src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Fri May 06 13:34:59 2011 +0200 (2011-05-06)
changeset 42709 e7af132d48fe
parent 42701 500e4a88675e
child 42722 626e292d22a7
permissions -rw-r--r--
allow each prover to specify its own formula kind for symbols occurring in the conjecture
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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 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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(* official TPTP syntax *)
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val tptp_tff_type_of_types = "$tType"
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val tptp_tff_bool_type = "$o"
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val tptp_false = "$false"
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val tptp_true = "$true"
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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datatype type_level =
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  All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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datatype type_system =
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  Simple 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 "mangled_") s of
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     SOME s => (Mangled_Monomorphic, s)
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   | NONE =>
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     case try (unprefix "mono_") s of
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       SOME s => (Monomorphic, s)
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     | NONE => (Polymorphic, s))
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  ||> (fn s =>
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          (* "_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 (polymorphism, (level, core)) =>
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         case (core, (polymorphism, level)) of
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           ("simple", (Polymorphic (* naja *), level)) => Simple level
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         | ("preds", extra) => Preds extra
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         | ("tags", extra) => Tags extra
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         | ("args", (_, All_Types (* naja *))) =>
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           Preds (polymorphism, Const_Arg_Types)
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         | ("erased", (Polymorphic, All_Types (* naja *))) =>
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           Preds (polymorphism, No_Types)
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         | _ => error ("Unknown type system: " ^ quote s ^ "."))
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fun polymorphism_of_type_sys (Simple _) = 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 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))
blanchet@42574
   318
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42568
   319
      | aux _ tm = tm
blanchet@42674
   320
  in aux true tm end
blanchet@42568
   321
blanchet@42562
   322
fun combformula_from_prop thy eq_as_iff =
blanchet@38282
   323
  let
blanchet@42568
   324
    fun do_term bs t atomic_types =
blanchet@41140
   325
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42568
   326
      |>> (introduce_proxies #> AAtom)
blanchet@42568
   327
      ||> union (op =) atomic_types
blanchet@38282
   328
    fun do_quant bs q s T t' =
blanchet@38518
   329
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   330
        do_formula ((s, T) :: bs) t'
blanchet@42562
   331
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   332
      end
blanchet@38282
   333
    and do_conn bs c t1 t2 =
blanchet@38282
   334
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   335
      #>> uncurry (mk_aconn c)
blanchet@38282
   336
    and do_formula bs t =
blanchet@38282
   337
      case t of
blanchet@42531
   338
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   339
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   340
        do_quant bs AForall s T t'
blanchet@38282
   341
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   342
        do_quant bs AExists s T t'
haftmann@38795
   343
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   344
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   345
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   346
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   347
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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   348
      | _ => do_term bs t
blanchet@38282
   349
  in do_formula [] end
blanchet@38282
   350
blanchet@38618
   351
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
blanchet@38282
   352
wenzelm@41491
   353
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   354
fun conceal_bounds Ts t =
blanchet@38282
   355
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   356
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   357
fun reveal_bounds Ts =
blanchet@38282
   358
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   359
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   360
blanchet@38608
   361
(* Removes the lambdas from an equation of the form "t = (%x. u)".
blanchet@39890
   362
   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
blanchet@38608
   363
fun extensionalize_term t =
blanchet@38608
   364
  let
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   365
    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
blanchet@38608
   366
      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
blanchet@38608
   367
                                        Type (_, [_, res_T])]))
blanchet@38608
   368
                    $ t2 $ Abs (var_s, var_T, t')) =
haftmann@38864
   369
        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
blanchet@38608
   370
          let val var_t = Var ((var_s, j), var_T) in
blanchet@38608
   371
            Const (s, T' --> T' --> res_T)
blanchet@38608
   372
              $ betapply (t2, var_t) $ subst_bound (var_t, t')
blanchet@38608
   373
            |> aux (j + 1)
blanchet@38608
   374
          end
blanchet@38608
   375
        else
blanchet@38608
   376
          t
blanchet@38608
   377
      | aux _ t = t
blanchet@38608
   378
  in aux (maxidx_of_term t + 1) t end
blanchet@38608
   379
blanchet@38282
   380
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   381
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   382
    if Meson.is_fol_term thy t then
blanchet@38491
   383
      t
blanchet@38491
   384
    else
blanchet@38491
   385
      let
blanchet@38491
   386
        fun aux Ts t =
blanchet@38491
   387
          case t of
blanchet@38491
   388
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   389
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   390
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   391
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   392
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   393
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   394
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   395
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   396
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   397
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   398
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   399
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   400
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   401
              $ t1 $ t2 =>
blanchet@38491
   402
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   403
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   404
                   t
blanchet@38491
   405
                 else
blanchet@38491
   406
                   t |> conceal_bounds Ts
blanchet@38491
   407
                     |> Envir.eta_contract
blanchet@38491
   408
                     |> cterm_of thy
blanchet@39890
   409
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   410
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   411
                     |> reveal_bounds Ts
blanchet@39370
   412
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   413
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   414
      handle THM _ =>
blanchet@38491
   415
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   416
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   417
             else HOLogic.true_const
blanchet@38491
   418
  end
blanchet@38282
   419
blanchet@38282
   420
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   421
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   422
fun freeze_term t =
blanchet@38282
   423
  let
blanchet@38282
   424
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   425
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   426
      | aux (Var ((s, i), T)) =
blanchet@38282
   427
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   428
      | aux t = t
blanchet@38282
   429
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   430
blanchet@40204
   431
(* making fact and conjecture formulas *)
blanchet@42640
   432
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   433
  let
wenzelm@42361
   434
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   435
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   436
              |> transform_elim_term
blanchet@41211
   437
              |> Object_Logic.atomize_term thy
blanchet@42563
   438
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   439
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@38282
   440
              |> extensionalize_term
blanchet@38282
   441
              |> presimp ? presimplify_term thy
blanchet@38282
   442
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   443
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   444
              |> kind <> Axiom ? freeze_term
blanchet@42562
   445
    val (combformula, atomic_types) =
blanchet@42562
   446
      combformula_from_prop thy eq_as_iff t []
blanchet@38282
   447
  in
blanchet@42640
   448
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   449
     atomic_types = atomic_types}
blanchet@38282
   450
  end
blanchet@38282
   451
blanchet@42640
   452
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   453
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   454
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   455
    NONE
blanchet@41990
   456
  | (_, formula) => SOME formula
blanchet@42561
   457
blanchet@42709
   458
fun make_conjecture ctxt prem_kind ts =
blanchet@38613
   459
  let val last = length ts - 1 in
blanchet@42709
   460
    map2 (fn j => fn t =>
blanchet@42709
   461
             let
blanchet@42709
   462
               val (kind, maybe_negate) =
blanchet@42709
   463
                 if j = last then
blanchet@42709
   464
                   (Conjecture, I)
blanchet@42709
   465
                 else
blanchet@42709
   466
                   (prem_kind,
blanchet@42709
   467
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   468
                    else I)
blanchet@42709
   469
              in
blanchet@42709
   470
                make_formula ctxt true true (string_of_int j) Chained kind t
blanchet@42709
   471
                |> maybe_negate
blanchet@42709
   472
              end)
blanchet@38613
   473
         (0 upto last) ts
blanchet@38613
   474
  end
blanchet@38282
   475
blanchet@42682
   476
(** Finite and infinite type inference **)
blanchet@42682
   477
blanchet@42682
   478
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   479
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   480
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   481
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   482
blanchet@42682
   483
fun datatype_constrs thy (T as Type (s, Ts)) =
blanchet@42682
   484
    (case Datatype.get_info thy s of
blanchet@42682
   485
       SOME {index, descr, ...} =>
blanchet@42682
   486
       let val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the in
blanchet@42682
   487
         map (apsnd (fn Us => map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
blanchet@42682
   488
             constrs
blanchet@42682
   489
       end
blanchet@42682
   490
     | NONE => [])
blanchet@42682
   491
  | datatype_constrs _ _ = []
blanchet@42682
   492
blanchet@42682
   493
(* Similar to "Nitpick_HOL.bounded_exact_card_of_type".
blanchet@42682
   494
   0 means infinite type, 1 means singleton type (e.g., "unit"), and 2 means
blanchet@42682
   495
   cardinality 2 or more. The specified default cardinality is returned if the
blanchet@42682
   496
   cardinality of the type can't be determined. *)
blanchet@42682
   497
fun tiny_card_of_type ctxt default_card T =
blanchet@42682
   498
  let
blanchet@42682
   499
    val max = 2 (* 1 would be too small for the "fun" case *)
blanchet@42698
   500
    fun aux slack avoid T =
blanchet@42682
   501
      (if member (op =) avoid T then
blanchet@42682
   502
         0
blanchet@42682
   503
       else case T of
blanchet@42682
   504
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@42698
   505
         (case (aux slack avoid T1, aux slack avoid T2) of
blanchet@42698
   506
            (k, 1) => if slack andalso k = 0 then 0 else 1
blanchet@42682
   507
          | (0, _) => 0
blanchet@42682
   508
          | (_, 0) => 0
blanchet@42682
   509
          | (k1, k2) =>
blanchet@42682
   510
            if k1 >= max orelse k2 >= max then max
blanchet@42682
   511
            else Int.min (max, Integer.pow k2 k1))
blanchet@42682
   512
       | @{typ bool} => 2 (* optimization *)
blanchet@42697
   513
       | @{typ nat} => 0 (* optimization *)
blanchet@42697
   514
       | @{typ int} => 0 (* optimization *)
blanchet@42697
   515
       | Type (s, _) =>
blanchet@42682
   516
         let val thy = Proof_Context.theory_of ctxt in
blanchet@42682
   517
           case datatype_constrs thy T of
blanchet@42697
   518
             constrs as _ :: _ =>
blanchet@42682
   519
             let
blanchet@42682
   520
               val constr_cards =
blanchet@42698
   521
                 map (Integer.prod o map (aux slack (T :: avoid)) o binder_types
blanchet@42682
   522
                      o snd) constrs
blanchet@42682
   523
             in
blanchet@42682
   524
               if exists (curry (op =) 0) constr_cards then 0
blanchet@42682
   525
               else Int.min (max, Integer.sum constr_cards)
blanchet@42682
   526
             end
blanchet@42697
   527
           | [] =>
blanchet@42697
   528
             case Typedef.get_info ctxt s of
blanchet@42697
   529
               ({abs_type, rep_type, ...}, _) :: _ =>
blanchet@42697
   530
               (* We cheat here by assuming that typedef types are infinite if
blanchet@42697
   531
                  their underlying type is infinite. This is unsound in general
blanchet@42697
   532
                  but it's hard to think of a realistic example where this would
blanchet@42698
   533
                  not be the case. We are also slack with representation types:
blanchet@42701
   534
                  If a representation type has the form "sigma => tau", we
blanchet@42701
   535
                  consider it enough to check "sigma" for infiniteness. (Look
blanchet@42701
   536
                  for "slack" in this function.) *)
blanchet@42697
   537
               (case varify_and_instantiate_type ctxt
blanchet@42697
   538
                         (Logic.varifyT_global abs_type) T
blanchet@42697
   539
                         (Logic.varifyT_global rep_type)
blanchet@42698
   540
                     |> aux true avoid of
blanchet@42697
   541
                  0 => 0
blanchet@42697
   542
                | 1 => 1
blanchet@42697
   543
                | _ => default_card)
blanchet@42697
   544
             | [] => default_card
blanchet@42682
   545
         end
blanchet@42698
   546
       | TFree _ =>
blanchet@42698
   547
         (* Very slightly unsound: Type variables are assumed not to be
blanchet@42701
   548
            constrained to cardinality 1. (In practice, the user would most
blanchet@42701
   549
            likely have used "unit" directly anyway.) *)
blanchet@42698
   550
         if default_card = 1 then 2 else default_card
blanchet@42682
   551
       | _ => default_card)
blanchet@42698
   552
  in Int.min (max, aux false [] T) end
blanchet@42682
   553
blanchet@42682
   554
fun is_type_surely_finite ctxt T = tiny_card_of_type ctxt 0 T <> 0
blanchet@42682
   555
fun is_type_surely_infinite ctxt T = tiny_card_of_type ctxt 1 T = 0
blanchet@42682
   556
blanchet@42682
   557
fun should_encode_type _ _ All_Types _ = true
blanchet@42682
   558
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   559
  | should_encode_type _ nonmono_Ts Nonmonotonic_Types T =
blanchet@42682
   560
    exists (curry Type.raw_instance T) nonmono_Ts
blanchet@42682
   561
  | should_encode_type _ _ _ _ = false
blanchet@42682
   562
blanchet@42682
   563
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level)) T =
blanchet@42682
   564
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   565
  | should_predicate_on_type _ _ _ _ = false
blanchet@42682
   566
blanchet@42682
   567
fun should_tag_with_type ctxt nonmono_Ts (Tags (_, level)) T =
blanchet@42682
   568
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   569
  | should_tag_with_type _ _ _ _ = false
blanchet@42682
   570
blanchet@42682
   571
val homo_infinite_T = @{typ ind} (* any infinite type *)
blanchet@42682
   572
blanchet@42682
   573
fun homogenized_type ctxt nonmono_Ts level T =
blanchet@42682
   574
  if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
blanchet@42682
   575
blanchet@42573
   576
(** "hBOOL" and "hAPP" **)
blanchet@41313
   577
blanchet@42574
   578
type sym_info =
blanchet@42563
   579
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   580
blanchet@42574
   581
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   582
  let
blanchet@42558
   583
    fun aux top_level tm =
blanchet@42558
   584
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   585
        (case head of
blanchet@42563
   586
           CombConst ((s, _), T, _) =>
blanchet@42558
   587
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   588
             I
blanchet@42558
   589
           else
blanchet@42563
   590
             let val ary = length args in
blanchet@42558
   591
               Symtab.map_default
blanchet@42558
   592
                   (s, {pred_sym = true,
blanchet@42563
   593
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   594
                        max_ary = 0, typ = SOME T})
blanchet@42563
   595
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   596
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   597
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   598
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   599
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   600
            end
blanchet@42558
   601
         | _ => I)
blanchet@42558
   602
        #> fold (aux false) args
blanchet@42558
   603
      end
blanchet@42558
   604
  in aux true end
blanchet@42674
   605
fun add_fact_syms_to_table explicit_apply =
blanchet@42680
   606
  fact_lift (formula_fold true (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   607
blanchet@42675
   608
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   609
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   610
   (make_fixed_const predicator_base,
blanchet@42563
   611
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   612
  ([tptp_false, tptp_true]
blanchet@42563
   613
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   614
blanchet@42544
   615
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   616
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   617
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   618
blanchet@42558
   619
fun min_arity_of sym_tab s =
blanchet@42558
   620
  case Symtab.lookup sym_tab s of
blanchet@42574
   621
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   622
  | NONE =>
blanchet@42558
   623
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   624
      SOME s =>
blanchet@42570
   625
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   626
        if s = predicator_base then 1
blanchet@42547
   627
        else if s = explicit_app_base then 2
blanchet@42547
   628
        else if s = type_pred_base then 1
blanchet@42557
   629
        else 0
blanchet@42547
   630
      end
blanchet@42544
   631
    | NONE => 0
blanchet@38282
   632
blanchet@38282
   633
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   634
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   635
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   636
   arguments and is used as a predicate. *)
blanchet@42558
   637
fun is_pred_sym sym_tab s =
blanchet@42558
   638
  case Symtab.lookup sym_tab s of
blanchet@42574
   639
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   640
    pred_sym andalso min_ary = max_ary
blanchet@42558
   641
  | NONE => false
blanchet@38282
   642
blanchet@42568
   643
val predicator_combconst =
blanchet@42568
   644
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   645
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   646
blanchet@42568
   647
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   648
  case strip_combterm_comb tm of
blanchet@42542
   649
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   650
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   651
  | _ => predicator tm
blanchet@42542
   652
blanchet@42544
   653
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   654
blanchet@42544
   655
fun explicit_app arg head =
blanchet@42544
   656
  let
blanchet@42562
   657
    val head_T = combtyp_of head
blanchet@42693
   658
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   659
    val explicit_app =
blanchet@42562
   660
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42693
   661
                 [arg_T, res_T])
blanchet@42544
   662
  in list_app explicit_app [head, arg] end
blanchet@42544
   663
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   664
blanchet@42565
   665
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   666
  let
blanchet@42544
   667
    fun aux tm =
blanchet@42544
   668
      case strip_combterm_comb tm of
blanchet@42544
   669
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   670
        args |> map aux
blanchet@42557
   671
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   672
             |>> list_app head
blanchet@42544
   673
             |-> list_explicit_app
blanchet@42544
   674
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   675
  in aux end
blanchet@38282
   676
blanchet@42701
   677
fun impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42573
   678
  let
blanchet@42573
   679
    fun aux (CombApp tmp) = CombApp (pairself aux tmp)
blanchet@42574
   680
      | aux (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   681
        let
blanchet@42701
   682
          val level = level_of_type_sys type_sys
blanchet@42701
   683
          val (T, T_args) =
blanchet@42701
   684
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   685
               anyway, by distinguishing overloads only on the homogenized
blanchet@42701
   686
               result type. *)
blanchet@42701
   687
            if s = const_prefix ^ explicit_app_base andalso
blanchet@42701
   688
               not (is_type_sys_virtually_sound type_sys) then
blanchet@42701
   689
              T_args |> map (homogenized_type ctxt nonmono_Ts level)
blanchet@42701
   690
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42701
   691
                                    (T --> T, tl Ts)
blanchet@42701
   692
                                  end)
blanchet@42701
   693
            else
blanchet@42701
   694
              (T, T_args)
blanchet@42701
   695
        in
blanchet@42701
   696
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   697
             NONE => (name, T_args)
blanchet@42701
   698
           | SOME s'' =>
blanchet@42701
   699
             let val s'' = invert_const s'' in
blanchet@42701
   700
               case type_arg_policy type_sys s'' of
blanchet@42701
   701
                 No_Type_Args => (name, [])
blanchet@42701
   702
               | Explicit_Type_Args => (name, T_args)
blanchet@42701
   703
               | Mangled_Type_Args => (mangled_const_name T_args name, [])
blanchet@42701
   704
             end)
blanchet@42701
   705
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   706
        end
blanchet@42573
   707
      | aux tm = tm
blanchet@42573
   708
  in aux end
blanchet@42573
   709
blanchet@42701
   710
fun repair_combterm ctxt nonmono_Ts type_sys sym_tab =
blanchet@42565
   711
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   712
  #> introduce_predicators_in_combterm sym_tab
blanchet@42701
   713
  #> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42701
   714
fun repair_fact ctxt nonmono_Ts type_sys sym_tab =
blanchet@42701
   715
  update_combformula (formula_map
blanchet@42701
   716
      (repair_combterm ctxt nonmono_Ts type_sys sym_tab))
blanchet@42573
   717
blanchet@42573
   718
(** Helper facts **)
blanchet@42573
   719
blanchet@42573
   720
fun ti_ti_helper_fact () =
blanchet@42573
   721
  let
blanchet@42573
   722
    fun var s = ATerm (`I s, [])
blanchet@42589
   723
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   724
  in
blanchet@42612
   725
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   726
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42573
   727
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   728
  end
blanchet@42573
   729
blanchet@42574
   730
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   731
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   732
    SOME mangled_s =>
blanchet@42573
   733
    let
blanchet@42573
   734
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   735
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42579
   736
      fun dub_and_inst c needs_some_types (th, j) =
blanchet@42579
   737
        ((c ^ "_" ^ string_of_int j ^ (if needs_some_types then "T" else ""),
blanchet@42640
   738
          Chained),
blanchet@42573
   739
         let val t = th |> prop_of in
blanchet@42589
   740
           t |> (general_type_arg_policy type_sys = Mangled_Type_Args andalso
blanchet@42573
   741
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   742
                ? (case typ of
blanchet@42573
   743
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   744
                   | NONE => I)
blanchet@42573
   745
         end)
blanchet@42573
   746
      fun make_facts eq_as_iff =
blanchet@42573
   747
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42589
   748
      val has_some_types = is_type_sys_fairly_sound type_sys
blanchet@42573
   749
    in
blanchet@42573
   750
      metis_helpers
blanchet@42579
   751
      |> maps (fn (metis_s, (needs_some_types, ths)) =>
blanchet@42573
   752
                  if metis_s <> unmangled_s orelse
blanchet@42589
   753
                     (needs_some_types andalso not has_some_types) then
blanchet@42573
   754
                    []
blanchet@42573
   755
                  else
blanchet@42573
   756
                    ths ~~ (1 upto length ths)
blanchet@42579
   757
                    |> map (dub_and_inst mangled_s needs_some_types)
blanchet@42579
   758
                    |> make_facts (not needs_some_types))
blanchet@42573
   759
    end
blanchet@42573
   760
  | NONE => []
blanchet@42573
   761
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   762
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   763
blanchet@42573
   764
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   765
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   766
blanchet@42709
   767
fun translate_formulas ctxt prem_kind type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   768
  let
blanchet@42573
   769
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   770
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   771
    val (facts, fact_names) =
blanchet@42573
   772
      rich_facts
blanchet@42573
   773
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   774
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   775
      |> ListPair.unzip
blanchet@42573
   776
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   777
       boost an ATP's performance (for some reason). *)
blanchet@42573
   778
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   779
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   780
    val all_ts = goal_t :: fact_ts
blanchet@42573
   781
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   782
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   783
    val tycons = type_consts_of_terms thy all_ts
blanchet@42709
   784
    val conjs = make_conjecture ctxt prem_kind (hyp_ts @ [concl_t])
blanchet@42573
   785
    val (supers', arity_clauses) =
blanchet@42589
   786
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   787
      else make_arity_clauses thy tycons supers
blanchet@42573
   788
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   789
  in
blanchet@42573
   790
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   791
  end
blanchet@42573
   792
blanchet@42573
   793
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   794
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   795
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   796
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   797
blanchet@42573
   798
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   799
blanchet@42701
   800
fun type_pred_combatom ctxt nonmono_Ts type_sys T tm =
blanchet@42573
   801
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T]),
blanchet@42573
   802
           tm)
blanchet@42701
   803
  |> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42573
   804
  |> AAtom
blanchet@42573
   805
blanchet@42680
   806
fun formula_from_combformula ctxt nonmono_Ts type_sys =
blanchet@42573
   807
  let
blanchet@42589
   808
    fun tag_with_type type_sys T tm =
blanchet@42589
   809
      CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42701
   810
      |> impose_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42589
   811
      |> do_term true
blanchet@42589
   812
      |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42589
   813
    and do_term top_level u =
blanchet@42573
   814
      let
blanchet@42573
   815
        val (head, args) = strip_combterm_comb u
blanchet@42574
   816
        val (x, T_args) =
blanchet@42573
   817
          case head of
blanchet@42574
   818
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42573
   819
          | CombVar (name, _) => (name, [])
blanchet@42573
   820
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42574
   821
        val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42573
   822
                          map (do_term false) args)
blanchet@42574
   823
        val T = combtyp_of u
blanchet@42573
   824
      in
blanchet@42680
   825
        t |> (if not top_level andalso
blanchet@42680
   826
                should_tag_with_type ctxt nonmono_Ts type_sys T then
blanchet@42589
   827
                tag_with_type type_sys T
blanchet@42573
   828
              else
blanchet@42573
   829
                I)
blanchet@42573
   830
      end
blanchet@42573
   831
    val do_bound_type =
blanchet@42682
   832
      case type_sys of
blanchet@42684
   833
        Simple level =>
blanchet@42682
   834
        SOME o mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42682
   835
      | _ => K NONE
blanchet@42573
   836
    fun do_out_of_bound_type (s, T) =
blanchet@42680
   837
      if should_predicate_on_type ctxt nonmono_Ts type_sys T then
blanchet@42701
   838
        type_pred_combatom ctxt nonmono_Ts type_sys T (CombVar (s, T))
blanchet@42573
   839
        |> do_formula |> SOME
blanchet@42573
   840
      else
blanchet@42573
   841
        NONE
blanchet@42573
   842
    and do_formula (AQuant (q, xs, phi)) =
blanchet@42573
   843
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42574
   844
                                      | SOME T => do_bound_type T)),
blanchet@42573
   845
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42573
   846
                    (map_filter
blanchet@42573
   847
                         (fn (_, NONE) => NONE
blanchet@42574
   848
                           | (s, SOME T) => do_out_of_bound_type (s, T)) xs)
blanchet@42573
   849
                    (do_formula phi))
blanchet@42573
   850
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42573
   851
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42573
   852
  in do_formula end
blanchet@42573
   853
blanchet@42680
   854
fun formula_for_fact ctxt nonmono_Ts type_sys
blanchet@42573
   855
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42573
   856
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42573
   857
                (atp_type_literals_for_types type_sys Axiom atomic_types))
blanchet@42680
   858
           (formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42573
   859
                (close_combformula_universally combformula))
blanchet@42573
   860
  |> close_formula_universally
blanchet@42573
   861
blanchet@42640
   862
fun useful_isabelle_info s = SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42640
   863
blanchet@42573
   864
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   865
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   866
   the remote provers might care. *)
blanchet@42680
   867
fun formula_line_for_fact ctxt prefix nonmono_Ts type_sys
blanchet@42640
   868
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   869
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   870
                     else string_of_int j ^ "_") ^
blanchet@42647
   871
           ascii_of name,
blanchet@42680
   872
           kind, formula_for_fact ctxt nonmono_Ts type_sys formula, NONE,
blanchet@42640
   873
           if generate_useful_info then
blanchet@42640
   874
             case locality of
blanchet@42640
   875
               Intro => useful_isabelle_info "intro"
blanchet@42640
   876
             | Elim => useful_isabelle_info "elim"
blanchet@42640
   877
             | Simp => useful_isabelle_info "simp"
blanchet@42640
   878
             | _ => NONE
blanchet@42640
   879
           else
blanchet@42640
   880
             NONE)
blanchet@42573
   881
blanchet@42573
   882
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@42573
   883
                                                       superclass, ...}) =
blanchet@42573
   884
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   885
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   886
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   887
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42573
   888
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   889
  end
blanchet@42573
   890
blanchet@42573
   891
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   892
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   893
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   894
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   895
blanchet@42573
   896
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@42573
   897
                                                ...}) =
blanchet@42577
   898
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   899
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42573
   900
                          o fo_literal_from_arity_literal) premLits)
blanchet@42573
   901
                    (formula_from_fo_literal
blanchet@42573
   902
                         (fo_literal_from_arity_literal conclLit))
blanchet@42573
   903
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   904
blanchet@42680
   905
fun formula_line_for_conjecture ctxt nonmono_Ts type_sys
blanchet@42573
   906
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   907
  Formula (conjecture_prefix ^ name, kind,
blanchet@42680
   908
           formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42573
   909
                                    (close_combformula_universally combformula)
blanchet@42573
   910
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   911
blanchet@42573
   912
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   913
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   914
               |> map fo_literal_from_type_literal
blanchet@42573
   915
blanchet@42573
   916
fun formula_line_for_free_type j lit =
blanchet@42577
   917
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   918
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   919
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   920
  let
blanchet@42573
   921
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   922
    val lits = fold (union (op =)) litss []
blanchet@42573
   923
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   924
blanchet@42573
   925
(** Symbol declarations **)
blanchet@42544
   926
blanchet@42677
   927
fun insert_type get_T x xs =
blanchet@42677
   928
  let val T = get_T x in
blanchet@42677
   929
    if exists (curry Type.raw_instance T o get_T) xs then xs
blanchet@42677
   930
    else x :: filter_out ((fn T' => Type.raw_instance (T', T)) o get_T) xs
blanchet@42677
   931
  end
blanchet@42677
   932
blanchet@42574
   933
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   934
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42645
   935
  not (String.isPrefix "$" s) andalso
blanchet@42684
   936
  ((case type_sys of Simple _ => true | _ => false) orelse not pred_sym)
blanchet@38282
   937
blanchet@42698
   938
fun sym_decl_table_for_facts type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
   939
  let
blanchet@42698
   940
    fun add_combterm in_conj tm =
blanchet@42574
   941
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   942
        (case head of
blanchet@42574
   943
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   944
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   945
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   946
               Symtab.map_default (s, [])
blanchet@42698
   947
                   (insert_type #3 (s', T_args, T, pred_sym, length args,
blanchet@42698
   948
                                    in_conj))
blanchet@42574
   949
             else
blanchet@42574
   950
               I
blanchet@42574
   951
           end
blanchet@42574
   952
         | _ => I)
blanchet@42698
   953
        #> fold (add_combterm in_conj) args
blanchet@42574
   954
      end
blanchet@42698
   955
    fun add_fact in_conj =
blanchet@42698
   956
      fact_lift (formula_fold true (K (add_combterm in_conj)))
blanchet@42698
   957
  in
blanchet@42698
   958
    Symtab.empty
blanchet@42698
   959
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
   960
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
   961
  end
blanchet@42533
   962
blanchet@42677
   963
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42677
   964
    String.isPrefix bound_var_prefix s
blanchet@42677
   965
  | is_var_or_bound_var (CombVar _) = true
blanchet@42677
   966
  | is_var_or_bound_var _ = false
blanchet@42677
   967
blanchet@42685
   968
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
   969
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42680
   970
fun add_combterm_nonmonotonic_types _ (SOME false) _ = I
blanchet@42680
   971
  | add_combterm_nonmonotonic_types ctxt _
blanchet@42680
   972
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
   973
                  tm2)) =
blanchet@42680
   974
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42680
   975
     not (is_type_surely_infinite ctxt T)) ? insert_type I T
blanchet@42680
   976
  | add_combterm_nonmonotonic_types _ _ _ = I
blanchet@42680
   977
fun add_fact_nonmonotonic_types ctxt ({kind, combformula, ...}
blanchet@42680
   978
                                      : translated_formula) =
blanchet@42680
   979
  formula_fold (kind <> Conjecture) (add_combterm_nonmonotonic_types ctxt)
blanchet@42680
   980
               combformula
blanchet@42680
   981
fun add_nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42680
   982
  level_of_type_sys type_sys = Nonmonotonic_Types
blanchet@42700
   983
  (* in case helper "True_or_False" is included (FIXME) *)
blanchet@42700
   984
  ? (insert_type I @{typ bool}
blanchet@42682
   985
     #> fold (add_fact_nonmonotonic_types ctxt) facts)
blanchet@42677
   986
blanchet@42574
   987
fun n_ary_strip_type 0 T = ([], T)
blanchet@42574
   988
  | n_ary_strip_type n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42574
   989
    n_ary_strip_type (n - 1) ran_T |>> cons dom_T
blanchet@42574
   990
  | n_ary_strip_type _ _ = raise Fail "unexpected non-function"
blanchet@42533
   991
blanchet@42698
   992
fun result_type_of_decl (_, _, T, _, ary, _) = n_ary_strip_type ary T |> snd
blanchet@42579
   993
blanchet@42698
   994
fun decl_line_for_sym s (s', _, T, pred_sym, ary, _) =
blanchet@42579
   995
  let val (arg_Ts, res_T) = n_ary_strip_type ary T in
blanchet@42612
   996
    Decl (sym_decl_prefix ^ s, (s, s'), map mangled_type_name arg_Ts,
blanchet@42579
   997
          if pred_sym then `I tptp_tff_bool_type else mangled_type_name res_T)
blanchet@42579
   998
  end
blanchet@42579
   999
blanchet@42592
  1000
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
  1001
blanchet@42709
  1002
fun formula_line_for_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys n s j
blanchet@42698
  1003
                              (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1004
  let
blanchet@42709
  1005
    val (kind, maybe_negate) =
blanchet@42709
  1006
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1007
      else (Axiom, I)
blanchet@42579
  1008
    val (arg_Ts, res_T) = n_ary_strip_type ary T
blanchet@42579
  1009
    val bound_names =
blanchet@42579
  1010
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42579
  1011
    val bound_tms =
blanchet@42579
  1012
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
  1013
    val bound_Ts =
blanchet@42592
  1014
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
  1015
                             else NONE)
blanchet@42579
  1016
  in
blanchet@42612
  1017
    Formula (sym_decl_prefix ^ s ^
blanchet@42709
  1018
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1019
             CombConst ((s, s'), T, T_args)
blanchet@42579
  1020
             |> fold (curry (CombApp o swap)) bound_tms
blanchet@42701
  1021
             |> type_pred_combatom ctxt nonmono_Ts type_sys res_T
blanchet@42579
  1022
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42680
  1023
             |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42709
  1024
             |> close_formula_universally
blanchet@42709
  1025
             |> maybe_negate,
blanchet@42579
  1026
             NONE, NONE)
blanchet@42579
  1027
  end
blanchet@42579
  1028
blanchet@42709
  1029
fun problem_lines_for_sym_decls ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1030
                                (s, decls) =
blanchet@42682
  1031
  case type_sys of
blanchet@42684
  1032
    Simple _ => map (decl_line_for_sym s) decls
blanchet@42682
  1033
  | _ =>
blanchet@42574
  1034
    let
blanchet@42579
  1035
      val decls =
blanchet@42579
  1036
        case decls of
blanchet@42579
  1037
          decl :: (decls' as _ :: _) =>
blanchet@42592
  1038
          let val T = result_type_of_decl decl in
blanchet@42592
  1039
            if forall ((fn T' => Type.raw_instance (T', T))
blanchet@42592
  1040
                       o result_type_of_decl) decls' then
blanchet@42592
  1041
              [decl]
blanchet@42592
  1042
            else
blanchet@42592
  1043
              decls
blanchet@42592
  1044
          end
blanchet@42579
  1045
        | _ => decls
blanchet@42579
  1046
      val n = length decls
blanchet@42579
  1047
      val decls =
blanchet@42680
  1048
        decls |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42579
  1049
                         o result_type_of_decl)
blanchet@42574
  1050
    in
blanchet@42709
  1051
      (0 upto length decls - 1, decls)
blanchet@42709
  1052
      |-> map2 (formula_line_for_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1053
                                          n s)
blanchet@42574
  1054
    end
blanchet@42579
  1055
blanchet@42709
  1056
fun problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1057
                                     sym_decl_tab =
blanchet@42709
  1058
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt conj_sym_kind
blanchet@42709
  1059
                                                        nonmono_Ts type_sys)
blanchet@42574
  1060
                  sym_decl_tab []
blanchet@42543
  1061
blanchet@42543
  1062
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
  1063
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
  1064
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
  1065
    fold add_tff_types_in_formula phis
blanchet@42543
  1066
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
  1067
blanchet@42562
  1068
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
  1069
    union (op =) (res_T :: arg_Ts)
blanchet@42577
  1070
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
  1071
    add_tff_types_in_formula phi
blanchet@42543
  1072
blanchet@42543
  1073
fun tff_types_in_problem problem =
blanchet@42543
  1074
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
  1075
blanchet@42545
  1076
fun decl_line_for_tff_type (s, s') =
blanchet@42568
  1077
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
  1078
blanchet@42543
  1079
val type_declsN = "Types"
blanchet@42544
  1080
val sym_declsN = "Symbol types"
blanchet@41157
  1081
val factsN = "Relevant facts"
blanchet@41157
  1082
val class_relsN = "Class relationships"
blanchet@42543
  1083
val aritiesN = "Arities"
blanchet@41157
  1084
val helpersN = "Helper facts"
blanchet@41157
  1085
val conjsN = "Conjectures"
blanchet@41313
  1086
val free_typesN = "Type variables"
blanchet@41157
  1087
blanchet@41157
  1088
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
  1089
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
  1090
    if heading = needle then j
blanchet@41157
  1091
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
  1092
blanchet@42709
  1093
fun prepare_atp_problem ctxt conj_sym_kind prem_kind type_sys explicit_apply
blanchet@42709
  1094
                        hyp_ts concl_t facts =
blanchet@38282
  1095
  let
blanchet@41313
  1096
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42709
  1097
      translate_formulas ctxt prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1098
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42682
  1099
    val nonmono_Ts =
blanchet@42682
  1100
      [] |> fold (add_nonmonotonic_types_for_facts ctxt type_sys) [facts, conjs]
blanchet@42701
  1101
    val repair = repair_fact ctxt nonmono_Ts type_sys sym_tab
blanchet@42682
  1102
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1103
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1104
    val helpers =
blanchet@42682
  1105
      repaired_sym_tab |> helper_facts_for_sym_table ctxt type_sys |> map repair
blanchet@42680
  1106
    val sym_decl_lines =
blanchet@42698
  1107
      (conjs, facts) (* FIXME: what if "True_or_False" is among helpers? *)
blanchet@42680
  1108
      |> sym_decl_table_for_facts type_sys repaired_sym_tab
blanchet@42709
  1109
      |> problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42522
  1110
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1111
       Flotter hack. *)
blanchet@38282
  1112
    val problem =
blanchet@42561
  1113
      [(sym_declsN, sym_decl_lines),
blanchet@42680
  1114
       (factsN, map (formula_line_for_fact ctxt fact_prefix nonmono_Ts type_sys)
blanchet@42180
  1115
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1116
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1117
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42680
  1118
       (helpersN, map (formula_line_for_fact ctxt helper_prefix nonmono_Ts
blanchet@42680
  1119
                                             type_sys)
blanchet@42563
  1120
                      (0 upto length helpers - 1 ~~ helpers)
blanchet@42579
  1121
                  |> (case type_sys of
blanchet@42589
  1122
                        Tags (Polymorphic, level) =>
blanchet@42687
  1123
                        is_type_level_partial level
blanchet@42589
  1124
                        ? cons (ti_ti_helper_fact ())
blanchet@42579
  1125
                      | _ => I)),
blanchet@42680
  1126
       (conjsN, map (formula_line_for_conjecture ctxt nonmono_Ts type_sys)
blanchet@42680
  1127
                    conjs),
blanchet@42545
  1128
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1129
    val problem =
blanchet@42561
  1130
      problem
blanchet@42682
  1131
      |> (case type_sys of
blanchet@42684
  1132
            Simple _ =>
blanchet@42561
  1133
            cons (type_declsN,
blanchet@42561
  1134
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42682
  1135
          | _ => I)
blanchet@42646
  1136
    val (problem, pool) =
blanchet@42646
  1137
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@38282
  1138
  in
blanchet@38282
  1139
    (problem,
blanchet@38282
  1140
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1141
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1142
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
  1143
     fact_names |> Vector.fromList)
blanchet@38282
  1144
  end
blanchet@38282
  1145
blanchet@41313
  1146
(* FUDGE *)
blanchet@41313
  1147
val conj_weight = 0.0
blanchet@41770
  1148
val hyp_weight = 0.1
blanchet@41770
  1149
val fact_min_weight = 0.2
blanchet@41313
  1150
val fact_max_weight = 1.0
blanchet@42608
  1151
val type_info_default_weight = 0.8
blanchet@41313
  1152
blanchet@41313
  1153
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
  1154
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
  1155
  #> fold (add_term_weights weight) tms
blanchet@42577
  1156
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42680
  1157
    formula_fold true (K (add_term_weights weight)) phi
blanchet@42528
  1158
  | add_problem_line_weights _ _ = I
blanchet@41313
  1159
blanchet@41313
  1160
fun add_conjectures_weights [] = I
blanchet@41313
  1161
  | add_conjectures_weights conjs =
blanchet@41313
  1162
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1163
      add_problem_line_weights conj_weight conj
blanchet@41313
  1164
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1165
    end
blanchet@41313
  1166
blanchet@41313
  1167
fun add_facts_weights facts =
blanchet@41313
  1168
  let
blanchet@41313
  1169
    val num_facts = length facts
blanchet@41313
  1170
    fun weight_of j =
blanchet@41313
  1171
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1172
                        / Real.fromInt num_facts
blanchet@41313
  1173
  in
blanchet@41313
  1174
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1175
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1176
  end
blanchet@41313
  1177
blanchet@41313
  1178
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1179
fun atp_problem_weights problem =
blanchet@42608
  1180
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1181
    Symtab.empty
blanchet@42608
  1182
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1183
    |> add_facts_weights (get factsN)
blanchet@42608
  1184
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1185
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1186
    |> Symtab.dest
blanchet@42608
  1187
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1188
  end
blanchet@41313
  1189
blanchet@38282
  1190
end;