src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Wed May 04 15:35:05 2011 +0200 (2011-05-04)
changeset 42677 25496cd3c199
parent 42675 223153bb68a1
child 42680 b6c27cf04fe9
permissions -rw-r--r--
monotonic type inference in ATP Sledgehammer problems -- based on Claessen & al.'s CADE 2011 paper, Sect. 2.3.
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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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    Many_Typed |
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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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  Many_Typed |
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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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           ("many_typed", (Polymorphic (* naja *), All_Types)) =>
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           Many_Typed
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         | ("preds", extra) => Preds extra
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         | ("tags", extra) => Tags extra
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         | ("const_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 Many_Typed = 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 Many_Typed = All_Types
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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 s =
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  s = All_Types orelse s = 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 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 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 (not pos) phi
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      | aux pos (AConn (AImplies, [phi1, phi2])) =
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        aux (not pos) phi1 #> aux pos phi2
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      | aux pos (AConn (c, phis)) =
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        if member (op =) [AAnd, AOr] c then fold (aux pos) phis
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        else raise Fail "unexpected connective with unknown polarities"
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      | aux pos (AAtom tm) = f pos tm
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  in aux true 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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      ||> union (op =) atomic_types
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   319
    fun do_quant bs q s T t' =
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   320
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   321
        do_formula ((s, T) :: bs) t'
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   322
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
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   323
      end
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   324
    and do_conn bs c t1 t2 =
blanchet@38282
   325
      do_formula bs t1 ##>> do_formula bs t2
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   326
      #>> uncurry (mk_aconn c)
blanchet@38282
   327
    and do_formula bs t =
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   328
      case t of
blanchet@42531
   329
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
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   330
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   331
        do_quant bs AForall s T t'
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   332
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   333
        do_quant bs AExists s T t'
haftmann@38795
   334
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   335
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   336
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   337
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
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   338
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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   339
      | _ => do_term bs t
blanchet@38282
   340
  in do_formula [] end
blanchet@38282
   341
blanchet@38618
   342
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
blanchet@38282
   343
wenzelm@41491
   344
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   345
fun conceal_bounds Ts t =
blanchet@38282
   346
  subst_bounds (map (Free o apfst concealed_bound_name)
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   347
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   348
fun reveal_bounds Ts =
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   349
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   350
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   351
blanchet@38608
   352
(* Removes the lambdas from an equation of the form "t = (%x. u)".
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   353
   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
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   354
fun extensionalize_term t =
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   355
  let
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   356
    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
blanchet@38608
   357
      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
blanchet@38608
   358
                                        Type (_, [_, res_T])]))
blanchet@38608
   359
                    $ t2 $ Abs (var_s, var_T, t')) =
haftmann@38864
   360
        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
blanchet@38608
   361
          let val var_t = Var ((var_s, j), var_T) in
blanchet@38608
   362
            Const (s, T' --> T' --> res_T)
blanchet@38608
   363
              $ betapply (t2, var_t) $ subst_bound (var_t, t')
blanchet@38608
   364
            |> aux (j + 1)
blanchet@38608
   365
          end
blanchet@38608
   366
        else
blanchet@38608
   367
          t
blanchet@38608
   368
      | aux _ t = t
blanchet@38608
   369
  in aux (maxidx_of_term t + 1) t end
blanchet@38608
   370
blanchet@38282
   371
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   372
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   373
    if Meson.is_fol_term thy t then
blanchet@38491
   374
      t
blanchet@38491
   375
    else
blanchet@38491
   376
      let
blanchet@38491
   377
        fun aux Ts t =
blanchet@38491
   378
          case t of
blanchet@38491
   379
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   380
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   381
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   382
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   383
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   384
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   385
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   386
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   387
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   388
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   389
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   390
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   391
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   392
              $ t1 $ t2 =>
blanchet@38491
   393
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   394
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   395
                   t
blanchet@38491
   396
                 else
blanchet@38491
   397
                   t |> conceal_bounds Ts
blanchet@38491
   398
                     |> Envir.eta_contract
blanchet@38491
   399
                     |> cterm_of thy
blanchet@39890
   400
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   401
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   402
                     |> reveal_bounds Ts
blanchet@39370
   403
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   404
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   405
      handle THM _ =>
blanchet@38491
   406
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   407
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   408
             else HOLogic.true_const
blanchet@38491
   409
  end
blanchet@38282
   410
blanchet@38282
   411
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   412
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   413
fun freeze_term t =
blanchet@38282
   414
  let
blanchet@38282
   415
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   416
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   417
      | aux (Var ((s, i), T)) =
blanchet@38282
   418
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   419
      | aux t = t
blanchet@38282
   420
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   421
blanchet@40204
   422
(* making fact and conjecture formulas *)
blanchet@42640
   423
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   424
  let
wenzelm@42361
   425
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   426
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   427
              |> transform_elim_term
blanchet@41211
   428
              |> Object_Logic.atomize_term thy
blanchet@42563
   429
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   430
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@38282
   431
              |> extensionalize_term
blanchet@38282
   432
              |> presimp ? presimplify_term thy
blanchet@38282
   433
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   434
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   435
              |> kind <> Axiom ? freeze_term
blanchet@42562
   436
    val (combformula, atomic_types) =
blanchet@42562
   437
      combformula_from_prop thy eq_as_iff t []
blanchet@38282
   438
  in
blanchet@42640
   439
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   440
     atomic_types = atomic_types}
blanchet@38282
   441
  end
blanchet@38282
   442
blanchet@42640
   443
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   444
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   445
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   446
    NONE
blanchet@41990
   447
  | (_, formula) => SOME formula
blanchet@42561
   448
blanchet@42544
   449
fun make_conjecture ctxt ts =
blanchet@38613
   450
  let val last = length ts - 1 in
blanchet@42640
   451
    map2 (fn j => make_formula ctxt true true (string_of_int j) Chained
blanchet@38613
   452
                               (if j = last then Conjecture else Hypothesis))
blanchet@38613
   453
         (0 upto last) ts
blanchet@38613
   454
  end
blanchet@38282
   455
blanchet@42573
   456
(** "hBOOL" and "hAPP" **)
blanchet@41313
   457
blanchet@42574
   458
type sym_info =
blanchet@42563
   459
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   460
blanchet@42574
   461
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   462
  let
blanchet@42558
   463
    fun aux top_level tm =
blanchet@42558
   464
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   465
        (case head of
blanchet@42563
   466
           CombConst ((s, _), T, _) =>
blanchet@42558
   467
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   468
             I
blanchet@42558
   469
           else
blanchet@42563
   470
             let val ary = length args in
blanchet@42558
   471
               Symtab.map_default
blanchet@42558
   472
                   (s, {pred_sym = true,
blanchet@42563
   473
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   474
                        max_ary = 0, typ = SOME T})
blanchet@42563
   475
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   476
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   477
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   478
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   479
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   480
            end
blanchet@42558
   481
         | _ => I)
blanchet@42558
   482
        #> fold (aux false) args
blanchet@42558
   483
      end
blanchet@42558
   484
  in aux true end
blanchet@42674
   485
fun add_fact_syms_to_table explicit_apply =
blanchet@42677
   486
  fact_lift (formula_fold (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   487
blanchet@42675
   488
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   489
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   490
   (make_fixed_const predicator_base,
blanchet@42563
   491
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   492
  ([tptp_false, tptp_true]
blanchet@42563
   493
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   494
blanchet@42544
   495
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   496
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   497
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   498
blanchet@42558
   499
fun min_arity_of sym_tab s =
blanchet@42558
   500
  case Symtab.lookup sym_tab s of
blanchet@42574
   501
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   502
  | NONE =>
blanchet@42558
   503
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   504
      SOME s =>
blanchet@42570
   505
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   506
        if s = predicator_base then 1
blanchet@42547
   507
        else if s = explicit_app_base then 2
blanchet@42547
   508
        else if s = type_pred_base then 1
blanchet@42557
   509
        else 0
blanchet@42547
   510
      end
blanchet@42544
   511
    | NONE => 0
blanchet@38282
   512
blanchet@38282
   513
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   514
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   515
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   516
   arguments and is used as a predicate. *)
blanchet@42558
   517
fun is_pred_sym sym_tab s =
blanchet@42558
   518
  case Symtab.lookup sym_tab s of
blanchet@42574
   519
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   520
    pred_sym andalso min_ary = max_ary
blanchet@42558
   521
  | NONE => false
blanchet@38282
   522
blanchet@42568
   523
val predicator_combconst =
blanchet@42568
   524
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   525
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   526
blanchet@42568
   527
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   528
  case strip_combterm_comb tm of
blanchet@42542
   529
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   530
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   531
  | _ => predicator tm
blanchet@42542
   532
blanchet@42544
   533
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   534
blanchet@42544
   535
fun explicit_app arg head =
blanchet@42544
   536
  let
blanchet@42562
   537
    val head_T = combtyp_of head
blanchet@42562
   538
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   539
    val explicit_app =
blanchet@42562
   540
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42562
   541
                 [arg_T, res_T])
blanchet@42544
   542
  in list_app explicit_app [head, arg] end
blanchet@42544
   543
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   544
blanchet@42565
   545
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   546
  let
blanchet@42544
   547
    fun aux tm =
blanchet@42544
   548
      case strip_combterm_comb tm of
blanchet@42544
   549
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   550
        args |> map aux
blanchet@42557
   551
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   552
             |>> list_app head
blanchet@42544
   553
             |-> list_explicit_app
blanchet@42544
   554
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   555
  in aux end
blanchet@38282
   556
blanchet@42573
   557
fun impose_type_arg_policy_in_combterm type_sys =
blanchet@42573
   558
  let
blanchet@42573
   559
    fun aux (CombApp tmp) = CombApp (pairself aux tmp)
blanchet@42574
   560
      | aux (CombConst (name as (s, _), T, T_args)) =
blanchet@42573
   561
        (case strip_prefix_and_unascii const_prefix s of
blanchet@42574
   562
           NONE => (name, T_args)
blanchet@42573
   563
         | SOME s'' =>
blanchet@42573
   564
           let val s'' = invert_const s'' in
blanchet@42573
   565
             case type_arg_policy type_sys s'' of
blanchet@42573
   566
               No_Type_Args => (name, [])
blanchet@42574
   567
             | Explicit_Type_Args => (name, T_args)
blanchet@42589
   568
             | Mangled_Type_Args => (mangled_const_name T_args name, [])
blanchet@42573
   569
           end)
blanchet@42574
   570
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42573
   571
      | aux tm = tm
blanchet@42573
   572
  in aux end
blanchet@42573
   573
blanchet@42573
   574
fun repair_combterm type_sys sym_tab =
blanchet@42565
   575
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   576
  #> introduce_predicators_in_combterm sym_tab
blanchet@42573
   577
  #> impose_type_arg_policy_in_combterm type_sys
blanchet@42674
   578
fun repair_fact type_sys sym_tab =
blanchet@42674
   579
  update_combformula (formula_map (repair_combterm type_sys sym_tab))
blanchet@42573
   580
blanchet@42573
   581
(** Helper facts **)
blanchet@42573
   582
blanchet@42573
   583
fun ti_ti_helper_fact () =
blanchet@42573
   584
  let
blanchet@42573
   585
    fun var s = ATerm (`I s, [])
blanchet@42589
   586
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   587
  in
blanchet@42612
   588
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   589
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42573
   590
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   591
  end
blanchet@42573
   592
blanchet@42574
   593
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   594
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   595
    SOME mangled_s =>
blanchet@42573
   596
    let
blanchet@42573
   597
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   598
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42579
   599
      fun dub_and_inst c needs_some_types (th, j) =
blanchet@42579
   600
        ((c ^ "_" ^ string_of_int j ^ (if needs_some_types then "T" else ""),
blanchet@42640
   601
          Chained),
blanchet@42573
   602
         let val t = th |> prop_of in
blanchet@42589
   603
           t |> (general_type_arg_policy type_sys = Mangled_Type_Args andalso
blanchet@42573
   604
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   605
                ? (case typ of
blanchet@42573
   606
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   607
                   | NONE => I)
blanchet@42573
   608
         end)
blanchet@42573
   609
      fun make_facts eq_as_iff =
blanchet@42573
   610
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42589
   611
      val has_some_types = is_type_sys_fairly_sound type_sys
blanchet@42573
   612
    in
blanchet@42573
   613
      metis_helpers
blanchet@42579
   614
      |> maps (fn (metis_s, (needs_some_types, ths)) =>
blanchet@42573
   615
                  if metis_s <> unmangled_s orelse
blanchet@42589
   616
                     (needs_some_types andalso not has_some_types) then
blanchet@42573
   617
                    []
blanchet@42573
   618
                  else
blanchet@42573
   619
                    ths ~~ (1 upto length ths)
blanchet@42579
   620
                    |> map (dub_and_inst mangled_s needs_some_types)
blanchet@42579
   621
                    |> make_facts (not needs_some_types))
blanchet@42573
   622
    end
blanchet@42573
   623
  | NONE => []
blanchet@42573
   624
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   625
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   626
blanchet@42573
   627
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   628
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   629
blanchet@42573
   630
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   631
  let
blanchet@42573
   632
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   633
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   634
    val (facts, fact_names) =
blanchet@42573
   635
      rich_facts
blanchet@42573
   636
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   637
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   638
      |> ListPair.unzip
blanchet@42573
   639
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   640
       boost an ATP's performance (for some reason). *)
blanchet@42573
   641
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   642
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   643
    val all_ts = goal_t :: fact_ts
blanchet@42573
   644
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   645
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   646
    val tycons = type_consts_of_terms thy all_ts
blanchet@42573
   647
    val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
blanchet@42573
   648
    val (supers', arity_clauses) =
blanchet@42589
   649
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   650
      else make_arity_clauses thy tycons supers
blanchet@42573
   651
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   652
  in
blanchet@42573
   653
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   654
  end
blanchet@42573
   655
blanchet@42573
   656
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   657
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   658
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   659
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   660
blanchet@42573
   661
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   662
blanchet@42573
   663
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42573
   664
   considered dangerous because their "exhaust" properties can easily lead to
blanchet@42573
   665
   unsound ATP proofs. The checks below are an (unsound) approximation of
blanchet@42573
   666
   finiteness. *)
blanchet@42573
   667
blanchet@42589
   668
fun is_dtyp_finite _ (Datatype_Aux.DtTFree _) = true
blanchet@42589
   669
  | is_dtyp_finite ctxt (Datatype_Aux.DtType (s, Us)) =
blanchet@42589
   670
    is_type_constr_finite ctxt s andalso forall (is_dtyp_finite ctxt) Us
blanchet@42589
   671
  | is_dtyp_finite _ (Datatype_Aux.DtRec _) = false
blanchet@42589
   672
and is_type_finite ctxt (Type (s, Ts)) =
blanchet@42589
   673
    is_type_constr_finite ctxt s andalso forall (is_type_finite ctxt) Ts
blanchet@42589
   674
  | is_type_finite _ _ = false
blanchet@42589
   675
and is_type_constr_finite ctxt s =
blanchet@42573
   676
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42573
   677
    case Datatype_Data.get_info thy s of
blanchet@42573
   678
      SOME {descr, ...} =>
blanchet@42573
   679
      forall (fn (_, (_, _, constrs)) =>
blanchet@42589
   680
                 forall (forall (is_dtyp_finite ctxt) o snd) constrs) descr
blanchet@42573
   681
    | NONE =>
blanchet@42573
   682
      case Typedef.get_info ctxt s of
blanchet@42589
   683
        ({rep_type, ...}, _) :: _ => is_type_finite ctxt rep_type
blanchet@42573
   684
      | [] => true
blanchet@42573
   685
  end
blanchet@42573
   686
blanchet@42589
   687
fun should_encode_type _ All_Types _ = true
blanchet@42589
   688
  | should_encode_type ctxt Finite_Types T = is_type_finite ctxt T
blanchet@42589
   689
  | should_encode_type _ Nonmonotonic_Types _ =
blanchet@42589
   690
    error "Monotonicity inference not implemented yet."
blanchet@42589
   691
  | should_encode_type _ _ _ = false
blanchet@42589
   692
blanchet@42589
   693
fun should_predicate_on_type ctxt (Preds (_, level)) T =
blanchet@42589
   694
    should_encode_type ctxt level T
blanchet@42589
   695
  | should_predicate_on_type _ _ _ = false
blanchet@42579
   696
blanchet@42579
   697
fun should_tag_with_type ctxt (Tags (_, level)) T =
blanchet@42579
   698
    should_encode_type ctxt level T
blanchet@42573
   699
  | should_tag_with_type _ _ _ = false
blanchet@42573
   700
blanchet@42573
   701
fun type_pred_combatom type_sys T tm =
blanchet@42573
   702
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T]),
blanchet@42573
   703
           tm)
blanchet@42573
   704
  |> impose_type_arg_policy_in_combterm type_sys
blanchet@42573
   705
  |> AAtom
blanchet@42573
   706
blanchet@42573
   707
fun formula_from_combformula ctxt type_sys =
blanchet@42573
   708
  let
blanchet@42589
   709
    fun tag_with_type type_sys T tm =
blanchet@42589
   710
      CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42589
   711
      |> impose_type_arg_policy_in_combterm type_sys
blanchet@42589
   712
      |> do_term true
blanchet@42589
   713
      |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42589
   714
    and do_term top_level u =
blanchet@42573
   715
      let
blanchet@42573
   716
        val (head, args) = strip_combterm_comb u
blanchet@42574
   717
        val (x, T_args) =
blanchet@42573
   718
          case head of
blanchet@42574
   719
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42573
   720
          | CombVar (name, _) => (name, [])
blanchet@42573
   721
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42574
   722
        val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42573
   723
                          map (do_term false) args)
blanchet@42574
   724
        val T = combtyp_of u
blanchet@42573
   725
      in
blanchet@42574
   726
        t |> (if not top_level andalso should_tag_with_type ctxt type_sys T then
blanchet@42589
   727
                tag_with_type type_sys T
blanchet@42573
   728
              else
blanchet@42573
   729
                I)
blanchet@42573
   730
      end
blanchet@42573
   731
    val do_bound_type =
blanchet@42573
   732
      if type_sys = Many_Typed then SOME o mangled_type_name else K NONE
blanchet@42573
   733
    fun do_out_of_bound_type (s, T) =
blanchet@42579
   734
      if should_predicate_on_type ctxt type_sys T then
blanchet@42573
   735
        type_pred_combatom type_sys T (CombVar (s, T))
blanchet@42573
   736
        |> do_formula |> SOME
blanchet@42573
   737
      else
blanchet@42573
   738
        NONE
blanchet@42573
   739
    and do_formula (AQuant (q, xs, phi)) =
blanchet@42573
   740
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42574
   741
                                      | SOME T => do_bound_type T)),
blanchet@42573
   742
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42573
   743
                    (map_filter
blanchet@42573
   744
                         (fn (_, NONE) => NONE
blanchet@42574
   745
                           | (s, SOME T) => do_out_of_bound_type (s, T)) xs)
blanchet@42573
   746
                    (do_formula phi))
blanchet@42573
   747
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42573
   748
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42573
   749
  in do_formula end
blanchet@42573
   750
blanchet@42573
   751
fun formula_for_fact ctxt type_sys
blanchet@42573
   752
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42573
   753
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42573
   754
                (atp_type_literals_for_types type_sys Axiom atomic_types))
blanchet@42573
   755
           (formula_from_combformula ctxt type_sys
blanchet@42573
   756
                (close_combformula_universally combformula))
blanchet@42573
   757
  |> close_formula_universally
blanchet@42573
   758
blanchet@42640
   759
fun useful_isabelle_info s = SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42640
   760
blanchet@42573
   761
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   762
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   763
   the remote provers might care. *)
blanchet@42573
   764
fun formula_line_for_fact ctxt prefix type_sys
blanchet@42640
   765
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42647
   766
  Formula (prefix ^
blanchet@42647
   767
           (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42647
   768
            else string_of_int j ^ "_") ^
blanchet@42647
   769
           ascii_of name,
blanchet@42647
   770
           kind, formula_for_fact ctxt type_sys formula, NONE,
blanchet@42640
   771
           if generate_useful_info then
blanchet@42640
   772
             case locality of
blanchet@42640
   773
               Intro => useful_isabelle_info "intro"
blanchet@42640
   774
             | Elim => useful_isabelle_info "elim"
blanchet@42640
   775
             | Simp => useful_isabelle_info "simp"
blanchet@42640
   776
             | _ => NONE
blanchet@42640
   777
           else
blanchet@42640
   778
             NONE)
blanchet@42573
   779
blanchet@42573
   780
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@42573
   781
                                                       superclass, ...}) =
blanchet@42573
   782
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   783
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   784
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   785
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42573
   786
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   787
  end
blanchet@42573
   788
blanchet@42573
   789
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   790
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   791
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   792
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   793
blanchet@42573
   794
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@42573
   795
                                                ...}) =
blanchet@42577
   796
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   797
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42573
   798
                          o fo_literal_from_arity_literal) premLits)
blanchet@42573
   799
                    (formula_from_fo_literal
blanchet@42573
   800
                         (fo_literal_from_arity_literal conclLit))
blanchet@42573
   801
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   802
blanchet@42573
   803
fun formula_line_for_conjecture ctxt type_sys
blanchet@42573
   804
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   805
  Formula (conjecture_prefix ^ name, kind,
blanchet@42573
   806
           formula_from_combformula ctxt type_sys
blanchet@42573
   807
                                    (close_combformula_universally combformula)
blanchet@42573
   808
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   809
blanchet@42573
   810
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   811
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   812
               |> map fo_literal_from_type_literal
blanchet@42573
   813
blanchet@42573
   814
fun formula_line_for_free_type j lit =
blanchet@42577
   815
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   816
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   817
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   818
  let
blanchet@42573
   819
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   820
    val lits = fold (union (op =)) litss []
blanchet@42573
   821
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   822
blanchet@42573
   823
(** Symbol declarations **)
blanchet@42544
   824
blanchet@42677
   825
fun insert_type get_T x xs =
blanchet@42677
   826
  let val T = get_T x in
blanchet@42677
   827
    if exists (curry Type.raw_instance T o get_T) xs then xs
blanchet@42677
   828
    else x :: filter_out ((fn T' => Type.raw_instance (T', T)) o get_T) xs
blanchet@42677
   829
  end
blanchet@42677
   830
blanchet@42574
   831
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   832
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42645
   833
  not (String.isPrefix "$" s) andalso
blanchet@42574
   834
  (type_sys = Many_Typed orelse not pred_sym)
blanchet@38282
   835
blanchet@42574
   836
fun add_combterm_syms_to_decl_table type_sys repaired_sym_tab =
blanchet@42574
   837
  let
blanchet@42677
   838
    fun declare_sym decl decls =
blanchet@42677
   839
      (* FIXME: use "insert_type" in all cases? *)
blanchet@42579
   840
      case type_sys of
blanchet@42677
   841
        Preds (Polymorphic, All_Types) => insert_type #3 decl decls
blanchet@42579
   842
      | _ => insert (op =) decl decls
blanchet@42576
   843
    fun do_term tm =
blanchet@42574
   844
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   845
        (case head of
blanchet@42574
   846
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   847
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   848
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   849
               Symtab.map_default (s, [])
blanchet@42576
   850
                   (declare_sym (s', T_args, T, pred_sym, length args))
blanchet@42574
   851
             else
blanchet@42574
   852
               I
blanchet@42574
   853
           end
blanchet@42574
   854
         | _ => I)
blanchet@42576
   855
        #> fold do_term args
blanchet@42574
   856
      end
blanchet@42576
   857
  in do_term end
blanchet@42574
   858
fun add_fact_syms_to_decl_table type_sys repaired_sym_tab =
blanchet@42574
   859
  fact_lift (formula_fold
blanchet@42677
   860
      (K (add_combterm_syms_to_decl_table type_sys repaired_sym_tab)))
blanchet@42574
   861
fun sym_decl_table_for_facts type_sys repaired_sym_tab facts =
blanchet@42589
   862
  Symtab.empty |> is_type_sys_fairly_sound type_sys
blanchet@42574
   863
                  ? fold (add_fact_syms_to_decl_table type_sys repaired_sym_tab)
blanchet@42574
   864
                         facts
blanchet@42533
   865
blanchet@42677
   866
(* FIXME: use CombVar not CombConst for bound variables? *)
blanchet@42677
   867
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42677
   868
    String.isPrefix bound_var_prefix s
blanchet@42677
   869
  | is_var_or_bound_var (CombVar _) = true
blanchet@42677
   870
  | is_var_or_bound_var _ = false
blanchet@42677
   871
blanchet@42677
   872
fun add_combterm_nonmonotonic_types true
blanchet@42677
   873
        (CombApp (CombConst (("equal", _), Type (_, [T, _]), _),
blanchet@42677
   874
                  CombApp (tm1, tm2))) =
blanchet@42677
   875
    exists is_var_or_bound_var [tm1, tm2] ? insert_type I T
blanchet@42677
   876
  | add_combterm_nonmonotonic_types _ _ = I
blanchet@42677
   877
blanchet@42677
   878
val add_fact_nonmonotonic_types =
blanchet@42677
   879
  fact_lift (formula_fold add_combterm_nonmonotonic_types)
blanchet@42677
   880
fun nonmonotonic_types_for_facts type_sys facts =
blanchet@42677
   881
  [] |> level_of_type_sys type_sys = Nonmonotonic_Types
blanchet@42677
   882
        ? fold add_fact_nonmonotonic_types facts
blanchet@42677
   883
blanchet@42574
   884
fun n_ary_strip_type 0 T = ([], T)
blanchet@42574
   885
  | n_ary_strip_type n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42574
   886
    n_ary_strip_type (n - 1) ran_T |>> cons dom_T
blanchet@42574
   887
  | n_ary_strip_type _ _ = raise Fail "unexpected non-function"
blanchet@42533
   888
blanchet@42579
   889
fun result_type_of_decl (_, _, T, _, ary) = n_ary_strip_type ary T |> snd
blanchet@42579
   890
blanchet@42579
   891
fun decl_line_for_sym_decl s (s', _, T, pred_sym, ary) =
blanchet@42579
   892
  let val (arg_Ts, res_T) = n_ary_strip_type ary T in
blanchet@42612
   893
    Decl (sym_decl_prefix ^ s, (s, s'), map mangled_type_name arg_Ts,
blanchet@42579
   894
          if pred_sym then `I tptp_tff_bool_type else mangled_type_name res_T)
blanchet@42579
   895
  end
blanchet@42579
   896
blanchet@42592
   897
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
   898
blanchet@42579
   899
fun formula_line_for_sym_decl ctxt type_sys n s j (s', T_args, T, _, ary) =
blanchet@42579
   900
  let
blanchet@42579
   901
    val (arg_Ts, res_T) = n_ary_strip_type ary T
blanchet@42579
   902
    val bound_names =
blanchet@42579
   903
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42579
   904
    val bound_tms =
blanchet@42579
   905
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
   906
    val bound_Ts =
blanchet@42592
   907
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
   908
                             else NONE)
blanchet@42579
   909
  in
blanchet@42612
   910
    Formula (sym_decl_prefix ^ s ^
blanchet@42612
   911
             (if n > 1 then "_" ^ string_of_int j else ""), Axiom,
blanchet@42579
   912
             CombConst ((s, s'), T, T_args)
blanchet@42579
   913
             |> fold (curry (CombApp o swap)) bound_tms
blanchet@42579
   914
             |> type_pred_combatom type_sys res_T
blanchet@42579
   915
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42586
   916
             |> formula_from_combformula ctxt type_sys
blanchet@42586
   917
             |> close_formula_universally,
blanchet@42579
   918
             NONE, NONE)
blanchet@42579
   919
  end
blanchet@42579
   920
blanchet@42579
   921
fun problem_lines_for_sym_decls ctxt type_sys (s, decls) =
blanchet@42574
   922
  if type_sys = Many_Typed then
blanchet@42579
   923
    map (decl_line_for_sym_decl s) decls
blanchet@42574
   924
  else
blanchet@42574
   925
    let
blanchet@42579
   926
      val decls =
blanchet@42579
   927
        case decls of
blanchet@42579
   928
          decl :: (decls' as _ :: _) =>
blanchet@42592
   929
          let val T = result_type_of_decl decl in
blanchet@42592
   930
            if forall ((fn T' => Type.raw_instance (T', T))
blanchet@42592
   931
                       o result_type_of_decl) decls' then
blanchet@42592
   932
              [decl]
blanchet@42592
   933
            else
blanchet@42592
   934
              decls
blanchet@42592
   935
          end
blanchet@42579
   936
        | _ => decls
blanchet@42579
   937
      val n = length decls
blanchet@42579
   938
      val decls =
blanchet@42579
   939
        decls |> filter (should_predicate_on_type ctxt type_sys
blanchet@42579
   940
                         o result_type_of_decl)
blanchet@42574
   941
    in
blanchet@42579
   942
      map2 (formula_line_for_sym_decl ctxt type_sys n s)
blanchet@42579
   943
           (0 upto length decls - 1) decls
blanchet@42574
   944
    end
blanchet@42579
   945
blanchet@42574
   946
fun problem_lines_for_sym_decl_table ctxt type_sys sym_decl_tab =
blanchet@42574
   947
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt type_sys)
blanchet@42574
   948
                  sym_decl_tab []
blanchet@42543
   949
blanchet@42543
   950
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
   951
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
   952
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
   953
    fold add_tff_types_in_formula phis
blanchet@42543
   954
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
   955
blanchet@42562
   956
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
   957
    union (op =) (res_T :: arg_Ts)
blanchet@42577
   958
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
   959
    add_tff_types_in_formula phi
blanchet@42543
   960
blanchet@42543
   961
fun tff_types_in_problem problem =
blanchet@42543
   962
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
   963
blanchet@42545
   964
fun decl_line_for_tff_type (s, s') =
blanchet@42568
   965
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
   966
blanchet@42543
   967
val type_declsN = "Types"
blanchet@42544
   968
val sym_declsN = "Symbol types"
blanchet@41157
   969
val factsN = "Relevant facts"
blanchet@41157
   970
val class_relsN = "Class relationships"
blanchet@42543
   971
val aritiesN = "Arities"
blanchet@41157
   972
val helpersN = "Helper facts"
blanchet@41157
   973
val conjsN = "Conjectures"
blanchet@41313
   974
val free_typesN = "Type variables"
blanchet@41157
   975
blanchet@41157
   976
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
   977
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
   978
    if heading = needle then j
blanchet@41157
   979
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
   980
blanchet@42568
   981
fun prepare_atp_problem ctxt type_sys explicit_apply hyp_ts concl_t facts =
blanchet@38282
   982
  let
blanchet@41313
   983
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
   984
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@42563
   985
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42565
   986
    val (conjs, facts) =
blanchet@42573
   987
      (conjs, facts) |> pairself (map (repair_fact type_sys sym_tab))
blanchet@42677
   988
    val conjs_and_facts = conjs @ facts
blanchet@42677
   989
    val repaired_sym_tab = conjs_and_facts |> sym_table_for_facts false
blanchet@42561
   990
    val sym_decl_lines =
blanchet@42677
   991
      conjs_and_facts
blanchet@42574
   992
      |> sym_decl_table_for_facts type_sys repaired_sym_tab
blanchet@42574
   993
      |> problem_lines_for_sym_decl_table ctxt type_sys
blanchet@42573
   994
    val helpers =
blanchet@42573
   995
      helper_facts_for_sym_table ctxt type_sys repaired_sym_tab
blanchet@42573
   996
      |> map (repair_fact type_sys sym_tab)
blanchet@42677
   997
    val nonmonotonic_Ts =
blanchet@42677
   998
      nonmonotonic_types_for_facts type_sys (helpers @ conjs_and_facts)
blanchet@42522
   999
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1000
       Flotter hack. *)
blanchet@38282
  1001
    val problem =
blanchet@42561
  1002
      [(sym_declsN, sym_decl_lines),
blanchet@42545
  1003
       (factsN, map (formula_line_for_fact ctxt fact_prefix type_sys)
blanchet@42180
  1004
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1005
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1006
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42561
  1007
       (helpersN, map (formula_line_for_fact ctxt helper_prefix type_sys)
blanchet@42563
  1008
                      (0 upto length helpers - 1 ~~ helpers)
blanchet@42579
  1009
                  |> (case type_sys of
blanchet@42589
  1010
                        Tags (Polymorphic, level) =>
blanchet@42589
  1011
                        member (op =) [Finite_Types, Nonmonotonic_Types] level
blanchet@42589
  1012
                        ? cons (ti_ti_helper_fact ())
blanchet@42579
  1013
                      | _ => I)),
blanchet@42545
  1014
       (conjsN, map (formula_line_for_conjecture ctxt type_sys) conjs),
blanchet@42545
  1015
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1016
    val problem =
blanchet@42561
  1017
      problem
blanchet@42561
  1018
      |> (if type_sys = Many_Typed then
blanchet@42561
  1019
            cons (type_declsN,
blanchet@42561
  1020
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42561
  1021
          else
blanchet@42561
  1022
            I)
blanchet@42646
  1023
    val (problem, pool) =
blanchet@42646
  1024
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@38282
  1025
  in
blanchet@38282
  1026
    (problem,
blanchet@38282
  1027
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1028
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1029
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
  1030
     fact_names |> Vector.fromList)
blanchet@38282
  1031
  end
blanchet@38282
  1032
blanchet@41313
  1033
(* FUDGE *)
blanchet@41313
  1034
val conj_weight = 0.0
blanchet@41770
  1035
val hyp_weight = 0.1
blanchet@41770
  1036
val fact_min_weight = 0.2
blanchet@41313
  1037
val fact_max_weight = 1.0
blanchet@42608
  1038
val type_info_default_weight = 0.8
blanchet@41313
  1039
blanchet@41313
  1040
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
  1041
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
  1042
  #> fold (add_term_weights weight) tms
blanchet@42577
  1043
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42677
  1044
    formula_fold (K (add_term_weights weight)) phi
blanchet@42528
  1045
  | add_problem_line_weights _ _ = I
blanchet@41313
  1046
blanchet@41313
  1047
fun add_conjectures_weights [] = I
blanchet@41313
  1048
  | add_conjectures_weights conjs =
blanchet@41313
  1049
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1050
      add_problem_line_weights conj_weight conj
blanchet@41313
  1051
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1052
    end
blanchet@41313
  1053
blanchet@41313
  1054
fun add_facts_weights facts =
blanchet@41313
  1055
  let
blanchet@41313
  1056
    val num_facts = length facts
blanchet@41313
  1057
    fun weight_of j =
blanchet@41313
  1058
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1059
                        / Real.fromInt num_facts
blanchet@41313
  1060
  in
blanchet@41313
  1061
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1062
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1063
  end
blanchet@41313
  1064
blanchet@41313
  1065
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1066
fun atp_problem_weights problem =
blanchet@42608
  1067
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1068
    Symtab.empty
blanchet@42608
  1069
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1070
    |> add_facts_weights (get factsN)
blanchet@42608
  1071
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1072
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1073
    |> Symtab.dest
blanchet@42608
  1074
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1075
  end
blanchet@41313
  1076
blanchet@38282
  1077
end;