src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Tue May 24 00:01:33 2011 +0200 (2011-05-24)
changeset 42956 9aeb0f6ad971
parent 42951 40bf0173fbed
child 42962 3b50fdeb6cfc
permissions -rw-r--r--
filter Waldmeister facts better -- and don't encode type classes as predicates, since it doesn't like conditional equations
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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 type_sys s =
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  if s = @{const_name HOL.eq} orelse
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     (s = explicit_app_base andalso
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      level_of_type_sys type_sys = Const_Arg_Types) then
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    No_Type_Args
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  else
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    general_type_arg_policy type_sys
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fun atp_type_literals_for_types format type_sys kind Ts =
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  if level_of_type_sys type_sys = No_Types orelse format = CNF_UEQ then
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    []
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  else
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    Ts |> type_literals_for_types
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       |> filter (fn TyLitVar _ => kind <> Conjecture
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                   | TyLitFree _ => kind = Conjecture)
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fun mk_aconns c phis =
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  let val (phis', phi') = split_last phis in
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    fold_rev (mk_aconn c) phis' phi'
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  end
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fun mk_ahorn [] phi = phi
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  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
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fun mk_aquant _ [] phi = phi
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  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
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    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
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  | mk_aquant q xs phi = AQuant (q, xs, phi)
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fun close_universally atom_vars phi =
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  let
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    fun formula_vars bounds (AQuant (_, xs, phi)) =
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        formula_vars (map fst xs @ bounds) phi
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      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
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      | formula_vars bounds (AAtom tm) =
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        union (op =) (atom_vars tm []
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                      |> filter_out (member (op =) bounds o fst))
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  in mk_aquant AForall (formula_vars [] phi []) phi end
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fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
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  | combterm_vars (CombConst _) = I
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  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
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fun close_combformula_universally phi = close_universally combterm_vars phi
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fun term_vars (ATerm (name as (s, _), tms)) =
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  is_atp_variable s ? insert (op =) (name, NONE)
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  #> fold term_vars tms
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fun close_formula_universally phi = close_universally term_vars phi
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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
blanchet@42542
   315
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   316
                    [] >> ATerm) x
blanchet@42542
   317
and parse_mangled_types x =
blanchet@42542
   318
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   319
blanchet@42542
   320
fun unmangled_type s =
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   321
  s |> suffix ")" |> raw_explode
blanchet@42542
   322
    |> Scan.finite Symbol.stopper
blanchet@42542
   323
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   324
                                                quote s)) parse_mangled_type))
blanchet@42542
   325
    |> fst
blanchet@42542
   326
blanchet@42561
   327
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   328
fun unmangled_const s =
blanchet@42542
   329
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   330
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   331
  end
blanchet@42542
   332
blanchet@42674
   333
fun introduce_proxies tm =
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   334
  let
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   335
    fun aux top_level (CombApp (tm1, tm2)) =
blanchet@42568
   336
        CombApp (aux top_level tm1, aux false tm2)
blanchet@42574
   337
      | aux top_level (CombConst (name as (s, s'), T, T_args)) =
blanchet@42570
   338
        (case proxify_const s of
blanchet@42568
   339
           SOME proxy_base =>
blanchet@42568
   340
           if top_level then
blanchet@42568
   341
             (case s of
blanchet@42568
   342
                "c_False" => (tptp_false, s')
blanchet@42568
   343
              | "c_True" => (tptp_true, s')
blanchet@42568
   344
              | _ => name, [])
blanchet@42569
   345
           else
blanchet@42574
   346
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   347
          | NONE => (name, T_args))
blanchet@42574
   348
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42568
   349
      | aux _ tm = tm
blanchet@42674
   350
  in aux true tm end
blanchet@42568
   351
blanchet@42562
   352
fun combformula_from_prop thy eq_as_iff =
blanchet@38282
   353
  let
blanchet@42568
   354
    fun do_term bs t atomic_types =
blanchet@41140
   355
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42568
   356
      |>> (introduce_proxies #> AAtom)
blanchet@42568
   357
      ||> union (op =) atomic_types
blanchet@38282
   358
    fun do_quant bs q s T t' =
blanchet@38518
   359
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   360
        do_formula ((s, T) :: bs) t'
blanchet@42562
   361
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   362
      end
blanchet@38282
   363
    and do_conn bs c t1 t2 =
blanchet@38282
   364
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   365
      #>> uncurry (mk_aconn c)
blanchet@38282
   366
    and do_formula bs t =
blanchet@38282
   367
      case t of
blanchet@42531
   368
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   369
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   370
        do_quant bs AForall s T t'
blanchet@38282
   371
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   372
        do_quant bs AExists s T t'
haftmann@38795
   373
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   374
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   375
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   376
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   377
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   378
      | _ => do_term bs t
blanchet@38282
   379
  in do_formula [] end
blanchet@38282
   380
blanchet@42750
   381
fun presimplify_term ctxt =
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   382
  Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@42750
   383
  #> Meson.presimplify ctxt
blanchet@42750
   384
  #> prop_of
blanchet@38282
   385
wenzelm@41491
   386
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   387
fun conceal_bounds Ts t =
blanchet@38282
   388
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   389
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   390
fun reveal_bounds Ts =
blanchet@38282
   391
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   392
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   393
blanchet@42747
   394
fun extensionalize_term ctxt t =
blanchet@42747
   395
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42747
   396
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@42747
   397
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   398
  end
blanchet@38608
   399
blanchet@38282
   400
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   401
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   402
    if Meson.is_fol_term thy t then
blanchet@38491
   403
      t
blanchet@38491
   404
    else
blanchet@38491
   405
      let
blanchet@38491
   406
        fun aux Ts t =
blanchet@38491
   407
          case t of
blanchet@38491
   408
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   409
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   410
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   411
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   412
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   413
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   414
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   415
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   416
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   417
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   418
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   419
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   420
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   421
              $ t1 $ t2 =>
blanchet@38491
   422
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   423
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   424
                   t
blanchet@38491
   425
                 else
blanchet@38491
   426
                   t |> conceal_bounds Ts
blanchet@38491
   427
                     |> Envir.eta_contract
blanchet@38491
   428
                     |> cterm_of thy
blanchet@39890
   429
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   430
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   431
                     |> reveal_bounds Ts
blanchet@39370
   432
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   433
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   434
      handle THM _ =>
blanchet@38491
   435
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   436
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   437
             else HOLogic.true_const
blanchet@38491
   438
  end
blanchet@38282
   439
blanchet@38282
   440
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   441
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   442
fun freeze_term t =
blanchet@38282
   443
  let
blanchet@38282
   444
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   445
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   446
      | aux (Var ((s, i), T)) =
blanchet@38282
   447
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   448
      | aux t = t
blanchet@38282
   449
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   450
blanchet@40204
   451
(* making fact and conjecture formulas *)
blanchet@42640
   452
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   453
  let
wenzelm@42361
   454
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   455
    val t = t |> Envir.beta_eta_contract
blanchet@42944
   456
              |> transform_elim_prop
blanchet@41211
   457
              |> Object_Logic.atomize_term thy
blanchet@42563
   458
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   459
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@42742
   460
              |> Raw_Simplifier.rewrite_term thy
blanchet@42742
   461
                     (Meson.unfold_set_const_simps ctxt) []
blanchet@42747
   462
              |> extensionalize_term ctxt
blanchet@42750
   463
              |> presimp ? presimplify_term ctxt
blanchet@38282
   464
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   465
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   466
              |> kind <> Axiom ? freeze_term
blanchet@42836
   467
    val (combformula, atomic_types) = combformula_from_prop thy eq_as_iff t []
blanchet@38282
   468
  in
blanchet@42640
   469
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   470
     atomic_types = atomic_types}
blanchet@38282
   471
  end
blanchet@38282
   472
blanchet@42640
   473
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   474
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   475
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   476
    NONE
blanchet@41990
   477
  | (_, formula) => SOME formula
blanchet@42561
   478
blanchet@42709
   479
fun make_conjecture ctxt prem_kind ts =
blanchet@38613
   480
  let val last = length ts - 1 in
blanchet@42709
   481
    map2 (fn j => fn t =>
blanchet@42709
   482
             let
blanchet@42709
   483
               val (kind, maybe_negate) =
blanchet@42709
   484
                 if j = last then
blanchet@42709
   485
                   (Conjecture, I)
blanchet@42709
   486
                 else
blanchet@42709
   487
                   (prem_kind,
blanchet@42709
   488
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   489
                    else I)
blanchet@42709
   490
              in
blanchet@42881
   491
                make_formula ctxt true true (string_of_int j) General kind t
blanchet@42709
   492
                |> maybe_negate
blanchet@42709
   493
              end)
blanchet@38613
   494
         (0 upto last) ts
blanchet@38613
   495
  end
blanchet@38282
   496
blanchet@42682
   497
(** Finite and infinite type inference **)
blanchet@42682
   498
blanchet@42886
   499
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
blanchet@42886
   500
  | deep_freeze_atyp T = T
blanchet@42886
   501
val deep_freeze_type = map_atyps deep_freeze_atyp
blanchet@42886
   502
blanchet@42886
   503
val type_instance = Sign.typ_instance o Proof_Context.theory_of
blanchet@42886
   504
blanchet@42682
   505
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   506
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   507
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   508
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   509
blanchet@42886
   510
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
blanchet@42886
   511
    exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
blanchet@42836
   512
  | should_encode_type _ _ All_Types _ = true
blanchet@42682
   513
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   514
  | should_encode_type _ _ _ _ = false
blanchet@42682
   515
blanchet@42837
   516
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
   517
                             should_predicate_on_var T =
blanchet@42878
   518
    (heaviness = Heavy orelse should_predicate_on_var ()) andalso
blanchet@42878
   519
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
   520
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
   521
blanchet@42836
   522
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42836
   523
    String.isPrefix bound_var_prefix s
blanchet@42836
   524
  | is_var_or_bound_var (CombVar _) = true
blanchet@42836
   525
  | is_var_or_bound_var _ = false
blanchet@42836
   526
blanchet@42829
   527
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
blanchet@42829
   528
blanchet@42829
   529
fun should_tag_with_type _ _ _ Top_Level _ _ = false
blanchet@42837
   530
  | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
blanchet@42837
   531
    (case heaviness of
blanchet@42837
   532
       Heavy => should_encode_type ctxt nonmono_Ts level T
blanchet@42837
   533
     | Light =>
blanchet@42836
   534
       case (site, is_var_or_bound_var u) of
blanchet@42836
   535
         (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
blanchet@42829
   536
       | _ => false)
blanchet@42829
   537
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
   538
blanchet@42682
   539
val homo_infinite_T = @{typ ind} (* any infinite type *)
blanchet@42682
   540
blanchet@42682
   541
fun homogenized_type ctxt nonmono_Ts level T =
blanchet@42682
   542
  if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
blanchet@42682
   543
blanchet@42573
   544
(** "hBOOL" and "hAPP" **)
blanchet@41313
   545
blanchet@42574
   546
type sym_info =
blanchet@42563
   547
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   548
blanchet@42574
   549
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   550
  let
blanchet@42558
   551
    fun aux top_level tm =
blanchet@42558
   552
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   553
        (case head of
blanchet@42563
   554
           CombConst ((s, _), T, _) =>
blanchet@42558
   555
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   556
             I
blanchet@42558
   557
           else
blanchet@42563
   558
             let val ary = length args in
blanchet@42558
   559
               Symtab.map_default
blanchet@42558
   560
                   (s, {pred_sym = true,
blanchet@42563
   561
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   562
                        max_ary = 0, typ = SOME T})
blanchet@42563
   563
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   564
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   565
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   566
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   567
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   568
            end
blanchet@42558
   569
         | _ => I)
blanchet@42558
   570
        #> fold (aux false) args
blanchet@42558
   571
      end
blanchet@42558
   572
  in aux true end
blanchet@42674
   573
fun add_fact_syms_to_table explicit_apply =
blanchet@42834
   574
  fact_lift (formula_fold NONE (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   575
blanchet@42675
   576
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   577
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   578
   (make_fixed_const predicator_base,
blanchet@42563
   579
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   580
  ([tptp_false, tptp_true]
blanchet@42563
   581
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   582
blanchet@42544
   583
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   584
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   585
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   586
blanchet@42558
   587
fun min_arity_of sym_tab s =
blanchet@42558
   588
  case Symtab.lookup sym_tab s of
blanchet@42574
   589
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   590
  | NONE =>
blanchet@42558
   591
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   592
      SOME s =>
blanchet@42570
   593
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   594
        if s = predicator_base then 1
blanchet@42547
   595
        else if s = explicit_app_base then 2
blanchet@42547
   596
        else if s = type_pred_base then 1
blanchet@42557
   597
        else 0
blanchet@42547
   598
      end
blanchet@42544
   599
    | NONE => 0
blanchet@38282
   600
blanchet@38282
   601
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   602
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   603
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   604
   arguments and is used as a predicate. *)
blanchet@42558
   605
fun is_pred_sym sym_tab s =
blanchet@42558
   606
  case Symtab.lookup sym_tab s of
blanchet@42574
   607
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   608
    pred_sym andalso min_ary = max_ary
blanchet@42558
   609
  | NONE => false
blanchet@38282
   610
blanchet@42568
   611
val predicator_combconst =
blanchet@42568
   612
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   613
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   614
blanchet@42568
   615
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   616
  case strip_combterm_comb tm of
blanchet@42542
   617
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   618
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   619
  | _ => predicator tm
blanchet@42542
   620
blanchet@42544
   621
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   622
blanchet@42544
   623
fun explicit_app arg head =
blanchet@42544
   624
  let
blanchet@42562
   625
    val head_T = combtyp_of head
blanchet@42693
   626
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   627
    val explicit_app =
blanchet@42562
   628
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42693
   629
                 [arg_T, res_T])
blanchet@42544
   630
  in list_app explicit_app [head, arg] end
blanchet@42544
   631
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   632
blanchet@42565
   633
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   634
  let
blanchet@42544
   635
    fun aux tm =
blanchet@42544
   636
      case strip_combterm_comb tm of
blanchet@42544
   637
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   638
        args |> map aux
blanchet@42557
   639
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   640
             |>> list_app head
blanchet@42544
   641
             |-> list_explicit_app
blanchet@42544
   642
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   643
  in aux end
blanchet@38282
   644
blanchet@42753
   645
fun chop_fun 0 T = ([], T)
blanchet@42753
   646
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
   647
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
   648
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
   649
blanchet@42780
   650
fun filter_type_args _ _ _ [] = []
blanchet@42780
   651
  | filter_type_args thy s arity T_args =
blanchet@42834
   652
    let
blanchet@42834
   653
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42834
   654
      val U = if s = explicit_app_base then
blanchet@42834
   655
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
   656
              else
blanchet@42834
   657
                s |> Sign.the_const_type thy
blanchet@42834
   658
    in
blanchet@42781
   659
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
   660
        [] => []
blanchet@42781
   661
      | res_U_vars =>
blanchet@42781
   662
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
   663
          U_args ~~ T_args
blanchet@42781
   664
          |> map_filter (fn (U, T) =>
blanchet@42781
   665
                            if member (op =) res_U_vars (dest_TVar U) then
blanchet@42781
   666
                              SOME T
blanchet@42781
   667
                            else
blanchet@42781
   668
                              NONE)
blanchet@42781
   669
        end
blanchet@42780
   670
    end
blanchet@42780
   671
    handle TYPE _ => T_args
blanchet@42753
   672
blanchet@42753
   673
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42753
   674
  let
blanchet@42753
   675
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
   676
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
   677
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
   678
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   679
        let
blanchet@42701
   680
          val level = level_of_type_sys type_sys
blanchet@42701
   681
          val (T, T_args) =
blanchet@42701
   682
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   683
               anyway, by distinguishing overloads only on the homogenized
blanchet@42837
   684
               result type. Don't do it for lightweight type systems, though,
blanchet@42837
   685
               since it leads to too many unsound proofs. *)
blanchet@42701
   686
            if s = const_prefix ^ explicit_app_base andalso
blanchet@42726
   687
               length T_args = 2 andalso
blanchet@42836
   688
               not (is_type_sys_virtually_sound type_sys) andalso
blanchet@42837
   689
               heaviness_of_type_sys type_sys = Heavy then
blanchet@42701
   690
              T_args |> map (homogenized_type ctxt nonmono_Ts level)
blanchet@42701
   691
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42831
   692
                                    (T --> T, tl Ts)
blanchet@42701
   693
                                  end)
blanchet@42701
   694
            else
blanchet@42701
   695
              (T, T_args)
blanchet@42701
   696
        in
blanchet@42701
   697
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   698
             NONE => (name, T_args)
blanchet@42701
   699
           | SOME s'' =>
blanchet@42753
   700
             let
blanchet@42753
   701
               val s'' = invert_const s''
blanchet@42831
   702
               fun filtered_T_args false = T_args
blanchet@42831
   703
                 | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@42753
   704
             in
blanchet@42701
   705
               case type_arg_policy type_sys s'' of
blanchet@42831
   706
                 Explicit_Type_Args drop_args =>
blanchet@42831
   707
                 (name, filtered_T_args drop_args)
blanchet@42831
   708
               | Mangled_Type_Args drop_args =>
blanchet@42831
   709
                 (mangled_const_name (filtered_T_args drop_args) name, [])
blanchet@42753
   710
               | No_Type_Args => (name, [])
blanchet@42701
   711
             end)
blanchet@42701
   712
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   713
        end
blanchet@42753
   714
      | aux _ tm = tm
blanchet@42753
   715
  in aux 0 end
blanchet@42573
   716
blanchet@42701
   717
fun repair_combterm ctxt nonmono_Ts type_sys sym_tab =
blanchet@42565
   718
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   719
  #> introduce_predicators_in_combterm sym_tab
blanchet@42753
   720
  #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42701
   721
fun repair_fact ctxt nonmono_Ts type_sys sym_tab =
blanchet@42701
   722
  update_combformula (formula_map
blanchet@42701
   723
      (repair_combterm ctxt nonmono_Ts type_sys sym_tab))
blanchet@42573
   724
blanchet@42573
   725
(** Helper facts **)
blanchet@42573
   726
blanchet@42573
   727
fun ti_ti_helper_fact () =
blanchet@42573
   728
  let
blanchet@42573
   729
    fun var s = ATerm (`I s, [])
blanchet@42589
   730
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   731
  in
blanchet@42612
   732
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   733
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42879
   734
             |> close_formula_universally, simp_info, NONE)
blanchet@42573
   735
  end
blanchet@42573
   736
blanchet@42574
   737
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   738
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   739
    SOME mangled_s =>
blanchet@42573
   740
    let
blanchet@42573
   741
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   742
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42893
   743
      fun dub_and_inst c needs_fairly_sound (th, j) =
blanchet@42881
   744
        ((c ^ "_" ^ string_of_int j ^
blanchet@42893
   745
          (if needs_fairly_sound then typed_helper_suffix
blanchet@42881
   746
           else untyped_helper_suffix),
blanchet@42881
   747
          General),
blanchet@42573
   748
         let val t = th |> prop_of in
blanchet@42753
   749
           t |> ((case general_type_arg_policy type_sys of
blanchet@42753
   750
                    Mangled_Type_Args _ => true
blanchet@42753
   751
                  | _ => false) andalso
blanchet@42573
   752
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   753
                ? (case typ of
blanchet@42573
   754
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   755
                   | NONE => I)
blanchet@42573
   756
         end)
blanchet@42573
   757
      fun make_facts eq_as_iff =
blanchet@42573
   758
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42893
   759
      val fairly_sound = is_type_sys_fairly_sound type_sys
blanchet@42573
   760
    in
blanchet@42573
   761
      metis_helpers
blanchet@42894
   762
      |> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
blanchet@42573
   763
                  if metis_s <> unmangled_s orelse
blanchet@42894
   764
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
   765
                    []
blanchet@42573
   766
                  else
blanchet@42573
   767
                    ths ~~ (1 upto length ths)
blanchet@42893
   768
                    |> map (dub_and_inst mangled_s needs_fairly_sound)
blanchet@42893
   769
                    |> make_facts (not needs_fairly_sound))
blanchet@42573
   770
    end
blanchet@42573
   771
  | NONE => []
blanchet@42573
   772
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   773
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   774
blanchet@42573
   775
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   776
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   777
blanchet@42709
   778
fun translate_formulas ctxt prem_kind type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   779
  let
blanchet@42573
   780
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   781
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   782
    val (facts, fact_names) =
blanchet@42573
   783
      rich_facts
blanchet@42573
   784
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   785
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   786
      |> ListPair.unzip
blanchet@42573
   787
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   788
       boost an ATP's performance (for some reason). *)
blanchet@42573
   789
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   790
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   791
    val all_ts = goal_t :: fact_ts
blanchet@42573
   792
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   793
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   794
    val tycons = type_consts_of_terms thy all_ts
blanchet@42709
   795
    val conjs = make_conjecture ctxt prem_kind (hyp_ts @ [concl_t])
blanchet@42573
   796
    val (supers', arity_clauses) =
blanchet@42589
   797
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   798
      else make_arity_clauses thy tycons supers
blanchet@42573
   799
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   800
  in
blanchet@42573
   801
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   802
  end
blanchet@42573
   803
blanchet@42573
   804
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   805
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   806
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   807
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   808
blanchet@42573
   809
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   810
blanchet@42878
   811
fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
blanchet@42834
   812
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T])
blanchet@42834
   813
           |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
blanchet@42573
   814
           tm)
blanchet@42573
   815
blanchet@42878
   816
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@42878
   817
  | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@42878
   818
    accum orelse (s = "equal" andalso member (op =) tms (ATerm (name, [])))
blanchet@42878
   819
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
blanchet@42878
   820
  | is_var_nonmonotonic_in_formula pos phi _ name =
blanchet@42878
   821
    formula_fold pos (var_occurs_positively_naked_in_term name) phi false
blanchet@42834
   822
blanchet@42829
   823
fun tag_with_type ctxt nonmono_Ts type_sys T tm =
blanchet@42829
   824
  CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42829
   825
  |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42829
   826
  |> term_from_combterm ctxt nonmono_Ts type_sys Top_Level
blanchet@42829
   827
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42829
   828
and term_from_combterm ctxt nonmono_Ts type_sys site u =
blanchet@42573
   829
  let
blanchet@42829
   830
    val (head, args) = strip_combterm_comb u
blanchet@42829
   831
    val (x as (s, _), T_args) =
blanchet@42829
   832
      case head of
blanchet@42829
   833
        CombConst (name, _, T_args) => (name, T_args)
blanchet@42829
   834
      | CombVar (name, _) => (name, [])
blanchet@42829
   835
      | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42829
   836
    val arg_site = if site = Top_Level andalso s = "equal" then Eq_Arg
blanchet@42829
   837
                   else Elsewhere
blanchet@42829
   838
    val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42829
   839
                      map (term_from_combterm ctxt nonmono_Ts type_sys arg_site)
blanchet@42829
   840
                          args)
blanchet@42829
   841
    val T = combtyp_of u
blanchet@42829
   842
  in
blanchet@42829
   843
    t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
blanchet@42829
   844
            tag_with_type ctxt nonmono_Ts type_sys T
blanchet@42829
   845
          else
blanchet@42829
   846
            I)
blanchet@42829
   847
  end
blanchet@42834
   848
and formula_from_combformula ctxt nonmono_Ts type_sys should_predicate_on_var =
blanchet@42829
   849
  let
blanchet@42878
   850
    val do_term = term_from_combterm ctxt nonmono_Ts type_sys Top_Level
blanchet@42573
   851
    val do_bound_type =
blanchet@42682
   852
      case type_sys of
blanchet@42722
   853
        Simple_Types level =>
blanchet@42682
   854
        SOME o mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42682
   855
      | _ => K NONE
blanchet@42878
   856
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@42834
   857
      if should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42878
   858
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@42834
   859
        CombVar (name, T)
blanchet@42878
   860
        |> type_pred_combterm ctxt nonmono_Ts type_sys T
blanchet@42878
   861
        |> do_term |> AAtom |> SOME
blanchet@42573
   862
      else
blanchet@42573
   863
        NONE
blanchet@42878
   864
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
   865
        let
blanchet@42878
   866
          val phi = phi |> do_formula pos
blanchet@42878
   867
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
   868
        in
blanchet@42834
   869
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
   870
                                        | SOME T => do_bound_type T)),
blanchet@42834
   871
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
   872
                      (map_filter
blanchet@42834
   873
                           (fn (_, NONE) => NONE
blanchet@42834
   874
                             | (s, SOME T) =>
blanchet@42878
   875
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
   876
                           xs)
blanchet@42834
   877
                      phi)
blanchet@42834
   878
        end
blanchet@42878
   879
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@42878
   880
      | do_formula _ (AAtom tm) = AAtom (do_term tm)
blanchet@42878
   881
  in do_formula o SOME end
blanchet@42573
   882
blanchet@42956
   883
fun bound_atomic_types format type_sys Ts =
blanchet@42727
   884
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42956
   885
                (atp_type_literals_for_types format type_sys Axiom Ts))
blanchet@42727
   886
blanchet@42956
   887
fun formula_for_fact ctxt format nonmono_Ts type_sys
blanchet@42573
   888
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   889
  combformula
blanchet@42727
   890
  |> close_combformula_universally
blanchet@42727
   891
  |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42878
   892
                              is_var_nonmonotonic_in_formula true
blanchet@42956
   893
  |> bound_atomic_types format type_sys atomic_types
blanchet@42573
   894
  |> close_formula_universally
blanchet@42573
   895
blanchet@42573
   896
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   897
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   898
   the remote provers might care. *)
blanchet@42956
   899
fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
blanchet@42640
   900
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   901
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   902
                     else string_of_int j ^ "_") ^
blanchet@42647
   903
           ascii_of name,
blanchet@42956
   904
           kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
blanchet@42879
   905
           case locality of
blanchet@42879
   906
             Intro => intro_info
blanchet@42879
   907
           | Elim => elim_info
blanchet@42879
   908
           | Simp => simp_info
blanchet@42879
   909
           | _ => NONE)
blanchet@42573
   910
blanchet@42939
   911
fun formula_line_for_class_rel_clause
blanchet@42939
   912
        (ClassRelClause {name, subclass, superclass, ...}) =
blanchet@42573
   913
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   914
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   915
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   916
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42879
   917
             |> close_formula_universally, intro_info, NONE)
blanchet@42573
   918
  end
blanchet@42573
   919
blanchet@42573
   920
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   921
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   922
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   923
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   924
blanchet@42939
   925
fun formula_line_for_arity_clause
blanchet@42939
   926
        (ArityClause {name, prem_lits, concl_lits, ...}) =
blanchet@42577
   927
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   928
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42895
   929
                          o fo_literal_from_arity_literal) prem_lits)
blanchet@42573
   930
                    (formula_from_fo_literal
blanchet@42895
   931
                         (fo_literal_from_arity_literal concl_lits))
blanchet@42879
   932
           |> close_formula_universally, intro_info, NONE)
blanchet@42573
   933
blanchet@42680
   934
fun formula_line_for_conjecture ctxt nonmono_Ts type_sys
blanchet@42573
   935
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   936
  Formula (conjecture_prefix ^ name, kind,
blanchet@42680
   937
           formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42939
   938
               is_var_nonmonotonic_in_formula false
blanchet@42939
   939
               (close_combformula_universally combformula)
blanchet@42573
   940
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   941
blanchet@42956
   942
fun free_type_literals format type_sys
blanchet@42956
   943
                       ({atomic_types, ...} : translated_formula) =
blanchet@42956
   944
  atomic_types |> atp_type_literals_for_types format type_sys Conjecture
blanchet@42573
   945
               |> map fo_literal_from_type_literal
blanchet@42573
   946
blanchet@42573
   947
fun formula_line_for_free_type j lit =
blanchet@42577
   948
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   949
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42956
   950
fun formula_lines_for_free_types format type_sys facts =
blanchet@42573
   951
  let
blanchet@42956
   952
    val litss = map (free_type_literals format type_sys) facts
blanchet@42573
   953
    val lits = fold (union (op =)) litss []
blanchet@42573
   954
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   955
blanchet@42573
   956
(** Symbol declarations **)
blanchet@42544
   957
blanchet@42886
   958
fun insert_type ctxt get_T x xs =
blanchet@42677
   959
  let val T = get_T x in
blanchet@42886
   960
    if exists (curry (type_instance ctxt) T o get_T) xs then xs
blanchet@42886
   961
    else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
blanchet@42677
   962
  end
blanchet@42677
   963
blanchet@42574
   964
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   965
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42753
   966
  not (String.isPrefix tptp_special_prefix s) andalso
blanchet@42894
   967
  (case type_sys of
blanchet@42894
   968
     Simple_Types _ => true
blanchet@42894
   969
   | Tags (_, _, Light) => true
blanchet@42894
   970
   | _ => not pred_sym)
blanchet@38282
   971
blanchet@42886
   972
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
   973
  let
blanchet@42698
   974
    fun add_combterm in_conj tm =
blanchet@42574
   975
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   976
        (case head of
blanchet@42574
   977
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   978
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   979
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   980
               Symtab.map_default (s, [])
blanchet@42886
   981
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
   982
                                         in_conj))
blanchet@42574
   983
             else
blanchet@42574
   984
               I
blanchet@42574
   985
           end
blanchet@42574
   986
         | _ => I)
blanchet@42698
   987
        #> fold (add_combterm in_conj) args
blanchet@42574
   988
      end
blanchet@42698
   989
    fun add_fact in_conj =
blanchet@42834
   990
      fact_lift (formula_fold NONE (K (add_combterm in_conj)))
blanchet@42698
   991
  in
blanchet@42698
   992
    Symtab.empty
blanchet@42698
   993
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
   994
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
   995
  end
blanchet@42533
   996
blanchet@42886
   997
(* These types witness that the type classes they belong to allow infinite
blanchet@42886
   998
   models and hence that any types with these type classes is monotonic. *)
blanchet@42886
   999
val known_infinite_types = [@{typ nat}, @{typ int}, @{typ "nat => bool"}]
blanchet@42886
  1000
blanchet@42685
  1001
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  1002
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42886
  1003
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
blanchet@42829
  1004
  | add_combterm_nonmonotonic_types ctxt level _
blanchet@42680
  1005
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
  1006
                  tm2)) =
blanchet@42680
  1007
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
  1008
     (case level of
blanchet@42886
  1009
        Nonmonotonic_Types =>
blanchet@42886
  1010
        not (is_type_surely_infinite ctxt known_infinite_types T)
blanchet@42829
  1011
      | Finite_Types => is_type_surely_finite ctxt T
blanchet@42886
  1012
      | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
blanchet@42829
  1013
  | add_combterm_nonmonotonic_types _ _ _ _ = I
blanchet@42829
  1014
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
blanchet@42829
  1015
                                            : translated_formula) =
blanchet@42834
  1016
  formula_fold (SOME (kind <> Conjecture))
blanchet@42829
  1017
               (add_combterm_nonmonotonic_types ctxt level) combformula
blanchet@42886
  1018
fun nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42829
  1019
  let val level = level_of_type_sys type_sys in
blanchet@42886
  1020
    if level = Nonmonotonic_Types orelse level = Finite_Types then
blanchet@42886
  1021
      [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
blanchet@42886
  1022
         (* We must add "bool" in case the helper "True_or_False" is added
blanchet@42886
  1023
            later. In addition, several places in the code rely on the list of
blanchet@42886
  1024
            nonmonotonic types not being empty. *)
blanchet@42886
  1025
         |> insert_type ctxt I @{typ bool}
blanchet@42886
  1026
    else
blanchet@42886
  1027
      []
blanchet@42829
  1028
  end
blanchet@42677
  1029
blanchet@42754
  1030
fun decl_line_for_sym ctxt nonmono_Ts level s (s', _, T, pred_sym, ary, _) =
blanchet@42754
  1031
  let
blanchet@42754
  1032
    val translate_type =
blanchet@42754
  1033
      mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42754
  1034
    val (arg_tys, res_ty) =
blanchet@42754
  1035
      T |> chop_fun ary |>> map translate_type ||> translate_type
blanchet@42754
  1036
  in
blanchet@42754
  1037
    Decl (sym_decl_prefix ^ s, (s, s'), arg_tys,
blanchet@42754
  1038
          if pred_sym then `I tptp_tff_bool_type else res_ty)
blanchet@42579
  1039
  end
blanchet@42579
  1040
blanchet@42592
  1041
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
  1042
blanchet@42956
  1043
fun formula_line_for_pred_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1044
                                   n s j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1045
  let
blanchet@42709
  1046
    val (kind, maybe_negate) =
blanchet@42709
  1047
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1048
      else (Axiom, I)
blanchet@42753
  1049
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42579
  1050
    val bound_names =
blanchet@42579
  1051
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1052
    val bounds =
blanchet@42579
  1053
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
  1054
    val bound_Ts =
blanchet@42592
  1055
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
  1056
                             else NONE)
blanchet@42579
  1057
  in
blanchet@42612
  1058
    Formula (sym_decl_prefix ^ s ^
blanchet@42709
  1059
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1060
             CombConst ((s, s'), T, T_args)
blanchet@42829
  1061
             |> fold (curry (CombApp o swap)) bounds
blanchet@42878
  1062
             |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
blanchet@42878
  1063
             |> AAtom
blanchet@42579
  1064
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42878
  1065
             |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42878
  1066
                                         (K (K (K (K true)))) true
blanchet@42956
  1067
             |> n > 1 ? bound_atomic_types format type_sys (atyps_of T)
blanchet@42709
  1068
             |> close_formula_universally
blanchet@42709
  1069
             |> maybe_negate,
blanchet@42879
  1070
             intro_info, NONE)
blanchet@42579
  1071
  end
blanchet@42579
  1072
blanchet@42956
  1073
fun formula_lines_for_tag_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1074
        n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1075
  let
blanchet@42829
  1076
    val ident_base =
blanchet@42829
  1077
      sym_decl_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1078
    val (kind, maybe_negate) =
blanchet@42852
  1079
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1080
      else (Axiom, I)
blanchet@42829
  1081
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1082
    val bound_names =
blanchet@42829
  1083
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1084
    val bounds = bound_names |> map (fn name => ATerm (name, []))
blanchet@42829
  1085
    fun const args = ATerm ((s, s'), map fo_term_from_typ T_args @ args)
blanchet@42830
  1086
    val atomic_Ts = atyps_of T
blanchet@42834
  1087
    fun eq tms =
blanchet@42834
  1088
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@42834
  1089
       else AAtom (ATerm (`I "equal", tms)))
blanchet@42956
  1090
      |> bound_atomic_types format type_sys atomic_Ts
blanchet@42830
  1091
      |> close_formula_universally
blanchet@42852
  1092
      |> maybe_negate
blanchet@42836
  1093
    val should_encode = should_encode_type ctxt nonmono_Ts All_Types
blanchet@42829
  1094
    val tag_with = tag_with_type ctxt nonmono_Ts type_sys
blanchet@42829
  1095
    val add_formula_for_res =
blanchet@42829
  1096
      if should_encode res_T then
blanchet@42852
  1097
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42834
  1098
                       eq [tag_with res_T (const bounds), const bounds],
blanchet@42879
  1099
                       simp_info, NONE))
blanchet@42829
  1100
      else
blanchet@42829
  1101
        I
blanchet@42829
  1102
    fun add_formula_for_arg k =
blanchet@42829
  1103
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1104
        if should_encode arg_T then
blanchet@42829
  1105
          case chop k bounds of
blanchet@42829
  1106
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1107
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42834
  1108
                           eq [const (bounds1 @ tag_with arg_T bound ::
blanchet@42834
  1109
                                      bounds2),
blanchet@42834
  1110
                               const bounds],
blanchet@42879
  1111
                           simp_info, NONE))
blanchet@42829
  1112
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1113
        else
blanchet@42829
  1114
          I
blanchet@42829
  1115
      end
blanchet@42829
  1116
  in
blanchet@42834
  1117
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1118
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1119
  end
blanchet@42829
  1120
blanchet@42836
  1121
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1122
blanchet@42956
  1123
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1124
                                (s, decls) =
blanchet@42682
  1125
  case type_sys of
blanchet@42754
  1126
    Simple_Types level => map (decl_line_for_sym ctxt nonmono_Ts level s) decls
blanchet@42829
  1127
  | Preds _ =>
blanchet@42574
  1128
    let
blanchet@42579
  1129
      val decls =
blanchet@42579
  1130
        case decls of
blanchet@42579
  1131
          decl :: (decls' as _ :: _) =>
blanchet@42592
  1132
          let val T = result_type_of_decl decl in
blanchet@42886
  1133
            if forall (curry (type_instance ctxt o swap) T
blanchet@42592
  1134
                       o result_type_of_decl) decls' then
blanchet@42592
  1135
              [decl]
blanchet@42592
  1136
            else
blanchet@42592
  1137
              decls
blanchet@42592
  1138
          end
blanchet@42579
  1139
        | _ => decls
blanchet@42579
  1140
      val n = length decls
blanchet@42579
  1141
      val decls =
blanchet@42834
  1142
        decls
blanchet@42834
  1143
        |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
blanchet@42834
  1144
                   o result_type_of_decl)
blanchet@42574
  1145
    in
blanchet@42709
  1146
      (0 upto length decls - 1, decls)
blanchet@42956
  1147
      |-> map2 (formula_line_for_pred_sym_decl ctxt format conj_sym_kind
blanchet@42956
  1148
                                               nonmono_Ts type_sys n s)
blanchet@42574
  1149
    end
blanchet@42837
  1150
  | Tags (_, _, heaviness) =>
blanchet@42837
  1151
    (case heaviness of
blanchet@42837
  1152
       Heavy => []
blanchet@42837
  1153
     | Light =>
blanchet@42829
  1154
       let val n = length decls in
blanchet@42829
  1155
         (0 upto n - 1 ~~ decls)
blanchet@42956
  1156
         |> maps (formula_lines_for_tag_sym_decl ctxt format conj_sym_kind
blanchet@42956
  1157
                                                 nonmono_Ts type_sys n s)
blanchet@42829
  1158
       end)
blanchet@42579
  1159
blanchet@42956
  1160
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@42956
  1161
                                     type_sys sym_decl_tab =
blanchet@42956
  1162
  Symtab.fold_rev
blanchet@42956
  1163
      (append o problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
blanchet@42956
  1164
                                            type_sys)
blanchet@42956
  1165
      sym_decl_tab []
blanchet@42543
  1166
blanchet@42543
  1167
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
  1168
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
  1169
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
  1170
    fold add_tff_types_in_formula phis
blanchet@42543
  1171
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
  1172
blanchet@42562
  1173
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
  1174
    union (op =) (res_T :: arg_Ts)
blanchet@42577
  1175
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
  1176
    add_tff_types_in_formula phi
blanchet@42543
  1177
blanchet@42543
  1178
fun tff_types_in_problem problem =
blanchet@42543
  1179
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
  1180
blanchet@42545
  1181
fun decl_line_for_tff_type (s, s') =
blanchet@42568
  1182
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
  1183
blanchet@42837
  1184
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
blanchet@42831
  1185
    level = Nonmonotonic_Types orelse level = Finite_Types
blanchet@42831
  1186
  | should_add_ti_ti_helper _ = false
blanchet@42831
  1187
blanchet@42939
  1188
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  1189
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  1190
    if heading = needle then j
blanchet@42939
  1191
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  1192
blanchet@42543
  1193
val type_declsN = "Types"
blanchet@42544
  1194
val sym_declsN = "Symbol types"
blanchet@41157
  1195
val factsN = "Relevant facts"
blanchet@41157
  1196
val class_relsN = "Class relationships"
blanchet@42543
  1197
val aritiesN = "Arities"
blanchet@41157
  1198
val helpersN = "Helper facts"
blanchet@41157
  1199
val conjsN = "Conjectures"
blanchet@41313
  1200
val free_typesN = "Type variables"
blanchet@41157
  1201
blanchet@42939
  1202
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
blanchet@42939
  1203
                        explicit_apply hyp_ts concl_t facts =
blanchet@38282
  1204
  let
blanchet@41313
  1205
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42709
  1206
      translate_formulas ctxt prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1207
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42886
  1208
    val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
blanchet@42701
  1209
    val repair = repair_fact ctxt nonmono_Ts type_sys sym_tab
blanchet@42682
  1210
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1211
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1212
    val helpers =
blanchet@42682
  1213
      repaired_sym_tab |> helper_facts_for_sym_table ctxt type_sys |> map repair
blanchet@42894
  1214
    val lavish_nonmono_Ts =
blanchet@42894
  1215
      if null nonmono_Ts orelse
blanchet@42894
  1216
         polymorphism_of_type_sys type_sys <> Polymorphic then
blanchet@42894
  1217
        nonmono_Ts
blanchet@42894
  1218
      else
blanchet@42894
  1219
        [TVar (("'a", 0), HOLogic.typeS)]
blanchet@42680
  1220
    val sym_decl_lines =
blanchet@42731
  1221
      (conjs, helpers @ facts)
blanchet@42886
  1222
      |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
blanchet@42956
  1223
      |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
blanchet@42956
  1224
                                          lavish_nonmono_Ts type_sys
blanchet@42881
  1225
    val helper_lines =
blanchet@42956
  1226
      0 upto length helpers - 1 ~~ helpers
blanchet@42956
  1227
      |> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
blanchet@42956
  1228
                                    type_sys)
blanchet@42956
  1229
      |> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
blanchet@42956
  1230
          else I)
blanchet@42522
  1231
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1232
       Flotter hack. *)
blanchet@38282
  1233
    val problem =
blanchet@42561
  1234
      [(sym_declsN, sym_decl_lines),
blanchet@42956
  1235
       (factsN,
blanchet@42956
  1236
        map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
blanchet@42956
  1237
            (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1238
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1239
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42881
  1240
       (helpersN, helper_lines),
blanchet@42680
  1241
       (conjsN, map (formula_line_for_conjecture ctxt nonmono_Ts type_sys)
blanchet@42680
  1242
                    conjs),
blanchet@42956
  1243
       (free_typesN,
blanchet@42956
  1244
        formula_lines_for_free_types format type_sys (facts @ conjs))]
blanchet@42543
  1245
    val problem =
blanchet@42561
  1246
      problem
blanchet@42682
  1247
      |> (case type_sys of
blanchet@42722
  1248
            Simple_Types _ =>
blanchet@42561
  1249
            cons (type_declsN,
blanchet@42561
  1250
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42682
  1251
          | _ => I)
blanchet@42939
  1252
    val problem =
blanchet@42939
  1253
      problem |> (if format = CNF_UEQ then filter_cnf_ueq_problem else I)
blanchet@42646
  1254
    val (problem, pool) =
blanchet@42646
  1255
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@42881
  1256
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  1257
    val typed_helpers =
blanchet@42881
  1258
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  1259
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  1260
                     else NONE)
blanchet@42881
  1261
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  1262
                  ~~ helpers)
blanchet@42778
  1263
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1264
      if min_ary > 0 then
blanchet@42755
  1265
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1266
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1267
        | NONE => I
blanchet@42755
  1268
      else
blanchet@42755
  1269
        I
blanchet@38282
  1270
  in
blanchet@38282
  1271
    (problem,
blanchet@38282
  1272
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1273
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1274
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1275
     fact_names |> Vector.fromList,
blanchet@42881
  1276
     typed_helpers,
blanchet@42755
  1277
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1278
  end
blanchet@38282
  1279
blanchet@41313
  1280
(* FUDGE *)
blanchet@41313
  1281
val conj_weight = 0.0
blanchet@41770
  1282
val hyp_weight = 0.1
blanchet@41770
  1283
val fact_min_weight = 0.2
blanchet@41313
  1284
val fact_max_weight = 1.0
blanchet@42608
  1285
val type_info_default_weight = 0.8
blanchet@41313
  1286
blanchet@41313
  1287
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42734
  1288
  (not (is_atp_variable s) andalso s <> "equal" andalso
blanchet@42753
  1289
   not (String.isPrefix tptp_special_prefix s)) ? Symtab.default (s, weight)
blanchet@41313
  1290
  #> fold (add_term_weights weight) tms
blanchet@42577
  1291
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1292
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1293
  | add_problem_line_weights _ _ = I
blanchet@41313
  1294
blanchet@41313
  1295
fun add_conjectures_weights [] = I
blanchet@41313
  1296
  | add_conjectures_weights conjs =
blanchet@41313
  1297
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1298
      add_problem_line_weights conj_weight conj
blanchet@41313
  1299
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1300
    end
blanchet@41313
  1301
blanchet@41313
  1302
fun add_facts_weights facts =
blanchet@41313
  1303
  let
blanchet@41313
  1304
    val num_facts = length facts
blanchet@41313
  1305
    fun weight_of j =
blanchet@41313
  1306
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1307
                        / Real.fromInt num_facts
blanchet@41313
  1308
  in
blanchet@41313
  1309
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1310
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1311
  end
blanchet@41313
  1312
blanchet@41313
  1313
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1314
fun atp_problem_weights problem =
blanchet@42608
  1315
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1316
    Symtab.empty
blanchet@42608
  1317
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1318
    |> add_facts_weights (get factsN)
blanchet@42608
  1319
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1320
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1321
    |> Symtab.dest
blanchet@42608
  1322
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1323
  end
blanchet@41313
  1324
blanchet@38282
  1325
end;