src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Fri May 27 10:30:07 2011 +0200 (2011-05-27)
changeset 42994 fe291ab75eb5
parent 42966 4e2d6c1e5392
child 42998 1c80902d0456
permissions -rw-r--r--
towards supporting non-simply-typed encodings for TFF and THF (for orthogonality and experiments)
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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 = "type_"
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val sym_decl_prefix = "sym_"
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val fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val class_rel_clause_prefix = "crel_";
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val arity_clause_prefix = "arity_"
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val tfree_prefix = "tfree_"
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val 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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fun aconn_fold pos f (ANot, [phi]) = f (Option.map not pos) phi
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  | aconn_fold pos f (AImplies, [phi1, phi2]) =
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    f (Option.map not pos) phi1 #> f pos phi2
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  | aconn_fold pos f (AAnd, phis) = fold (f pos) phis
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  | aconn_fold pos f (AOr, phis) = fold (f pos) phis
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  | aconn_fold _ f (_, phis) = fold (f NONE) phis
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fun aconn_map pos f (ANot, [phi]) = AConn (ANot, [f (Option.map not pos) phi])
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  | aconn_map pos f (AImplies, [phi1, phi2]) =
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    AConn (AImplies, [f (Option.map not pos) phi1, f pos phi2])
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  | aconn_map pos f (AAnd, phis) = AConn (AAnd, map (f pos) phis)
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  | aconn_map pos f (AOr, phis) = AConn (AOr, map (f pos) phis)
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  | aconn_map _ f (c, phis) = AConn (c, map (f NONE) phis)
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fun formula_fold pos f =
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  let
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    fun aux pos (AQuant (_, _, phi)) = aux pos phi
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      | aux pos (AConn conn) = aconn_fold pos aux conn
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      | aux pos (AAtom tm) = f pos tm
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  in aux pos end
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type translated_formula =
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  {name: string,
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   locality: locality,
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   kind: formula_kind,
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   combformula: (name, typ, combterm) formula,
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   atomic_types: typ list}
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fun update_combformula f ({name, locality, kind, combformula, atomic_types}
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                          : translated_formula) =
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  {name = name, locality = locality, kind = kind, combformula = f combformula,
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   atomic_types = atomic_types} : translated_formula
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fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
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(* 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_atp_variable s ? insert (op =) (name, NONE)
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  #> fold term_vars tms
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fun close_formula_universally phi = close_universally term_vars phi
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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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fun ho_type_from_fo_term higher_order pred_sym ary =
blanchet@42963
   315
  let
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   316
    fun to_atype ty =
blanchet@42963
   317
      AType ((make_simple_type (generic_mangled_type_name fst ty),
blanchet@42963
   318
              generic_mangled_type_name snd ty))
blanchet@42963
   319
    fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
blanchet@42994
   320
    fun to_fo 0 ty =
blanchet@42963
   321
        if pred_sym then AType (`I tptp_bool_type) else to_atype ty
blanchet@42994
   322
      | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
blanchet@42994
   323
    fun to_ho (ty as ATerm ((s, _), tys)) =
blanchet@42994
   324
      if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
blanchet@42994
   325
  in if higher_order then to_ho else to_fo ary end
blanchet@42963
   326
blanchet@42994
   327
fun mangled_type higher_order pred_sym ary =
blanchet@42994
   328
  ho_type_from_fo_term higher_order pred_sym ary o fo_term_from_typ higher_order
blanchet@42963
   329
blanchet@42994
   330
fun mangled_const_name T_args (s, s') =
blanchet@42963
   331
  let
blanchet@42994
   332
    val ty_args = map (fo_term_from_typ false) T_args
blanchet@42963
   333
    fun type_suffix f g =
blanchet@42963
   334
      fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42963
   335
                o generic_mangled_type_name f) ty_args ""
blanchet@42963
   336
  in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
blanchet@42542
   337
blanchet@42542
   338
val parse_mangled_ident =
blanchet@42542
   339
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   340
blanchet@42542
   341
fun parse_mangled_type x =
blanchet@42542
   342
  (parse_mangled_ident
blanchet@42542
   343
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   344
                    [] >> ATerm) x
blanchet@42542
   345
and parse_mangled_types x =
blanchet@42542
   346
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   347
blanchet@42542
   348
fun unmangled_type s =
blanchet@42542
   349
  s |> suffix ")" |> raw_explode
blanchet@42542
   350
    |> Scan.finite Symbol.stopper
blanchet@42542
   351
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   352
                                                quote s)) parse_mangled_type))
blanchet@42542
   353
    |> fst
blanchet@42542
   354
blanchet@42561
   355
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   356
fun unmangled_const s =
blanchet@42542
   357
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   358
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   359
  end
blanchet@42542
   360
blanchet@42994
   361
fun introduce_proxies format type_sys tm =
blanchet@42568
   362
  let
blanchet@42963
   363
    fun aux ary top_level (CombApp (tm1, tm2)) =
blanchet@42963
   364
        CombApp (aux (ary + 1) top_level tm1, aux 0 false tm2)
blanchet@42963
   365
      | aux ary top_level (CombConst (name as (s, s'), T, T_args)) =
blanchet@42570
   366
        (case proxify_const s of
blanchet@42568
   367
           SOME proxy_base =>
blanchet@42963
   368
           (* Proxies are not needed in THF, except for partially applied
blanchet@42963
   369
              equality since THF does not provide any syntax for it. *)
blanchet@42963
   370
           if top_level orelse
blanchet@42994
   371
              (is_setting_higher_order format type_sys andalso
blanchet@42994
   372
               (s <> "equal" orelse ary = 2)) then
blanchet@42568
   373
             (case s of
blanchet@42568
   374
                "c_False" => (tptp_false, s')
blanchet@42568
   375
              | "c_True" => (tptp_true, s')
blanchet@42568
   376
              | _ => name, [])
blanchet@42569
   377
           else
blanchet@42574
   378
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   379
          | NONE => (name, T_args))
blanchet@42574
   380
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42963
   381
      | aux _ _ tm = tm
blanchet@42963
   382
  in aux 0 true tm end
blanchet@42568
   383
blanchet@42994
   384
fun combformula_from_prop thy format type_sys eq_as_iff =
blanchet@38282
   385
  let
blanchet@42568
   386
    fun do_term bs t atomic_types =
blanchet@41140
   387
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42994
   388
      |>> (introduce_proxies format type_sys #> AAtom)
blanchet@42568
   389
      ||> union (op =) atomic_types
blanchet@38282
   390
    fun do_quant bs q s T t' =
blanchet@38518
   391
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   392
        do_formula ((s, T) :: bs) t'
blanchet@42562
   393
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   394
      end
blanchet@38282
   395
    and do_conn bs c t1 t2 =
blanchet@38282
   396
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   397
      #>> uncurry (mk_aconn c)
blanchet@38282
   398
    and do_formula bs t =
blanchet@38282
   399
      case t of
blanchet@42531
   400
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   401
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   402
        do_quant bs AForall s T t'
blanchet@38282
   403
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   404
        do_quant bs AExists s T t'
haftmann@38795
   405
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   406
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   407
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   408
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   409
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   410
      | _ => do_term bs t
blanchet@38282
   411
  in do_formula [] end
blanchet@38282
   412
blanchet@42750
   413
fun presimplify_term ctxt =
blanchet@42750
   414
  Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@42750
   415
  #> Meson.presimplify ctxt
blanchet@42750
   416
  #> prop_of
blanchet@38282
   417
wenzelm@41491
   418
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   419
fun conceal_bounds Ts t =
blanchet@38282
   420
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   421
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   422
fun reveal_bounds Ts =
blanchet@38282
   423
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   424
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   425
blanchet@42747
   426
fun extensionalize_term ctxt t =
blanchet@42747
   427
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42747
   428
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@42747
   429
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   430
  end
blanchet@38608
   431
blanchet@38282
   432
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   433
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   434
    if Meson.is_fol_term thy t then
blanchet@38491
   435
      t
blanchet@38491
   436
    else
blanchet@38491
   437
      let
blanchet@38491
   438
        fun aux Ts t =
blanchet@38491
   439
          case t of
blanchet@38491
   440
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   441
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   442
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   443
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   444
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   445
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   446
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   447
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   448
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   449
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   450
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   451
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   452
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   453
              $ t1 $ t2 =>
blanchet@38491
   454
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   455
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   456
                   t
blanchet@38491
   457
                 else
blanchet@38491
   458
                   t |> conceal_bounds Ts
blanchet@38491
   459
                     |> Envir.eta_contract
blanchet@38491
   460
                     |> cterm_of thy
blanchet@39890
   461
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   462
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   463
                     |> reveal_bounds Ts
blanchet@39370
   464
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   465
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   466
      handle THM _ =>
blanchet@38491
   467
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   468
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   469
             else HOLogic.true_const
blanchet@38491
   470
  end
blanchet@38282
   471
blanchet@38282
   472
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   473
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   474
fun freeze_term t =
blanchet@38282
   475
  let
blanchet@38282
   476
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   477
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   478
      | aux (Var ((s, i), T)) =
blanchet@38282
   479
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   480
      | aux t = t
blanchet@38282
   481
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   482
blanchet@40204
   483
(* making fact and conjecture formulas *)
blanchet@42994
   484
fun make_formula ctxt format type_sys eq_as_iff presimp name loc kind t =
blanchet@38282
   485
  let
wenzelm@42361
   486
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   487
    val t = t |> Envir.beta_eta_contract
blanchet@42944
   488
              |> transform_elim_prop
blanchet@41211
   489
              |> Object_Logic.atomize_term thy
blanchet@42563
   490
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   491
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@42742
   492
              |> Raw_Simplifier.rewrite_term thy
blanchet@42742
   493
                     (Meson.unfold_set_const_simps ctxt) []
blanchet@42747
   494
              |> extensionalize_term ctxt
blanchet@42750
   495
              |> presimp ? presimplify_term ctxt
blanchet@38282
   496
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   497
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   498
              |> kind <> Axiom ? freeze_term
blanchet@42962
   499
    val (combformula, atomic_types) =
blanchet@42994
   500
      combformula_from_prop thy format type_sys eq_as_iff t []
blanchet@38282
   501
  in
blanchet@42640
   502
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   503
     atomic_types = atomic_types}
blanchet@38282
   504
  end
blanchet@38282
   505
blanchet@42994
   506
fun make_fact ctxt format type_sys keep_trivial eq_as_iff presimp
blanchet@42994
   507
              ((name, loc), t) =
blanchet@42962
   508
  case (keep_trivial,
blanchet@42994
   509
        make_formula ctxt format type_sys eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   510
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   511
    NONE
blanchet@41990
   512
  | (_, formula) => SOME formula
blanchet@42561
   513
blanchet@42994
   514
fun make_conjecture ctxt format prem_kind type_sys ts =
blanchet@38613
   515
  let val last = length ts - 1 in
blanchet@42709
   516
    map2 (fn j => fn t =>
blanchet@42709
   517
             let
blanchet@42709
   518
               val (kind, maybe_negate) =
blanchet@42709
   519
                 if j = last then
blanchet@42709
   520
                   (Conjecture, I)
blanchet@42709
   521
                 else
blanchet@42709
   522
                   (prem_kind,
blanchet@42709
   523
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   524
                    else I)
blanchet@42709
   525
              in
blanchet@42994
   526
                t |> make_formula ctxt format type_sys true true
blanchet@42994
   527
                                  (string_of_int j) General kind
blanchet@42962
   528
                  |> maybe_negate
blanchet@42709
   529
              end)
blanchet@38613
   530
         (0 upto last) ts
blanchet@38613
   531
  end
blanchet@38282
   532
blanchet@42682
   533
(** Finite and infinite type inference **)
blanchet@42682
   534
blanchet@42886
   535
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
blanchet@42886
   536
  | deep_freeze_atyp T = T
blanchet@42886
   537
val deep_freeze_type = map_atyps deep_freeze_atyp
blanchet@42886
   538
blanchet@42886
   539
val type_instance = Sign.typ_instance o Proof_Context.theory_of
blanchet@42886
   540
blanchet@42682
   541
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   542
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   543
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   544
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   545
blanchet@42886
   546
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
blanchet@42886
   547
    exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
blanchet@42836
   548
  | should_encode_type _ _ All_Types _ = true
blanchet@42682
   549
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   550
  | should_encode_type _ _ _ _ = false
blanchet@42682
   551
blanchet@42837
   552
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
   553
                             should_predicate_on_var T =
blanchet@42878
   554
    (heaviness = Heavy orelse should_predicate_on_var ()) andalso
blanchet@42878
   555
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
   556
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
   557
blanchet@42836
   558
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42836
   559
    String.isPrefix bound_var_prefix s
blanchet@42836
   560
  | is_var_or_bound_var (CombVar _) = true
blanchet@42836
   561
  | is_var_or_bound_var _ = false
blanchet@42836
   562
blanchet@42829
   563
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
blanchet@42829
   564
blanchet@42829
   565
fun should_tag_with_type _ _ _ Top_Level _ _ = false
blanchet@42837
   566
  | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
blanchet@42837
   567
    (case heaviness of
blanchet@42837
   568
       Heavy => should_encode_type ctxt nonmono_Ts level T
blanchet@42837
   569
     | Light =>
blanchet@42836
   570
       case (site, is_var_or_bound_var u) of
blanchet@42836
   571
         (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
blanchet@42829
   572
       | _ => false)
blanchet@42829
   573
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
   574
blanchet@42994
   575
fun homogenized_type ctxt nonmono_Ts level =
blanchet@42994
   576
  let
blanchet@42994
   577
    val should_encode = should_encode_type ctxt nonmono_Ts level
blanchet@42994
   578
    fun homo 0 T = if should_encode T then T else homo_infinite_type
blanchet@42994
   579
      | homo ary (Type (@{type_name fun}, [T1, T2])) =
blanchet@42994
   580
        homo 0 T1 --> homo (ary - 1) T2
blanchet@42994
   581
      | homo _ _ = raise Fail "expected function type"
blanchet@42994
   582
  in homo end
blanchet@42682
   583
blanchet@42573
   584
(** "hBOOL" and "hAPP" **)
blanchet@41313
   585
blanchet@42574
   586
type sym_info =
blanchet@42563
   587
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   588
blanchet@42574
   589
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   590
  let
blanchet@42558
   591
    fun aux top_level tm =
blanchet@42558
   592
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   593
        (case head of
blanchet@42563
   594
           CombConst ((s, _), T, _) =>
blanchet@42558
   595
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   596
             I
blanchet@42558
   597
           else
blanchet@42563
   598
             let val ary = length args in
blanchet@42558
   599
               Symtab.map_default
blanchet@42558
   600
                   (s, {pred_sym = true,
blanchet@42563
   601
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   602
                        max_ary = 0, typ = SOME T})
blanchet@42563
   603
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   604
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   605
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   606
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   607
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   608
            end
blanchet@42558
   609
         | _ => I)
blanchet@42558
   610
        #> fold (aux false) args
blanchet@42558
   611
      end
blanchet@42558
   612
  in aux true end
blanchet@42674
   613
fun add_fact_syms_to_table explicit_apply =
blanchet@42834
   614
  fact_lift (formula_fold NONE (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   615
blanchet@42675
   616
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   617
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42966
   618
   (make_fixed_const predicator_name,
blanchet@42563
   619
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   620
  ([tptp_false, tptp_true]
blanchet@42563
   621
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   622
blanchet@42544
   623
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   624
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   625
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   626
blanchet@42558
   627
fun min_arity_of sym_tab s =
blanchet@42558
   628
  case Symtab.lookup sym_tab s of
blanchet@42574
   629
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   630
  | NONE =>
blanchet@42558
   631
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   632
      SOME s =>
blanchet@42570
   633
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42966
   634
        if s = predicator_name then 1
blanchet@42966
   635
        else if s = app_op_name then 2
blanchet@42966
   636
        else if s = type_pred_name then 1
blanchet@42557
   637
        else 0
blanchet@42547
   638
      end
blanchet@42544
   639
    | NONE => 0
blanchet@38282
   640
blanchet@38282
   641
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   642
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   643
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   644
   arguments and is used as a predicate. *)
blanchet@42558
   645
fun is_pred_sym sym_tab s =
blanchet@42558
   646
  case Symtab.lookup sym_tab s of
blanchet@42574
   647
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   648
    pred_sym andalso min_ary = max_ary
blanchet@42558
   649
  | NONE => false
blanchet@38282
   650
blanchet@42568
   651
val predicator_combconst =
blanchet@42966
   652
  CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
blanchet@42568
   653
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   654
blanchet@42568
   655
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   656
  case strip_combterm_comb tm of
blanchet@42542
   657
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   658
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   659
  | _ => predicator tm
blanchet@42542
   660
blanchet@42544
   661
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   662
blanchet@42544
   663
fun explicit_app arg head =
blanchet@42544
   664
  let
blanchet@42562
   665
    val head_T = combtyp_of head
blanchet@42693
   666
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   667
    val explicit_app =
blanchet@42966
   668
      CombConst (`make_fixed_const app_op_name, head_T --> head_T,
blanchet@42693
   669
                 [arg_T, res_T])
blanchet@42544
   670
  in list_app explicit_app [head, arg] end
blanchet@42544
   671
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   672
blanchet@42565
   673
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   674
  let
blanchet@42544
   675
    fun aux tm =
blanchet@42544
   676
      case strip_combterm_comb tm of
blanchet@42544
   677
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   678
        args |> map aux
blanchet@42557
   679
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   680
             |>> list_app head
blanchet@42544
   681
             |-> list_explicit_app
blanchet@42544
   682
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   683
  in aux end
blanchet@38282
   684
blanchet@42753
   685
fun chop_fun 0 T = ([], T)
blanchet@42753
   686
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
   687
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
   688
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
   689
blanchet@42780
   690
fun filter_type_args _ _ _ [] = []
blanchet@42780
   691
  | filter_type_args thy s arity T_args =
blanchet@42834
   692
    let
blanchet@42834
   693
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42966
   694
      val U = if s = app_op_name then
blanchet@42834
   695
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
   696
              else
blanchet@42834
   697
                s |> Sign.the_const_type thy
blanchet@42834
   698
    in
blanchet@42781
   699
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
   700
        [] => []
blanchet@42781
   701
      | res_U_vars =>
blanchet@42781
   702
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
   703
          U_args ~~ T_args
blanchet@42781
   704
          |> map_filter (fn (U, T) =>
blanchet@42781
   705
                            if member (op =) res_U_vars (dest_TVar U) then
blanchet@42781
   706
                              SOME T
blanchet@42781
   707
                            else
blanchet@42781
   708
                              NONE)
blanchet@42781
   709
        end
blanchet@42780
   710
    end
blanchet@42780
   711
    handle TYPE _ => T_args
blanchet@42753
   712
blanchet@42994
   713
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42753
   714
  let
blanchet@42753
   715
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
   716
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
   717
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
   718
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   719
        let
blanchet@42701
   720
          val level = level_of_type_sys type_sys
blanchet@42701
   721
          val (T, T_args) =
blanchet@42701
   722
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   723
               anyway, by distinguishing overloads only on the homogenized
blanchet@42837
   724
               result type. Don't do it for lightweight type systems, though,
blanchet@42837
   725
               since it leads to too many unsound proofs. *)
blanchet@42966
   726
            if s = const_prefix ^ app_op_name andalso
blanchet@42726
   727
               length T_args = 2 andalso
blanchet@42836
   728
               not (is_type_sys_virtually_sound type_sys) andalso
blanchet@42837
   729
               heaviness_of_type_sys type_sys = Heavy then
blanchet@42994
   730
              T_args |> map (homogenized_type ctxt nonmono_Ts level 0)
blanchet@42701
   731
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42831
   732
                                    (T --> T, tl Ts)
blanchet@42701
   733
                                  end)
blanchet@42701
   734
            else
blanchet@42701
   735
              (T, T_args)
blanchet@42701
   736
        in
blanchet@42701
   737
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   738
             NONE => (name, T_args)
blanchet@42701
   739
           | SOME s'' =>
blanchet@42753
   740
             let
blanchet@42753
   741
               val s'' = invert_const s''
blanchet@42831
   742
               fun filtered_T_args false = T_args
blanchet@42831
   743
                 | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@42753
   744
             in
blanchet@42701
   745
               case type_arg_policy type_sys s'' of
blanchet@42831
   746
                 Explicit_Type_Args drop_args =>
blanchet@42831
   747
                 (name, filtered_T_args drop_args)
blanchet@42831
   748
               | Mangled_Type_Args drop_args =>
blanchet@42994
   749
                 (mangled_const_name (filtered_T_args drop_args) name, [])
blanchet@42753
   750
               | No_Type_Args => (name, [])
blanchet@42701
   751
             end)
blanchet@42701
   752
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   753
        end
blanchet@42753
   754
      | aux _ tm = tm
blanchet@42753
   755
  in aux 0 end
blanchet@42573
   756
blanchet@42962
   757
fun repair_combterm ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42994
   758
  not (is_setting_higher_order format type_sys)
blanchet@42994
   759
  ? (introduce_explicit_apps_in_combterm sym_tab
blanchet@42994
   760
     #> introduce_predicators_in_combterm sym_tab)
blanchet@42994
   761
  #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
   762
fun repair_fact ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42701
   763
  update_combformula (formula_map
blanchet@42962
   764
      (repair_combterm ctxt format nonmono_Ts type_sys sym_tab))
blanchet@42573
   765
blanchet@42573
   766
(** Helper facts **)
blanchet@42573
   767
blanchet@42573
   768
fun ti_ti_helper_fact () =
blanchet@42573
   769
  let
blanchet@42573
   770
    fun var s = ATerm (`I s, [])
blanchet@42589
   771
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   772
  in
blanchet@42612
   773
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   774
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42879
   775
             |> close_formula_universally, simp_info, NONE)
blanchet@42573
   776
  end
blanchet@42573
   777
blanchet@42962
   778
fun helper_facts_for_sym ctxt format type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   779
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   780
    SOME mangled_s =>
blanchet@42573
   781
    let
blanchet@42573
   782
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   783
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42893
   784
      fun dub_and_inst c needs_fairly_sound (th, j) =
blanchet@42881
   785
        ((c ^ "_" ^ string_of_int j ^
blanchet@42893
   786
          (if needs_fairly_sound then typed_helper_suffix
blanchet@42881
   787
           else untyped_helper_suffix),
blanchet@42881
   788
          General),
blanchet@42573
   789
         let val t = th |> prop_of in
blanchet@42753
   790
           t |> ((case general_type_arg_policy type_sys of
blanchet@42753
   791
                    Mangled_Type_Args _ => true
blanchet@42753
   792
                  | _ => false) andalso
blanchet@42573
   793
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   794
                ? (case typ of
blanchet@42573
   795
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   796
                   | NONE => I)
blanchet@42573
   797
         end)
blanchet@42573
   798
      fun make_facts eq_as_iff =
blanchet@42994
   799
        map_filter (make_fact ctxt format type_sys false eq_as_iff false)
blanchet@42893
   800
      val fairly_sound = is_type_sys_fairly_sound type_sys
blanchet@42573
   801
    in
blanchet@42573
   802
      metis_helpers
blanchet@42894
   803
      |> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
blanchet@42573
   804
                  if metis_s <> unmangled_s orelse
blanchet@42894
   805
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
   806
                    []
blanchet@42573
   807
                  else
blanchet@42573
   808
                    ths ~~ (1 upto length ths)
blanchet@42893
   809
                    |> map (dub_and_inst mangled_s needs_fairly_sound)
blanchet@42893
   810
                    |> make_facts (not needs_fairly_sound))
blanchet@42573
   811
    end
blanchet@42573
   812
  | NONE => []
blanchet@42962
   813
fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
blanchet@42962
   814
  Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
blanchet@42962
   815
                  []
blanchet@42573
   816
blanchet@42994
   817
fun translate_atp_fact ctxt format type_sys keep_trivial =
blanchet@42994
   818
  `(make_fact ctxt format type_sys keep_trivial true true o apsnd prop_of)
blanchet@42573
   819
blanchet@42962
   820
fun translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t
blanchet@42962
   821
                       rich_facts =
blanchet@42573
   822
  let
blanchet@42573
   823
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   824
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   825
    val (facts, fact_names) =
blanchet@42573
   826
      rich_facts
blanchet@42573
   827
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   828
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   829
      |> ListPair.unzip
blanchet@42573
   830
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   831
       boost an ATP's performance (for some reason). *)
blanchet@42573
   832
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   833
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   834
    val all_ts = goal_t :: fact_ts
blanchet@42573
   835
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   836
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   837
    val tycons = type_consts_of_terms thy all_ts
blanchet@42994
   838
    val conjs =
blanchet@42994
   839
      hyp_ts @ [concl_t] |> make_conjecture ctxt format prem_kind type_sys
blanchet@42573
   840
    val (supers', arity_clauses) =
blanchet@42589
   841
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   842
      else make_arity_clauses thy tycons supers
blanchet@42573
   843
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   844
  in
blanchet@42573
   845
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   846
  end
blanchet@42573
   847
blanchet@42573
   848
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   849
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   850
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   851
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   852
blanchet@42573
   853
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   854
blanchet@42994
   855
fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
blanchet@42966
   856
  CombApp (CombConst (`make_fixed_const type_pred_name, T --> @{typ bool}, [T])
blanchet@42994
   857
           |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
blanchet@42573
   858
           tm)
blanchet@42573
   859
blanchet@42878
   860
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@42878
   861
  | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@42878
   862
    accum orelse (s = "equal" andalso member (op =) tms (ATerm (name, [])))
blanchet@42878
   863
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
blanchet@42878
   864
  | is_var_nonmonotonic_in_formula pos phi _ name =
blanchet@42878
   865
    formula_fold pos (var_occurs_positively_naked_in_term name) phi false
blanchet@42834
   866
blanchet@42994
   867
fun mk_const_aterm x T_args args =
blanchet@42994
   868
  ATerm (x, map (fo_term_from_typ false) T_args @ args)
blanchet@42994
   869
blanchet@42962
   870
fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
blanchet@42829
   871
  CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42994
   872
  |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
   873
  |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42829
   874
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42962
   875
and term_from_combterm ctxt format nonmono_Ts type_sys =
blanchet@42573
   876
  let
blanchet@42962
   877
    fun aux site u =
blanchet@42962
   878
      let
blanchet@42962
   879
        val (head, args) = strip_combterm_comb u
blanchet@42962
   880
        val (x as (s, _), T_args) =
blanchet@42962
   881
          case head of
blanchet@42962
   882
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42962
   883
          | CombVar (name, _) => (name, [])
blanchet@42962
   884
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42962
   885
        val arg_site = if site = Top_Level andalso s = "equal" then Eq_Arg
blanchet@42962
   886
                       else Elsewhere
blanchet@42994
   887
        val t = mk_const_aterm x T_args (map (aux arg_site) args)
blanchet@42962
   888
        val T = combtyp_of u
blanchet@42962
   889
      in
blanchet@42962
   890
        t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
blanchet@42962
   891
                tag_with_type ctxt format nonmono_Ts type_sys T
blanchet@42962
   892
              else
blanchet@42962
   893
                I)
blanchet@42962
   894
      end
blanchet@42962
   895
  in aux end
blanchet@42962
   896
and formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42962
   897
                             should_predicate_on_var =
blanchet@42829
   898
  let
blanchet@42994
   899
    val higher_order = is_setting_higher_order format type_sys
blanchet@42962
   900
    val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42573
   901
    val do_bound_type =
blanchet@42682
   902
      case type_sys of
blanchet@42722
   903
        Simple_Types level =>
blanchet@42994
   904
        homogenized_type ctxt nonmono_Ts level 0
blanchet@42994
   905
        #> mangled_type higher_order false 0 #> SOME
blanchet@42682
   906
      | _ => K NONE
blanchet@42878
   907
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@42834
   908
      if should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42878
   909
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@42834
   910
        CombVar (name, T)
blanchet@42994
   911
        |> type_pred_combterm ctxt nonmono_Ts type_sys T
blanchet@42878
   912
        |> do_term |> AAtom |> SOME
blanchet@42573
   913
      else
blanchet@42573
   914
        NONE
blanchet@42878
   915
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
   916
        let
blanchet@42878
   917
          val phi = phi |> do_formula pos
blanchet@42878
   918
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
   919
        in
blanchet@42834
   920
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
   921
                                        | SOME T => do_bound_type T)),
blanchet@42834
   922
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
   923
                      (map_filter
blanchet@42834
   924
                           (fn (_, NONE) => NONE
blanchet@42834
   925
                             | (s, SOME T) =>
blanchet@42878
   926
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
   927
                           xs)
blanchet@42834
   928
                      phi)
blanchet@42834
   929
        end
blanchet@42878
   930
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@42878
   931
      | do_formula _ (AAtom tm) = AAtom (do_term tm)
blanchet@42878
   932
  in do_formula o SOME end
blanchet@42573
   933
blanchet@42956
   934
fun bound_atomic_types format type_sys Ts =
blanchet@42727
   935
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42956
   936
                (atp_type_literals_for_types format type_sys Axiom Ts))
blanchet@42727
   937
blanchet@42956
   938
fun formula_for_fact ctxt format nonmono_Ts type_sys
blanchet@42573
   939
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   940
  combformula
blanchet@42727
   941
  |> close_combformula_universally
blanchet@42962
   942
  |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
   943
                              is_var_nonmonotonic_in_formula true
blanchet@42956
   944
  |> bound_atomic_types format type_sys atomic_types
blanchet@42573
   945
  |> close_formula_universally
blanchet@42573
   946
blanchet@42573
   947
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   948
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   949
   the remote provers might care. *)
blanchet@42956
   950
fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
blanchet@42640
   951
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   952
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   953
                     else string_of_int j ^ "_") ^
blanchet@42647
   954
           ascii_of name,
blanchet@42956
   955
           kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
blanchet@42879
   956
           case locality of
blanchet@42879
   957
             Intro => intro_info
blanchet@42879
   958
           | Elim => elim_info
blanchet@42879
   959
           | Simp => simp_info
blanchet@42879
   960
           | _ => NONE)
blanchet@42573
   961
blanchet@42939
   962
fun formula_line_for_class_rel_clause
blanchet@42939
   963
        (ClassRelClause {name, subclass, superclass, ...}) =
blanchet@42573
   964
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   965
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   966
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   967
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42879
   968
             |> close_formula_universally, intro_info, NONE)
blanchet@42573
   969
  end
blanchet@42573
   970
blanchet@42573
   971
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   972
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   973
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   974
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   975
blanchet@42939
   976
fun formula_line_for_arity_clause
blanchet@42939
   977
        (ArityClause {name, prem_lits, concl_lits, ...}) =
blanchet@42577
   978
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   979
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42895
   980
                          o fo_literal_from_arity_literal) prem_lits)
blanchet@42573
   981
                    (formula_from_fo_literal
blanchet@42895
   982
                         (fo_literal_from_arity_literal concl_lits))
blanchet@42879
   983
           |> close_formula_universally, intro_info, NONE)
blanchet@42573
   984
blanchet@42962
   985
fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
blanchet@42573
   986
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   987
  Formula (conjecture_prefix ^ name, kind,
blanchet@42962
   988
           formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42939
   989
               is_var_nonmonotonic_in_formula false
blanchet@42939
   990
               (close_combformula_universally combformula)
blanchet@42573
   991
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   992
blanchet@42956
   993
fun free_type_literals format type_sys
blanchet@42956
   994
                       ({atomic_types, ...} : translated_formula) =
blanchet@42956
   995
  atomic_types |> atp_type_literals_for_types format type_sys Conjecture
blanchet@42573
   996
               |> map fo_literal_from_type_literal
blanchet@42573
   997
blanchet@42573
   998
fun formula_line_for_free_type j lit =
blanchet@42577
   999
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
  1000
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42956
  1001
fun formula_lines_for_free_types format type_sys facts =
blanchet@42573
  1002
  let
blanchet@42956
  1003
    val litss = map (free_type_literals format type_sys) facts
blanchet@42573
  1004
    val lits = fold (union (op =)) litss []
blanchet@42573
  1005
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
  1006
blanchet@42573
  1007
(** Symbol declarations **)
blanchet@42544
  1008
blanchet@42886
  1009
fun insert_type ctxt get_T x xs =
blanchet@42677
  1010
  let val T = get_T x in
blanchet@42886
  1011
    if exists (curry (type_instance ctxt) T o get_T) xs then xs
blanchet@42886
  1012
    else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
blanchet@42677
  1013
  end
blanchet@42677
  1014
blanchet@42574
  1015
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
  1016
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42753
  1017
  not (String.isPrefix tptp_special_prefix s) andalso
blanchet@42894
  1018
  (case type_sys of
blanchet@42894
  1019
     Simple_Types _ => true
blanchet@42894
  1020
   | Tags (_, _, Light) => true
blanchet@42894
  1021
   | _ => not pred_sym)
blanchet@38282
  1022
blanchet@42886
  1023
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
  1024
  let
blanchet@42698
  1025
    fun add_combterm in_conj tm =
blanchet@42574
  1026
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
  1027
        (case head of
blanchet@42574
  1028
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
  1029
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
  1030
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
  1031
               Symtab.map_default (s, [])
blanchet@42886
  1032
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
  1033
                                         in_conj))
blanchet@42574
  1034
             else
blanchet@42574
  1035
               I
blanchet@42574
  1036
           end
blanchet@42574
  1037
         | _ => I)
blanchet@42698
  1038
        #> fold (add_combterm in_conj) args
blanchet@42574
  1039
      end
blanchet@42698
  1040
    fun add_fact in_conj =
blanchet@42834
  1041
      fact_lift (formula_fold NONE (K (add_combterm in_conj)))
blanchet@42698
  1042
  in
blanchet@42698
  1043
    Symtab.empty
blanchet@42698
  1044
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
  1045
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
  1046
  end
blanchet@42533
  1047
blanchet@42886
  1048
(* These types witness that the type classes they belong to allow infinite
blanchet@42886
  1049
   models and hence that any types with these type classes is monotonic. *)
blanchet@42886
  1050
val known_infinite_types = [@{typ nat}, @{typ int}, @{typ "nat => bool"}]
blanchet@42886
  1051
blanchet@42685
  1052
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  1053
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42886
  1054
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
blanchet@42829
  1055
  | add_combterm_nonmonotonic_types ctxt level _
blanchet@42680
  1056
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
  1057
                  tm2)) =
blanchet@42680
  1058
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
  1059
     (case level of
blanchet@42886
  1060
        Nonmonotonic_Types =>
blanchet@42886
  1061
        not (is_type_surely_infinite ctxt known_infinite_types T)
blanchet@42829
  1062
      | Finite_Types => is_type_surely_finite ctxt T
blanchet@42886
  1063
      | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
blanchet@42829
  1064
  | add_combterm_nonmonotonic_types _ _ _ _ = I
blanchet@42829
  1065
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
blanchet@42829
  1066
                                            : translated_formula) =
blanchet@42834
  1067
  formula_fold (SOME (kind <> Conjecture))
blanchet@42829
  1068
               (add_combterm_nonmonotonic_types ctxt level) combformula
blanchet@42886
  1069
fun nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42829
  1070
  let val level = level_of_type_sys type_sys in
blanchet@42886
  1071
    if level = Nonmonotonic_Types orelse level = Finite_Types then
blanchet@42886
  1072
      [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
blanchet@42886
  1073
         (* We must add "bool" in case the helper "True_or_False" is added
blanchet@42886
  1074
            later. In addition, several places in the code rely on the list of
blanchet@42886
  1075
            nonmonotonic types not being empty. *)
blanchet@42886
  1076
         |> insert_type ctxt I @{typ bool}
blanchet@42886
  1077
    else
blanchet@42886
  1078
      []
blanchet@42829
  1079
  end
blanchet@42677
  1080
blanchet@42994
  1081
fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
blanchet@42994
  1082
                      (s', T_args, T, pred_sym, ary, _) =
blanchet@42994
  1083
  let
blanchet@42994
  1084
    val (higher_order, T_arg_Ts, level) =
blanchet@42994
  1085
      case type_sys of
blanchet@42994
  1086
        Simple_Types level => (format = THF, [], level)
blanchet@42994
  1087
      | _ => (false, replicate (length T_args) homo_infinite_type, No_Types)
blanchet@42994
  1088
  in
blanchet@42994
  1089
    Decl (type_decl_prefix ^ s, (s, s'),
blanchet@42994
  1090
          (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
blanchet@42994
  1091
          |> mangled_type higher_order pred_sym (length T_arg_Ts + ary))
blanchet@42994
  1092
  end
blanchet@42579
  1093
blanchet@42592
  1094
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
  1095
blanchet@42956
  1096
fun formula_line_for_pred_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1097
                                   n s j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1098
  let
blanchet@42709
  1099
    val (kind, maybe_negate) =
blanchet@42709
  1100
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1101
      else (Axiom, I)
blanchet@42753
  1102
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42579
  1103
    val bound_names =
blanchet@42579
  1104
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1105
    val bounds =
blanchet@42579
  1106
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
  1107
    val bound_Ts =
blanchet@42592
  1108
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
  1109
                             else NONE)
blanchet@42579
  1110
  in
blanchet@42612
  1111
    Formula (sym_decl_prefix ^ s ^
blanchet@42709
  1112
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1113
             CombConst ((s, s'), T, T_args)
blanchet@42829
  1114
             |> fold (curry (CombApp o swap)) bounds
blanchet@42994
  1115
             |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
blanchet@42963
  1116
             |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42962
  1117
             |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
  1118
                                         (K (K (K (K true)))) true
blanchet@42956
  1119
             |> n > 1 ? bound_atomic_types format type_sys (atyps_of T)
blanchet@42709
  1120
             |> close_formula_universally
blanchet@42709
  1121
             |> maybe_negate,
blanchet@42879
  1122
             intro_info, NONE)
blanchet@42579
  1123
  end
blanchet@42579
  1124
blanchet@42956
  1125
fun formula_lines_for_tag_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1126
        n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1127
  let
blanchet@42829
  1128
    val ident_base =
blanchet@42829
  1129
      sym_decl_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1130
    val (kind, maybe_negate) =
blanchet@42852
  1131
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1132
      else (Axiom, I)
blanchet@42829
  1133
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1134
    val bound_names =
blanchet@42829
  1135
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1136
    val bounds = bound_names |> map (fn name => ATerm (name, []))
blanchet@42994
  1137
    val cst = mk_const_aterm (s, s') T_args
blanchet@42830
  1138
    val atomic_Ts = atyps_of T
blanchet@42834
  1139
    fun eq tms =
blanchet@42834
  1140
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@42834
  1141
       else AAtom (ATerm (`I "equal", tms)))
blanchet@42956
  1142
      |> bound_atomic_types format type_sys atomic_Ts
blanchet@42830
  1143
      |> close_formula_universally
blanchet@42852
  1144
      |> maybe_negate
blanchet@42836
  1145
    val should_encode = should_encode_type ctxt nonmono_Ts All_Types
blanchet@42962
  1146
    val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
blanchet@42829
  1147
    val add_formula_for_res =
blanchet@42829
  1148
      if should_encode res_T then
blanchet@42852
  1149
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42994
  1150
                       eq [tag_with res_T (cst bounds), cst bounds],
blanchet@42879
  1151
                       simp_info, NONE))
blanchet@42829
  1152
      else
blanchet@42829
  1153
        I
blanchet@42829
  1154
    fun add_formula_for_arg k =
blanchet@42829
  1155
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1156
        if should_encode arg_T then
blanchet@42829
  1157
          case chop k bounds of
blanchet@42829
  1158
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1159
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42994
  1160
                           eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
blanchet@42994
  1161
                               cst bounds],
blanchet@42879
  1162
                           simp_info, NONE))
blanchet@42829
  1163
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1164
        else
blanchet@42829
  1165
          I
blanchet@42829
  1166
      end
blanchet@42829
  1167
  in
blanchet@42834
  1168
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1169
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1170
  end
blanchet@42829
  1171
blanchet@42836
  1172
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1173
blanchet@42956
  1174
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1175
                                (s, decls) =
blanchet@42994
  1176
  (if member (op =) [TFF, THF] format then
blanchet@42994
  1177
     decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
blanchet@42994
  1178
   else
blanchet@42994
  1179
     []) @
blanchet@42994
  1180
  (case type_sys of
blanchet@42994
  1181
     Simple_Types _ => []
blanchet@42994
  1182
   | Preds _ =>
blanchet@42994
  1183
     let
blanchet@42994
  1184
       val decls =
blanchet@42994
  1185
         case decls of
blanchet@42994
  1186
           decl :: (decls' as _ :: _) =>
blanchet@42994
  1187
           let val T = result_type_of_decl decl in
blanchet@42994
  1188
             if forall (curry (type_instance ctxt o swap) T
blanchet@42994
  1189
                        o result_type_of_decl) decls' then
blanchet@42994
  1190
               [decl]
blanchet@42994
  1191
             else
blanchet@42994
  1192
               decls
blanchet@42994
  1193
           end
blanchet@42994
  1194
         | _ => decls
blanchet@42994
  1195
       val n = length decls
blanchet@42994
  1196
       val decls =
blanchet@42994
  1197
         decls
blanchet@42994
  1198
         |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
blanchet@42994
  1199
                    o result_type_of_decl)
blanchet@42994
  1200
     in
blanchet@42994
  1201
       (0 upto length decls - 1, decls)
blanchet@42994
  1202
       |-> map2 (formula_line_for_pred_sym_decl ctxt format conj_sym_kind
blanchet@42994
  1203
                                                nonmono_Ts type_sys n s)
blanchet@42994
  1204
     end
blanchet@42994
  1205
   | Tags (_, _, heaviness) =>
blanchet@42994
  1206
     (case heaviness of
blanchet@42994
  1207
        Heavy => []
blanchet@42994
  1208
      | Light =>
blanchet@42994
  1209
        let val n = length decls in
blanchet@42994
  1210
          (0 upto n - 1 ~~ decls)
blanchet@42994
  1211
          |> maps (formula_lines_for_tag_sym_decl ctxt format conj_sym_kind
blanchet@42994
  1212
                                                  nonmono_Ts type_sys n s)
blanchet@42994
  1213
        end))
blanchet@42579
  1214
blanchet@42956
  1215
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@42956
  1216
                                     type_sys sym_decl_tab =
blanchet@42956
  1217
  Symtab.fold_rev
blanchet@42956
  1218
      (append o problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
blanchet@42956
  1219
                                            type_sys)
blanchet@42956
  1220
      sym_decl_tab []
blanchet@42543
  1221
blanchet@42963
  1222
fun add_simple_types_in_type (AFun (ty1, ty2)) =
blanchet@42963
  1223
    fold add_simple_types_in_type [ty1, ty2]
blanchet@42963
  1224
  | add_simple_types_in_type (AType name) = insert (op =) name
blanchet@42963
  1225
blanchet@42962
  1226
fun add_simple_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42963
  1227
    fold add_simple_types_in_type (map_filter snd xs)
blanchet@42963
  1228
    #> add_simple_types_in_formula phi
blanchet@42962
  1229
  | add_simple_types_in_formula (AConn (_, phis)) =
blanchet@42962
  1230
    fold add_simple_types_in_formula phis
blanchet@42962
  1231
  | add_simple_types_in_formula (AAtom _) = I
blanchet@42539
  1232
blanchet@42963
  1233
fun add_simple_types_in_problem_line (Decl (_, _, ty)) =
blanchet@42963
  1234
    add_simple_types_in_type ty
blanchet@42962
  1235
  | add_simple_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42962
  1236
    add_simple_types_in_formula phi
blanchet@42543
  1237
blanchet@42962
  1238
fun simple_types_in_problem problem =
blanchet@42962
  1239
  fold (fold add_simple_types_in_problem_line o snd) problem []
blanchet@42962
  1240
  |> filter_out (String.isPrefix tptp_special_prefix o fst)
blanchet@42543
  1241
blanchet@42962
  1242
fun decl_line_for_simple_type (s, s') =
blanchet@42963
  1243
  Decl (type_decl_prefix ^ s, (s, s'), AType (`I tptp_type_of_types))
blanchet@42543
  1244
blanchet@42837
  1245
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
blanchet@42831
  1246
    level = Nonmonotonic_Types orelse level = Finite_Types
blanchet@42831
  1247
  | should_add_ti_ti_helper _ = false
blanchet@42831
  1248
blanchet@42939
  1249
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  1250
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  1251
    if heading = needle then j
blanchet@42939
  1252
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  1253
blanchet@42543
  1254
val type_declsN = "Types"
blanchet@42544
  1255
val sym_declsN = "Symbol types"
blanchet@41157
  1256
val factsN = "Relevant facts"
blanchet@41157
  1257
val class_relsN = "Class relationships"
blanchet@42543
  1258
val aritiesN = "Arities"
blanchet@41157
  1259
val helpersN = "Helper facts"
blanchet@41157
  1260
val conjsN = "Conjectures"
blanchet@41313
  1261
val free_typesN = "Type variables"
blanchet@41157
  1262
blanchet@42939
  1263
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
blanchet@42939
  1264
                        explicit_apply hyp_ts concl_t facts =
blanchet@38282
  1265
  let
blanchet@41313
  1266
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42962
  1267
      translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1268
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42886
  1269
    val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
blanchet@42962
  1270
    val repair = repair_fact ctxt format nonmono_Ts type_sys sym_tab
blanchet@42682
  1271
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1272
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1273
    val helpers =
blanchet@42962
  1274
      repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
blanchet@42962
  1275
                       |> map repair
blanchet@42894
  1276
    val lavish_nonmono_Ts =
blanchet@42894
  1277
      if null nonmono_Ts orelse
blanchet@42894
  1278
         polymorphism_of_type_sys type_sys <> Polymorphic then
blanchet@42894
  1279
        nonmono_Ts
blanchet@42894
  1280
      else
blanchet@42894
  1281
        [TVar (("'a", 0), HOLogic.typeS)]
blanchet@42680
  1282
    val sym_decl_lines =
blanchet@42731
  1283
      (conjs, helpers @ facts)
blanchet@42886
  1284
      |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
blanchet@42956
  1285
      |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
blanchet@42956
  1286
                                          lavish_nonmono_Ts type_sys
blanchet@42881
  1287
    val helper_lines =
blanchet@42956
  1288
      0 upto length helpers - 1 ~~ helpers
blanchet@42956
  1289
      |> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
blanchet@42956
  1290
                                    type_sys)
blanchet@42956
  1291
      |> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
blanchet@42956
  1292
          else I)
blanchet@42522
  1293
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1294
       Flotter hack. *)
blanchet@38282
  1295
    val problem =
blanchet@42561
  1296
      [(sym_declsN, sym_decl_lines),
blanchet@42956
  1297
       (factsN,
blanchet@42956
  1298
        map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
blanchet@42956
  1299
            (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1300
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1301
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42881
  1302
       (helpersN, helper_lines),
blanchet@42962
  1303
       (conjsN,
blanchet@42962
  1304
        map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
blanchet@42962
  1305
            conjs),
blanchet@42956
  1306
       (free_typesN,
blanchet@42956
  1307
        formula_lines_for_free_types format type_sys (facts @ conjs))]
blanchet@42543
  1308
    val problem =
blanchet@42561
  1309
      problem
blanchet@42682
  1310
      |> (case type_sys of
blanchet@42722
  1311
            Simple_Types _ =>
blanchet@42962
  1312
            cons (type_declsN, problem |> simple_types_in_problem
blanchet@42962
  1313
                                       |> map decl_line_for_simple_type)
blanchet@42682
  1314
          | _ => I)
blanchet@42939
  1315
    val problem =
blanchet@42939
  1316
      problem |> (if format = CNF_UEQ then filter_cnf_ueq_problem else I)
blanchet@42646
  1317
    val (problem, pool) =
blanchet@42646
  1318
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@42881
  1319
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  1320
    val typed_helpers =
blanchet@42881
  1321
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  1322
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  1323
                     else NONE)
blanchet@42881
  1324
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  1325
                  ~~ helpers)
blanchet@42778
  1326
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1327
      if min_ary > 0 then
blanchet@42755
  1328
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1329
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1330
        | NONE => I
blanchet@42755
  1331
      else
blanchet@42755
  1332
        I
blanchet@38282
  1333
  in
blanchet@38282
  1334
    (problem,
blanchet@38282
  1335
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1336
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1337
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1338
     fact_names |> Vector.fromList,
blanchet@42881
  1339
     typed_helpers,
blanchet@42755
  1340
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1341
  end
blanchet@38282
  1342
blanchet@41313
  1343
(* FUDGE *)
blanchet@41313
  1344
val conj_weight = 0.0
blanchet@41770
  1345
val hyp_weight = 0.1
blanchet@41770
  1346
val fact_min_weight = 0.2
blanchet@41313
  1347
val fact_max_weight = 1.0
blanchet@42608
  1348
val type_info_default_weight = 0.8
blanchet@41313
  1349
blanchet@41313
  1350
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42734
  1351
  (not (is_atp_variable s) andalso s <> "equal" andalso
blanchet@42753
  1352
   not (String.isPrefix tptp_special_prefix s)) ? Symtab.default (s, weight)
blanchet@41313
  1353
  #> fold (add_term_weights weight) tms
blanchet@42577
  1354
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1355
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1356
  | add_problem_line_weights _ _ = I
blanchet@41313
  1357
blanchet@41313
  1358
fun add_conjectures_weights [] = I
blanchet@41313
  1359
  | add_conjectures_weights conjs =
blanchet@41313
  1360
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1361
      add_problem_line_weights conj_weight conj
blanchet@41313
  1362
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1363
    end
blanchet@41313
  1364
blanchet@41313
  1365
fun add_facts_weights facts =
blanchet@41313
  1366
  let
blanchet@41313
  1367
    val num_facts = length facts
blanchet@41313
  1368
    fun weight_of j =
blanchet@41313
  1369
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1370
                        / Real.fromInt num_facts
blanchet@41313
  1371
  in
blanchet@41313
  1372
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1373
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1374
  end
blanchet@41313
  1375
blanchet@41313
  1376
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1377
fun atp_problem_weights problem =
blanchet@42608
  1378
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1379
    Symtab.empty
blanchet@42608
  1380
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1381
    |> add_facts_weights (get factsN)
blanchet@42608
  1382
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1383
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1384
    |> Symtab.dest
blanchet@42608
  1385
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1386
  end
blanchet@41313
  1387
blanchet@38282
  1388
end;