src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Thu May 12 15:29:19 2011 +0200 (2011-05-12)
changeset 42747 f132d13fcf75
parent 42742 369dfc819056
child 42750 c8b1d9ee3758
permissions -rw-r--r--
use the same code for extensionalization in Metis and Sledgehammer and generalize that code so that it gracefully handles negations (e.g. negated conjecture), formulas of the form (%x. t) = u, etc.
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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 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_system =
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    Simple_Types of type_level |
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    Preds of polymorphism * type_level |
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    Tags of polymorphism * type_level
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  type translated_formula
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  val readable_names : bool Config.T
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  val fact_prefix : string
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  val conjecture_prefix : string
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  val predicator_base : string
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  val explicit_app_base : string
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  val type_pred_base : string
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  val tff_type_prefix : string
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  val type_sys_from_string : string -> type_system
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  val polymorphism_of_type_sys : type_system -> polymorphism
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  val level_of_type_sys : type_system -> type_level
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  val is_type_sys_virtually_sound : type_system -> bool
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  val is_type_sys_fairly_sound : type_system -> bool
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  val num_atp_type_args : theory -> type_system -> string -> int
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  val unmangled_const : string -> string * string fo_term list
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  val translate_atp_fact :
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    Proof.context -> bool -> (string * locality) * thm
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    -> translated_formula option * ((string * locality) * thm)
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  val prepare_atp_problem :
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    Proof.context -> formula_kind -> formula_kind -> type_system -> bool
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    -> term list -> term
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    -> (translated_formula option * ((string * 'a) * thm)) list
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    -> string problem * string Symtab.table * int * int
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       * (string * 'a) list vector
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  val atp_problem_weights : string problem -> (string * real) list
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end;
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structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
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struct
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open ATP_Problem
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open Metis_Translate
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open Sledgehammer_Util
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open Sledgehammer_Filter
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(* experimental *)
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val generate_useful_info = false
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(* Readable names are often much shorter, especially if types are mangled in
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   names. Also, the logic for generating legal SNARK sort names is only
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   implemented for readable names. Finally, readable names are, well, more
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   readable. For these reason, they are enabled by default. *)
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val readable_names =
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  Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
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val type_decl_prefix = "type_"
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val sym_decl_prefix = "sym_"
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val fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val class_rel_clause_prefix = "crel_";
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val arity_clause_prefix = "arity_"
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val tfree_prefix = "tfree_"
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val predicator_base = "hBOOL"
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val explicit_app_base = "hAPP"
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val type_pred_base = "is"
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val tff_type_prefix = "ty_"
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fun make_tff_type s = tff_type_prefix ^ ascii_of s
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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datatype type_level =
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  All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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datatype type_system =
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  Simple_Types of type_level |
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  Preds of polymorphism * type_level |
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  Tags of polymorphism * type_level
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fun 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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  |> (fn (poly, (level, core)) =>
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         case (core, (poly, level)) of
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           ("simple_types", (NONE, level)) => Simple_Types level
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         | ("preds", (SOME poly, level)) => Preds (poly, level)
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         | ("tags", (SOME poly, level)) => Tags (poly, level)
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         | ("args", (SOME poly, All_Types (* naja *))) =>
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           Preds (poly, Const_Arg_Types)
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         | ("erased", (NONE, All_Types (* naja *))) =>
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           Preds (Polymorphic, No_Types)
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         | _ => 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 is_type_level_virtually_sound level =
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  level = All_Types orelse level = Nonmonotonic_Types
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val is_type_sys_virtually_sound =
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  is_type_level_virtually_sound o level_of_type_sys
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fun is_type_level_fairly_sound level =
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  is_type_level_virtually_sound level orelse level = Finite_Types
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val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
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fun is_type_level_partial level =
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  level = Nonmonotonic_Types orelse level = Finite_Types
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fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
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  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
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  | formula_map f (AAtom tm) = AAtom (f tm)
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fun formula_fold pos f =
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  let
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    fun aux pos (AQuant (_, _, phi)) = aux pos phi
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      | aux pos (AConn (ANot, [phi])) = aux (Option.map not pos) phi
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      | aux pos (AConn (AImplies, [phi1, phi2])) =
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        aux (Option.map not pos) phi1 #> aux pos phi2
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      | aux pos (AConn (AAnd, phis)) = fold (aux pos) phis
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      | aux pos (AConn (AOr, phis)) = fold (aux pos) phis
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      | aux _ (AConn (_, phis)) = fold (aux NONE) phis
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      | aux pos (AAtom tm) = f pos tm
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  in aux (SOME pos) end
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type translated_formula =
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  {name: string,
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   locality: locality,
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   kind: formula_kind,
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   combformula: (name, typ, combterm) formula,
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   atomic_types: typ list}
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fun update_combformula f ({name, locality, kind, combformula, atomic_types}
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                          : translated_formula) =
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  {name = name, locality = locality, kind = kind, combformula = f combformula,
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   atomic_types = atomic_types} : translated_formula
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fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
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val boring_consts = [explicit_app_base, @{const_name Metis.fequal}]
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fun should_omit_type_args type_sys s =
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  s <> type_pred_base andalso s <> type_tag_name andalso
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  (s = @{const_name HOL.eq} orelse level_of_type_sys type_sys = No_Types orelse
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   (case type_sys of
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      Tags (_, All_Types) => true
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    | _ => polymorphism_of_type_sys type_sys <> Mangled_Monomorphic andalso
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           member (op =) boring_consts s))
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datatype type_arg_policy = No_Type_Args | Explicit_Type_Args | Mangled_Type_Args
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fun general_type_arg_policy type_sys =
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  if level_of_type_sys type_sys = No_Types then
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    No_Type_Args
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  else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
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    Mangled_Type_Args
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  else
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    Explicit_Type_Args
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fun type_arg_policy type_sys s =
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  if should_omit_type_args type_sys s then No_Type_Args
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  else general_type_arg_policy type_sys
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fun num_atp_type_args thy type_sys s =
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  if type_arg_policy type_sys s = Explicit_Type_Args then num_type_args thy s
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  else 0
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fun atp_type_literals_for_types type_sys kind Ts =
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  if level_of_type_sys type_sys = No_Types then
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    []
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  else
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    Ts |> type_literals_for_types
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       |> filter (fn TyLitVar _ => kind <> Conjecture
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                   | TyLitFree _ => kind = Conjecture)
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fun mk_anot phi = AConn (ANot, [phi])
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
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fun mk_aconns c phis =
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  let val (phis', phi') = split_last phis in
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    fold_rev (mk_aconn c) phis' phi'
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  end
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fun mk_ahorn [] phi = phi
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  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
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fun mk_aquant _ [] phi = phi
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  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
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    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
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  | mk_aquant q xs phi = AQuant (q, xs, phi)
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fun close_universally atom_vars phi =
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  let
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    fun formula_vars bounds (AQuant (_, xs, phi)) =
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        formula_vars (map fst xs @ bounds) phi
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      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
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      | formula_vars bounds (AAtom tm) =
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        union (op =) (atom_vars tm []
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                      |> filter_out (member (op =) bounds o fst))
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  in mk_aquant AForall (formula_vars [] phi []) phi end
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fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
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  | combterm_vars (CombConst _) = I
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  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
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fun close_combformula_universally phi = close_universally combterm_vars phi
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fun term_vars (ATerm (name as (s, _), tms)) =
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  is_atp_variable s ? insert (op =) (name, NONE)
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  #> fold term_vars tms
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fun close_formula_universally phi = close_universally term_vars phi
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fun fo_term_from_typ (Type (s, Ts)) =
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    ATerm (`make_fixed_type_const s, map fo_term_from_typ Ts)
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  | fo_term_from_typ (TFree (s, _)) =
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    ATerm (`make_fixed_type_var s, [])
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  | fo_term_from_typ (TVar ((x as (s, _)), _)) =
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    ATerm ((make_schematic_type_var x, s), [])
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(* This shouldn't clash with anything else. *)
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val mangled_type_sep = "\000"
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fun generic_mangled_type_name f (ATerm (name, [])) = f name
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  | generic_mangled_type_name f (ATerm (name, tys)) =
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    f name ^ "(" ^ commas (map (generic_mangled_type_name f) tys) ^ ")"
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val mangled_type_name =
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  fo_term_from_typ
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  #> (fn ty => (make_tff_type (generic_mangled_type_name fst ty),
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                generic_mangled_type_name snd ty))
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fun generic_mangled_type_suffix f g Ts =
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  fold_rev (curry (op ^) o g o prefix mangled_type_sep
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            o generic_mangled_type_name f) Ts ""
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fun mangled_const_name T_args (s, s') =
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  let val ty_args = map fo_term_from_typ T_args in
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    (s ^ generic_mangled_type_suffix fst ascii_of ty_args,
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     s' ^ generic_mangled_type_suffix snd I ty_args)
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  end
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val parse_mangled_ident =
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  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
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fun parse_mangled_type x =
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  (parse_mangled_ident
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   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
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                    [] >> ATerm) x
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and parse_mangled_types x =
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  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
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fun unmangled_type s =
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  s |> suffix ")" |> raw_explode
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    |> Scan.finite Symbol.stopper
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           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
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                                                quote s)) parse_mangled_type))
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    |> fst
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val unmangled_const_name = space_explode mangled_type_sep #> hd
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fun unmangled_const s =
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  let val ss = space_explode mangled_type_sep s in
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    (hd ss, map unmangled_type (tl ss))
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  end
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fun introduce_proxies tm =
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  let
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    fun aux top_level (CombApp (tm1, tm2)) =
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        CombApp (aux top_level tm1, aux false tm2)
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      | aux top_level (CombConst (name as (s, s'), T, T_args)) =
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        (case proxify_const s of
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           SOME proxy_base =>
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           if top_level then
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             (case s of
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                "c_False" => (tptp_false, s')
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              | "c_True" => (tptp_true, s')
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              | _ => name, [])
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           else
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             (proxy_base |>> prefix const_prefix, T_args)
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          | NONE => (name, T_args))
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        |> (fn (name, T_args) => CombConst (name, T, T_args))
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   316
      | aux _ tm = tm
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   317
  in aux true tm end
blanchet@42568
   318
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   319
fun combformula_from_prop thy eq_as_iff =
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   320
  let
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   321
    fun do_term bs t atomic_types =
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   322
      combterm_from_term thy bs (Envir.eta_contract t)
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   323
      |>> (introduce_proxies #> AAtom)
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   324
      ||> union (op =) atomic_types
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   325
    fun do_quant bs q s T t' =
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   326
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   327
        do_formula ((s, T) :: bs) t'
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   328
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
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   329
      end
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   330
    and do_conn bs c t1 t2 =
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   331
      do_formula bs t1 ##>> do_formula bs t2
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   332
      #>> uncurry (mk_aconn c)
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   333
    and do_formula bs t =
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   334
      case t of
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   335
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
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   336
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   337
        do_quant bs AForall s T t'
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   338
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   339
        do_quant bs AExists s T t'
haftmann@38795
   340
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   341
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   342
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   343
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
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   344
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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   345
      | _ => do_term bs t
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   346
  in do_formula [] end
blanchet@38282
   347
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   348
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
blanchet@38282
   349
wenzelm@41491
   350
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
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   351
fun conceal_bounds Ts t =
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   352
  subst_bounds (map (Free o apfst concealed_bound_name)
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   353
                    (0 upto length Ts - 1 ~~ Ts), t)
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   354
fun reveal_bounds Ts =
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   355
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   356
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   357
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   358
fun extensionalize_term ctxt t =
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   359
  let val thy = Proof_Context.theory_of ctxt in
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   360
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
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   361
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   362
  end
blanchet@38608
   363
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   364
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   365
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   366
    if Meson.is_fol_term thy t then
blanchet@38491
   367
      t
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   368
    else
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   369
      let
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   370
        fun aux Ts t =
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   371
          case t of
blanchet@38491
   372
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   373
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   374
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   375
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   376
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   377
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   378
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   379
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   380
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   381
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   382
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   383
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   384
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   385
              $ t1 $ t2 =>
blanchet@38491
   386
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   387
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   388
                   t
blanchet@38491
   389
                 else
blanchet@38491
   390
                   t |> conceal_bounds Ts
blanchet@38491
   391
                     |> Envir.eta_contract
blanchet@38491
   392
                     |> cterm_of thy
blanchet@39890
   393
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   394
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   395
                     |> reveal_bounds Ts
blanchet@39370
   396
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   397
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   398
      handle THM _ =>
blanchet@38491
   399
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   400
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   401
             else HOLogic.true_const
blanchet@38491
   402
  end
blanchet@38282
   403
blanchet@38282
   404
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   405
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   406
fun freeze_term t =
blanchet@38282
   407
  let
blanchet@38282
   408
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   409
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   410
      | aux (Var ((s, i), T)) =
blanchet@38282
   411
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   412
      | aux t = t
blanchet@38282
   413
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   414
blanchet@40204
   415
(* making fact and conjecture formulas *)
blanchet@42640
   416
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   417
  let
wenzelm@42361
   418
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   419
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   420
              |> transform_elim_term
blanchet@41211
   421
              |> Object_Logic.atomize_term thy
blanchet@42563
   422
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   423
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@42742
   424
              |> Raw_Simplifier.rewrite_term thy
blanchet@42742
   425
                     (Meson.unfold_set_const_simps ctxt) []
blanchet@42747
   426
              |> extensionalize_term ctxt
blanchet@38282
   427
              |> presimp ? presimplify_term thy
blanchet@38282
   428
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   429
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   430
              |> kind <> Axiom ? freeze_term
blanchet@42562
   431
    val (combformula, atomic_types) =
blanchet@42562
   432
      combformula_from_prop thy eq_as_iff t []
blanchet@38282
   433
  in
blanchet@42640
   434
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   435
     atomic_types = atomic_types}
blanchet@38282
   436
  end
blanchet@38282
   437
blanchet@42640
   438
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   439
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   440
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   441
    NONE
blanchet@41990
   442
  | (_, formula) => SOME formula
blanchet@42561
   443
blanchet@42709
   444
fun make_conjecture ctxt prem_kind ts =
blanchet@38613
   445
  let val last = length ts - 1 in
blanchet@42709
   446
    map2 (fn j => fn t =>
blanchet@42709
   447
             let
blanchet@42709
   448
               val (kind, maybe_negate) =
blanchet@42709
   449
                 if j = last then
blanchet@42709
   450
                   (Conjecture, I)
blanchet@42709
   451
                 else
blanchet@42709
   452
                   (prem_kind,
blanchet@42709
   453
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   454
                    else I)
blanchet@42709
   455
              in
blanchet@42709
   456
                make_formula ctxt true true (string_of_int j) Chained kind t
blanchet@42709
   457
                |> maybe_negate
blanchet@42709
   458
              end)
blanchet@38613
   459
         (0 upto last) ts
blanchet@38613
   460
  end
blanchet@38282
   461
blanchet@42682
   462
(** Finite and infinite type inference **)
blanchet@42682
   463
blanchet@42682
   464
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   465
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   466
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   467
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   468
blanchet@42682
   469
fun should_encode_type _ _ All_Types _ = true
blanchet@42682
   470
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   471
  | should_encode_type _ nonmono_Ts Nonmonotonic_Types T =
blanchet@42682
   472
    exists (curry Type.raw_instance T) nonmono_Ts
blanchet@42682
   473
  | should_encode_type _ _ _ _ = false
blanchet@42682
   474
blanchet@42682
   475
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level)) T =
blanchet@42682
   476
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   477
  | should_predicate_on_type _ _ _ _ = false
blanchet@42682
   478
blanchet@42682
   479
fun should_tag_with_type ctxt nonmono_Ts (Tags (_, level)) T =
blanchet@42682
   480
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   481
  | should_tag_with_type _ _ _ _ = false
blanchet@42682
   482
blanchet@42682
   483
val homo_infinite_T = @{typ ind} (* any infinite type *)
blanchet@42682
   484
blanchet@42682
   485
fun homogenized_type ctxt nonmono_Ts level T =
blanchet@42682
   486
  if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
blanchet@42682
   487
blanchet@42573
   488
(** "hBOOL" and "hAPP" **)
blanchet@41313
   489
blanchet@42574
   490
type sym_info =
blanchet@42563
   491
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   492
blanchet@42574
   493
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   494
  let
blanchet@42558
   495
    fun aux top_level tm =
blanchet@42558
   496
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   497
        (case head of
blanchet@42563
   498
           CombConst ((s, _), T, _) =>
blanchet@42558
   499
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   500
             I
blanchet@42558
   501
           else
blanchet@42563
   502
             let val ary = length args in
blanchet@42558
   503
               Symtab.map_default
blanchet@42558
   504
                   (s, {pred_sym = true,
blanchet@42563
   505
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   506
                        max_ary = 0, typ = SOME T})
blanchet@42563
   507
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   508
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   509
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   510
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   511
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   512
            end
blanchet@42558
   513
         | _ => I)
blanchet@42558
   514
        #> fold (aux false) args
blanchet@42558
   515
      end
blanchet@42558
   516
  in aux true end
blanchet@42674
   517
fun add_fact_syms_to_table explicit_apply =
blanchet@42680
   518
  fact_lift (formula_fold true (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   519
blanchet@42675
   520
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   521
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   522
   (make_fixed_const predicator_base,
blanchet@42563
   523
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   524
  ([tptp_false, tptp_true]
blanchet@42563
   525
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   526
blanchet@42544
   527
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   528
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   529
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   530
blanchet@42558
   531
fun min_arity_of sym_tab s =
blanchet@42558
   532
  case Symtab.lookup sym_tab s of
blanchet@42574
   533
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   534
  | NONE =>
blanchet@42558
   535
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   536
      SOME s =>
blanchet@42570
   537
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   538
        if s = predicator_base then 1
blanchet@42547
   539
        else if s = explicit_app_base then 2
blanchet@42547
   540
        else if s = type_pred_base then 1
blanchet@42557
   541
        else 0
blanchet@42547
   542
      end
blanchet@42544
   543
    | NONE => 0
blanchet@38282
   544
blanchet@38282
   545
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   546
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   547
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   548
   arguments and is used as a predicate. *)
blanchet@42558
   549
fun is_pred_sym sym_tab s =
blanchet@42558
   550
  case Symtab.lookup sym_tab s of
blanchet@42574
   551
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   552
    pred_sym andalso min_ary = max_ary
blanchet@42558
   553
  | NONE => false
blanchet@38282
   554
blanchet@42568
   555
val predicator_combconst =
blanchet@42568
   556
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   557
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   558
blanchet@42568
   559
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   560
  case strip_combterm_comb tm of
blanchet@42542
   561
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   562
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   563
  | _ => predicator tm
blanchet@42542
   564
blanchet@42544
   565
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   566
blanchet@42544
   567
fun explicit_app arg head =
blanchet@42544
   568
  let
blanchet@42562
   569
    val head_T = combtyp_of head
blanchet@42693
   570
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   571
    val explicit_app =
blanchet@42562
   572
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42693
   573
                 [arg_T, res_T])
blanchet@42544
   574
  in list_app explicit_app [head, arg] end
blanchet@42544
   575
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   576
blanchet@42565
   577
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   578
  let
blanchet@42544
   579
    fun aux tm =
blanchet@42544
   580
      case strip_combterm_comb tm of
blanchet@42544
   581
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   582
        args |> map aux
blanchet@42557
   583
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   584
             |>> list_app head
blanchet@42544
   585
             |-> list_explicit_app
blanchet@42544
   586
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   587
  in aux end
blanchet@38282
   588
blanchet@42701
   589
fun impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42573
   590
  let
blanchet@42573
   591
    fun aux (CombApp tmp) = CombApp (pairself aux tmp)
blanchet@42574
   592
      | aux (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   593
        let
blanchet@42701
   594
          val level = level_of_type_sys type_sys
blanchet@42701
   595
          val (T, T_args) =
blanchet@42701
   596
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   597
               anyway, by distinguishing overloads only on the homogenized
blanchet@42701
   598
               result type. *)
blanchet@42701
   599
            if s = const_prefix ^ explicit_app_base andalso
blanchet@42726
   600
               length T_args = 2 andalso
blanchet@42701
   601
               not (is_type_sys_virtually_sound type_sys) then
blanchet@42701
   602
              T_args |> map (homogenized_type ctxt nonmono_Ts level)
blanchet@42701
   603
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42701
   604
                                    (T --> T, tl Ts)
blanchet@42701
   605
                                  end)
blanchet@42701
   606
            else
blanchet@42701
   607
              (T, T_args)
blanchet@42701
   608
        in
blanchet@42701
   609
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   610
             NONE => (name, T_args)
blanchet@42701
   611
           | SOME s'' =>
blanchet@42701
   612
             let val s'' = invert_const s'' in
blanchet@42701
   613
               case type_arg_policy type_sys s'' of
blanchet@42701
   614
                 No_Type_Args => (name, [])
blanchet@42701
   615
               | Explicit_Type_Args => (name, T_args)
blanchet@42701
   616
               | Mangled_Type_Args => (mangled_const_name T_args name, [])
blanchet@42701
   617
             end)
blanchet@42701
   618
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   619
        end
blanchet@42573
   620
      | aux tm = tm
blanchet@42573
   621
  in aux end
blanchet@42573
   622
blanchet@42701
   623
fun repair_combterm ctxt nonmono_Ts type_sys sym_tab =
blanchet@42565
   624
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   625
  #> introduce_predicators_in_combterm sym_tab
blanchet@42701
   626
  #> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42701
   627
fun repair_fact ctxt nonmono_Ts type_sys sym_tab =
blanchet@42701
   628
  update_combformula (formula_map
blanchet@42701
   629
      (repair_combterm ctxt nonmono_Ts type_sys sym_tab))
blanchet@42573
   630
blanchet@42573
   631
(** Helper facts **)
blanchet@42573
   632
blanchet@42573
   633
fun ti_ti_helper_fact () =
blanchet@42573
   634
  let
blanchet@42573
   635
    fun var s = ATerm (`I s, [])
blanchet@42589
   636
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   637
  in
blanchet@42612
   638
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   639
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42573
   640
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   641
  end
blanchet@42573
   642
blanchet@42574
   643
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   644
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   645
    SOME mangled_s =>
blanchet@42573
   646
    let
blanchet@42573
   647
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   648
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42579
   649
      fun dub_and_inst c needs_some_types (th, j) =
blanchet@42579
   650
        ((c ^ "_" ^ string_of_int j ^ (if needs_some_types then "T" else ""),
blanchet@42640
   651
          Chained),
blanchet@42573
   652
         let val t = th |> prop_of in
blanchet@42589
   653
           t |> (general_type_arg_policy type_sys = Mangled_Type_Args andalso
blanchet@42573
   654
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   655
                ? (case typ of
blanchet@42573
   656
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   657
                   | NONE => I)
blanchet@42573
   658
         end)
blanchet@42573
   659
      fun make_facts eq_as_iff =
blanchet@42573
   660
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42589
   661
      val has_some_types = is_type_sys_fairly_sound type_sys
blanchet@42573
   662
    in
blanchet@42573
   663
      metis_helpers
blanchet@42579
   664
      |> maps (fn (metis_s, (needs_some_types, ths)) =>
blanchet@42573
   665
                  if metis_s <> unmangled_s orelse
blanchet@42589
   666
                     (needs_some_types andalso not has_some_types) then
blanchet@42573
   667
                    []
blanchet@42573
   668
                  else
blanchet@42573
   669
                    ths ~~ (1 upto length ths)
blanchet@42579
   670
                    |> map (dub_and_inst mangled_s needs_some_types)
blanchet@42579
   671
                    |> make_facts (not needs_some_types))
blanchet@42573
   672
    end
blanchet@42573
   673
  | NONE => []
blanchet@42573
   674
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   675
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   676
blanchet@42573
   677
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   678
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   679
blanchet@42709
   680
fun translate_formulas ctxt prem_kind type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   681
  let
blanchet@42573
   682
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   683
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   684
    val (facts, fact_names) =
blanchet@42573
   685
      rich_facts
blanchet@42573
   686
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   687
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   688
      |> ListPair.unzip
blanchet@42573
   689
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   690
       boost an ATP's performance (for some reason). *)
blanchet@42573
   691
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   692
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   693
    val all_ts = goal_t :: fact_ts
blanchet@42573
   694
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   695
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   696
    val tycons = type_consts_of_terms thy all_ts
blanchet@42709
   697
    val conjs = make_conjecture ctxt prem_kind (hyp_ts @ [concl_t])
blanchet@42573
   698
    val (supers', arity_clauses) =
blanchet@42589
   699
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   700
      else make_arity_clauses thy tycons supers
blanchet@42573
   701
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   702
  in
blanchet@42573
   703
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   704
  end
blanchet@42573
   705
blanchet@42573
   706
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   707
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   708
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   709
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   710
blanchet@42573
   711
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   712
blanchet@42701
   713
fun type_pred_combatom ctxt nonmono_Ts type_sys T tm =
blanchet@42573
   714
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T]),
blanchet@42573
   715
           tm)
blanchet@42701
   716
  |> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42573
   717
  |> AAtom
blanchet@42573
   718
blanchet@42680
   719
fun formula_from_combformula ctxt nonmono_Ts type_sys =
blanchet@42573
   720
  let
blanchet@42589
   721
    fun tag_with_type type_sys T tm =
blanchet@42589
   722
      CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42701
   723
      |> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42589
   724
      |> do_term true
blanchet@42589
   725
      |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42589
   726
    and do_term top_level u =
blanchet@42573
   727
      let
blanchet@42573
   728
        val (head, args) = strip_combterm_comb u
blanchet@42574
   729
        val (x, T_args) =
blanchet@42573
   730
          case head of
blanchet@42574
   731
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42573
   732
          | CombVar (name, _) => (name, [])
blanchet@42573
   733
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42574
   734
        val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42573
   735
                          map (do_term false) args)
blanchet@42574
   736
        val T = combtyp_of u
blanchet@42573
   737
      in
blanchet@42680
   738
        t |> (if not top_level andalso
blanchet@42680
   739
                should_tag_with_type ctxt nonmono_Ts type_sys T then
blanchet@42589
   740
                tag_with_type type_sys T
blanchet@42573
   741
              else
blanchet@42573
   742
                I)
blanchet@42573
   743
      end
blanchet@42573
   744
    val do_bound_type =
blanchet@42682
   745
      case type_sys of
blanchet@42722
   746
        Simple_Types level =>
blanchet@42682
   747
        SOME o mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42682
   748
      | _ => K NONE
blanchet@42573
   749
    fun do_out_of_bound_type (s, T) =
blanchet@42680
   750
      if should_predicate_on_type ctxt nonmono_Ts type_sys T then
blanchet@42701
   751
        type_pred_combatom ctxt nonmono_Ts type_sys T (CombVar (s, T))
blanchet@42573
   752
        |> do_formula |> SOME
blanchet@42573
   753
      else
blanchet@42573
   754
        NONE
blanchet@42573
   755
    and do_formula (AQuant (q, xs, phi)) =
blanchet@42573
   756
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42574
   757
                                      | SOME T => do_bound_type T)),
blanchet@42573
   758
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42573
   759
                    (map_filter
blanchet@42573
   760
                         (fn (_, NONE) => NONE
blanchet@42574
   761
                           | (s, SOME T) => do_out_of_bound_type (s, T)) xs)
blanchet@42573
   762
                    (do_formula phi))
blanchet@42573
   763
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42573
   764
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42573
   765
  in do_formula end
blanchet@42573
   766
blanchet@42727
   767
fun bound_atomic_types type_sys Ts =
blanchet@42727
   768
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42727
   769
                (atp_type_literals_for_types type_sys Axiom Ts))
blanchet@42727
   770
blanchet@42680
   771
fun formula_for_fact ctxt nonmono_Ts type_sys
blanchet@42573
   772
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   773
  combformula
blanchet@42727
   774
  |> close_combformula_universally
blanchet@42727
   775
  |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42727
   776
  |> bound_atomic_types type_sys atomic_types
blanchet@42573
   777
  |> close_formula_universally
blanchet@42573
   778
blanchet@42640
   779
fun useful_isabelle_info s = SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42640
   780
blanchet@42573
   781
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   782
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   783
   the remote provers might care. *)
blanchet@42680
   784
fun formula_line_for_fact ctxt prefix nonmono_Ts type_sys
blanchet@42640
   785
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   786
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   787
                     else string_of_int j ^ "_") ^
blanchet@42647
   788
           ascii_of name,
blanchet@42680
   789
           kind, formula_for_fact ctxt nonmono_Ts type_sys formula, NONE,
blanchet@42640
   790
           if generate_useful_info then
blanchet@42640
   791
             case locality of
blanchet@42640
   792
               Intro => useful_isabelle_info "intro"
blanchet@42640
   793
             | Elim => useful_isabelle_info "elim"
blanchet@42640
   794
             | Simp => useful_isabelle_info "simp"
blanchet@42640
   795
             | _ => NONE
blanchet@42640
   796
           else
blanchet@42640
   797
             NONE)
blanchet@42573
   798
blanchet@42573
   799
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@42573
   800
                                                       superclass, ...}) =
blanchet@42573
   801
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   802
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   803
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   804
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42573
   805
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   806
  end
blanchet@42573
   807
blanchet@42573
   808
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   809
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   810
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   811
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   812
blanchet@42573
   813
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@42573
   814
                                                ...}) =
blanchet@42577
   815
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   816
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42573
   817
                          o fo_literal_from_arity_literal) premLits)
blanchet@42573
   818
                    (formula_from_fo_literal
blanchet@42573
   819
                         (fo_literal_from_arity_literal conclLit))
blanchet@42573
   820
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   821
blanchet@42680
   822
fun formula_line_for_conjecture ctxt nonmono_Ts type_sys
blanchet@42573
   823
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   824
  Formula (conjecture_prefix ^ name, kind,
blanchet@42680
   825
           formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42573
   826
                                    (close_combformula_universally combformula)
blanchet@42573
   827
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   828
blanchet@42573
   829
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   830
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   831
               |> map fo_literal_from_type_literal
blanchet@42573
   832
blanchet@42573
   833
fun formula_line_for_free_type j lit =
blanchet@42577
   834
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   835
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   836
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   837
  let
blanchet@42573
   838
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   839
    val lits = fold (union (op =)) litss []
blanchet@42573
   840
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   841
blanchet@42573
   842
(** Symbol declarations **)
blanchet@42544
   843
blanchet@42677
   844
fun insert_type get_T x xs =
blanchet@42677
   845
  let val T = get_T x in
blanchet@42677
   846
    if exists (curry Type.raw_instance T o get_T) xs then xs
blanchet@42677
   847
    else x :: filter_out ((fn T' => Type.raw_instance (T', T)) o get_T) xs
blanchet@42677
   848
  end
blanchet@42677
   849
blanchet@42574
   850
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   851
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42645
   852
  not (String.isPrefix "$" s) andalso
blanchet@42722
   853
  ((case type_sys of Simple_Types _ => true | _ => false) orelse not pred_sym)
blanchet@38282
   854
blanchet@42698
   855
fun sym_decl_table_for_facts type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
   856
  let
blanchet@42698
   857
    fun add_combterm in_conj tm =
blanchet@42574
   858
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   859
        (case head of
blanchet@42574
   860
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   861
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   862
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   863
               Symtab.map_default (s, [])
blanchet@42698
   864
                   (insert_type #3 (s', T_args, T, pred_sym, length args,
blanchet@42698
   865
                                    in_conj))
blanchet@42574
   866
             else
blanchet@42574
   867
               I
blanchet@42574
   868
           end
blanchet@42574
   869
         | _ => I)
blanchet@42698
   870
        #> fold (add_combterm in_conj) args
blanchet@42574
   871
      end
blanchet@42698
   872
    fun add_fact in_conj =
blanchet@42698
   873
      fact_lift (formula_fold true (K (add_combterm in_conj)))
blanchet@42698
   874
  in
blanchet@42698
   875
    Symtab.empty
blanchet@42698
   876
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
   877
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
   878
  end
blanchet@42533
   879
blanchet@42677
   880
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42677
   881
    String.isPrefix bound_var_prefix s
blanchet@42677
   882
  | is_var_or_bound_var (CombVar _) = true
blanchet@42677
   883
  | is_var_or_bound_var _ = false
blanchet@42677
   884
blanchet@42685
   885
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
   886
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42680
   887
fun add_combterm_nonmonotonic_types _ (SOME false) _ = I
blanchet@42680
   888
  | add_combterm_nonmonotonic_types ctxt _
blanchet@42680
   889
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
   890
                  tm2)) =
blanchet@42680
   891
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42680
   892
     not (is_type_surely_infinite ctxt T)) ? insert_type I T
blanchet@42680
   893
  | add_combterm_nonmonotonic_types _ _ _ = I
blanchet@42680
   894
fun add_fact_nonmonotonic_types ctxt ({kind, combformula, ...}
blanchet@42680
   895
                                      : translated_formula) =
blanchet@42680
   896
  formula_fold (kind <> Conjecture) (add_combterm_nonmonotonic_types ctxt)
blanchet@42680
   897
               combformula
blanchet@42680
   898
fun add_nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42680
   899
  level_of_type_sys type_sys = Nonmonotonic_Types
blanchet@42731
   900
  ? (fold (add_fact_nonmonotonic_types ctxt) facts
blanchet@42731
   901
     (* in case helper "True_or_False" is included *)
blanchet@42731
   902
     #> insert_type I @{typ bool})
blanchet@42677
   903
blanchet@42574
   904
fun n_ary_strip_type 0 T = ([], T)
blanchet@42574
   905
  | n_ary_strip_type n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42574
   906
    n_ary_strip_type (n - 1) ran_T |>> cons dom_T
blanchet@42574
   907
  | n_ary_strip_type _ _ = raise Fail "unexpected non-function"
blanchet@42533
   908
blanchet@42698
   909
fun result_type_of_decl (_, _, T, _, ary, _) = n_ary_strip_type ary T |> snd
blanchet@42579
   910
blanchet@42698
   911
fun decl_line_for_sym s (s', _, T, pred_sym, ary, _) =
blanchet@42579
   912
  let val (arg_Ts, res_T) = n_ary_strip_type ary T in
blanchet@42612
   913
    Decl (sym_decl_prefix ^ s, (s, s'), map mangled_type_name arg_Ts,
blanchet@42579
   914
          if pred_sym then `I tptp_tff_bool_type else mangled_type_name res_T)
blanchet@42579
   915
  end
blanchet@42579
   916
blanchet@42592
   917
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
   918
blanchet@42709
   919
fun formula_line_for_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys n s j
blanchet@42698
   920
                              (s', T_args, T, _, ary, in_conj) =
blanchet@42579
   921
  let
blanchet@42709
   922
    val (kind, maybe_negate) =
blanchet@42709
   923
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
   924
      else (Axiom, I)
blanchet@42579
   925
    val (arg_Ts, res_T) = n_ary_strip_type ary T
blanchet@42579
   926
    val bound_names =
blanchet@42579
   927
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42579
   928
    val bound_tms =
blanchet@42579
   929
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
   930
    val bound_Ts =
blanchet@42592
   931
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
   932
                             else NONE)
blanchet@42579
   933
  in
blanchet@42612
   934
    Formula (sym_decl_prefix ^ s ^
blanchet@42709
   935
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
   936
             CombConst ((s, s'), T, T_args)
blanchet@42579
   937
             |> fold (curry (CombApp o swap)) bound_tms
blanchet@42701
   938
             |> type_pred_combatom ctxt nonmono_Ts type_sys res_T
blanchet@42579
   939
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42680
   940
             |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42727
   941
             |> n > 1 ? bound_atomic_types type_sys (atyps_of T)
blanchet@42709
   942
             |> close_formula_universally
blanchet@42709
   943
             |> maybe_negate,
blanchet@42579
   944
             NONE, NONE)
blanchet@42579
   945
  end
blanchet@42579
   946
blanchet@42709
   947
fun problem_lines_for_sym_decls ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
   948
                                (s, decls) =
blanchet@42682
   949
  case type_sys of
blanchet@42722
   950
    Simple_Types _ => map (decl_line_for_sym s) decls
blanchet@42682
   951
  | _ =>
blanchet@42574
   952
    let
blanchet@42579
   953
      val decls =
blanchet@42579
   954
        case decls of
blanchet@42579
   955
          decl :: (decls' as _ :: _) =>
blanchet@42592
   956
          let val T = result_type_of_decl decl in
blanchet@42592
   957
            if forall ((fn T' => Type.raw_instance (T', T))
blanchet@42592
   958
                       o result_type_of_decl) decls' then
blanchet@42592
   959
              [decl]
blanchet@42592
   960
            else
blanchet@42592
   961
              decls
blanchet@42592
   962
          end
blanchet@42579
   963
        | _ => decls
blanchet@42579
   964
      val n = length decls
blanchet@42579
   965
      val decls =
blanchet@42680
   966
        decls |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42579
   967
                         o result_type_of_decl)
blanchet@42574
   968
    in
blanchet@42709
   969
      (0 upto length decls - 1, decls)
blanchet@42709
   970
      |-> map2 (formula_line_for_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
   971
                                          n s)
blanchet@42574
   972
    end
blanchet@42579
   973
blanchet@42709
   974
fun problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
   975
                                     sym_decl_tab =
blanchet@42709
   976
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt conj_sym_kind
blanchet@42709
   977
                                                        nonmono_Ts type_sys)
blanchet@42574
   978
                  sym_decl_tab []
blanchet@42543
   979
blanchet@42543
   980
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
   981
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
   982
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
   983
    fold add_tff_types_in_formula phis
blanchet@42543
   984
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
   985
blanchet@42562
   986
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
   987
    union (op =) (res_T :: arg_Ts)
blanchet@42577
   988
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
   989
    add_tff_types_in_formula phi
blanchet@42543
   990
blanchet@42543
   991
fun tff_types_in_problem problem =
blanchet@42543
   992
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
   993
blanchet@42545
   994
fun decl_line_for_tff_type (s, s') =
blanchet@42568
   995
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
   996
blanchet@42543
   997
val type_declsN = "Types"
blanchet@42544
   998
val sym_declsN = "Symbol types"
blanchet@41157
   999
val factsN = "Relevant facts"
blanchet@41157
  1000
val class_relsN = "Class relationships"
blanchet@42543
  1001
val aritiesN = "Arities"
blanchet@41157
  1002
val helpersN = "Helper facts"
blanchet@41157
  1003
val conjsN = "Conjectures"
blanchet@41313
  1004
val free_typesN = "Type variables"
blanchet@41157
  1005
blanchet@41157
  1006
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
  1007
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
  1008
    if heading = needle then j
blanchet@41157
  1009
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
  1010
blanchet@42709
  1011
fun prepare_atp_problem ctxt conj_sym_kind prem_kind type_sys explicit_apply
blanchet@42709
  1012
                        hyp_ts concl_t facts =
blanchet@38282
  1013
  let
blanchet@41313
  1014
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42709
  1015
      translate_formulas ctxt prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1016
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42682
  1017
    val nonmono_Ts =
blanchet@42682
  1018
      [] |> fold (add_nonmonotonic_types_for_facts ctxt type_sys) [facts, conjs]
blanchet@42701
  1019
    val repair = repair_fact ctxt nonmono_Ts type_sys sym_tab
blanchet@42682
  1020
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1021
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1022
    val helpers =
blanchet@42682
  1023
      repaired_sym_tab |> helper_facts_for_sym_table ctxt type_sys |> map repair
blanchet@42680
  1024
    val sym_decl_lines =
blanchet@42731
  1025
      (conjs, helpers @ facts)
blanchet@42680
  1026
      |> sym_decl_table_for_facts type_sys repaired_sym_tab
blanchet@42709
  1027
      |> problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42522
  1028
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1029
       Flotter hack. *)
blanchet@38282
  1030
    val problem =
blanchet@42561
  1031
      [(sym_declsN, sym_decl_lines),
blanchet@42680
  1032
       (factsN, map (formula_line_for_fact ctxt fact_prefix nonmono_Ts type_sys)
blanchet@42180
  1033
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1034
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1035
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42680
  1036
       (helpersN, map (formula_line_for_fact ctxt helper_prefix nonmono_Ts
blanchet@42680
  1037
                                             type_sys)
blanchet@42563
  1038
                      (0 upto length helpers - 1 ~~ helpers)
blanchet@42579
  1039
                  |> (case type_sys of
blanchet@42589
  1040
                        Tags (Polymorphic, level) =>
blanchet@42687
  1041
                        is_type_level_partial level
blanchet@42589
  1042
                        ? cons (ti_ti_helper_fact ())
blanchet@42579
  1043
                      | _ => I)),
blanchet@42680
  1044
       (conjsN, map (formula_line_for_conjecture ctxt nonmono_Ts type_sys)
blanchet@42680
  1045
                    conjs),
blanchet@42545
  1046
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1047
    val problem =
blanchet@42561
  1048
      problem
blanchet@42682
  1049
      |> (case type_sys of
blanchet@42722
  1050
            Simple_Types _ =>
blanchet@42561
  1051
            cons (type_declsN,
blanchet@42561
  1052
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42682
  1053
          | _ => I)
blanchet@42646
  1054
    val (problem, pool) =
blanchet@42646
  1055
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@38282
  1056
  in
blanchet@38282
  1057
    (problem,
blanchet@38282
  1058
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1059
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1060
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
  1061
     fact_names |> Vector.fromList)
blanchet@38282
  1062
  end
blanchet@38282
  1063
blanchet@41313
  1064
(* FUDGE *)
blanchet@41313
  1065
val conj_weight = 0.0
blanchet@41770
  1066
val hyp_weight = 0.1
blanchet@41770
  1067
val fact_min_weight = 0.2
blanchet@41313
  1068
val fact_max_weight = 1.0
blanchet@42608
  1069
val type_info_default_weight = 0.8
blanchet@41313
  1070
blanchet@41313
  1071
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42734
  1072
  (not (is_atp_variable s) andalso s <> "equal" andalso
blanchet@42734
  1073
   not (String.isPrefix "$" s)) ? Symtab.default (s, weight)
blanchet@41313
  1074
  #> fold (add_term_weights weight) tms
blanchet@42577
  1075
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42680
  1076
    formula_fold true (K (add_term_weights weight)) phi
blanchet@42528
  1077
  | add_problem_line_weights _ _ = I
blanchet@41313
  1078
blanchet@41313
  1079
fun add_conjectures_weights [] = I
blanchet@41313
  1080
  | add_conjectures_weights conjs =
blanchet@41313
  1081
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1082
      add_problem_line_weights conj_weight conj
blanchet@41313
  1083
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1084
    end
blanchet@41313
  1085
blanchet@41313
  1086
fun add_facts_weights facts =
blanchet@41313
  1087
  let
blanchet@41313
  1088
    val num_facts = length facts
blanchet@41313
  1089
    fun weight_of j =
blanchet@41313
  1090
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1091
                        / Real.fromInt num_facts
blanchet@41313
  1092
  in
blanchet@41313
  1093
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1094
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1095
  end
blanchet@41313
  1096
blanchet@41313
  1097
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1098
fun atp_problem_weights problem =
blanchet@42608
  1099
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1100
    Symtab.empty
blanchet@42608
  1101
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1102
    |> add_facts_weights (get factsN)
blanchet@42608
  1103
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1104
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1105
    |> Symtab.dest
blanchet@42608
  1106
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1107
  end
blanchet@41313
  1108
blanchet@38282
  1109
end;