src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Sun May 22 14:51:42 2011 +0200 (2011-05-22)
changeset 42944 9e620869a576
parent 42943 62a14c80d194
child 42951 40bf0173fbed
permissions -rw-r--r--
improved Waldmeister support -- even run it by default on unit equational goals
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
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    Author:     Fabian Immler, TU Muenchen
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    Author:     Makarius
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    Author:     Jasmin Blanchette, TU Muenchen
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Translation of HOL to FOL for Sledgehammer.
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*)
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signature SLEDGEHAMMER_ATP_TRANSLATE =
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sig
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  type 'a fo_term = 'a ATP_Problem.fo_term
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  type format = ATP_Problem.format
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  type formula_kind = ATP_Problem.formula_kind
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  type 'a problem = 'a ATP_Problem.problem
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  type locality = Sledgehammer_Filter.locality
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  datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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  datatype type_level =
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    All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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  datatype type_heaviness = Heavy | Light
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  datatype type_system =
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    Simple_Types of type_level |
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    Preds of polymorphism * type_level * type_heaviness |
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    Tags of polymorphism * type_level * type_heaviness
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  type translated_formula
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  val readable_names : bool Config.T
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  val fact_prefix : string
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  val conjecture_prefix : string
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  val helper_prefix : string
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  val typed_helper_suffix : string
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  val predicator_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 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 -> format -> formula_kind -> formula_kind -> type_system
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    -> bool -> term list -> term
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    -> (translated_formula option * ((string * 'a) * thm)) list
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    -> string problem * string Symtab.table * int * int
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       * (string * 'a) list vector * int list * int Symtab.table
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  val atp_problem_weights : string problem -> (string * real) list
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end;
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structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
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struct
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open ATP_Problem
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open Metis_Translate
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open Sledgehammer_Util
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open Sledgehammer_Filter
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(* experimental *)
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val generate_useful_info = false
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fun useful_isabelle_info s =
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  if generate_useful_info then
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    SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
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  else
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    NONE
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val intro_info = useful_isabelle_info "intro"
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val elim_info = useful_isabelle_info "elim"
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val simp_info = useful_isabelle_info "simp"
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(* Readable names are often much shorter, especially if types are mangled in
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   names. Also, the logic for generating legal SNARK sort names is only
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   implemented for readable names. Finally, readable names are, well, more
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   readable. For these reason, they are enabled by default. *)
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val readable_names =
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  Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
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val type_decl_prefix = "type_"
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val sym_decl_prefix = "sym_"
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val fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val class_rel_clause_prefix = "crel_";
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val arity_clause_prefix = "arity_"
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val tfree_prefix = "tfree_"
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val typed_helper_suffix = "_T"
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val untyped_helper_suffix = "_U"
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val predicator_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_heaviness = Heavy | Light
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datatype type_system =
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  Simple_Types of type_level |
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  Preds of polymorphism * type_level * type_heaviness |
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  Tags of polymorphism * type_level * type_heaviness
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fun try_unsuffixes ss s =
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  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
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fun type_sys_from_string s =
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  (case try (unprefix "poly_") s of
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     SOME s => (SOME Polymorphic, s)
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   | NONE =>
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     case try (unprefix "mono_") s of
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       SOME s => (SOME Monomorphic, s)
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     | NONE =>
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       case try (unprefix "mangled_") s of
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         SOME s => (SOME Mangled_Monomorphic, s)
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       | NONE => (NONE, s))
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  ||> (fn s =>
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          (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
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          case try_unsuffixes ["?", "_query"] s of
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            SOME s => (Nonmonotonic_Types, s)
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          | NONE =>
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            case try_unsuffixes ["!", "_bang"] s of
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              SOME s => (Finite_Types, s)
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            | NONE => (All_Types, s))
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  ||> apsnd (fn s =>
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                case try (unsuffix "_heavy") s of
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                  SOME s => (Heavy, s)
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                | NONE => (Light, s))
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  |> (fn (poly, (level, (heaviness, core))) =>
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         case (core, (poly, level, heaviness)) of
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           ("simple", (NONE, _, Light)) => Simple_Types level
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         | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
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         | ("tags", (SOME Polymorphic, All_Types, _)) =>
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           Tags (Polymorphic, All_Types, heaviness)
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         | ("tags", (SOME Polymorphic, _, _)) =>
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           (* The actual light encoding is very unsound. *)
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           Tags (Polymorphic, level, Heavy)
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         | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
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         | ("args", (SOME poly, All_Types (* naja *), Light)) =>
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           Preds (poly, Const_Arg_Types, Light)
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         | ("erased", (NONE, All_Types (* naja *), Light)) =>
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           Preds (Polymorphic, No_Types, Light)
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         | _ => raise Same.SAME)
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  handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
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fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
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  | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
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  | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
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fun level_of_type_sys (Simple_Types level) = level
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  | level_of_type_sys (Preds (_, level, _)) = level
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  | level_of_type_sys (Tags (_, level, _)) = level
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fun heaviness_of_type_sys (Simple_Types _) = Heavy
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  | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
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  | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
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fun is_type_level_virtually_sound level =
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  level = All_Types orelse level = Nonmonotonic_Types
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val is_type_sys_virtually_sound =
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  is_type_level_virtually_sound o level_of_type_sys
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fun is_type_level_fairly_sound level =
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  is_type_level_virtually_sound level orelse level = Finite_Types
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val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
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fun aconn_fold pos f (ANot, [phi]) = f (Option.map not pos) phi
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  | aconn_fold pos f (AImplies, [phi1, phi2]) =
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    f (Option.map not pos) phi1 #> f pos phi2
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  | aconn_fold pos f (AAnd, phis) = fold (f pos) phis
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  | aconn_fold pos f (AOr, phis) = fold (f pos) phis
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  | aconn_fold _ f (_, phis) = fold (f NONE) phis
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fun aconn_map pos f (ANot, [phi]) = AConn (ANot, [f (Option.map not pos) phi])
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  | aconn_map pos f (AImplies, [phi1, phi2]) =
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    AConn (AImplies, [f (Option.map not pos) phi1, f pos phi2])
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  | aconn_map pos f (AAnd, phis) = AConn (AAnd, map (f pos) phis)
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  | aconn_map pos f (AOr, phis) = AConn (AOr, map (f pos) phis)
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  | aconn_map _ f (c, phis) = AConn (c, map (f NONE) phis)
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fun formula_fold pos f =
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  let
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    fun aux pos (AQuant (_, _, phi)) = aux pos phi
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      | aux pos (AConn conn) = aconn_fold pos aux conn
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      | aux pos (AAtom tm) = f pos tm
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  in aux pos end
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type translated_formula =
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  {name: string,
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   locality: locality,
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   kind: formula_kind,
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   combformula: (name, typ, combterm) formula,
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   atomic_types: typ list}
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fun update_combformula f ({name, locality, kind, combformula, atomic_types}
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                          : translated_formula) =
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  {name = name, locality = locality, kind = kind, combformula = f combformula,
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   atomic_types = atomic_types} : translated_formula
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fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
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(* The Booleans indicate whether all type arguments should be kept. *)
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datatype type_arg_policy =
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  Explicit_Type_Args of bool |
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  Mangled_Type_Args of bool |
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  No_Type_Args
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fun should_drop_arg_type_args (Simple_Types _) =
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    false (* since TFF doesn't support overloading *)
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  | should_drop_arg_type_args type_sys =
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    level_of_type_sys type_sys = All_Types andalso
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    heaviness_of_type_sys type_sys = Heavy
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fun general_type_arg_policy type_sys =
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  if level_of_type_sys type_sys = No_Types then
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    No_Type_Args
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  else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
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    Mangled_Type_Args (should_drop_arg_type_args type_sys)
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  else
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    Explicit_Type_Args (should_drop_arg_type_args type_sys)
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fun type_arg_policy _ @{const_name HOL.eq} = No_Type_Args
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  | type_arg_policy type_sys _ = general_type_arg_policy type_sys
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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_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 ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
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    ^ ")"
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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
blanchet@42542
   314
blanchet@42542
   315
fun unmangled_type s =
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   316
  s |> suffix ")" |> raw_explode
blanchet@42542
   317
    |> Scan.finite Symbol.stopper
blanchet@42542
   318
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   319
                                                quote s)) parse_mangled_type))
blanchet@42542
   320
    |> fst
blanchet@42542
   321
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   322
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   323
fun unmangled_const s =
blanchet@42542
   324
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   325
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   326
  end
blanchet@42542
   327
blanchet@42674
   328
fun introduce_proxies tm =
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   329
  let
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   330
    fun aux top_level (CombApp (tm1, tm2)) =
blanchet@42568
   331
        CombApp (aux top_level tm1, aux false tm2)
blanchet@42574
   332
      | aux top_level (CombConst (name as (s, s'), T, T_args)) =
blanchet@42570
   333
        (case proxify_const s of
blanchet@42568
   334
           SOME proxy_base =>
blanchet@42568
   335
           if top_level then
blanchet@42568
   336
             (case s of
blanchet@42568
   337
                "c_False" => (tptp_false, s')
blanchet@42568
   338
              | "c_True" => (tptp_true, s')
blanchet@42568
   339
              | _ => name, [])
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   340
           else
blanchet@42574
   341
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   342
          | NONE => (name, T_args))
blanchet@42574
   343
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42568
   344
      | aux _ tm = tm
blanchet@42674
   345
  in aux true tm end
blanchet@42568
   346
blanchet@42562
   347
fun combformula_from_prop thy eq_as_iff =
blanchet@38282
   348
  let
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   349
    fun do_term bs t atomic_types =
blanchet@41140
   350
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42568
   351
      |>> (introduce_proxies #> AAtom)
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   352
      ||> union (op =) atomic_types
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   353
    fun do_quant bs q s T t' =
blanchet@38518
   354
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   355
        do_formula ((s, T) :: bs) t'
blanchet@42562
   356
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   357
      end
blanchet@38282
   358
    and do_conn bs c t1 t2 =
blanchet@38282
   359
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   360
      #>> uncurry (mk_aconn c)
blanchet@38282
   361
    and do_formula bs t =
blanchet@38282
   362
      case t of
blanchet@42531
   363
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   364
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   365
        do_quant bs AForall s T t'
blanchet@38282
   366
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   367
        do_quant bs AExists s T t'
haftmann@38795
   368
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   369
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   370
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   371
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   372
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   373
      | _ => do_term bs t
blanchet@38282
   374
  in do_formula [] end
blanchet@38282
   375
blanchet@42750
   376
fun presimplify_term ctxt =
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   377
  Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
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   378
  #> Meson.presimplify ctxt
blanchet@42750
   379
  #> prop_of
blanchet@38282
   380
wenzelm@41491
   381
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   382
fun conceal_bounds Ts t =
blanchet@38282
   383
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   384
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   385
fun reveal_bounds Ts =
blanchet@38282
   386
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   387
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   388
blanchet@42747
   389
fun extensionalize_term ctxt t =
blanchet@42747
   390
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42747
   391
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@42747
   392
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   393
  end
blanchet@38608
   394
blanchet@38282
   395
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   396
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   397
    if Meson.is_fol_term thy t then
blanchet@38491
   398
      t
blanchet@38491
   399
    else
blanchet@38491
   400
      let
blanchet@38491
   401
        fun aux Ts t =
blanchet@38491
   402
          case t of
blanchet@38491
   403
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   404
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   405
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   406
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   407
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   408
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   409
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   410
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   411
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   412
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   413
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   414
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   415
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   416
              $ t1 $ t2 =>
blanchet@38491
   417
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   418
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   419
                   t
blanchet@38491
   420
                 else
blanchet@38491
   421
                   t |> conceal_bounds Ts
blanchet@38491
   422
                     |> Envir.eta_contract
blanchet@38491
   423
                     |> cterm_of thy
blanchet@39890
   424
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   425
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   426
                     |> reveal_bounds Ts
blanchet@39370
   427
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   428
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   429
      handle THM _ =>
blanchet@38491
   430
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   431
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   432
             else HOLogic.true_const
blanchet@38491
   433
  end
blanchet@38282
   434
blanchet@38282
   435
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   436
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   437
fun freeze_term t =
blanchet@38282
   438
  let
blanchet@38282
   439
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   440
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   441
      | aux (Var ((s, i), T)) =
blanchet@38282
   442
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   443
      | aux t = t
blanchet@38282
   444
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   445
blanchet@40204
   446
(* making fact and conjecture formulas *)
blanchet@42640
   447
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   448
  let
wenzelm@42361
   449
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   450
    val t = t |> Envir.beta_eta_contract
blanchet@42944
   451
              |> transform_elim_prop
blanchet@41211
   452
              |> Object_Logic.atomize_term thy
blanchet@42563
   453
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   454
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@42742
   455
              |> Raw_Simplifier.rewrite_term thy
blanchet@42742
   456
                     (Meson.unfold_set_const_simps ctxt) []
blanchet@42747
   457
              |> extensionalize_term ctxt
blanchet@42750
   458
              |> presimp ? presimplify_term ctxt
blanchet@38282
   459
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   460
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   461
              |> kind <> Axiom ? freeze_term
blanchet@42836
   462
    val (combformula, atomic_types) = combformula_from_prop thy eq_as_iff t []
blanchet@38282
   463
  in
blanchet@42640
   464
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   465
     atomic_types = atomic_types}
blanchet@38282
   466
  end
blanchet@38282
   467
blanchet@42640
   468
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   469
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   470
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   471
    NONE
blanchet@41990
   472
  | (_, formula) => SOME formula
blanchet@42561
   473
blanchet@42709
   474
fun make_conjecture ctxt prem_kind ts =
blanchet@38613
   475
  let val last = length ts - 1 in
blanchet@42709
   476
    map2 (fn j => fn t =>
blanchet@42709
   477
             let
blanchet@42709
   478
               val (kind, maybe_negate) =
blanchet@42709
   479
                 if j = last then
blanchet@42709
   480
                   (Conjecture, I)
blanchet@42709
   481
                 else
blanchet@42709
   482
                   (prem_kind,
blanchet@42709
   483
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   484
                    else I)
blanchet@42709
   485
              in
blanchet@42881
   486
                make_formula ctxt true true (string_of_int j) General kind t
blanchet@42709
   487
                |> maybe_negate
blanchet@42709
   488
              end)
blanchet@38613
   489
         (0 upto last) ts
blanchet@38613
   490
  end
blanchet@38282
   491
blanchet@42682
   492
(** Finite and infinite type inference **)
blanchet@42682
   493
blanchet@42886
   494
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
blanchet@42886
   495
  | deep_freeze_atyp T = T
blanchet@42886
   496
val deep_freeze_type = map_atyps deep_freeze_atyp
blanchet@42886
   497
blanchet@42886
   498
val type_instance = Sign.typ_instance o Proof_Context.theory_of
blanchet@42886
   499
blanchet@42682
   500
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   501
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   502
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   503
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   504
blanchet@42886
   505
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
blanchet@42886
   506
    exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
blanchet@42836
   507
  | should_encode_type _ _ All_Types _ = true
blanchet@42682
   508
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   509
  | should_encode_type _ _ _ _ = false
blanchet@42682
   510
blanchet@42837
   511
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
   512
                             should_predicate_on_var T =
blanchet@42878
   513
    (heaviness = Heavy orelse should_predicate_on_var ()) andalso
blanchet@42878
   514
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
   515
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
   516
blanchet@42836
   517
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42836
   518
    String.isPrefix bound_var_prefix s
blanchet@42836
   519
  | is_var_or_bound_var (CombVar _) = true
blanchet@42836
   520
  | is_var_or_bound_var _ = false
blanchet@42836
   521
blanchet@42829
   522
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
blanchet@42829
   523
blanchet@42829
   524
fun should_tag_with_type _ _ _ Top_Level _ _ = false
blanchet@42837
   525
  | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
blanchet@42837
   526
    (case heaviness of
blanchet@42837
   527
       Heavy => should_encode_type ctxt nonmono_Ts level T
blanchet@42837
   528
     | Light =>
blanchet@42836
   529
       case (site, is_var_or_bound_var u) of
blanchet@42836
   530
         (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
blanchet@42829
   531
       | _ => false)
blanchet@42829
   532
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
   533
blanchet@42682
   534
val homo_infinite_T = @{typ ind} (* any infinite type *)
blanchet@42682
   535
blanchet@42682
   536
fun homogenized_type ctxt nonmono_Ts level T =
blanchet@42682
   537
  if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
blanchet@42682
   538
blanchet@42573
   539
(** "hBOOL" and "hAPP" **)
blanchet@41313
   540
blanchet@42574
   541
type sym_info =
blanchet@42563
   542
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   543
blanchet@42574
   544
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   545
  let
blanchet@42558
   546
    fun aux top_level tm =
blanchet@42558
   547
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   548
        (case head of
blanchet@42563
   549
           CombConst ((s, _), T, _) =>
blanchet@42558
   550
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   551
             I
blanchet@42558
   552
           else
blanchet@42563
   553
             let val ary = length args in
blanchet@42558
   554
               Symtab.map_default
blanchet@42558
   555
                   (s, {pred_sym = true,
blanchet@42563
   556
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   557
                        max_ary = 0, typ = SOME T})
blanchet@42563
   558
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   559
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   560
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   561
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   562
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   563
            end
blanchet@42558
   564
         | _ => I)
blanchet@42558
   565
        #> fold (aux false) args
blanchet@42558
   566
      end
blanchet@42558
   567
  in aux true end
blanchet@42674
   568
fun add_fact_syms_to_table explicit_apply =
blanchet@42834
   569
  fact_lift (formula_fold NONE (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   570
blanchet@42675
   571
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   572
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   573
   (make_fixed_const predicator_base,
blanchet@42563
   574
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   575
  ([tptp_false, tptp_true]
blanchet@42563
   576
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   577
blanchet@42544
   578
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   579
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   580
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   581
blanchet@42558
   582
fun min_arity_of sym_tab s =
blanchet@42558
   583
  case Symtab.lookup sym_tab s of
blanchet@42574
   584
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   585
  | NONE =>
blanchet@42558
   586
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   587
      SOME s =>
blanchet@42570
   588
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   589
        if s = predicator_base then 1
blanchet@42547
   590
        else if s = explicit_app_base then 2
blanchet@42547
   591
        else if s = type_pred_base then 1
blanchet@42557
   592
        else 0
blanchet@42547
   593
      end
blanchet@42544
   594
    | NONE => 0
blanchet@38282
   595
blanchet@38282
   596
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   597
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   598
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   599
   arguments and is used as a predicate. *)
blanchet@42558
   600
fun is_pred_sym sym_tab s =
blanchet@42558
   601
  case Symtab.lookup sym_tab s of
blanchet@42574
   602
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   603
    pred_sym andalso min_ary = max_ary
blanchet@42558
   604
  | NONE => false
blanchet@38282
   605
blanchet@42568
   606
val predicator_combconst =
blanchet@42568
   607
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   608
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   609
blanchet@42568
   610
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   611
  case strip_combterm_comb tm of
blanchet@42542
   612
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   613
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   614
  | _ => predicator tm
blanchet@42542
   615
blanchet@42544
   616
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   617
blanchet@42544
   618
fun explicit_app arg head =
blanchet@42544
   619
  let
blanchet@42562
   620
    val head_T = combtyp_of head
blanchet@42693
   621
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   622
    val explicit_app =
blanchet@42562
   623
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42693
   624
                 [arg_T, res_T])
blanchet@42544
   625
  in list_app explicit_app [head, arg] end
blanchet@42544
   626
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   627
blanchet@42565
   628
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   629
  let
blanchet@42544
   630
    fun aux tm =
blanchet@42544
   631
      case strip_combterm_comb tm of
blanchet@42544
   632
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   633
        args |> map aux
blanchet@42557
   634
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   635
             |>> list_app head
blanchet@42544
   636
             |-> list_explicit_app
blanchet@42544
   637
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   638
  in aux end
blanchet@38282
   639
blanchet@42753
   640
fun chop_fun 0 T = ([], T)
blanchet@42753
   641
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
   642
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
   643
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
   644
blanchet@42780
   645
fun filter_type_args _ _ _ [] = []
blanchet@42780
   646
  | filter_type_args thy s arity T_args =
blanchet@42834
   647
    let
blanchet@42834
   648
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42834
   649
      val U = if s = explicit_app_base then
blanchet@42834
   650
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
   651
              else
blanchet@42834
   652
                s |> Sign.the_const_type thy
blanchet@42834
   653
    in
blanchet@42781
   654
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
   655
        [] => []
blanchet@42781
   656
      | res_U_vars =>
blanchet@42781
   657
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
   658
          U_args ~~ T_args
blanchet@42781
   659
          |> map_filter (fn (U, T) =>
blanchet@42781
   660
                            if member (op =) res_U_vars (dest_TVar U) then
blanchet@42781
   661
                              SOME T
blanchet@42781
   662
                            else
blanchet@42781
   663
                              NONE)
blanchet@42781
   664
        end
blanchet@42780
   665
    end
blanchet@42780
   666
    handle TYPE _ => T_args
blanchet@42753
   667
blanchet@42753
   668
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42753
   669
  let
blanchet@42753
   670
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
   671
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
   672
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
   673
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   674
        let
blanchet@42701
   675
          val level = level_of_type_sys type_sys
blanchet@42701
   676
          val (T, T_args) =
blanchet@42701
   677
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   678
               anyway, by distinguishing overloads only on the homogenized
blanchet@42837
   679
               result type. Don't do it for lightweight type systems, though,
blanchet@42837
   680
               since it leads to too many unsound proofs. *)
blanchet@42701
   681
            if s = const_prefix ^ explicit_app_base andalso
blanchet@42726
   682
               length T_args = 2 andalso
blanchet@42836
   683
               not (is_type_sys_virtually_sound type_sys) andalso
blanchet@42837
   684
               heaviness_of_type_sys type_sys = Heavy then
blanchet@42701
   685
              T_args |> map (homogenized_type ctxt nonmono_Ts level)
blanchet@42701
   686
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42831
   687
                                    (T --> T, tl Ts)
blanchet@42701
   688
                                  end)
blanchet@42701
   689
            else
blanchet@42701
   690
              (T, T_args)
blanchet@42701
   691
        in
blanchet@42701
   692
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   693
             NONE => (name, T_args)
blanchet@42701
   694
           | SOME s'' =>
blanchet@42753
   695
             let
blanchet@42753
   696
               val s'' = invert_const s''
blanchet@42831
   697
               fun filtered_T_args false = T_args
blanchet@42831
   698
                 | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@42753
   699
             in
blanchet@42701
   700
               case type_arg_policy type_sys s'' of
blanchet@42831
   701
                 Explicit_Type_Args drop_args =>
blanchet@42831
   702
                 (name, filtered_T_args drop_args)
blanchet@42831
   703
               | Mangled_Type_Args drop_args =>
blanchet@42831
   704
                 (mangled_const_name (filtered_T_args drop_args) name, [])
blanchet@42753
   705
               | No_Type_Args => (name, [])
blanchet@42701
   706
             end)
blanchet@42701
   707
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   708
        end
blanchet@42753
   709
      | aux _ tm = tm
blanchet@42753
   710
  in aux 0 end
blanchet@42573
   711
blanchet@42701
   712
fun repair_combterm ctxt nonmono_Ts type_sys sym_tab =
blanchet@42565
   713
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   714
  #> introduce_predicators_in_combterm sym_tab
blanchet@42753
   715
  #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42701
   716
fun repair_fact ctxt nonmono_Ts type_sys sym_tab =
blanchet@42701
   717
  update_combformula (formula_map
blanchet@42701
   718
      (repair_combterm ctxt nonmono_Ts type_sys sym_tab))
blanchet@42573
   719
blanchet@42573
   720
(** Helper facts **)
blanchet@42573
   721
blanchet@42573
   722
fun ti_ti_helper_fact () =
blanchet@42573
   723
  let
blanchet@42573
   724
    fun var s = ATerm (`I s, [])
blanchet@42589
   725
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   726
  in
blanchet@42612
   727
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   728
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42879
   729
             |> close_formula_universally, simp_info, NONE)
blanchet@42573
   730
  end
blanchet@42573
   731
blanchet@42574
   732
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   733
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   734
    SOME mangled_s =>
blanchet@42573
   735
    let
blanchet@42573
   736
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   737
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42893
   738
      fun dub_and_inst c needs_fairly_sound (th, j) =
blanchet@42881
   739
        ((c ^ "_" ^ string_of_int j ^
blanchet@42893
   740
          (if needs_fairly_sound then typed_helper_suffix
blanchet@42881
   741
           else untyped_helper_suffix),
blanchet@42881
   742
          General),
blanchet@42573
   743
         let val t = th |> prop_of in
blanchet@42753
   744
           t |> ((case general_type_arg_policy type_sys of
blanchet@42753
   745
                    Mangled_Type_Args _ => true
blanchet@42753
   746
                  | _ => false) andalso
blanchet@42573
   747
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   748
                ? (case typ of
blanchet@42573
   749
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   750
                   | NONE => I)
blanchet@42573
   751
         end)
blanchet@42573
   752
      fun make_facts eq_as_iff =
blanchet@42573
   753
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42893
   754
      val fairly_sound = is_type_sys_fairly_sound type_sys
blanchet@42573
   755
    in
blanchet@42573
   756
      metis_helpers
blanchet@42894
   757
      |> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
blanchet@42573
   758
                  if metis_s <> unmangled_s orelse
blanchet@42894
   759
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
   760
                    []
blanchet@42573
   761
                  else
blanchet@42573
   762
                    ths ~~ (1 upto length ths)
blanchet@42893
   763
                    |> map (dub_and_inst mangled_s needs_fairly_sound)
blanchet@42893
   764
                    |> make_facts (not needs_fairly_sound))
blanchet@42573
   765
    end
blanchet@42573
   766
  | NONE => []
blanchet@42573
   767
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   768
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   769
blanchet@42573
   770
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   771
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   772
blanchet@42709
   773
fun translate_formulas ctxt prem_kind type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   774
  let
blanchet@42573
   775
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   776
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   777
    val (facts, fact_names) =
blanchet@42573
   778
      rich_facts
blanchet@42573
   779
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   780
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   781
      |> ListPair.unzip
blanchet@42573
   782
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   783
       boost an ATP's performance (for some reason). *)
blanchet@42573
   784
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   785
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   786
    val all_ts = goal_t :: fact_ts
blanchet@42573
   787
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   788
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   789
    val tycons = type_consts_of_terms thy all_ts
blanchet@42709
   790
    val conjs = make_conjecture ctxt prem_kind (hyp_ts @ [concl_t])
blanchet@42573
   791
    val (supers', arity_clauses) =
blanchet@42589
   792
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   793
      else make_arity_clauses thy tycons supers
blanchet@42573
   794
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   795
  in
blanchet@42573
   796
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   797
  end
blanchet@42573
   798
blanchet@42573
   799
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   800
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   801
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   802
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   803
blanchet@42573
   804
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   805
blanchet@42878
   806
fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
blanchet@42834
   807
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T])
blanchet@42834
   808
           |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
blanchet@42573
   809
           tm)
blanchet@42573
   810
blanchet@42878
   811
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@42878
   812
  | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@42878
   813
    accum orelse (s = "equal" andalso member (op =) tms (ATerm (name, [])))
blanchet@42878
   814
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
blanchet@42878
   815
  | is_var_nonmonotonic_in_formula pos phi _ name =
blanchet@42878
   816
    formula_fold pos (var_occurs_positively_naked_in_term name) phi false
blanchet@42834
   817
blanchet@42829
   818
fun tag_with_type ctxt nonmono_Ts type_sys T tm =
blanchet@42829
   819
  CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42829
   820
  |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42829
   821
  |> term_from_combterm ctxt nonmono_Ts type_sys Top_Level
blanchet@42829
   822
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42829
   823
and term_from_combterm ctxt nonmono_Ts type_sys site u =
blanchet@42573
   824
  let
blanchet@42829
   825
    val (head, args) = strip_combterm_comb u
blanchet@42829
   826
    val (x as (s, _), T_args) =
blanchet@42829
   827
      case head of
blanchet@42829
   828
        CombConst (name, _, T_args) => (name, T_args)
blanchet@42829
   829
      | CombVar (name, _) => (name, [])
blanchet@42829
   830
      | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42829
   831
    val arg_site = if site = Top_Level andalso s = "equal" then Eq_Arg
blanchet@42829
   832
                   else Elsewhere
blanchet@42829
   833
    val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42829
   834
                      map (term_from_combterm ctxt nonmono_Ts type_sys arg_site)
blanchet@42829
   835
                          args)
blanchet@42829
   836
    val T = combtyp_of u
blanchet@42829
   837
  in
blanchet@42829
   838
    t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
blanchet@42829
   839
            tag_with_type ctxt nonmono_Ts type_sys T
blanchet@42829
   840
          else
blanchet@42829
   841
            I)
blanchet@42829
   842
  end
blanchet@42834
   843
and formula_from_combformula ctxt nonmono_Ts type_sys should_predicate_on_var =
blanchet@42829
   844
  let
blanchet@42878
   845
    val do_term = term_from_combterm ctxt nonmono_Ts type_sys Top_Level
blanchet@42573
   846
    val do_bound_type =
blanchet@42682
   847
      case type_sys of
blanchet@42722
   848
        Simple_Types level =>
blanchet@42682
   849
        SOME o mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42682
   850
      | _ => K NONE
blanchet@42878
   851
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@42834
   852
      if should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42878
   853
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@42834
   854
        CombVar (name, T)
blanchet@42878
   855
        |> type_pred_combterm ctxt nonmono_Ts type_sys T
blanchet@42878
   856
        |> do_term |> AAtom |> SOME
blanchet@42573
   857
      else
blanchet@42573
   858
        NONE
blanchet@42878
   859
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
   860
        let
blanchet@42878
   861
          val phi = phi |> do_formula pos
blanchet@42878
   862
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
   863
        in
blanchet@42834
   864
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
   865
                                        | SOME T => do_bound_type T)),
blanchet@42834
   866
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
   867
                      (map_filter
blanchet@42834
   868
                           (fn (_, NONE) => NONE
blanchet@42834
   869
                             | (s, SOME T) =>
blanchet@42878
   870
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
   871
                           xs)
blanchet@42834
   872
                      phi)
blanchet@42834
   873
        end
blanchet@42878
   874
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@42878
   875
      | do_formula _ (AAtom tm) = AAtom (do_term tm)
blanchet@42878
   876
  in do_formula o SOME end
blanchet@42573
   877
blanchet@42727
   878
fun bound_atomic_types type_sys Ts =
blanchet@42727
   879
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42727
   880
                (atp_type_literals_for_types type_sys Axiom Ts))
blanchet@42727
   881
blanchet@42680
   882
fun formula_for_fact ctxt nonmono_Ts type_sys
blanchet@42573
   883
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   884
  combformula
blanchet@42727
   885
  |> close_combformula_universally
blanchet@42727
   886
  |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42878
   887
                              is_var_nonmonotonic_in_formula true
blanchet@42727
   888
  |> bound_atomic_types type_sys atomic_types
blanchet@42573
   889
  |> close_formula_universally
blanchet@42573
   890
blanchet@42573
   891
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   892
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   893
   the remote provers might care. *)
blanchet@42680
   894
fun formula_line_for_fact ctxt prefix nonmono_Ts type_sys
blanchet@42640
   895
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   896
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   897
                     else string_of_int j ^ "_") ^
blanchet@42647
   898
           ascii_of name,
blanchet@42680
   899
           kind, formula_for_fact ctxt nonmono_Ts type_sys formula, NONE,
blanchet@42879
   900
           case locality of
blanchet@42879
   901
             Intro => intro_info
blanchet@42879
   902
           | Elim => elim_info
blanchet@42879
   903
           | Simp => simp_info
blanchet@42879
   904
           | _ => NONE)
blanchet@42573
   905
blanchet@42939
   906
fun formula_line_for_class_rel_clause
blanchet@42939
   907
        (ClassRelClause {name, subclass, superclass, ...}) =
blanchet@42573
   908
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   909
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   910
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   911
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42879
   912
             |> close_formula_universally, intro_info, NONE)
blanchet@42573
   913
  end
blanchet@42573
   914
blanchet@42573
   915
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   916
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   917
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   918
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   919
blanchet@42939
   920
fun formula_line_for_arity_clause
blanchet@42939
   921
        (ArityClause {name, prem_lits, concl_lits, ...}) =
blanchet@42577
   922
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   923
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42895
   924
                          o fo_literal_from_arity_literal) prem_lits)
blanchet@42573
   925
                    (formula_from_fo_literal
blanchet@42895
   926
                         (fo_literal_from_arity_literal concl_lits))
blanchet@42879
   927
           |> close_formula_universally, intro_info, NONE)
blanchet@42573
   928
blanchet@42680
   929
fun formula_line_for_conjecture ctxt nonmono_Ts type_sys
blanchet@42573
   930
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   931
  Formula (conjecture_prefix ^ name, kind,
blanchet@42680
   932
           formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42939
   933
               is_var_nonmonotonic_in_formula false
blanchet@42939
   934
               (close_combformula_universally combformula)
blanchet@42573
   935
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   936
blanchet@42573
   937
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   938
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   939
               |> map fo_literal_from_type_literal
blanchet@42573
   940
blanchet@42573
   941
fun formula_line_for_free_type j lit =
blanchet@42577
   942
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   943
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   944
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   945
  let
blanchet@42573
   946
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   947
    val lits = fold (union (op =)) litss []
blanchet@42573
   948
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   949
blanchet@42573
   950
(** Symbol declarations **)
blanchet@42544
   951
blanchet@42886
   952
fun insert_type ctxt get_T x xs =
blanchet@42677
   953
  let val T = get_T x in
blanchet@42886
   954
    if exists (curry (type_instance ctxt) T o get_T) xs then xs
blanchet@42886
   955
    else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
blanchet@42677
   956
  end
blanchet@42677
   957
blanchet@42574
   958
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   959
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42753
   960
  not (String.isPrefix tptp_special_prefix s) andalso
blanchet@42894
   961
  (case type_sys of
blanchet@42894
   962
     Simple_Types _ => true
blanchet@42894
   963
   | Tags (_, _, Light) => true
blanchet@42894
   964
   | _ => not pred_sym)
blanchet@38282
   965
blanchet@42886
   966
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
   967
  let
blanchet@42698
   968
    fun add_combterm in_conj tm =
blanchet@42574
   969
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   970
        (case head of
blanchet@42574
   971
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   972
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   973
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   974
               Symtab.map_default (s, [])
blanchet@42886
   975
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
   976
                                         in_conj))
blanchet@42574
   977
             else
blanchet@42574
   978
               I
blanchet@42574
   979
           end
blanchet@42574
   980
         | _ => I)
blanchet@42698
   981
        #> fold (add_combterm in_conj) args
blanchet@42574
   982
      end
blanchet@42698
   983
    fun add_fact in_conj =
blanchet@42834
   984
      fact_lift (formula_fold NONE (K (add_combterm in_conj)))
blanchet@42698
   985
  in
blanchet@42698
   986
    Symtab.empty
blanchet@42698
   987
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
   988
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
   989
  end
blanchet@42533
   990
blanchet@42886
   991
(* These types witness that the type classes they belong to allow infinite
blanchet@42886
   992
   models and hence that any types with these type classes is monotonic. *)
blanchet@42886
   993
val known_infinite_types = [@{typ nat}, @{typ int}, @{typ "nat => bool"}]
blanchet@42886
   994
blanchet@42685
   995
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
   996
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42886
   997
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
blanchet@42829
   998
  | add_combterm_nonmonotonic_types ctxt level _
blanchet@42680
   999
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
  1000
                  tm2)) =
blanchet@42680
  1001
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
  1002
     (case level of
blanchet@42886
  1003
        Nonmonotonic_Types =>
blanchet@42886
  1004
        not (is_type_surely_infinite ctxt known_infinite_types T)
blanchet@42829
  1005
      | Finite_Types => is_type_surely_finite ctxt T
blanchet@42886
  1006
      | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
blanchet@42829
  1007
  | add_combterm_nonmonotonic_types _ _ _ _ = I
blanchet@42829
  1008
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
blanchet@42829
  1009
                                            : translated_formula) =
blanchet@42834
  1010
  formula_fold (SOME (kind <> Conjecture))
blanchet@42829
  1011
               (add_combterm_nonmonotonic_types ctxt level) combformula
blanchet@42886
  1012
fun nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42829
  1013
  let val level = level_of_type_sys type_sys in
blanchet@42886
  1014
    if level = Nonmonotonic_Types orelse level = Finite_Types then
blanchet@42886
  1015
      [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
blanchet@42886
  1016
         (* We must add "bool" in case the helper "True_or_False" is added
blanchet@42886
  1017
            later. In addition, several places in the code rely on the list of
blanchet@42886
  1018
            nonmonotonic types not being empty. *)
blanchet@42886
  1019
         |> insert_type ctxt I @{typ bool}
blanchet@42886
  1020
    else
blanchet@42886
  1021
      []
blanchet@42829
  1022
  end
blanchet@42677
  1023
blanchet@42754
  1024
fun decl_line_for_sym ctxt nonmono_Ts level s (s', _, T, pred_sym, ary, _) =
blanchet@42754
  1025
  let
blanchet@42754
  1026
    val translate_type =
blanchet@42754
  1027
      mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42754
  1028
    val (arg_tys, res_ty) =
blanchet@42754
  1029
      T |> chop_fun ary |>> map translate_type ||> translate_type
blanchet@42754
  1030
  in
blanchet@42754
  1031
    Decl (sym_decl_prefix ^ s, (s, s'), arg_tys,
blanchet@42754
  1032
          if pred_sym then `I tptp_tff_bool_type else res_ty)
blanchet@42579
  1033
  end
blanchet@42579
  1034
blanchet@42592
  1035
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
  1036
blanchet@42829
  1037
fun formula_line_for_pred_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys n s j
blanchet@42829
  1038
                                   (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1039
  let
blanchet@42709
  1040
    val (kind, maybe_negate) =
blanchet@42709
  1041
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1042
      else (Axiom, I)
blanchet@42753
  1043
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42579
  1044
    val bound_names =
blanchet@42579
  1045
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1046
    val bounds =
blanchet@42579
  1047
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
  1048
    val bound_Ts =
blanchet@42592
  1049
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
  1050
                             else NONE)
blanchet@42579
  1051
  in
blanchet@42612
  1052
    Formula (sym_decl_prefix ^ s ^
blanchet@42709
  1053
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1054
             CombConst ((s, s'), T, T_args)
blanchet@42829
  1055
             |> fold (curry (CombApp o swap)) bounds
blanchet@42878
  1056
             |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
blanchet@42878
  1057
             |> AAtom
blanchet@42579
  1058
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42878
  1059
             |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42878
  1060
                                         (K (K (K (K true)))) true
blanchet@42727
  1061
             |> n > 1 ? bound_atomic_types type_sys (atyps_of T)
blanchet@42709
  1062
             |> close_formula_universally
blanchet@42709
  1063
             |> maybe_negate,
blanchet@42879
  1064
             intro_info, NONE)
blanchet@42579
  1065
  end
blanchet@42579
  1066
blanchet@42852
  1067
fun formula_lines_for_tag_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys n s
blanchet@42852
  1068
                                  (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1069
  let
blanchet@42829
  1070
    val ident_base =
blanchet@42829
  1071
      sym_decl_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1072
    val (kind, maybe_negate) =
blanchet@42852
  1073
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1074
      else (Axiom, I)
blanchet@42829
  1075
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1076
    val bound_names =
blanchet@42829
  1077
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1078
    val bounds = bound_names |> map (fn name => ATerm (name, []))
blanchet@42829
  1079
    fun const args = ATerm ((s, s'), map fo_term_from_typ T_args @ args)
blanchet@42830
  1080
    val atomic_Ts = atyps_of T
blanchet@42834
  1081
    fun eq tms =
blanchet@42834
  1082
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@42834
  1083
       else AAtom (ATerm (`I "equal", tms)))
blanchet@42830
  1084
      |> bound_atomic_types type_sys atomic_Ts
blanchet@42830
  1085
      |> close_formula_universally
blanchet@42852
  1086
      |> maybe_negate
blanchet@42836
  1087
    val should_encode = should_encode_type ctxt nonmono_Ts All_Types
blanchet@42829
  1088
    val tag_with = tag_with_type ctxt nonmono_Ts type_sys
blanchet@42829
  1089
    val add_formula_for_res =
blanchet@42829
  1090
      if should_encode res_T then
blanchet@42852
  1091
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42834
  1092
                       eq [tag_with res_T (const bounds), const bounds],
blanchet@42879
  1093
                       simp_info, NONE))
blanchet@42829
  1094
      else
blanchet@42829
  1095
        I
blanchet@42829
  1096
    fun add_formula_for_arg k =
blanchet@42829
  1097
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1098
        if should_encode arg_T then
blanchet@42829
  1099
          case chop k bounds of
blanchet@42829
  1100
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1101
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42834
  1102
                           eq [const (bounds1 @ tag_with arg_T bound ::
blanchet@42834
  1103
                                      bounds2),
blanchet@42834
  1104
                               const bounds],
blanchet@42879
  1105
                           simp_info, NONE))
blanchet@42829
  1106
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1107
        else
blanchet@42829
  1108
          I
blanchet@42829
  1109
      end
blanchet@42829
  1110
  in
blanchet@42834
  1111
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1112
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1113
  end
blanchet@42829
  1114
blanchet@42836
  1115
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1116
blanchet@42709
  1117
fun problem_lines_for_sym_decls ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1118
                                (s, decls) =
blanchet@42682
  1119
  case type_sys of
blanchet@42754
  1120
    Simple_Types level => map (decl_line_for_sym ctxt nonmono_Ts level s) decls
blanchet@42829
  1121
  | Preds _ =>
blanchet@42574
  1122
    let
blanchet@42579
  1123
      val decls =
blanchet@42579
  1124
        case decls of
blanchet@42579
  1125
          decl :: (decls' as _ :: _) =>
blanchet@42592
  1126
          let val T = result_type_of_decl decl in
blanchet@42886
  1127
            if forall (curry (type_instance ctxt o swap) T
blanchet@42592
  1128
                       o result_type_of_decl) decls' then
blanchet@42592
  1129
              [decl]
blanchet@42592
  1130
            else
blanchet@42592
  1131
              decls
blanchet@42592
  1132
          end
blanchet@42579
  1133
        | _ => decls
blanchet@42579
  1134
      val n = length decls
blanchet@42579
  1135
      val decls =
blanchet@42834
  1136
        decls
blanchet@42834
  1137
        |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
blanchet@42834
  1138
                   o result_type_of_decl)
blanchet@42574
  1139
    in
blanchet@42709
  1140
      (0 upto length decls - 1, decls)
blanchet@42829
  1141
      |-> map2 (formula_line_for_pred_sym_decl ctxt conj_sym_kind nonmono_Ts
blanchet@42829
  1142
                                               type_sys n s)
blanchet@42574
  1143
    end
blanchet@42837
  1144
  | Tags (_, _, heaviness) =>
blanchet@42837
  1145
    (case heaviness of
blanchet@42837
  1146
       Heavy => []
blanchet@42837
  1147
     | Light =>
blanchet@42829
  1148
       let val n = length decls in
blanchet@42829
  1149
         (0 upto n - 1 ~~ decls)
blanchet@42852
  1150
         |> maps (formula_lines_for_tag_sym_decl ctxt conj_sym_kind nonmono_Ts
blanchet@42852
  1151
                                                 type_sys n s)
blanchet@42829
  1152
       end)
blanchet@42579
  1153
blanchet@42709
  1154
fun problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1155
                                     sym_decl_tab =
blanchet@42709
  1156
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt conj_sym_kind
blanchet@42709
  1157
                                                        nonmono_Ts type_sys)
blanchet@42574
  1158
                  sym_decl_tab []
blanchet@42543
  1159
blanchet@42543
  1160
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
  1161
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
  1162
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
  1163
    fold add_tff_types_in_formula phis
blanchet@42543
  1164
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
  1165
blanchet@42562
  1166
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
  1167
    union (op =) (res_T :: arg_Ts)
blanchet@42577
  1168
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
  1169
    add_tff_types_in_formula phi
blanchet@42543
  1170
blanchet@42543
  1171
fun tff_types_in_problem problem =
blanchet@42543
  1172
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
  1173
blanchet@42545
  1174
fun decl_line_for_tff_type (s, s') =
blanchet@42568
  1175
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
  1176
blanchet@42837
  1177
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
blanchet@42831
  1178
    level = Nonmonotonic_Types orelse level = Finite_Types
blanchet@42831
  1179
  | should_add_ti_ti_helper _ = false
blanchet@42831
  1180
blanchet@42939
  1181
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  1182
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  1183
    if heading = needle then j
blanchet@42939
  1184
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  1185
blanchet@42543
  1186
val type_declsN = "Types"
blanchet@42544
  1187
val sym_declsN = "Symbol types"
blanchet@41157
  1188
val factsN = "Relevant facts"
blanchet@41157
  1189
val class_relsN = "Class relationships"
blanchet@42543
  1190
val aritiesN = "Arities"
blanchet@41157
  1191
val helpersN = "Helper facts"
blanchet@41157
  1192
val conjsN = "Conjectures"
blanchet@41313
  1193
val free_typesN = "Type variables"
blanchet@41157
  1194
blanchet@42939
  1195
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
blanchet@42939
  1196
                        explicit_apply hyp_ts concl_t facts =
blanchet@38282
  1197
  let
blanchet@41313
  1198
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42709
  1199
      translate_formulas ctxt prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1200
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42886
  1201
    val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
blanchet@42701
  1202
    val repair = repair_fact ctxt nonmono_Ts type_sys sym_tab
blanchet@42682
  1203
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1204
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1205
    val helpers =
blanchet@42682
  1206
      repaired_sym_tab |> helper_facts_for_sym_table ctxt type_sys |> map repair
blanchet@42894
  1207
    val lavish_nonmono_Ts =
blanchet@42894
  1208
      if null nonmono_Ts orelse
blanchet@42894
  1209
         polymorphism_of_type_sys type_sys <> Polymorphic then
blanchet@42894
  1210
        nonmono_Ts
blanchet@42894
  1211
      else
blanchet@42894
  1212
        [TVar (("'a", 0), HOLogic.typeS)]
blanchet@42680
  1213
    val sym_decl_lines =
blanchet@42731
  1214
      (conjs, helpers @ facts)
blanchet@42886
  1215
      |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
blanchet@42894
  1216
      |> problem_lines_for_sym_decl_table ctxt conj_sym_kind lavish_nonmono_Ts
blanchet@42894
  1217
                                          type_sys
blanchet@42881
  1218
    val helper_lines =
blanchet@42894
  1219
      map (formula_line_for_fact ctxt helper_prefix lavish_nonmono_Ts type_sys)
blanchet@42881
  1220
          (0 upto length helpers - 1 ~~ helpers)
blanchet@42939
  1221
      |> (if should_add_ti_ti_helper type_sys then
blanchet@42939
  1222
            cons (ti_ti_helper_fact ())
blanchet@42939
  1223
          else
blanchet@42939
  1224
            I)
blanchet@42522
  1225
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1226
       Flotter hack. *)
blanchet@38282
  1227
    val problem =
blanchet@42561
  1228
      [(sym_declsN, sym_decl_lines),
blanchet@42680
  1229
       (factsN, map (formula_line_for_fact ctxt fact_prefix nonmono_Ts type_sys)
blanchet@42180
  1230
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1231
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1232
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42881
  1233
       (helpersN, helper_lines),
blanchet@42680
  1234
       (conjsN, map (formula_line_for_conjecture ctxt nonmono_Ts type_sys)
blanchet@42680
  1235
                    conjs),
blanchet@42545
  1236
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1237
    val problem =
blanchet@42561
  1238
      problem
blanchet@42682
  1239
      |> (case type_sys of
blanchet@42722
  1240
            Simple_Types _ =>
blanchet@42561
  1241
            cons (type_declsN,
blanchet@42561
  1242
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42682
  1243
          | _ => I)
blanchet@42939
  1244
    val problem =
blanchet@42939
  1245
      problem |> (if format = CNF_UEQ then filter_cnf_ueq_problem else I)
blanchet@42646
  1246
    val (problem, pool) =
blanchet@42646
  1247
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@42881
  1248
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  1249
    val typed_helpers =
blanchet@42881
  1250
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  1251
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  1252
                     else NONE)
blanchet@42881
  1253
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  1254
                  ~~ helpers)
blanchet@42778
  1255
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1256
      if min_ary > 0 then
blanchet@42755
  1257
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1258
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1259
        | NONE => I
blanchet@42755
  1260
      else
blanchet@42755
  1261
        I
blanchet@38282
  1262
  in
blanchet@38282
  1263
    (problem,
blanchet@38282
  1264
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1265
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1266
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1267
     fact_names |> Vector.fromList,
blanchet@42881
  1268
     typed_helpers,
blanchet@42755
  1269
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1270
  end
blanchet@38282
  1271
blanchet@41313
  1272
(* FUDGE *)
blanchet@41313
  1273
val conj_weight = 0.0
blanchet@41770
  1274
val hyp_weight = 0.1
blanchet@41770
  1275
val fact_min_weight = 0.2
blanchet@41313
  1276
val fact_max_weight = 1.0
blanchet@42608
  1277
val type_info_default_weight = 0.8
blanchet@41313
  1278
blanchet@41313
  1279
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42734
  1280
  (not (is_atp_variable s) andalso s <> "equal" andalso
blanchet@42753
  1281
   not (String.isPrefix tptp_special_prefix s)) ? Symtab.default (s, weight)
blanchet@41313
  1282
  #> fold (add_term_weights weight) tms
blanchet@42577
  1283
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1284
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1285
  | add_problem_line_weights _ _ = I
blanchet@41313
  1286
blanchet@41313
  1287
fun add_conjectures_weights [] = I
blanchet@41313
  1288
  | add_conjectures_weights conjs =
blanchet@41313
  1289
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1290
      add_problem_line_weights conj_weight conj
blanchet@41313
  1291
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1292
    end
blanchet@41313
  1293
blanchet@41313
  1294
fun add_facts_weights facts =
blanchet@41313
  1295
  let
blanchet@41313
  1296
    val num_facts = length facts
blanchet@41313
  1297
    fun weight_of j =
blanchet@41313
  1298
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1299
                        / Real.fromInt num_facts
blanchet@41313
  1300
  in
blanchet@41313
  1301
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1302
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1303
  end
blanchet@41313
  1304
blanchet@41313
  1305
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1306
fun atp_problem_weights problem =
blanchet@42608
  1307
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1308
    Symtab.empty
blanchet@42608
  1309
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1310
    |> add_facts_weights (get factsN)
blanchet@42608
  1311
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1312
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1313
    |> Symtab.dest
blanchet@42608
  1314
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1315
  end
blanchet@41313
  1316
blanchet@38282
  1317
end;