src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Fri May 27 10:30:07 2011 +0200 (2011-05-27)
changeset 43000 bd424c3dde46
parent 42998 1c80902d0456
child 43001 f3492698dfc7
permissions -rw-r--r--
cleaner handling of equality and proxies (esp. for THF)
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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 =
blanchet@42542
   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@42994
   341
fun introduce_proxies format type_sys tm =
blanchet@42568
   342
  let
blanchet@42963
   343
    fun aux ary top_level (CombApp (tm1, tm2)) =
blanchet@42963
   344
        CombApp (aux (ary + 1) top_level tm1, aux 0 false tm2)
blanchet@43000
   345
      | aux ary top_level (CombConst (name as (s, _), T, T_args)) =
blanchet@42570
   346
        (case proxify_const s of
blanchet@43000
   347
           SOME (proxy_ary, 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
blanchet@43000
   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@43000
   357
               (* Proxies are not needed in THF, but we generate them for "="
blanchet@43000
   358
                  when it is not fully applied to work around parsing bugs in
blanchet@43000
   359
                  the provers ("= @ x @ x" is challenging to some). *)
blanchet@43000
   360
               if is_tptp_equal s andalso ary = proxy_ary then
blanchet@43000
   361
                 (`I tptp_equal, [])
blanchet@43000
   362
               else
blanchet@43000
   363
                 (proxy_base |>> prefix const_prefix, T_args)
blanchet@43000
   364
             | _ => (name, [])
blanchet@42569
   365
           else
blanchet@42574
   366
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   367
          | NONE => (name, T_args))
blanchet@42574
   368
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42963
   369
      | aux _ _ tm = tm
blanchet@42963
   370
  in aux 0 true tm end
blanchet@42568
   371
blanchet@42994
   372
fun combformula_from_prop thy format type_sys eq_as_iff =
blanchet@38282
   373
  let
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   374
    fun do_term bs t atomic_types =
blanchet@41140
   375
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42994
   376
      |>> (introduce_proxies format type_sys #> AAtom)
blanchet@42568
   377
      ||> union (op =) atomic_types
blanchet@38282
   378
    fun do_quant bs q s T t' =
blanchet@38518
   379
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   380
        do_formula ((s, T) :: bs) t'
blanchet@42562
   381
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   382
      end
blanchet@38282
   383
    and do_conn bs c t1 t2 =
blanchet@38282
   384
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   385
      #>> uncurry (mk_aconn c)
blanchet@38282
   386
    and do_formula bs t =
blanchet@38282
   387
      case t of
blanchet@42531
   388
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   389
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   390
        do_quant bs AForall s T t'
blanchet@38282
   391
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   392
        do_quant bs AExists s T t'
haftmann@38795
   393
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   394
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   395
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   396
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   397
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   398
      | _ => do_term bs t
blanchet@38282
   399
  in do_formula [] end
blanchet@38282
   400
blanchet@42750
   401
fun presimplify_term ctxt =
blanchet@42750
   402
  Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@42750
   403
  #> Meson.presimplify ctxt
blanchet@42750
   404
  #> prop_of
blanchet@38282
   405
wenzelm@41491
   406
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   407
fun conceal_bounds Ts t =
blanchet@38282
   408
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   409
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   410
fun reveal_bounds Ts =
blanchet@38282
   411
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   412
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   413
blanchet@42747
   414
fun extensionalize_term ctxt t =
blanchet@42747
   415
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42747
   416
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@42747
   417
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   418
  end
blanchet@38608
   419
blanchet@38282
   420
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   421
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   422
    if Meson.is_fol_term thy t then
blanchet@38491
   423
      t
blanchet@38491
   424
    else
blanchet@38491
   425
      let
blanchet@38491
   426
        fun aux Ts t =
blanchet@38491
   427
          case t of
blanchet@38491
   428
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   429
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   430
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   431
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   432
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   433
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   434
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   435
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   436
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   437
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   438
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   439
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   440
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   441
              $ t1 $ t2 =>
blanchet@38491
   442
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   443
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   444
                   t
blanchet@38491
   445
                 else
blanchet@38491
   446
                   t |> conceal_bounds Ts
blanchet@38491
   447
                     |> Envir.eta_contract
blanchet@38491
   448
                     |> cterm_of thy
blanchet@39890
   449
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   450
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   451
                     |> reveal_bounds Ts
blanchet@39370
   452
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   453
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   454
      handle THM _ =>
blanchet@38491
   455
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   456
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   457
             else HOLogic.true_const
blanchet@38491
   458
  end
blanchet@38282
   459
blanchet@38282
   460
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   461
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   462
fun freeze_term t =
blanchet@38282
   463
  let
blanchet@38282
   464
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   465
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   466
      | aux (Var ((s, i), T)) =
blanchet@38282
   467
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   468
      | aux t = t
blanchet@38282
   469
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   470
blanchet@40204
   471
(* making fact and conjecture formulas *)
blanchet@42994
   472
fun make_formula ctxt format type_sys eq_as_iff presimp name loc kind t =
blanchet@38282
   473
  let
wenzelm@42361
   474
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   475
    val t = t |> Envir.beta_eta_contract
blanchet@42944
   476
              |> transform_elim_prop
blanchet@41211
   477
              |> Object_Logic.atomize_term thy
blanchet@42563
   478
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   479
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@42742
   480
              |> Raw_Simplifier.rewrite_term thy
blanchet@42742
   481
                     (Meson.unfold_set_const_simps ctxt) []
blanchet@42747
   482
              |> extensionalize_term ctxt
blanchet@42750
   483
              |> presimp ? presimplify_term ctxt
blanchet@38282
   484
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   485
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   486
              |> kind <> Axiom ? freeze_term
blanchet@42962
   487
    val (combformula, atomic_types) =
blanchet@42994
   488
      combformula_from_prop thy format type_sys eq_as_iff t []
blanchet@38282
   489
  in
blanchet@42640
   490
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   491
     atomic_types = atomic_types}
blanchet@38282
   492
  end
blanchet@38282
   493
blanchet@42994
   494
fun make_fact ctxt format type_sys keep_trivial eq_as_iff presimp
blanchet@42994
   495
              ((name, loc), t) =
blanchet@42962
   496
  case (keep_trivial,
blanchet@42994
   497
        make_formula ctxt format type_sys eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   498
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   499
    NONE
blanchet@41990
   500
  | (_, formula) => SOME formula
blanchet@42561
   501
blanchet@42994
   502
fun make_conjecture ctxt format prem_kind type_sys ts =
blanchet@38613
   503
  let val last = length ts - 1 in
blanchet@42709
   504
    map2 (fn j => fn t =>
blanchet@42709
   505
             let
blanchet@42709
   506
               val (kind, maybe_negate) =
blanchet@42709
   507
                 if j = last then
blanchet@42709
   508
                   (Conjecture, I)
blanchet@42709
   509
                 else
blanchet@42709
   510
                   (prem_kind,
blanchet@42709
   511
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   512
                    else I)
blanchet@42709
   513
              in
blanchet@42994
   514
                t |> make_formula ctxt format type_sys true true
blanchet@42994
   515
                                  (string_of_int j) General kind
blanchet@42962
   516
                  |> maybe_negate
blanchet@42709
   517
              end)
blanchet@38613
   518
         (0 upto last) ts
blanchet@38613
   519
  end
blanchet@38282
   520
blanchet@42682
   521
(** Finite and infinite type inference **)
blanchet@42682
   522
blanchet@42886
   523
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
blanchet@42886
   524
  | deep_freeze_atyp T = T
blanchet@42886
   525
val deep_freeze_type = map_atyps deep_freeze_atyp
blanchet@42886
   526
blanchet@42886
   527
val type_instance = Sign.typ_instance o Proof_Context.theory_of
blanchet@42886
   528
blanchet@42682
   529
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   530
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   531
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   532
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   533
blanchet@42886
   534
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
blanchet@42886
   535
    exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
blanchet@42836
   536
  | should_encode_type _ _ All_Types _ = true
blanchet@42682
   537
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   538
  | should_encode_type _ _ _ _ = false
blanchet@42682
   539
blanchet@42837
   540
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
   541
                             should_predicate_on_var T =
blanchet@42878
   542
    (heaviness = Heavy orelse should_predicate_on_var ()) andalso
blanchet@42878
   543
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
   544
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
   545
blanchet@42836
   546
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42836
   547
    String.isPrefix bound_var_prefix s
blanchet@42836
   548
  | is_var_or_bound_var (CombVar _) = true
blanchet@42836
   549
  | is_var_or_bound_var _ = false
blanchet@42836
   550
blanchet@42829
   551
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
blanchet@42829
   552
blanchet@42829
   553
fun should_tag_with_type _ _ _ Top_Level _ _ = false
blanchet@42837
   554
  | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
blanchet@42837
   555
    (case heaviness of
blanchet@42837
   556
       Heavy => should_encode_type ctxt nonmono_Ts level T
blanchet@42837
   557
     | Light =>
blanchet@42836
   558
       case (site, is_var_or_bound_var u) of
blanchet@42836
   559
         (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
blanchet@42829
   560
       | _ => false)
blanchet@42829
   561
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
   562
blanchet@42994
   563
fun homogenized_type ctxt nonmono_Ts level =
blanchet@42994
   564
  let
blanchet@42994
   565
    val should_encode = should_encode_type ctxt nonmono_Ts level
blanchet@42994
   566
    fun homo 0 T = if should_encode T then T else homo_infinite_type
blanchet@42994
   567
      | homo ary (Type (@{type_name fun}, [T1, T2])) =
blanchet@42994
   568
        homo 0 T1 --> homo (ary - 1) T2
blanchet@42994
   569
      | homo _ _ = raise Fail "expected function type"
blanchet@42994
   570
  in homo end
blanchet@42682
   571
blanchet@42573
   572
(** "hBOOL" and "hAPP" **)
blanchet@41313
   573
blanchet@42574
   574
type sym_info =
blanchet@42563
   575
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   576
blanchet@42574
   577
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   578
  let
blanchet@42558
   579
    fun aux top_level tm =
blanchet@42558
   580
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   581
        (case head of
blanchet@42563
   582
           CombConst ((s, _), T, _) =>
blanchet@42558
   583
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   584
             I
blanchet@42558
   585
           else
blanchet@42563
   586
             let val ary = length args in
blanchet@42558
   587
               Symtab.map_default
blanchet@42558
   588
                   (s, {pred_sym = true,
blanchet@42563
   589
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   590
                        max_ary = 0, typ = SOME T})
blanchet@42563
   591
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   592
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   593
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   594
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   595
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   596
            end
blanchet@42558
   597
         | _ => I)
blanchet@42558
   598
        #> fold (aux false) args
blanchet@42558
   599
      end
blanchet@42558
   600
  in aux true end
blanchet@42674
   601
fun add_fact_syms_to_table explicit_apply =
blanchet@42834
   602
  fact_lift (formula_fold NONE (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   603
blanchet@42675
   604
val default_sym_table_entries : (string * sym_info) list =
blanchet@43000
   605
  [(tptp_equal, {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@43000
   606
   (tptp_old_equal, {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42966
   607
   (make_fixed_const predicator_name,
blanchet@42563
   608
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   609
  ([tptp_false, tptp_true]
blanchet@42563
   610
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   611
blanchet@42544
   612
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   613
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   614
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   615
blanchet@42558
   616
fun min_arity_of sym_tab s =
blanchet@42558
   617
  case Symtab.lookup sym_tab s of
blanchet@42574
   618
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   619
  | NONE =>
blanchet@42558
   620
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   621
      SOME s =>
blanchet@42570
   622
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42966
   623
        if s = predicator_name then 1
blanchet@42966
   624
        else if s = app_op_name then 2
blanchet@42966
   625
        else if s = type_pred_name then 1
blanchet@42557
   626
        else 0
blanchet@42547
   627
      end
blanchet@42544
   628
    | NONE => 0
blanchet@38282
   629
blanchet@38282
   630
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   631
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   632
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   633
   arguments and is used as a predicate. *)
blanchet@42558
   634
fun is_pred_sym sym_tab s =
blanchet@42558
   635
  case Symtab.lookup sym_tab s of
blanchet@42574
   636
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   637
    pred_sym andalso min_ary = max_ary
blanchet@42558
   638
  | NONE => false
blanchet@38282
   639
blanchet@42568
   640
val predicator_combconst =
blanchet@42966
   641
  CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
blanchet@42568
   642
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   643
blanchet@42568
   644
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   645
  case strip_combterm_comb tm of
blanchet@42542
   646
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   647
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   648
  | _ => predicator tm
blanchet@42542
   649
blanchet@42544
   650
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   651
blanchet@42544
   652
fun explicit_app arg head =
blanchet@42544
   653
  let
blanchet@42562
   654
    val head_T = combtyp_of head
blanchet@42693
   655
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   656
    val explicit_app =
blanchet@42966
   657
      CombConst (`make_fixed_const app_op_name, head_T --> head_T,
blanchet@42693
   658
                 [arg_T, res_T])
blanchet@42544
   659
  in list_app explicit_app [head, arg] end
blanchet@42544
   660
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   661
blanchet@42565
   662
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   663
  let
blanchet@42544
   664
    fun aux tm =
blanchet@42544
   665
      case strip_combterm_comb tm of
blanchet@42544
   666
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   667
        args |> map aux
blanchet@42557
   668
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   669
             |>> list_app head
blanchet@42544
   670
             |-> list_explicit_app
blanchet@42544
   671
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   672
  in aux end
blanchet@38282
   673
blanchet@42753
   674
fun chop_fun 0 T = ([], T)
blanchet@42753
   675
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
   676
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
   677
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
   678
blanchet@42780
   679
fun filter_type_args _ _ _ [] = []
blanchet@42780
   680
  | filter_type_args thy s arity T_args =
blanchet@42834
   681
    let
blanchet@42834
   682
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42966
   683
      val U = if s = app_op_name then
blanchet@42834
   684
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
   685
              else
blanchet@42834
   686
                s |> Sign.the_const_type thy
blanchet@42834
   687
    in
blanchet@42781
   688
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
   689
        [] => []
blanchet@42781
   690
      | res_U_vars =>
blanchet@42781
   691
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
   692
          U_args ~~ T_args
blanchet@42781
   693
          |> map_filter (fn (U, T) =>
blanchet@42781
   694
                            if member (op =) res_U_vars (dest_TVar U) then
blanchet@42781
   695
                              SOME T
blanchet@42781
   696
                            else
blanchet@42781
   697
                              NONE)
blanchet@42781
   698
        end
blanchet@42780
   699
    end
blanchet@42780
   700
    handle TYPE _ => T_args
blanchet@42753
   701
blanchet@42994
   702
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42753
   703
  let
blanchet@42753
   704
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
   705
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
   706
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
   707
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   708
        let
blanchet@42701
   709
          val level = level_of_type_sys type_sys
blanchet@42701
   710
          val (T, T_args) =
blanchet@42701
   711
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   712
               anyway, by distinguishing overloads only on the homogenized
blanchet@42837
   713
               result type. Don't do it for lightweight type systems, though,
blanchet@42837
   714
               since it leads to too many unsound proofs. *)
blanchet@42966
   715
            if s = const_prefix ^ app_op_name andalso
blanchet@42726
   716
               length T_args = 2 andalso
blanchet@42836
   717
               not (is_type_sys_virtually_sound type_sys) andalso
blanchet@42837
   718
               heaviness_of_type_sys type_sys = Heavy then
blanchet@42994
   719
              T_args |> map (homogenized_type ctxt nonmono_Ts level 0)
blanchet@42701
   720
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42831
   721
                                    (T --> T, tl Ts)
blanchet@42701
   722
                                  end)
blanchet@42701
   723
            else
blanchet@42701
   724
              (T, T_args)
blanchet@42701
   725
        in
blanchet@42701
   726
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   727
             NONE => (name, T_args)
blanchet@42701
   728
           | SOME s'' =>
blanchet@42753
   729
             let
blanchet@42753
   730
               val s'' = invert_const s''
blanchet@42831
   731
               fun filtered_T_args false = T_args
blanchet@42831
   732
                 | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@42753
   733
             in
blanchet@42701
   734
               case type_arg_policy type_sys s'' of
blanchet@42831
   735
                 Explicit_Type_Args drop_args =>
blanchet@42831
   736
                 (name, filtered_T_args drop_args)
blanchet@42831
   737
               | Mangled_Type_Args drop_args =>
blanchet@42994
   738
                 (mangled_const_name (filtered_T_args drop_args) name, [])
blanchet@42753
   739
               | No_Type_Args => (name, [])
blanchet@42701
   740
             end)
blanchet@42701
   741
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   742
        end
blanchet@42753
   743
      | aux _ tm = tm
blanchet@42753
   744
  in aux 0 end
blanchet@42573
   745
blanchet@42962
   746
fun repair_combterm ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42994
   747
  not (is_setting_higher_order format type_sys)
blanchet@42994
   748
  ? (introduce_explicit_apps_in_combterm sym_tab
blanchet@42994
   749
     #> introduce_predicators_in_combterm sym_tab)
blanchet@42994
   750
  #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
   751
fun repair_fact ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42701
   752
  update_combformula (formula_map
blanchet@42962
   753
      (repair_combterm ctxt format nonmono_Ts type_sys sym_tab))
blanchet@42573
   754
blanchet@42573
   755
(** Helper facts **)
blanchet@42573
   756
blanchet@42573
   757
fun ti_ti_helper_fact () =
blanchet@42573
   758
  let
blanchet@42573
   759
    fun var s = ATerm (`I s, [])
blanchet@42589
   760
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   761
  in
blanchet@42612
   762
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@43000
   763
             AAtom (ATerm (`I tptp_equal, [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42879
   764
             |> close_formula_universally, simp_info, NONE)
blanchet@42573
   765
  end
blanchet@42573
   766
blanchet@42962
   767
fun helper_facts_for_sym ctxt format type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   768
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   769
    SOME mangled_s =>
blanchet@42573
   770
    let
blanchet@42573
   771
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   772
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42893
   773
      fun dub_and_inst c needs_fairly_sound (th, j) =
blanchet@42881
   774
        ((c ^ "_" ^ string_of_int j ^
blanchet@42893
   775
          (if needs_fairly_sound then typed_helper_suffix
blanchet@42881
   776
           else untyped_helper_suffix),
blanchet@42881
   777
          General),
blanchet@42573
   778
         let val t = th |> prop_of in
blanchet@42753
   779
           t |> ((case general_type_arg_policy type_sys of
blanchet@42753
   780
                    Mangled_Type_Args _ => true
blanchet@42753
   781
                  | _ => false) andalso
blanchet@42573
   782
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   783
                ? (case typ of
blanchet@42573
   784
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   785
                   | NONE => I)
blanchet@42573
   786
         end)
blanchet@42573
   787
      fun make_facts eq_as_iff =
blanchet@42994
   788
        map_filter (make_fact ctxt format type_sys false eq_as_iff false)
blanchet@42893
   789
      val fairly_sound = is_type_sys_fairly_sound type_sys
blanchet@42573
   790
    in
blanchet@42573
   791
      metis_helpers
blanchet@42894
   792
      |> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
blanchet@42573
   793
                  if metis_s <> unmangled_s orelse
blanchet@42894
   794
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
   795
                    []
blanchet@42573
   796
                  else
blanchet@42573
   797
                    ths ~~ (1 upto length ths)
blanchet@42893
   798
                    |> map (dub_and_inst mangled_s needs_fairly_sound)
blanchet@42893
   799
                    |> make_facts (not needs_fairly_sound))
blanchet@42573
   800
    end
blanchet@42573
   801
  | NONE => []
blanchet@42962
   802
fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
blanchet@42962
   803
  Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
blanchet@42962
   804
                  []
blanchet@42573
   805
blanchet@42994
   806
fun translate_atp_fact ctxt format type_sys keep_trivial =
blanchet@42994
   807
  `(make_fact ctxt format type_sys keep_trivial true true o apsnd prop_of)
blanchet@42573
   808
blanchet@42962
   809
fun translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t
blanchet@42962
   810
                       rich_facts =
blanchet@42573
   811
  let
blanchet@42573
   812
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   813
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   814
    val (facts, fact_names) =
blanchet@42573
   815
      rich_facts
blanchet@42573
   816
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   817
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   818
      |> ListPair.unzip
blanchet@42573
   819
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   820
       boost an ATP's performance (for some reason). *)
blanchet@42573
   821
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   822
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   823
    val all_ts = goal_t :: fact_ts
blanchet@42573
   824
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   825
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   826
    val tycons = type_consts_of_terms thy all_ts
blanchet@42994
   827
    val conjs =
blanchet@42994
   828
      hyp_ts @ [concl_t] |> make_conjecture ctxt format prem_kind type_sys
blanchet@42573
   829
    val (supers', arity_clauses) =
blanchet@42589
   830
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   831
      else make_arity_clauses thy tycons supers
blanchet@42573
   832
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   833
  in
blanchet@42573
   834
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   835
  end
blanchet@42573
   836
blanchet@42573
   837
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   838
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   839
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   840
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   841
blanchet@42573
   842
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   843
blanchet@42994
   844
fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
blanchet@42966
   845
  CombApp (CombConst (`make_fixed_const type_pred_name, T --> @{typ bool}, [T])
blanchet@42994
   846
           |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
blanchet@42573
   847
           tm)
blanchet@42573
   848
blanchet@42878
   849
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@42878
   850
  | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@43000
   851
    accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
blanchet@42878
   852
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
blanchet@42878
   853
  | is_var_nonmonotonic_in_formula pos phi _ name =
blanchet@42878
   854
    formula_fold pos (var_occurs_positively_naked_in_term name) phi false
blanchet@42834
   855
blanchet@42994
   856
fun mk_const_aterm x T_args args =
blanchet@42994
   857
  ATerm (x, map (fo_term_from_typ false) T_args @ args)
blanchet@42994
   858
blanchet@42962
   859
fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
blanchet@42829
   860
  CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42994
   861
  |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
   862
  |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42829
   863
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42962
   864
and term_from_combterm ctxt format nonmono_Ts type_sys =
blanchet@42573
   865
  let
blanchet@42962
   866
    fun aux site u =
blanchet@42962
   867
      let
blanchet@42962
   868
        val (head, args) = strip_combterm_comb u
blanchet@42962
   869
        val (x as (s, _), T_args) =
blanchet@42962
   870
          case head of
blanchet@42962
   871
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42962
   872
          | CombVar (name, _) => (name, [])
blanchet@42962
   873
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@43000
   874
        val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
blanchet@42962
   875
                       else Elsewhere
blanchet@42994
   876
        val t = mk_const_aterm x T_args (map (aux arg_site) args)
blanchet@42962
   877
        val T = combtyp_of u
blanchet@42962
   878
      in
blanchet@42962
   879
        t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
blanchet@42962
   880
                tag_with_type ctxt format nonmono_Ts type_sys T
blanchet@42962
   881
              else
blanchet@42962
   882
                I)
blanchet@42962
   883
      end
blanchet@42962
   884
  in aux end
blanchet@42962
   885
and formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42962
   886
                             should_predicate_on_var =
blanchet@42829
   887
  let
blanchet@42994
   888
    val higher_order = is_setting_higher_order format type_sys
blanchet@42962
   889
    val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42573
   890
    val do_bound_type =
blanchet@42682
   891
      case type_sys of
blanchet@42722
   892
        Simple_Types level =>
blanchet@42994
   893
        homogenized_type ctxt nonmono_Ts level 0
blanchet@42994
   894
        #> mangled_type higher_order false 0 #> SOME
blanchet@42682
   895
      | _ => K NONE
blanchet@42878
   896
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@42834
   897
      if should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42878
   898
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@42834
   899
        CombVar (name, T)
blanchet@42994
   900
        |> type_pred_combterm ctxt nonmono_Ts type_sys T
blanchet@42878
   901
        |> do_term |> AAtom |> SOME
blanchet@42573
   902
      else
blanchet@42573
   903
        NONE
blanchet@42878
   904
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
   905
        let
blanchet@42878
   906
          val phi = phi |> do_formula pos
blanchet@42878
   907
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
   908
        in
blanchet@42834
   909
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
   910
                                        | SOME T => do_bound_type T)),
blanchet@42834
   911
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
   912
                      (map_filter
blanchet@42834
   913
                           (fn (_, NONE) => NONE
blanchet@42834
   914
                             | (s, SOME T) =>
blanchet@42878
   915
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
   916
                           xs)
blanchet@42834
   917
                      phi)
blanchet@42834
   918
        end
blanchet@42878
   919
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@42878
   920
      | do_formula _ (AAtom tm) = AAtom (do_term tm)
blanchet@42878
   921
  in do_formula o SOME end
blanchet@42573
   922
blanchet@42956
   923
fun bound_atomic_types format type_sys Ts =
blanchet@42727
   924
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42956
   925
                (atp_type_literals_for_types format type_sys Axiom Ts))
blanchet@42727
   926
blanchet@42956
   927
fun formula_for_fact ctxt format nonmono_Ts type_sys
blanchet@42573
   928
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   929
  combformula
blanchet@42727
   930
  |> close_combformula_universally
blanchet@42962
   931
  |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
   932
                              is_var_nonmonotonic_in_formula true
blanchet@42956
   933
  |> bound_atomic_types format type_sys atomic_types
blanchet@42573
   934
  |> close_formula_universally
blanchet@42573
   935
blanchet@42573
   936
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   937
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   938
   the remote provers might care. *)
blanchet@42956
   939
fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
blanchet@42640
   940
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   941
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   942
                     else string_of_int j ^ "_") ^
blanchet@42647
   943
           ascii_of name,
blanchet@42956
   944
           kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
blanchet@42879
   945
           case locality of
blanchet@42879
   946
             Intro => intro_info
blanchet@42879
   947
           | Elim => elim_info
blanchet@42879
   948
           | Simp => simp_info
blanchet@42879
   949
           | _ => NONE)
blanchet@42573
   950
blanchet@42939
   951
fun formula_line_for_class_rel_clause
blanchet@42939
   952
        (ClassRelClause {name, subclass, superclass, ...}) =
blanchet@42573
   953
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   954
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   955
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   956
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42879
   957
             |> close_formula_universally, intro_info, NONE)
blanchet@42573
   958
  end
blanchet@42573
   959
blanchet@42573
   960
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   961
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   962
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   963
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   964
blanchet@42939
   965
fun formula_line_for_arity_clause
blanchet@42939
   966
        (ArityClause {name, prem_lits, concl_lits, ...}) =
blanchet@42577
   967
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   968
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42895
   969
                          o fo_literal_from_arity_literal) prem_lits)
blanchet@42573
   970
                    (formula_from_fo_literal
blanchet@42895
   971
                         (fo_literal_from_arity_literal concl_lits))
blanchet@42879
   972
           |> close_formula_universally, intro_info, NONE)
blanchet@42573
   973
blanchet@42962
   974
fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
blanchet@42573
   975
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   976
  Formula (conjecture_prefix ^ name, kind,
blanchet@42962
   977
           formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42939
   978
               is_var_nonmonotonic_in_formula false
blanchet@42939
   979
               (close_combformula_universally combformula)
blanchet@42573
   980
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   981
blanchet@42956
   982
fun free_type_literals format type_sys
blanchet@42956
   983
                       ({atomic_types, ...} : translated_formula) =
blanchet@42956
   984
  atomic_types |> atp_type_literals_for_types format type_sys Conjecture
blanchet@42573
   985
               |> map fo_literal_from_type_literal
blanchet@42573
   986
blanchet@42573
   987
fun formula_line_for_free_type j lit =
blanchet@42577
   988
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   989
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42956
   990
fun formula_lines_for_free_types format type_sys facts =
blanchet@42573
   991
  let
blanchet@42956
   992
    val litss = map (free_type_literals format type_sys) facts
blanchet@42573
   993
    val lits = fold (union (op =)) litss []
blanchet@42573
   994
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   995
blanchet@42573
   996
(** Symbol declarations **)
blanchet@42544
   997
blanchet@42886
   998
fun insert_type ctxt get_T x xs =
blanchet@42677
   999
  let val T = get_T x in
blanchet@42886
  1000
    if exists (curry (type_instance ctxt) T o get_T) xs then xs
blanchet@42886
  1001
    else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
blanchet@42677
  1002
  end
blanchet@42677
  1003
blanchet@42574
  1004
fun should_declare_sym type_sys pred_sym s =
blanchet@42998
  1005
  is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
blanchet@42894
  1006
  (case type_sys of
blanchet@42894
  1007
     Simple_Types _ => true
blanchet@42894
  1008
   | Tags (_, _, Light) => true
blanchet@42894
  1009
   | _ => not pred_sym)
blanchet@38282
  1010
blanchet@42886
  1011
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
  1012
  let
blanchet@42698
  1013
    fun add_combterm in_conj tm =
blanchet@42574
  1014
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
  1015
        (case head of
blanchet@42574
  1016
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
  1017
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
  1018
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
  1019
               Symtab.map_default (s, [])
blanchet@42886
  1020
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
  1021
                                         in_conj))
blanchet@42574
  1022
             else
blanchet@42574
  1023
               I
blanchet@42574
  1024
           end
blanchet@42574
  1025
         | _ => I)
blanchet@42698
  1026
        #> fold (add_combterm in_conj) args
blanchet@42574
  1027
      end
blanchet@42698
  1028
    fun add_fact in_conj =
blanchet@42834
  1029
      fact_lift (formula_fold NONE (K (add_combterm in_conj)))
blanchet@42698
  1030
  in
blanchet@42698
  1031
    Symtab.empty
blanchet@42698
  1032
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
  1033
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
  1034
  end
blanchet@42533
  1035
blanchet@42886
  1036
(* These types witness that the type classes they belong to allow infinite
blanchet@42886
  1037
   models and hence that any types with these type classes is monotonic. *)
blanchet@42886
  1038
val known_infinite_types = [@{typ nat}, @{typ int}, @{typ "nat => bool"}]
blanchet@42886
  1039
blanchet@42685
  1040
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  1041
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42886
  1042
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
blanchet@42829
  1043
  | add_combterm_nonmonotonic_types ctxt level _
blanchet@43000
  1044
        (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) =
blanchet@43000
  1045
    (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
  1046
     (case level of
blanchet@42886
  1047
        Nonmonotonic_Types =>
blanchet@42886
  1048
        not (is_type_surely_infinite ctxt known_infinite_types T)
blanchet@42829
  1049
      | Finite_Types => is_type_surely_finite ctxt T
blanchet@42886
  1050
      | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
blanchet@42829
  1051
  | add_combterm_nonmonotonic_types _ _ _ _ = I
blanchet@42829
  1052
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
blanchet@42829
  1053
                                            : translated_formula) =
blanchet@42834
  1054
  formula_fold (SOME (kind <> Conjecture))
blanchet@42829
  1055
               (add_combterm_nonmonotonic_types ctxt level) combformula
blanchet@42886
  1056
fun nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42829
  1057
  let val level = level_of_type_sys type_sys in
blanchet@42886
  1058
    if level = Nonmonotonic_Types orelse level = Finite_Types then
blanchet@42886
  1059
      [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
blanchet@42886
  1060
         (* We must add "bool" in case the helper "True_or_False" is added
blanchet@42886
  1061
            later. In addition, several places in the code rely on the list of
blanchet@42886
  1062
            nonmonotonic types not being empty. *)
blanchet@42886
  1063
         |> insert_type ctxt I @{typ bool}
blanchet@42886
  1064
    else
blanchet@42886
  1065
      []
blanchet@42829
  1066
  end
blanchet@42677
  1067
blanchet@42994
  1068
fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
blanchet@42994
  1069
                      (s', T_args, T, pred_sym, ary, _) =
blanchet@42994
  1070
  let
blanchet@42994
  1071
    val (higher_order, T_arg_Ts, level) =
blanchet@42994
  1072
      case type_sys of
blanchet@42994
  1073
        Simple_Types level => (format = THF, [], level)
blanchet@42994
  1074
      | _ => (false, replicate (length T_args) homo_infinite_type, No_Types)
blanchet@42994
  1075
  in
blanchet@42998
  1076
    Decl (sym_decl_prefix ^ s, (s, s'),
blanchet@42994
  1077
          (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
blanchet@42994
  1078
          |> mangled_type higher_order pred_sym (length T_arg_Ts + ary))
blanchet@42994
  1079
  end
blanchet@42579
  1080
blanchet@42592
  1081
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
  1082
blanchet@42956
  1083
fun formula_line_for_pred_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1084
                                   n s j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1085
  let
blanchet@42709
  1086
    val (kind, maybe_negate) =
blanchet@42709
  1087
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1088
      else (Axiom, I)
blanchet@42753
  1089
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42579
  1090
    val bound_names =
blanchet@42579
  1091
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1092
    val bounds =
blanchet@42579
  1093
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
  1094
    val bound_Ts =
blanchet@42592
  1095
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
  1096
                             else NONE)
blanchet@42579
  1097
  in
blanchet@42998
  1098
    Formula (sym_formula_prefix ^ s ^
blanchet@42709
  1099
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1100
             CombConst ((s, s'), T, T_args)
blanchet@42829
  1101
             |> fold (curry (CombApp o swap)) bounds
blanchet@42994
  1102
             |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
blanchet@42963
  1103
             |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42962
  1104
             |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
  1105
                                         (K (K (K (K true)))) true
blanchet@42956
  1106
             |> n > 1 ? bound_atomic_types format type_sys (atyps_of T)
blanchet@42709
  1107
             |> close_formula_universally
blanchet@42709
  1108
             |> maybe_negate,
blanchet@42879
  1109
             intro_info, NONE)
blanchet@42579
  1110
  end
blanchet@42579
  1111
blanchet@42956
  1112
fun formula_lines_for_tag_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1113
        n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1114
  let
blanchet@42829
  1115
    val ident_base =
blanchet@42998
  1116
      sym_formula_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1117
    val (kind, maybe_negate) =
blanchet@42852
  1118
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1119
      else (Axiom, I)
blanchet@42829
  1120
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1121
    val bound_names =
blanchet@42829
  1122
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1123
    val bounds = bound_names |> map (fn name => ATerm (name, []))
blanchet@42994
  1124
    val cst = mk_const_aterm (s, s') T_args
blanchet@42830
  1125
    val atomic_Ts = atyps_of T
blanchet@42834
  1126
    fun eq tms =
blanchet@42834
  1127
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@43000
  1128
       else AAtom (ATerm (`I tptp_equal, tms)))
blanchet@42956
  1129
      |> bound_atomic_types format type_sys atomic_Ts
blanchet@42830
  1130
      |> close_formula_universally
blanchet@42852
  1131
      |> maybe_negate
blanchet@42836
  1132
    val should_encode = should_encode_type ctxt nonmono_Ts All_Types
blanchet@42962
  1133
    val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
blanchet@42829
  1134
    val add_formula_for_res =
blanchet@42829
  1135
      if should_encode res_T then
blanchet@42852
  1136
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42994
  1137
                       eq [tag_with res_T (cst bounds), cst bounds],
blanchet@42879
  1138
                       simp_info, NONE))
blanchet@42829
  1139
      else
blanchet@42829
  1140
        I
blanchet@42829
  1141
    fun add_formula_for_arg k =
blanchet@42829
  1142
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1143
        if should_encode arg_T then
blanchet@42829
  1144
          case chop k bounds of
blanchet@42829
  1145
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1146
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42994
  1147
                           eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
blanchet@42994
  1148
                               cst bounds],
blanchet@42879
  1149
                           simp_info, NONE))
blanchet@42829
  1150
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1151
        else
blanchet@42829
  1152
          I
blanchet@42829
  1153
      end
blanchet@42829
  1154
  in
blanchet@42834
  1155
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1156
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1157
  end
blanchet@42829
  1158
blanchet@42836
  1159
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1160
blanchet@42956
  1161
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1162
                                (s, decls) =
blanchet@42998
  1163
  case type_sys of
blanchet@42998
  1164
    Simple_Types _ =>
blanchet@42998
  1165
    decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
blanchet@42998
  1166
  | Preds _ =>
blanchet@42998
  1167
    let
blanchet@42998
  1168
      val decls =
blanchet@42998
  1169
        case decls of
blanchet@42998
  1170
          decl :: (decls' as _ :: _) =>
blanchet@42998
  1171
          let val T = result_type_of_decl decl in
blanchet@42998
  1172
            if forall (curry (type_instance ctxt o swap) T
blanchet@42998
  1173
                       o result_type_of_decl) decls' then
blanchet@42998
  1174
              [decl]
blanchet@42998
  1175
            else
blanchet@42998
  1176
              decls
blanchet@42998
  1177
          end
blanchet@42998
  1178
        | _ => decls
blanchet@42998
  1179
      val n = length decls
blanchet@42998
  1180
      val decls =
blanchet@42998
  1181
        decls
blanchet@42998
  1182
        |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
blanchet@42998
  1183
                   o result_type_of_decl)
blanchet@42998
  1184
    in
blanchet@42998
  1185
      (0 upto length decls - 1, decls)
blanchet@42998
  1186
      |-> map2 (formula_line_for_pred_sym_decl ctxt format conj_sym_kind
blanchet@42998
  1187
                                               nonmono_Ts type_sys n s)
blanchet@42998
  1188
    end
blanchet@42998
  1189
  | Tags (_, _, heaviness) =>
blanchet@42998
  1190
    (case heaviness of
blanchet@42998
  1191
       Heavy => []
blanchet@42998
  1192
     | Light =>
blanchet@42998
  1193
       let val n = length decls in
blanchet@42998
  1194
         (0 upto n - 1 ~~ decls)
blanchet@42998
  1195
         |> maps (formula_lines_for_tag_sym_decl ctxt format conj_sym_kind
blanchet@42998
  1196
                                                 nonmono_Ts type_sys n s)
blanchet@42998
  1197
       end)
blanchet@42579
  1198
blanchet@42956
  1199
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@42956
  1200
                                     type_sys sym_decl_tab =
blanchet@42998
  1201
  sym_decl_tab
blanchet@42998
  1202
  |> Symtab.dest
blanchet@42998
  1203
  |> sort_wrt fst
blanchet@42998
  1204
  |> rpair []
blanchet@42998
  1205
  |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
blanchet@42998
  1206
                                                     nonmono_Ts type_sys)
blanchet@42543
  1207
blanchet@42837
  1208
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
blanchet@42831
  1209
    level = Nonmonotonic_Types orelse level = Finite_Types
blanchet@42831
  1210
  | should_add_ti_ti_helper _ = false
blanchet@42831
  1211
blanchet@42939
  1212
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  1213
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  1214
    if heading = needle then j
blanchet@42939
  1215
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  1216
blanchet@42998
  1217
val implicit_declsN = "Should-be-implicit typings"
blanchet@42998
  1218
val explicit_declsN = "Explicit typings"
blanchet@41157
  1219
val factsN = "Relevant facts"
blanchet@41157
  1220
val class_relsN = "Class relationships"
blanchet@42543
  1221
val aritiesN = "Arities"
blanchet@41157
  1222
val helpersN = "Helper facts"
blanchet@41157
  1223
val conjsN = "Conjectures"
blanchet@41313
  1224
val free_typesN = "Type variables"
blanchet@41157
  1225
blanchet@42939
  1226
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
blanchet@42939
  1227
                        explicit_apply hyp_ts concl_t facts =
blanchet@38282
  1228
  let
blanchet@41313
  1229
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42962
  1230
      translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1231
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42886
  1232
    val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
blanchet@42962
  1233
    val repair = repair_fact ctxt format nonmono_Ts type_sys sym_tab
blanchet@42682
  1234
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1235
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1236
    val helpers =
blanchet@42962
  1237
      repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
blanchet@42962
  1238
                       |> map repair
blanchet@42894
  1239
    val lavish_nonmono_Ts =
blanchet@42894
  1240
      if null nonmono_Ts orelse
blanchet@42894
  1241
         polymorphism_of_type_sys type_sys <> Polymorphic then
blanchet@42894
  1242
        nonmono_Ts
blanchet@42894
  1243
      else
blanchet@42894
  1244
        [TVar (("'a", 0), HOLogic.typeS)]
blanchet@42680
  1245
    val sym_decl_lines =
blanchet@42731
  1246
      (conjs, helpers @ facts)
blanchet@42886
  1247
      |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
blanchet@42956
  1248
      |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
blanchet@42956
  1249
                                          lavish_nonmono_Ts type_sys
blanchet@42881
  1250
    val helper_lines =
blanchet@42956
  1251
      0 upto length helpers - 1 ~~ helpers
blanchet@42956
  1252
      |> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
blanchet@42956
  1253
                                    type_sys)
blanchet@42956
  1254
      |> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
blanchet@42956
  1255
          else I)
blanchet@42522
  1256
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1257
       Flotter hack. *)
blanchet@38282
  1258
    val problem =
blanchet@42998
  1259
      [(explicit_declsN, sym_decl_lines),
blanchet@42956
  1260
       (factsN,
blanchet@42956
  1261
        map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
blanchet@42956
  1262
            (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1263
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1264
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42881
  1265
       (helpersN, helper_lines),
blanchet@42962
  1266
       (conjsN,
blanchet@42962
  1267
        map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
blanchet@42962
  1268
            conjs),
blanchet@42956
  1269
       (free_typesN,
blanchet@42956
  1270
        formula_lines_for_free_types format type_sys (facts @ conjs))]
blanchet@42543
  1271
    val problem =
blanchet@42561
  1272
      problem
blanchet@42998
  1273
      |> (if format = CNF_UEQ then filter_cnf_ueq_problem else I)
blanchet@42998
  1274
      |> (if is_format_typed format then
blanchet@42998
  1275
            declare_undeclared_syms_in_atp_problem type_decl_prefix
blanchet@42998
  1276
                                                   implicit_declsN
blanchet@42998
  1277
          else
blanchet@42998
  1278
            I)
blanchet@42646
  1279
    val (problem, pool) =
blanchet@42646
  1280
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@42881
  1281
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  1282
    val typed_helpers =
blanchet@42881
  1283
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  1284
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  1285
                     else NONE)
blanchet@42881
  1286
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  1287
                  ~~ helpers)
blanchet@42778
  1288
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1289
      if min_ary > 0 then
blanchet@42755
  1290
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1291
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1292
        | NONE => I
blanchet@42755
  1293
      else
blanchet@42755
  1294
        I
blanchet@38282
  1295
  in
blanchet@38282
  1296
    (problem,
blanchet@38282
  1297
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1298
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1299
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1300
     fact_names |> Vector.fromList,
blanchet@42881
  1301
     typed_helpers,
blanchet@42755
  1302
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1303
  end
blanchet@38282
  1304
blanchet@41313
  1305
(* FUDGE *)
blanchet@41313
  1306
val conj_weight = 0.0
blanchet@41770
  1307
val hyp_weight = 0.1
blanchet@41770
  1308
val fact_min_weight = 0.2
blanchet@41313
  1309
val fact_max_weight = 1.0
blanchet@42608
  1310
val type_info_default_weight = 0.8
blanchet@41313
  1311
blanchet@41313
  1312
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42998
  1313
  is_tptp_user_symbol s ? Symtab.default (s, weight)
blanchet@41313
  1314
  #> fold (add_term_weights weight) tms
blanchet@42577
  1315
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1316
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1317
  | add_problem_line_weights _ _ = I
blanchet@41313
  1318
blanchet@41313
  1319
fun add_conjectures_weights [] = I
blanchet@41313
  1320
  | add_conjectures_weights conjs =
blanchet@41313
  1321
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1322
      add_problem_line_weights conj_weight conj
blanchet@41313
  1323
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1324
    end
blanchet@41313
  1325
blanchet@41313
  1326
fun add_facts_weights facts =
blanchet@41313
  1327
  let
blanchet@41313
  1328
    val num_facts = length facts
blanchet@41313
  1329
    fun weight_of j =
blanchet@41313
  1330
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1331
                        / Real.fromInt num_facts
blanchet@41313
  1332
  in
blanchet@41313
  1333
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1334
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1335
  end
blanchet@41313
  1336
blanchet@41313
  1337
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1338
fun atp_problem_weights problem =
blanchet@42608
  1339
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1340
    Symtab.empty
blanchet@42608
  1341
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1342
    |> add_facts_weights (get factsN)
blanchet@42608
  1343
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42998
  1344
            [explicit_declsN, class_relsN, aritiesN]
blanchet@42608
  1345
    |> Symtab.dest
blanchet@42608
  1346
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1347
  end
blanchet@41313
  1348
blanchet@38282
  1349
end;