src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Fri May 27 10:30:08 2011 +0200 (2011-05-27)
changeset 43017 944b19ab6003
parent 43001 f3492698dfc7
child 43039 b967219cec78
permissions -rw-r--r--
removed THF equality proxy hack now that Geoff Sutcliffe has fixed SystemOnTPTP
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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 format = ATP_Problem.format
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  type formula_kind = ATP_Problem.formula_kind
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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_heaviness = Heavy | Light
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  datatype type_system =
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    Simple_Types of type_level |
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    Preds of polymorphism * type_level * type_heaviness |
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    Tags of polymorphism * type_level * type_heaviness
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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 helper_prefix : string
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  val typed_helper_suffix : string
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  val predicator_name : string
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  val app_op_name : string
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  val type_pred_name : string
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  val simple_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 unmangled_const : string -> string * string fo_term list
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  val translate_atp_fact :
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    Proof.context -> format -> type_system -> 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 -> format -> formula_kind -> formula_kind -> type_system
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    -> 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 * int list * int Symtab.table
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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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fun useful_isabelle_info s =
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  if generate_useful_info then
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    SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
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  else
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    NONE
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val intro_info = useful_isabelle_info "intro"
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val elim_info = useful_isabelle_info "elim"
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val simp_info = useful_isabelle_info "simp"
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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 = "ty_"
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val sym_decl_prefix = "sy_"
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val sym_formula_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 typed_helper_suffix = "_T"
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val untyped_helper_suffix = "_U"
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val predicator_name = "hBOOL"
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val app_op_name = "hAPP"
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val type_pred_name = "is"
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val simple_type_prefix = "ty_"
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fun make_simple_type s =
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  if s = tptp_bool_type orelse s = tptp_fun_type orelse
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     s = tptp_individual_type then
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    s
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  else
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    simple_type_prefix ^ ascii_of s
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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_heaviness = Heavy | Light
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datatype type_system =
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  Simple_Types of type_level |
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  Preds of polymorphism * type_level * type_heaviness |
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  Tags of polymorphism * type_level * type_heaviness
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fun try_unsuffixes ss s =
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  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
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fun type_sys_from_string s =
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  (case try (unprefix "poly_") s of
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     SOME s => (SOME Polymorphic, s)
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   | NONE =>
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     case try (unprefix "mono_") s of
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       SOME s => (SOME Monomorphic, s)
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     | NONE =>
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       case try (unprefix "mangled_") s of
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         SOME s => (SOME Mangled_Monomorphic, s)
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       | NONE => (NONE, s))
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  ||> (fn s =>
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          (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
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          case try_unsuffixes ["?", "_query"] s of
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            SOME s => (Nonmonotonic_Types, s)
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          | NONE =>
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            case try_unsuffixes ["!", "_bang"] s of
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              SOME s => (Finite_Types, s)
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            | NONE => (All_Types, s))
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  ||> apsnd (fn s =>
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                case try (unsuffix "_heavy") s of
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                  SOME s => (Heavy, s)
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                | NONE => (Light, s))
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  |> (fn (poly, (level, (heaviness, core))) =>
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         case (core, (poly, level, heaviness)) of
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           ("simple", (NONE, _, Light)) => Simple_Types level
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         | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
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         | ("tags", (SOME Polymorphic, All_Types, _)) =>
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           Tags (Polymorphic, All_Types, heaviness)
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         | ("tags", (SOME Polymorphic, _, _)) =>
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           (* The actual light encoding is very unsound. *)
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           Tags (Polymorphic, level, Heavy)
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         | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
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         | ("args", (SOME poly, All_Types (* naja *), Light)) =>
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           Preds (poly, Const_Arg_Types, Light)
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         | ("erased", (NONE, All_Types (* naja *), Light)) =>
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           Preds (Polymorphic, No_Types, Light)
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         | _ => raise Same.SAME)
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  handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
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fun polymorphism_of_type_sys (Simple_Types _) = 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_Types 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 heaviness_of_type_sys (Simple_Types _) = Heavy
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  | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
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  | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
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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_setting_higher_order THF (Simple_Types _) = true
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  | is_setting_higher_order _ _ = false
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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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(* The Booleans indicate whether all type arguments should be kept. *)
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datatype type_arg_policy =
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  Explicit_Type_Args of bool |
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  Mangled_Type_Args of bool |
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  No_Type_Args
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fun should_drop_arg_type_args (Simple_Types _) =
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    false (* since TFF doesn't support overloading *)
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  | should_drop_arg_type_args type_sys =
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    level_of_type_sys type_sys = All_Types andalso
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    heaviness_of_type_sys type_sys = Heavy
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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 (should_drop_arg_type_args type_sys)
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  else
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    Explicit_Type_Args (should_drop_arg_type_args type_sys)
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fun type_arg_policy type_sys s =
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  if s = @{const_name HOL.eq} orelse
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     (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
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    No_Type_Args
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  else
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    general_type_arg_policy type_sys
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fun atp_type_literals_for_types format type_sys kind Ts =
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  if level_of_type_sys type_sys = No_Types orelse format = CNF_UEQ 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_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_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
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fun close_formula_universally phi = close_universally term_vars phi
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val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
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val homo_infinite_type = Type (homo_infinite_type_name, [])
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fun fo_term_from_typ higher_order =
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  let
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    fun term (Type (s, Ts)) =
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      ATerm (case (higher_order, s) of
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               (true, @{type_name bool}) => `I tptp_bool_type
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             | (true, @{type_name fun}) => `I tptp_fun_type
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             | _ => if s = homo_infinite_type_name then `I tptp_individual_type
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                    else `make_fixed_type_const s,
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             map term Ts)
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    | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
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    | term (TVar ((x as (s, _)), _)) =
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      ATerm ((make_schematic_type_var x, s), [])
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  in term end
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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 ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
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    ^ ")"
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val bool_atype = AType (`I tptp_bool_type)
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fun ho_type_from_fo_term higher_order pred_sym ary =
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  let
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    fun to_atype ty =
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      AType ((make_simple_type (generic_mangled_type_name fst ty),
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              generic_mangled_type_name snd ty))
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    fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
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    fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
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      | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
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    fun to_ho (ty as ATerm ((s, _), tys)) =
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      if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
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  in if higher_order then to_ho else to_fo ary end
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fun mangled_type higher_order pred_sym ary =
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  ho_type_from_fo_term higher_order pred_sym ary o fo_term_from_typ higher_order
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fun mangled_const_name T_args (s, s') =
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  let
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    val ty_args = map (fo_term_from_typ false) T_args
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    fun type_suffix f g =
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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) ty_args ""
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  in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
blanchet@42542
   317
blanchet@42542
   318
val parse_mangled_ident =
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   319
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   320
blanchet@42542
   321
fun parse_mangled_type x =
blanchet@42542
   322
  (parse_mangled_ident
blanchet@42542
   323
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   324
                    [] >> ATerm) x
blanchet@42542
   325
and parse_mangled_types x =
blanchet@42542
   326
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   327
blanchet@42542
   328
fun unmangled_type s =
blanchet@42542
   329
  s |> suffix ")" |> raw_explode
blanchet@42542
   330
    |> Scan.finite Symbol.stopper
blanchet@42542
   331
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   332
                                                quote s)) parse_mangled_type))
blanchet@42542
   333
    |> fst
blanchet@42542
   334
blanchet@42561
   335
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   336
fun unmangled_const s =
blanchet@42542
   337
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   338
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   339
  end
blanchet@42542
   340
blanchet@43017
   341
fun introduce_proxies format type_sys =
blanchet@42568
   342
  let
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   343
    fun intro top_level (CombApp (tm1, tm2)) =
blanchet@43017
   344
        CombApp (intro top_level tm1, intro false tm2)
blanchet@43017
   345
      | intro top_level (CombConst (name as (s, _), T, T_args)) =
blanchet@42570
   346
        (case proxify_const s of
blanchet@43017
   347
           SOME (_, proxy_base) =>
blanchet@43000
   348
           if top_level orelse is_setting_higher_order format type_sys then
blanchet@43000
   349
             case (top_level, s) of
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   350
               (_, "c_False") => (`I tptp_false, [])
blanchet@43000
   351
             | (_, "c_True") => (`I tptp_true, [])
blanchet@43000
   352
             | (false, "c_Not") => (`I tptp_not, [])
blanchet@43000
   353
             | (false, "c_conj") => (`I tptp_and, [])
blanchet@43000
   354
             | (false, "c_disj") => (`I tptp_or, [])
blanchet@43000
   355
             | (false, "c_implies") => (`I tptp_implies, [])
blanchet@43000
   356
             | (false, s) =>
blanchet@43017
   357
               if is_tptp_equal s then (`I tptp_equal, [])
blanchet@43017
   358
               else (proxy_base |>> prefix const_prefix, T_args)
blanchet@43000
   359
             | _ => (name, [])
blanchet@42569
   360
           else
blanchet@42574
   361
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   362
          | NONE => (name, T_args))
blanchet@42574
   363
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@43017
   364
      | intro _ tm = tm
blanchet@43017
   365
  in intro true end
blanchet@42568
   366
blanchet@42994
   367
fun combformula_from_prop thy format type_sys eq_as_iff =
blanchet@38282
   368
  let
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   369
    fun do_term bs t atomic_types =
blanchet@41140
   370
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42994
   371
      |>> (introduce_proxies format type_sys #> AAtom)
blanchet@42568
   372
      ||> union (op =) atomic_types
blanchet@38282
   373
    fun do_quant bs q s T t' =
blanchet@38518
   374
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   375
        do_formula ((s, T) :: bs) t'
blanchet@42562
   376
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   377
      end
blanchet@38282
   378
    and do_conn bs c t1 t2 =
blanchet@38282
   379
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   380
      #>> uncurry (mk_aconn c)
blanchet@38282
   381
    and do_formula bs t =
blanchet@38282
   382
      case t of
blanchet@42531
   383
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   384
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   385
        do_quant bs AForall s T t'
blanchet@38282
   386
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   387
        do_quant bs AExists s T t'
haftmann@38795
   388
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   389
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   390
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   391
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   392
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   393
      | _ => do_term bs t
blanchet@38282
   394
  in do_formula [] end
blanchet@38282
   395
blanchet@42750
   396
fun presimplify_term ctxt =
blanchet@42750
   397
  Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@42750
   398
  #> Meson.presimplify ctxt
blanchet@42750
   399
  #> prop_of
blanchet@38282
   400
wenzelm@41491
   401
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   402
fun conceal_bounds Ts t =
blanchet@38282
   403
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   404
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   405
fun reveal_bounds Ts =
blanchet@38282
   406
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   407
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   408
blanchet@42747
   409
fun extensionalize_term ctxt t =
blanchet@42747
   410
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42747
   411
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@42747
   412
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   413
  end
blanchet@38608
   414
blanchet@38282
   415
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   416
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   417
    if Meson.is_fol_term thy t then
blanchet@38491
   418
      t
blanchet@38491
   419
    else
blanchet@38491
   420
      let
blanchet@38491
   421
        fun aux Ts t =
blanchet@38491
   422
          case t of
blanchet@38491
   423
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   424
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   425
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   426
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   427
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   428
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   429
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   430
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   431
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   432
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   433
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   434
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   435
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   436
              $ t1 $ t2 =>
blanchet@38491
   437
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   438
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   439
                   t
blanchet@38491
   440
                 else
blanchet@38491
   441
                   t |> conceal_bounds Ts
blanchet@38491
   442
                     |> Envir.eta_contract
blanchet@38491
   443
                     |> cterm_of thy
blanchet@39890
   444
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   445
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   446
                     |> reveal_bounds Ts
blanchet@39370
   447
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   448
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   449
      handle THM _ =>
blanchet@38491
   450
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   451
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   452
             else HOLogic.true_const
blanchet@38491
   453
  end
blanchet@38282
   454
blanchet@38282
   455
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   456
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   457
fun freeze_term t =
blanchet@38282
   458
  let
blanchet@38282
   459
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   460
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   461
      | aux (Var ((s, i), T)) =
blanchet@38282
   462
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   463
      | aux t = t
blanchet@38282
   464
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   465
blanchet@40204
   466
(* making fact and conjecture formulas *)
blanchet@42994
   467
fun make_formula ctxt format type_sys eq_as_iff presimp name loc kind t =
blanchet@38282
   468
  let
wenzelm@42361
   469
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   470
    val t = t |> Envir.beta_eta_contract
blanchet@42944
   471
              |> transform_elim_prop
blanchet@41211
   472
              |> Object_Logic.atomize_term thy
blanchet@42563
   473
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   474
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@42742
   475
              |> Raw_Simplifier.rewrite_term thy
blanchet@42742
   476
                     (Meson.unfold_set_const_simps ctxt) []
blanchet@42747
   477
              |> extensionalize_term ctxt
blanchet@42750
   478
              |> presimp ? presimplify_term ctxt
blanchet@38282
   479
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   480
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   481
              |> kind <> Axiom ? freeze_term
blanchet@42962
   482
    val (combformula, atomic_types) =
blanchet@42994
   483
      combformula_from_prop thy format type_sys eq_as_iff t []
blanchet@38282
   484
  in
blanchet@42640
   485
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   486
     atomic_types = atomic_types}
blanchet@38282
   487
  end
blanchet@38282
   488
blanchet@42994
   489
fun make_fact ctxt format type_sys keep_trivial eq_as_iff presimp
blanchet@42994
   490
              ((name, loc), t) =
blanchet@42962
   491
  case (keep_trivial,
blanchet@42994
   492
        make_formula ctxt format type_sys eq_as_iff presimp name loc Axiom t) of
blanchet@43001
   493
    (false, formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...}) =>
blanchet@43001
   494
    if s = tptp_true then NONE else SOME formula
blanchet@41990
   495
  | (_, formula) => SOME formula
blanchet@42561
   496
blanchet@42994
   497
fun make_conjecture ctxt format prem_kind type_sys ts =
blanchet@38613
   498
  let val last = length ts - 1 in
blanchet@42709
   499
    map2 (fn j => fn t =>
blanchet@42709
   500
             let
blanchet@42709
   501
               val (kind, maybe_negate) =
blanchet@42709
   502
                 if j = last then
blanchet@42709
   503
                   (Conjecture, I)
blanchet@42709
   504
                 else
blanchet@42709
   505
                   (prem_kind,
blanchet@42709
   506
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   507
                    else I)
blanchet@42709
   508
              in
blanchet@42994
   509
                t |> make_formula ctxt format type_sys true true
blanchet@42994
   510
                                  (string_of_int j) General kind
blanchet@42962
   511
                  |> maybe_negate
blanchet@42709
   512
              end)
blanchet@38613
   513
         (0 upto last) ts
blanchet@38613
   514
  end
blanchet@38282
   515
blanchet@42682
   516
(** Finite and infinite type inference **)
blanchet@42682
   517
blanchet@42886
   518
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
blanchet@42886
   519
  | deep_freeze_atyp T = T
blanchet@42886
   520
val deep_freeze_type = map_atyps deep_freeze_atyp
blanchet@42886
   521
blanchet@42886
   522
val type_instance = Sign.typ_instance o Proof_Context.theory_of
blanchet@42886
   523
blanchet@42682
   524
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   525
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   526
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   527
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   528
blanchet@42886
   529
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
blanchet@42886
   530
    exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
blanchet@42836
   531
  | should_encode_type _ _ All_Types _ = true
blanchet@42682
   532
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   533
  | should_encode_type _ _ _ _ = false
blanchet@42682
   534
blanchet@42837
   535
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
   536
                             should_predicate_on_var T =
blanchet@42878
   537
    (heaviness = Heavy orelse should_predicate_on_var ()) andalso
blanchet@42878
   538
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
   539
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
   540
blanchet@42836
   541
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42836
   542
    String.isPrefix bound_var_prefix s
blanchet@42836
   543
  | is_var_or_bound_var (CombVar _) = true
blanchet@42836
   544
  | is_var_or_bound_var _ = false
blanchet@42836
   545
blanchet@42829
   546
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
blanchet@42829
   547
blanchet@42829
   548
fun should_tag_with_type _ _ _ Top_Level _ _ = false
blanchet@42837
   549
  | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
blanchet@42837
   550
    (case heaviness of
blanchet@42837
   551
       Heavy => should_encode_type ctxt nonmono_Ts level T
blanchet@42837
   552
     | Light =>
blanchet@42836
   553
       case (site, is_var_or_bound_var u) of
blanchet@42836
   554
         (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
blanchet@42829
   555
       | _ => false)
blanchet@42829
   556
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
   557
blanchet@42994
   558
fun homogenized_type ctxt nonmono_Ts level =
blanchet@42994
   559
  let
blanchet@42994
   560
    val should_encode = should_encode_type ctxt nonmono_Ts level
blanchet@42994
   561
    fun homo 0 T = if should_encode T then T else homo_infinite_type
blanchet@42994
   562
      | homo ary (Type (@{type_name fun}, [T1, T2])) =
blanchet@42994
   563
        homo 0 T1 --> homo (ary - 1) T2
blanchet@42994
   564
      | homo _ _ = raise Fail "expected function type"
blanchet@42994
   565
  in homo end
blanchet@42682
   566
blanchet@42573
   567
(** "hBOOL" and "hAPP" **)
blanchet@41313
   568
blanchet@42574
   569
type sym_info =
blanchet@42563
   570
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   571
blanchet@42574
   572
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   573
  let
blanchet@42558
   574
    fun aux top_level tm =
blanchet@42558
   575
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   576
        (case head of
blanchet@42563
   577
           CombConst ((s, _), T, _) =>
blanchet@42558
   578
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   579
             I
blanchet@42558
   580
           else
blanchet@42563
   581
             let val ary = length args in
blanchet@42558
   582
               Symtab.map_default
blanchet@42558
   583
                   (s, {pred_sym = true,
blanchet@42563
   584
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   585
                        max_ary = 0, typ = SOME T})
blanchet@42563
   586
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   587
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   588
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   589
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   590
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   591
            end
blanchet@42558
   592
         | _ => I)
blanchet@42558
   593
        #> fold (aux false) args
blanchet@42558
   594
      end
blanchet@42558
   595
  in aux true end
blanchet@42674
   596
fun add_fact_syms_to_table explicit_apply =
blanchet@42834
   597
  fact_lift (formula_fold NONE (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   598
blanchet@42675
   599
val default_sym_table_entries : (string * sym_info) list =
blanchet@43000
   600
  [(tptp_equal, {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@43000
   601
   (tptp_old_equal, {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42966
   602
   (make_fixed_const predicator_name,
blanchet@42563
   603
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   604
  ([tptp_false, tptp_true]
blanchet@42563
   605
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   606
blanchet@42544
   607
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   608
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   609
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   610
blanchet@42558
   611
fun min_arity_of sym_tab s =
blanchet@42558
   612
  case Symtab.lookup sym_tab s of
blanchet@42574
   613
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   614
  | NONE =>
blanchet@42558
   615
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   616
      SOME s =>
blanchet@42570
   617
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42966
   618
        if s = predicator_name then 1
blanchet@42966
   619
        else if s = app_op_name then 2
blanchet@42966
   620
        else if s = type_pred_name then 1
blanchet@42557
   621
        else 0
blanchet@42547
   622
      end
blanchet@42544
   623
    | NONE => 0
blanchet@38282
   624
blanchet@38282
   625
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   626
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   627
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   628
   arguments and is used as a predicate. *)
blanchet@42558
   629
fun is_pred_sym sym_tab s =
blanchet@42558
   630
  case Symtab.lookup sym_tab s of
blanchet@42574
   631
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   632
    pred_sym andalso min_ary = max_ary
blanchet@42558
   633
  | NONE => false
blanchet@38282
   634
blanchet@42568
   635
val predicator_combconst =
blanchet@42966
   636
  CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
blanchet@42568
   637
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   638
blanchet@42568
   639
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   640
  case strip_combterm_comb tm of
blanchet@42542
   641
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   642
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   643
  | _ => predicator tm
blanchet@42542
   644
blanchet@42544
   645
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   646
blanchet@42544
   647
fun explicit_app arg head =
blanchet@42544
   648
  let
blanchet@42562
   649
    val head_T = combtyp_of head
blanchet@42693
   650
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   651
    val explicit_app =
blanchet@42966
   652
      CombConst (`make_fixed_const app_op_name, head_T --> head_T,
blanchet@42693
   653
                 [arg_T, res_T])
blanchet@42544
   654
  in list_app explicit_app [head, arg] end
blanchet@42544
   655
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   656
blanchet@42565
   657
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   658
  let
blanchet@42544
   659
    fun aux tm =
blanchet@42544
   660
      case strip_combterm_comb tm of
blanchet@42544
   661
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   662
        args |> map aux
blanchet@42557
   663
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   664
             |>> list_app head
blanchet@42544
   665
             |-> list_explicit_app
blanchet@42544
   666
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   667
  in aux end
blanchet@38282
   668
blanchet@42753
   669
fun chop_fun 0 T = ([], T)
blanchet@42753
   670
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
   671
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
   672
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
   673
blanchet@42780
   674
fun filter_type_args _ _ _ [] = []
blanchet@42780
   675
  | filter_type_args thy s arity T_args =
blanchet@42834
   676
    let
blanchet@42834
   677
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42966
   678
      val U = if s = app_op_name then
blanchet@42834
   679
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
   680
              else
blanchet@42834
   681
                s |> Sign.the_const_type thy
blanchet@42834
   682
    in
blanchet@42781
   683
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
   684
        [] => []
blanchet@42781
   685
      | res_U_vars =>
blanchet@42781
   686
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
   687
          U_args ~~ T_args
blanchet@42781
   688
          |> map_filter (fn (U, T) =>
blanchet@42781
   689
                            if member (op =) res_U_vars (dest_TVar U) then
blanchet@42781
   690
                              SOME T
blanchet@42781
   691
                            else
blanchet@42781
   692
                              NONE)
blanchet@42781
   693
        end
blanchet@42780
   694
    end
blanchet@42780
   695
    handle TYPE _ => T_args
blanchet@42753
   696
blanchet@42994
   697
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42753
   698
  let
blanchet@42753
   699
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
   700
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
   701
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
   702
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   703
        let
blanchet@42701
   704
          val level = level_of_type_sys type_sys
blanchet@42701
   705
          val (T, T_args) =
blanchet@42701
   706
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   707
               anyway, by distinguishing overloads only on the homogenized
blanchet@42837
   708
               result type. Don't do it for lightweight type systems, though,
blanchet@42837
   709
               since it leads to too many unsound proofs. *)
blanchet@42966
   710
            if s = const_prefix ^ app_op_name andalso
blanchet@42726
   711
               length T_args = 2 andalso
blanchet@42836
   712
               not (is_type_sys_virtually_sound type_sys) andalso
blanchet@42837
   713
               heaviness_of_type_sys type_sys = Heavy then
blanchet@42994
   714
              T_args |> map (homogenized_type ctxt nonmono_Ts level 0)
blanchet@42701
   715
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42831
   716
                                    (T --> T, tl Ts)
blanchet@42701
   717
                                  end)
blanchet@42701
   718
            else
blanchet@42701
   719
              (T, T_args)
blanchet@42701
   720
        in
blanchet@42701
   721
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   722
             NONE => (name, T_args)
blanchet@42701
   723
           | SOME s'' =>
blanchet@42753
   724
             let
blanchet@42753
   725
               val s'' = invert_const s''
blanchet@42831
   726
               fun filtered_T_args false = T_args
blanchet@42831
   727
                 | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@42753
   728
             in
blanchet@42701
   729
               case type_arg_policy type_sys s'' of
blanchet@42831
   730
                 Explicit_Type_Args drop_args =>
blanchet@42831
   731
                 (name, filtered_T_args drop_args)
blanchet@42831
   732
               | Mangled_Type_Args drop_args =>
blanchet@42994
   733
                 (mangled_const_name (filtered_T_args drop_args) name, [])
blanchet@42753
   734
               | No_Type_Args => (name, [])
blanchet@42701
   735
             end)
blanchet@42701
   736
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   737
        end
blanchet@42753
   738
      | aux _ tm = tm
blanchet@42753
   739
  in aux 0 end
blanchet@42573
   740
blanchet@42962
   741
fun repair_combterm ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42994
   742
  not (is_setting_higher_order format type_sys)
blanchet@42994
   743
  ? (introduce_explicit_apps_in_combterm sym_tab
blanchet@42994
   744
     #> introduce_predicators_in_combterm sym_tab)
blanchet@42994
   745
  #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
   746
fun repair_fact ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42701
   747
  update_combformula (formula_map
blanchet@42962
   748
      (repair_combterm ctxt format nonmono_Ts type_sys sym_tab))
blanchet@42573
   749
blanchet@42573
   750
(** Helper facts **)
blanchet@42573
   751
blanchet@42573
   752
fun ti_ti_helper_fact () =
blanchet@42573
   753
  let
blanchet@42573
   754
    fun var s = ATerm (`I s, [])
blanchet@42589
   755
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   756
  in
blanchet@42612
   757
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@43000
   758
             AAtom (ATerm (`I tptp_equal, [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42879
   759
             |> close_formula_universally, simp_info, NONE)
blanchet@42573
   760
  end
blanchet@42573
   761
blanchet@42962
   762
fun helper_facts_for_sym ctxt format type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   763
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   764
    SOME mangled_s =>
blanchet@42573
   765
    let
blanchet@42573
   766
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   767
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42893
   768
      fun dub_and_inst c needs_fairly_sound (th, j) =
blanchet@42881
   769
        ((c ^ "_" ^ string_of_int j ^
blanchet@42893
   770
          (if needs_fairly_sound then typed_helper_suffix
blanchet@42881
   771
           else untyped_helper_suffix),
blanchet@42881
   772
          General),
blanchet@42573
   773
         let val t = th |> prop_of in
blanchet@42753
   774
           t |> ((case general_type_arg_policy type_sys of
blanchet@42753
   775
                    Mangled_Type_Args _ => true
blanchet@42753
   776
                  | _ => false) andalso
blanchet@42573
   777
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   778
                ? (case typ of
blanchet@42573
   779
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   780
                   | NONE => I)
blanchet@42573
   781
         end)
blanchet@42573
   782
      fun make_facts eq_as_iff =
blanchet@42994
   783
        map_filter (make_fact ctxt format type_sys false eq_as_iff false)
blanchet@42893
   784
      val fairly_sound = is_type_sys_fairly_sound type_sys
blanchet@42573
   785
    in
blanchet@42573
   786
      metis_helpers
blanchet@42894
   787
      |> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
blanchet@42573
   788
                  if metis_s <> unmangled_s orelse
blanchet@42894
   789
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
   790
                    []
blanchet@42573
   791
                  else
blanchet@42573
   792
                    ths ~~ (1 upto length ths)
blanchet@42893
   793
                    |> map (dub_and_inst mangled_s needs_fairly_sound)
blanchet@42893
   794
                    |> make_facts (not needs_fairly_sound))
blanchet@42573
   795
    end
blanchet@42573
   796
  | NONE => []
blanchet@42962
   797
fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
blanchet@42962
   798
  Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
blanchet@42962
   799
                  []
blanchet@42573
   800
blanchet@42994
   801
fun translate_atp_fact ctxt format type_sys keep_trivial =
blanchet@42994
   802
  `(make_fact ctxt format type_sys keep_trivial true true o apsnd prop_of)
blanchet@42573
   803
blanchet@42962
   804
fun translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t
blanchet@42962
   805
                       rich_facts =
blanchet@42573
   806
  let
blanchet@42573
   807
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   808
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   809
    val (facts, fact_names) =
blanchet@42573
   810
      rich_facts
blanchet@42573
   811
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   812
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   813
      |> ListPair.unzip
blanchet@42573
   814
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   815
       boost an ATP's performance (for some reason). *)
blanchet@42573
   816
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   817
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   818
    val all_ts = goal_t :: fact_ts
blanchet@42573
   819
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   820
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   821
    val tycons = type_consts_of_terms thy all_ts
blanchet@42994
   822
    val conjs =
blanchet@42994
   823
      hyp_ts @ [concl_t] |> make_conjecture ctxt format prem_kind type_sys
blanchet@42573
   824
    val (supers', arity_clauses) =
blanchet@42589
   825
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   826
      else make_arity_clauses thy tycons supers
blanchet@42573
   827
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   828
  in
blanchet@42573
   829
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   830
  end
blanchet@42573
   831
blanchet@42573
   832
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   833
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   834
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   835
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   836
blanchet@42573
   837
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   838
blanchet@42994
   839
fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
blanchet@42966
   840
  CombApp (CombConst (`make_fixed_const type_pred_name, T --> @{typ bool}, [T])
blanchet@42994
   841
           |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
blanchet@42573
   842
           tm)
blanchet@42573
   843
blanchet@42878
   844
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@42878
   845
  | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@43000
   846
    accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
blanchet@42878
   847
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
blanchet@42878
   848
  | is_var_nonmonotonic_in_formula pos phi _ name =
blanchet@42878
   849
    formula_fold pos (var_occurs_positively_naked_in_term name) phi false
blanchet@42834
   850
blanchet@42994
   851
fun mk_const_aterm x T_args args =
blanchet@42994
   852
  ATerm (x, map (fo_term_from_typ false) T_args @ args)
blanchet@42994
   853
blanchet@42962
   854
fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
blanchet@42829
   855
  CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42994
   856
  |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
   857
  |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42829
   858
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42962
   859
and term_from_combterm ctxt format nonmono_Ts type_sys =
blanchet@42573
   860
  let
blanchet@42962
   861
    fun aux site u =
blanchet@42962
   862
      let
blanchet@42962
   863
        val (head, args) = strip_combterm_comb u
blanchet@42962
   864
        val (x as (s, _), T_args) =
blanchet@42962
   865
          case head of
blanchet@42962
   866
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42962
   867
          | CombVar (name, _) => (name, [])
blanchet@42962
   868
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@43000
   869
        val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
blanchet@42962
   870
                       else Elsewhere
blanchet@42994
   871
        val t = mk_const_aterm x T_args (map (aux arg_site) args)
blanchet@42962
   872
        val T = combtyp_of u
blanchet@42962
   873
      in
blanchet@42962
   874
        t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
blanchet@42962
   875
                tag_with_type ctxt format nonmono_Ts type_sys T
blanchet@42962
   876
              else
blanchet@42962
   877
                I)
blanchet@42962
   878
      end
blanchet@42962
   879
  in aux end
blanchet@42962
   880
and formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42962
   881
                             should_predicate_on_var =
blanchet@42829
   882
  let
blanchet@42994
   883
    val higher_order = is_setting_higher_order format type_sys
blanchet@42962
   884
    val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42573
   885
    val do_bound_type =
blanchet@42682
   886
      case type_sys of
blanchet@42722
   887
        Simple_Types level =>
blanchet@42994
   888
        homogenized_type ctxt nonmono_Ts level 0
blanchet@42994
   889
        #> mangled_type higher_order false 0 #> SOME
blanchet@42682
   890
      | _ => K NONE
blanchet@42878
   891
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@42834
   892
      if should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42878
   893
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@42834
   894
        CombVar (name, T)
blanchet@42994
   895
        |> type_pred_combterm ctxt nonmono_Ts type_sys T
blanchet@42878
   896
        |> do_term |> AAtom |> SOME
blanchet@42573
   897
      else
blanchet@42573
   898
        NONE
blanchet@42878
   899
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
   900
        let
blanchet@42878
   901
          val phi = phi |> do_formula pos
blanchet@42878
   902
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
   903
        in
blanchet@42834
   904
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
   905
                                        | SOME T => do_bound_type T)),
blanchet@42834
   906
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
   907
                      (map_filter
blanchet@42834
   908
                           (fn (_, NONE) => NONE
blanchet@42834
   909
                             | (s, SOME T) =>
blanchet@42878
   910
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
   911
                           xs)
blanchet@42834
   912
                      phi)
blanchet@42834
   913
        end
blanchet@42878
   914
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@42878
   915
      | do_formula _ (AAtom tm) = AAtom (do_term tm)
blanchet@42878
   916
  in do_formula o SOME end
blanchet@42573
   917
blanchet@42956
   918
fun bound_atomic_types format type_sys Ts =
blanchet@42727
   919
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42956
   920
                (atp_type_literals_for_types format type_sys Axiom Ts))
blanchet@42727
   921
blanchet@42956
   922
fun formula_for_fact ctxt format nonmono_Ts type_sys
blanchet@42573
   923
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   924
  combformula
blanchet@42727
   925
  |> close_combformula_universally
blanchet@42962
   926
  |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
   927
                              is_var_nonmonotonic_in_formula true
blanchet@42956
   928
  |> bound_atomic_types format type_sys atomic_types
blanchet@42573
   929
  |> close_formula_universally
blanchet@42573
   930
blanchet@42573
   931
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   932
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   933
   the remote provers might care. *)
blanchet@42956
   934
fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
blanchet@42640
   935
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   936
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   937
                     else string_of_int j ^ "_") ^
blanchet@42647
   938
           ascii_of name,
blanchet@42956
   939
           kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
blanchet@42879
   940
           case locality of
blanchet@42879
   941
             Intro => intro_info
blanchet@42879
   942
           | Elim => elim_info
blanchet@42879
   943
           | Simp => simp_info
blanchet@42879
   944
           | _ => NONE)
blanchet@42573
   945
blanchet@42939
   946
fun formula_line_for_class_rel_clause
blanchet@42939
   947
        (ClassRelClause {name, subclass, superclass, ...}) =
blanchet@42573
   948
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   949
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   950
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   951
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42879
   952
             |> close_formula_universally, intro_info, NONE)
blanchet@42573
   953
  end
blanchet@42573
   954
blanchet@42573
   955
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   956
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   957
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   958
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   959
blanchet@42939
   960
fun formula_line_for_arity_clause
blanchet@42939
   961
        (ArityClause {name, prem_lits, concl_lits, ...}) =
blanchet@42577
   962
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   963
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42895
   964
                          o fo_literal_from_arity_literal) prem_lits)
blanchet@42573
   965
                    (formula_from_fo_literal
blanchet@42895
   966
                         (fo_literal_from_arity_literal concl_lits))
blanchet@42879
   967
           |> close_formula_universally, intro_info, NONE)
blanchet@42573
   968
blanchet@42962
   969
fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
blanchet@42573
   970
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   971
  Formula (conjecture_prefix ^ name, kind,
blanchet@42962
   972
           formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42939
   973
               is_var_nonmonotonic_in_formula false
blanchet@42939
   974
               (close_combformula_universally combformula)
blanchet@42573
   975
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   976
blanchet@42956
   977
fun free_type_literals format type_sys
blanchet@42956
   978
                       ({atomic_types, ...} : translated_formula) =
blanchet@42956
   979
  atomic_types |> atp_type_literals_for_types format type_sys Conjecture
blanchet@42573
   980
               |> map fo_literal_from_type_literal
blanchet@42573
   981
blanchet@42573
   982
fun formula_line_for_free_type j lit =
blanchet@42577
   983
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   984
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42956
   985
fun formula_lines_for_free_types format type_sys facts =
blanchet@42573
   986
  let
blanchet@42956
   987
    val litss = map (free_type_literals format type_sys) facts
blanchet@42573
   988
    val lits = fold (union (op =)) litss []
blanchet@42573
   989
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   990
blanchet@42573
   991
(** Symbol declarations **)
blanchet@42544
   992
blanchet@42886
   993
fun insert_type ctxt get_T x xs =
blanchet@42677
   994
  let val T = get_T x in
blanchet@42886
   995
    if exists (curry (type_instance ctxt) T o get_T) xs then xs
blanchet@42886
   996
    else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
blanchet@42677
   997
  end
blanchet@42677
   998
blanchet@42574
   999
fun should_declare_sym type_sys pred_sym s =
blanchet@42998
  1000
  is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
blanchet@42894
  1001
  (case type_sys of
blanchet@42894
  1002
     Simple_Types _ => true
blanchet@42894
  1003
   | Tags (_, _, Light) => true
blanchet@42894
  1004
   | _ => not pred_sym)
blanchet@38282
  1005
blanchet@42886
  1006
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
  1007
  let
blanchet@42698
  1008
    fun add_combterm in_conj tm =
blanchet@42574
  1009
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
  1010
        (case head of
blanchet@42574
  1011
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
  1012
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
  1013
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
  1014
               Symtab.map_default (s, [])
blanchet@42886
  1015
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
  1016
                                         in_conj))
blanchet@42574
  1017
             else
blanchet@42574
  1018
               I
blanchet@42574
  1019
           end
blanchet@42574
  1020
         | _ => I)
blanchet@42698
  1021
        #> fold (add_combterm in_conj) args
blanchet@42574
  1022
      end
blanchet@42698
  1023
    fun add_fact in_conj =
blanchet@42834
  1024
      fact_lift (formula_fold NONE (K (add_combterm in_conj)))
blanchet@42698
  1025
  in
blanchet@42698
  1026
    Symtab.empty
blanchet@42698
  1027
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
  1028
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
  1029
  end
blanchet@42533
  1030
blanchet@42886
  1031
(* These types witness that the type classes they belong to allow infinite
blanchet@42886
  1032
   models and hence that any types with these type classes is monotonic. *)
blanchet@42886
  1033
val known_infinite_types = [@{typ nat}, @{typ int}, @{typ "nat => bool"}]
blanchet@42886
  1034
blanchet@42685
  1035
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  1036
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42886
  1037
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
blanchet@42829
  1038
  | add_combterm_nonmonotonic_types ctxt level _
blanchet@43000
  1039
        (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) =
blanchet@43000
  1040
    (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
  1041
     (case level of
blanchet@42886
  1042
        Nonmonotonic_Types =>
blanchet@42886
  1043
        not (is_type_surely_infinite ctxt known_infinite_types T)
blanchet@42829
  1044
      | Finite_Types => is_type_surely_finite ctxt T
blanchet@42886
  1045
      | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
blanchet@42829
  1046
  | add_combterm_nonmonotonic_types _ _ _ _ = I
blanchet@42829
  1047
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
blanchet@42829
  1048
                                            : translated_formula) =
blanchet@42834
  1049
  formula_fold (SOME (kind <> Conjecture))
blanchet@42829
  1050
               (add_combterm_nonmonotonic_types ctxt level) combformula
blanchet@42886
  1051
fun nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42829
  1052
  let val level = level_of_type_sys type_sys in
blanchet@42886
  1053
    if level = Nonmonotonic_Types orelse level = Finite_Types then
blanchet@42886
  1054
      [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
blanchet@42886
  1055
         (* We must add "bool" in case the helper "True_or_False" is added
blanchet@42886
  1056
            later. In addition, several places in the code rely on the list of
blanchet@42886
  1057
            nonmonotonic types not being empty. *)
blanchet@42886
  1058
         |> insert_type ctxt I @{typ bool}
blanchet@42886
  1059
    else
blanchet@42886
  1060
      []
blanchet@42829
  1061
  end
blanchet@42677
  1062
blanchet@42994
  1063
fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
blanchet@42994
  1064
                      (s', T_args, T, pred_sym, ary, _) =
blanchet@42994
  1065
  let
blanchet@42994
  1066
    val (higher_order, T_arg_Ts, level) =
blanchet@42994
  1067
      case type_sys of
blanchet@42994
  1068
        Simple_Types level => (format = THF, [], level)
blanchet@42994
  1069
      | _ => (false, replicate (length T_args) homo_infinite_type, No_Types)
blanchet@42994
  1070
  in
blanchet@42998
  1071
    Decl (sym_decl_prefix ^ s, (s, s'),
blanchet@42994
  1072
          (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
blanchet@42994
  1073
          |> mangled_type higher_order pred_sym (length T_arg_Ts + ary))
blanchet@42994
  1074
  end
blanchet@42579
  1075
blanchet@42592
  1076
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
  1077
blanchet@42956
  1078
fun formula_line_for_pred_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1079
                                   n s j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1080
  let
blanchet@42709
  1081
    val (kind, maybe_negate) =
blanchet@42709
  1082
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1083
      else (Axiom, I)
blanchet@42753
  1084
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42579
  1085
    val bound_names =
blanchet@42579
  1086
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1087
    val bounds =
blanchet@42579
  1088
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
  1089
    val bound_Ts =
blanchet@42592
  1090
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
  1091
                             else NONE)
blanchet@42579
  1092
  in
blanchet@42998
  1093
    Formula (sym_formula_prefix ^ s ^
blanchet@42709
  1094
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1095
             CombConst ((s, s'), T, T_args)
blanchet@42829
  1096
             |> fold (curry (CombApp o swap)) bounds
blanchet@42994
  1097
             |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
blanchet@42963
  1098
             |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42962
  1099
             |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
  1100
                                         (K (K (K (K true)))) true
blanchet@42956
  1101
             |> n > 1 ? bound_atomic_types format type_sys (atyps_of T)
blanchet@42709
  1102
             |> close_formula_universally
blanchet@42709
  1103
             |> maybe_negate,
blanchet@42879
  1104
             intro_info, NONE)
blanchet@42579
  1105
  end
blanchet@42579
  1106
blanchet@42956
  1107
fun formula_lines_for_tag_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1108
        n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1109
  let
blanchet@42829
  1110
    val ident_base =
blanchet@42998
  1111
      sym_formula_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1112
    val (kind, maybe_negate) =
blanchet@42852
  1113
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1114
      else (Axiom, I)
blanchet@42829
  1115
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1116
    val bound_names =
blanchet@42829
  1117
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1118
    val bounds = bound_names |> map (fn name => ATerm (name, []))
blanchet@42994
  1119
    val cst = mk_const_aterm (s, s') T_args
blanchet@42830
  1120
    val atomic_Ts = atyps_of T
blanchet@42834
  1121
    fun eq tms =
blanchet@42834
  1122
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@43000
  1123
       else AAtom (ATerm (`I tptp_equal, tms)))
blanchet@42956
  1124
      |> bound_atomic_types format type_sys atomic_Ts
blanchet@42830
  1125
      |> close_formula_universally
blanchet@42852
  1126
      |> maybe_negate
blanchet@42836
  1127
    val should_encode = should_encode_type ctxt nonmono_Ts All_Types
blanchet@42962
  1128
    val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
blanchet@42829
  1129
    val add_formula_for_res =
blanchet@42829
  1130
      if should_encode res_T then
blanchet@42852
  1131
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42994
  1132
                       eq [tag_with res_T (cst bounds), cst bounds],
blanchet@42879
  1133
                       simp_info, NONE))
blanchet@42829
  1134
      else
blanchet@42829
  1135
        I
blanchet@42829
  1136
    fun add_formula_for_arg k =
blanchet@42829
  1137
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1138
        if should_encode arg_T then
blanchet@42829
  1139
          case chop k bounds of
blanchet@42829
  1140
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1141
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42994
  1142
                           eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
blanchet@42994
  1143
                               cst bounds],
blanchet@42879
  1144
                           simp_info, NONE))
blanchet@42829
  1145
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1146
        else
blanchet@42829
  1147
          I
blanchet@42829
  1148
      end
blanchet@42829
  1149
  in
blanchet@42834
  1150
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1151
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1152
  end
blanchet@42829
  1153
blanchet@42836
  1154
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1155
blanchet@42956
  1156
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1157
                                (s, decls) =
blanchet@42998
  1158
  case type_sys of
blanchet@42998
  1159
    Simple_Types _ =>
blanchet@42998
  1160
    decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
blanchet@42998
  1161
  | Preds _ =>
blanchet@42998
  1162
    let
blanchet@42998
  1163
      val decls =
blanchet@42998
  1164
        case decls of
blanchet@42998
  1165
          decl :: (decls' as _ :: _) =>
blanchet@42998
  1166
          let val T = result_type_of_decl decl in
blanchet@42998
  1167
            if forall (curry (type_instance ctxt o swap) T
blanchet@42998
  1168
                       o result_type_of_decl) decls' then
blanchet@42998
  1169
              [decl]
blanchet@42998
  1170
            else
blanchet@42998
  1171
              decls
blanchet@42998
  1172
          end
blanchet@42998
  1173
        | _ => decls
blanchet@42998
  1174
      val n = length decls
blanchet@42998
  1175
      val decls =
blanchet@42998
  1176
        decls
blanchet@42998
  1177
        |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
blanchet@42998
  1178
                   o result_type_of_decl)
blanchet@42998
  1179
    in
blanchet@42998
  1180
      (0 upto length decls - 1, decls)
blanchet@42998
  1181
      |-> map2 (formula_line_for_pred_sym_decl ctxt format conj_sym_kind
blanchet@42998
  1182
                                               nonmono_Ts type_sys n s)
blanchet@42998
  1183
    end
blanchet@42998
  1184
  | Tags (_, _, heaviness) =>
blanchet@42998
  1185
    (case heaviness of
blanchet@42998
  1186
       Heavy => []
blanchet@42998
  1187
     | Light =>
blanchet@42998
  1188
       let val n = length decls in
blanchet@42998
  1189
         (0 upto n - 1 ~~ decls)
blanchet@42998
  1190
         |> maps (formula_lines_for_tag_sym_decl ctxt format conj_sym_kind
blanchet@42998
  1191
                                                 nonmono_Ts type_sys n s)
blanchet@42998
  1192
       end)
blanchet@42579
  1193
blanchet@42956
  1194
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@42956
  1195
                                     type_sys sym_decl_tab =
blanchet@42998
  1196
  sym_decl_tab
blanchet@42998
  1197
  |> Symtab.dest
blanchet@42998
  1198
  |> sort_wrt fst
blanchet@42998
  1199
  |> rpair []
blanchet@42998
  1200
  |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
blanchet@42998
  1201
                                                     nonmono_Ts type_sys)
blanchet@42543
  1202
blanchet@42837
  1203
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
blanchet@42831
  1204
    level = Nonmonotonic_Types orelse level = Finite_Types
blanchet@42831
  1205
  | should_add_ti_ti_helper _ = false
blanchet@42831
  1206
blanchet@42939
  1207
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  1208
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  1209
    if heading = needle then j
blanchet@42939
  1210
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  1211
blanchet@42998
  1212
val implicit_declsN = "Should-be-implicit typings"
blanchet@42998
  1213
val explicit_declsN = "Explicit typings"
blanchet@41157
  1214
val factsN = "Relevant facts"
blanchet@41157
  1215
val class_relsN = "Class relationships"
blanchet@42543
  1216
val aritiesN = "Arities"
blanchet@41157
  1217
val helpersN = "Helper facts"
blanchet@41157
  1218
val conjsN = "Conjectures"
blanchet@41313
  1219
val free_typesN = "Type variables"
blanchet@41157
  1220
blanchet@42939
  1221
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
blanchet@42939
  1222
                        explicit_apply hyp_ts concl_t facts =
blanchet@38282
  1223
  let
blanchet@41313
  1224
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42962
  1225
      translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1226
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42886
  1227
    val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
blanchet@42962
  1228
    val repair = repair_fact ctxt format nonmono_Ts type_sys sym_tab
blanchet@42682
  1229
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1230
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1231
    val helpers =
blanchet@42962
  1232
      repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
blanchet@42962
  1233
                       |> map repair
blanchet@42894
  1234
    val lavish_nonmono_Ts =
blanchet@42894
  1235
      if null nonmono_Ts orelse
blanchet@42894
  1236
         polymorphism_of_type_sys type_sys <> Polymorphic then
blanchet@42894
  1237
        nonmono_Ts
blanchet@42894
  1238
      else
blanchet@42894
  1239
        [TVar (("'a", 0), HOLogic.typeS)]
blanchet@42680
  1240
    val sym_decl_lines =
blanchet@42731
  1241
      (conjs, helpers @ facts)
blanchet@42886
  1242
      |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
blanchet@42956
  1243
      |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
blanchet@42956
  1244
                                          lavish_nonmono_Ts type_sys
blanchet@42881
  1245
    val helper_lines =
blanchet@42956
  1246
      0 upto length helpers - 1 ~~ helpers
blanchet@42956
  1247
      |> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
blanchet@42956
  1248
                                    type_sys)
blanchet@42956
  1249
      |> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
blanchet@42956
  1250
          else I)
blanchet@42522
  1251
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1252
       Flotter hack. *)
blanchet@38282
  1253
    val problem =
blanchet@42998
  1254
      [(explicit_declsN, sym_decl_lines),
blanchet@42956
  1255
       (factsN,
blanchet@42956
  1256
        map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
blanchet@42956
  1257
            (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1258
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1259
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42881
  1260
       (helpersN, helper_lines),
blanchet@42962
  1261
       (conjsN,
blanchet@42962
  1262
        map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
blanchet@42962
  1263
            conjs),
blanchet@42956
  1264
       (free_typesN,
blanchet@42956
  1265
        formula_lines_for_free_types format type_sys (facts @ conjs))]
blanchet@42543
  1266
    val problem =
blanchet@42561
  1267
      problem
blanchet@42998
  1268
      |> (if format = CNF_UEQ then filter_cnf_ueq_problem else I)
blanchet@42998
  1269
      |> (if is_format_typed format then
blanchet@42998
  1270
            declare_undeclared_syms_in_atp_problem type_decl_prefix
blanchet@42998
  1271
                                                   implicit_declsN
blanchet@42998
  1272
          else
blanchet@42998
  1273
            I)
blanchet@42646
  1274
    val (problem, pool) =
blanchet@42646
  1275
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@42881
  1276
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  1277
    val typed_helpers =
blanchet@42881
  1278
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  1279
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  1280
                     else NONE)
blanchet@42881
  1281
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  1282
                  ~~ helpers)
blanchet@42778
  1283
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1284
      if min_ary > 0 then
blanchet@42755
  1285
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1286
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1287
        | NONE => I
blanchet@42755
  1288
      else
blanchet@42755
  1289
        I
blanchet@38282
  1290
  in
blanchet@38282
  1291
    (problem,
blanchet@38282
  1292
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1293
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1294
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1295
     fact_names |> Vector.fromList,
blanchet@42881
  1296
     typed_helpers,
blanchet@42755
  1297
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1298
  end
blanchet@38282
  1299
blanchet@41313
  1300
(* FUDGE *)
blanchet@41313
  1301
val conj_weight = 0.0
blanchet@41770
  1302
val hyp_weight = 0.1
blanchet@41770
  1303
val fact_min_weight = 0.2
blanchet@41313
  1304
val fact_max_weight = 1.0
blanchet@42608
  1305
val type_info_default_weight = 0.8
blanchet@41313
  1306
blanchet@41313
  1307
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42998
  1308
  is_tptp_user_symbol s ? Symtab.default (s, weight)
blanchet@41313
  1309
  #> fold (add_term_weights weight) tms
blanchet@42577
  1310
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1311
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1312
  | add_problem_line_weights _ _ = I
blanchet@41313
  1313
blanchet@41313
  1314
fun add_conjectures_weights [] = I
blanchet@41313
  1315
  | add_conjectures_weights conjs =
blanchet@41313
  1316
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1317
      add_problem_line_weights conj_weight conj
blanchet@41313
  1318
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1319
    end
blanchet@41313
  1320
blanchet@41313
  1321
fun add_facts_weights facts =
blanchet@41313
  1322
  let
blanchet@41313
  1323
    val num_facts = length facts
blanchet@41313
  1324
    fun weight_of j =
blanchet@41313
  1325
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1326
                        / Real.fromInt num_facts
blanchet@41313
  1327
  in
blanchet@41313
  1328
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1329
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1330
  end
blanchet@41313
  1331
blanchet@41313
  1332
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1333
fun atp_problem_weights problem =
blanchet@42608
  1334
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1335
    Symtab.empty
blanchet@42608
  1336
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1337
    |> add_facts_weights (get factsN)
blanchet@42608
  1338
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42998
  1339
            [explicit_declsN, class_relsN, aritiesN]
blanchet@42608
  1340
    |> Symtab.dest
blanchet@42608
  1341
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1342
  end
blanchet@41313
  1343
blanchet@38282
  1344
end;