blanchet@42545
  1079
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1080
    val problem =
blanchet@42561
  1081
      problem
blanchet@42682
  1082
      |> (case type_sys of
blanchet@42684
  1083
            Simple _ =>
blanchet@42561
  1084
            cons (type_declsN,
blanchet@42561
  1085
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42682
  1086
          | _ => I)
blanchet@42646
  1087
    val (problem, pool) =
blanchet@42646
  1088
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@38282
  1089
  in
blanchet@38282
  1090
    (problem,
blanchet@38282
  1091
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1092
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1093
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
  1094
     fact_names |> Vector.fromList)
blanchet@38282
  1095
  end
blanchet@38282
  1096
blanchet@41313
  1097
(* FUDGE *)
blanchet@41313
  1098
val conj_weight = 0.0
blanchet@41770
  1099
val hyp_weight = 0.1
blanchet@41770
  1100
val fact_min_weight = 0.2
blanchet@41313
  1101
val fact_max_weight = 1.0
blanchet@42608
  1102
val type_info_default_weight = 0.8
blanchet@41313
  1103
blanchet@41313
  1104
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
  1105
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
  1106
  #> fold (add_term_weights weight) tms
blanchet@42577
  1107
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42680
  1108
    formula_fold true (K (add_term_weights weight)) phi
blanchet@42528
  1109
  | add_problem_line_weights _ _ = I
blanchet@41313
  1110
blanchet@41313
  1111
fun add_conjectures_weights [] = I
blanchet@41313
  1112
  | add_conjectures_weights conjs =
blanchet@41313
  1113
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1114
      add_problem_line_weights conj_weight conj
blanchet@41313
  1115
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1116
    end
blanchet@41313
  1117
blanchet@41313
  1118
fun add_facts_weights facts =
blanchet@41313
  1119
  let
blanchet@41313
  1120
    val num_facts = length facts
blanchet@41313
  1121
    fun weight_of j =
blanchet@41313
  1122
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1123
                        / Real.fromInt num_facts
blanchet@41313
  1124
  in
blanchet@41313
  1125
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1126
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1127
  end
blanchet@41313
  1128
blanchet@41313
  1129
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1130
fun atp_problem_weights problem =
blanchet@42608
  1131
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1132
    Symtab.empty
blanchet@42608
  1133
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1134
    |> add_facts_weights (get factsN)
blanchet@42608
  1135
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1136
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1137
    |> Symtab.dest
blanchet@42608
  1138
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1139
  end
blanchet@41313
  1140
blanchet@38282
  1141
end;