src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Fri May 20 12:47:58 2011 +0200 (2011-05-20)
changeset 42878 85ac4c12a4b7
parent 42855 b48529f41888
child 42879 3b9669b11d33
permissions -rw-r--r--
slightly fewer type predicates introduced in the lightweight encoding, based on the observation that only universal positive equalities are dangerous
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
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    Author:     Fabian Immler, TU Muenchen
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    Author:     Makarius
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    Author:     Jasmin Blanchette, TU Muenchen
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Translation of HOL to FOL for Sledgehammer.
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*)
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signature SLEDGEHAMMER_ATP_TRANSLATE =
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sig
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  type 'a fo_term = 'a ATP_Problem.fo_term
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  type formula_kind = ATP_Problem.formula_kind
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  type 'a problem = 'a ATP_Problem.problem
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  type locality = Sledgehammer_Filter.locality
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  datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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  datatype type_level =
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    All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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  datatype type_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 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 -> formula_kind -> formula_kind -> type_system -> bool
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    -> term list -> term
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    -> (translated_formula option * ((string * 'a) * thm)) list
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    -> string problem * string Symtab.table * int * int
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       * (string * 'a) list vector * 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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(* Readable names are often much shorter, especially if types are mangled in
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   names. Also, the logic for generating legal SNARK sort names is only
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   implemented for readable names. Finally, readable names are, well, more
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   readable. For these reason, they are enabled by default. *)
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val readable_names =
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  Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
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val type_decl_prefix = "type_"
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val sym_decl_prefix = "sym_"
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val fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val class_rel_clause_prefix = "crel_";
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val arity_clause_prefix = "arity_"
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val tfree_prefix = "tfree_"
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val predicator_base = "hBOOL"
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val explicit_app_base = "hAPP"
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val type_pred_base = "is"
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val tff_type_prefix = "ty_"
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fun make_tff_type s = tff_type_prefix ^ ascii_of s
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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datatype type_level =
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  All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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datatype type_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 Polymorphic, _, _)) =>
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           if level = All_Types then Preds (Polymorphic, level, heaviness)
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           else raise Same.SAME
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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, Finite_Types, _)) =>
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           (* The light encoding yields too many unsound proofs. *)
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           Tags (Polymorphic, Finite_Types, Heavy)
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         | ("tags", (SOME Polymorphic, _, _)) => raise Same.SAME
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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 formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
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  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
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  | formula_map f (AAtom tm) = AAtom (f tm)
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fun 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_anot phi = AConn (ANot, [phi])
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
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fun mk_aconns c phis =
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  let val (phis', phi') = split_last phis in
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    fold_rev (mk_aconn c) phis' phi'
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  end
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fun mk_ahorn [] phi = phi
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  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
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fun mk_aquant _ [] phi = phi
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  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
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    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
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  | mk_aquant q xs phi = AQuant (q, xs, phi)
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fun close_universally atom_vars phi =
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  let
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    fun formula_vars bounds (AQuant (_, xs, phi)) =
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        formula_vars (map fst xs @ bounds) phi
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      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
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      | formula_vars bounds (AAtom tm) =
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        union (op =) (atom_vars tm []
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                      |> filter_out (member (op =) bounds o fst))
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  in mk_aquant AForall (formula_vars [] phi []) phi end
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fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
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  | combterm_vars (CombConst _) = I
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  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
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fun close_combformula_universally phi = close_universally combterm_vars phi
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fun term_vars (ATerm (name as (s, _), tms)) =
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  is_atp_variable s ? insert (op =) (name, NONE)
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  #> fold term_vars tms
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fun close_formula_universally phi = close_universally term_vars phi
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fun fo_term_from_typ (Type (s, Ts)) =
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    ATerm (`make_fixed_type_const s, map fo_term_from_typ Ts)
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  | fo_term_from_typ (TFree (s, _)) =
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    ATerm (`make_fixed_type_var s, [])
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  | fo_term_from_typ (TVar ((x as (s, _)), _)) =
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    ATerm ((make_schematic_type_var x, s), [])
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(* This shouldn't clash with anything else. *)
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val mangled_type_sep = "\000"
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fun generic_mangled_type_name f (ATerm (name, [])) = f name
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  | generic_mangled_type_name f (ATerm (name, tys)) =
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    f name ^ "(" ^ 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
   308
blanchet@42542
   309
fun unmangled_type s =
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   310
  s |> suffix ")" |> raw_explode
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   311
    |> Scan.finite Symbol.stopper
blanchet@42542
   312
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   313
                                                quote s)) parse_mangled_type))
blanchet@42542
   314
    |> fst
blanchet@42542
   315
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   316
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   317
fun unmangled_const s =
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   318
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   319
    (hd ss, map unmangled_type (tl ss))
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   320
  end
blanchet@42542
   321
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   322
fun introduce_proxies tm =
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   323
  let
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   324
    fun aux top_level (CombApp (tm1, tm2)) =
blanchet@42568
   325
        CombApp (aux top_level tm1, aux false tm2)
blanchet@42574
   326
      | aux top_level (CombConst (name as (s, s'), T, T_args)) =
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   327
        (case proxify_const s of
blanchet@42568
   328
           SOME proxy_base =>
blanchet@42568
   329
           if top_level then
blanchet@42568
   330
             (case s of
blanchet@42568
   331
                "c_False" => (tptp_false, s')
blanchet@42568
   332
              | "c_True" => (tptp_true, s')
blanchet@42568
   333
              | _ => name, [])
blanchet@42569
   334
           else
blanchet@42574
   335
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   336
          | NONE => (name, T_args))
blanchet@42574
   337
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42568
   338
      | aux _ tm = tm
blanchet@42674
   339
  in aux true tm end
blanchet@42568
   340
blanchet@42562
   341
fun combformula_from_prop thy eq_as_iff =
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   342
  let
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   343
    fun do_term bs t atomic_types =
blanchet@41140
   344
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42568
   345
      |>> (introduce_proxies #> AAtom)
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   346
      ||> union (op =) atomic_types
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   347
    fun do_quant bs q s T t' =
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   348
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   349
        do_formula ((s, T) :: bs) t'
blanchet@42562
   350
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
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   351
      end
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   352
    and do_conn bs c t1 t2 =
blanchet@38282
   353
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   354
      #>> uncurry (mk_aconn c)
blanchet@38282
   355
    and do_formula bs t =
blanchet@38282
   356
      case t of
blanchet@42531
   357
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
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   358
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   359
        do_quant bs AForall s T t'
blanchet@38282
   360
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   361
        do_quant bs AExists s T t'
haftmann@38795
   362
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   363
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   364
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   365
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   366
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   367
      | _ => do_term bs t
blanchet@38282
   368
  in do_formula [] end
blanchet@38282
   369
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   370
fun presimplify_term ctxt =
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   371
  Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
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   372
  #> Meson.presimplify ctxt
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   373
  #> prop_of
blanchet@38282
   374
wenzelm@41491
   375
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   376
fun conceal_bounds Ts t =
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   377
  subst_bounds (map (Free o apfst concealed_bound_name)
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   378
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   379
fun reveal_bounds Ts =
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   380
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   381
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   382
blanchet@42747
   383
fun extensionalize_term ctxt t =
blanchet@42747
   384
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42747
   385
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@42747
   386
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   387
  end
blanchet@38608
   388
blanchet@38282
   389
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   390
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   391
    if Meson.is_fol_term thy t then
blanchet@38491
   392
      t
blanchet@38491
   393
    else
blanchet@38491
   394
      let
blanchet@38491
   395
        fun aux Ts t =
blanchet@38491
   396
          case t of
blanchet@38491
   397
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   398
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   399
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   400
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   401
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   402
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   403
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   404
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   405
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   406
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   407
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   408
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   409
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   410
              $ t1 $ t2 =>
blanchet@38491
   411
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   412
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   413
                   t
blanchet@38491
   414
                 else
blanchet@38491
   415
                   t |> conceal_bounds Ts
blanchet@38491
   416
                     |> Envir.eta_contract
blanchet@38491
   417
                     |> cterm_of thy
blanchet@39890
   418
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   419
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   420
                     |> reveal_bounds Ts
blanchet@39370
   421
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   422
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   423
      handle THM _ =>
blanchet@38491
   424
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   425
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   426
             else HOLogic.true_const
blanchet@38491
   427
  end
blanchet@38282
   428
blanchet@38282
   429
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   430
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   431
fun freeze_term t =
blanchet@38282
   432
  let
blanchet@38282
   433
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   434
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   435
      | aux (Var ((s, i), T)) =
blanchet@38282
   436
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   437
      | aux t = t
blanchet@38282
   438
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   439
blanchet@40204
   440
(* making fact and conjecture formulas *)
blanchet@42640
   441
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   442
  let
wenzelm@42361
   443
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   444
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   445
              |> transform_elim_term
blanchet@41211
   446
              |> Object_Logic.atomize_term thy
blanchet@42563
   447
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   448
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@42742
   449
              |> Raw_Simplifier.rewrite_term thy
blanchet@42742
   450
                     (Meson.unfold_set_const_simps ctxt) []
blanchet@42747
   451
              |> extensionalize_term ctxt
blanchet@42750
   452
              |> presimp ? presimplify_term ctxt
blanchet@38282
   453
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   454
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   455
              |> kind <> Axiom ? freeze_term
blanchet@42836
   456
    val (combformula, atomic_types) = combformula_from_prop thy eq_as_iff t []
blanchet@38282
   457
  in
blanchet@42640
   458
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   459
     atomic_types = atomic_types}
blanchet@38282
   460
  end
blanchet@38282
   461
blanchet@42640
   462
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   463
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   464
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   465
    NONE
blanchet@41990
   466
  | (_, formula) => SOME formula
blanchet@42561
   467
blanchet@42709
   468
fun make_conjecture ctxt prem_kind ts =
blanchet@38613
   469
  let val last = length ts - 1 in
blanchet@42709
   470
    map2 (fn j => fn t =>
blanchet@42709
   471
             let
blanchet@42709
   472
               val (kind, maybe_negate) =
blanchet@42709
   473
                 if j = last then
blanchet@42709
   474
                   (Conjecture, I)
blanchet@42709
   475
                 else
blanchet@42709
   476
                   (prem_kind,
blanchet@42709
   477
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   478
                    else I)
blanchet@42709
   479
              in
blanchet@42709
   480
                make_formula ctxt true true (string_of_int j) Chained kind t
blanchet@42709
   481
                |> maybe_negate
blanchet@42709
   482
              end)
blanchet@38613
   483
         (0 upto last) ts
blanchet@38613
   484
  end
blanchet@38282
   485
blanchet@42682
   486
(** Finite and infinite type inference **)
blanchet@42682
   487
blanchet@42682
   488
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   489
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   490
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   491
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   492
blanchet@42836
   493
fun should_encode_type _ (nonmono_Ts as _ :: _) _ T =
blanchet@42836
   494
    exists (curry Type.raw_instance T) nonmono_Ts
blanchet@42836
   495
  | should_encode_type _ _ All_Types _ = true
blanchet@42682
   496
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   497
  | should_encode_type _ _ _ _ = false
blanchet@42682
   498
blanchet@42837
   499
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
   500
                             should_predicate_on_var T =
blanchet@42878
   501
    (heaviness = Heavy orelse should_predicate_on_var ()) andalso
blanchet@42878
   502
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
   503
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
   504
blanchet@42836
   505
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42836
   506
    String.isPrefix bound_var_prefix s
blanchet@42836
   507
  | is_var_or_bound_var (CombVar _) = true
blanchet@42836
   508
  | is_var_or_bound_var _ = false
blanchet@42836
   509
blanchet@42829
   510
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
blanchet@42829
   511
blanchet@42829
   512
fun should_tag_with_type _ _ _ Top_Level _ _ = false
blanchet@42837
   513
  | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
blanchet@42837
   514
    (case heaviness of
blanchet@42837
   515
       Heavy => should_encode_type ctxt nonmono_Ts level T
blanchet@42837
   516
     | Light =>
blanchet@42836
   517
       case (site, is_var_or_bound_var u) of
blanchet@42836
   518
         (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
blanchet@42829
   519
       | _ => false)
blanchet@42829
   520
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
   521
blanchet@42682
   522
val homo_infinite_T = @{typ ind} (* any infinite type *)
blanchet@42682
   523
blanchet@42682
   524
fun homogenized_type ctxt nonmono_Ts level T =
blanchet@42682
   525
  if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
blanchet@42682
   526
blanchet@42573
   527
(** "hBOOL" and "hAPP" **)
blanchet@41313
   528
blanchet@42574
   529
type sym_info =
blanchet@42563
   530
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   531
blanchet@42574
   532
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   533
  let
blanchet@42558
   534
    fun aux top_level tm =
blanchet@42558
   535
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   536
        (case head of
blanchet@42563
   537
           CombConst ((s, _), T, _) =>
blanchet@42558
   538
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   539
             I
blanchet@42558
   540
           else
blanchet@42563
   541
             let val ary = length args in
blanchet@42558
   542
               Symtab.map_default
blanchet@42558
   543
                   (s, {pred_sym = true,
blanchet@42563
   544
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   545
                        max_ary = 0, typ = SOME T})
blanchet@42563
   546
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   547
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   548
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   549
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   550
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   551
            end
blanchet@42558
   552
         | _ => I)
blanchet@42558
   553
        #> fold (aux false) args
blanchet@42558
   554
      end
blanchet@42558
   555
  in aux true end
blanchet@42674
   556
fun add_fact_syms_to_table explicit_apply =
blanchet@42834
   557
  fact_lift (formula_fold NONE (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   558
blanchet@42675
   559
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   560
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   561
   (make_fixed_const predicator_base,
blanchet@42563
   562
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   563
  ([tptp_false, tptp_true]
blanchet@42563
   564
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   565
blanchet@42544
   566
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   567
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   568
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   569
blanchet@42558
   570
fun min_arity_of sym_tab s =
blanchet@42558
   571
  case Symtab.lookup sym_tab s of
blanchet@42574
   572
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   573
  | NONE =>
blanchet@42558
   574
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   575
      SOME s =>
blanchet@42570
   576
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   577
        if s = predicator_base then 1
blanchet@42547
   578
        else if s = explicit_app_base then 2
blanchet@42547
   579
        else if s = type_pred_base then 1
blanchet@42557
   580
        else 0
blanchet@42547
   581
      end
blanchet@42544
   582
    | NONE => 0
blanchet@38282
   583
blanchet@38282
   584
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   585
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   586
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   587
   arguments and is used as a predicate. *)
blanchet@42558
   588
fun is_pred_sym sym_tab s =
blanchet@42558
   589
  case Symtab.lookup sym_tab s of
blanchet@42574
   590
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   591
    pred_sym andalso min_ary = max_ary
blanchet@42558
   592
  | NONE => false
blanchet@38282
   593
blanchet@42568
   594
val predicator_combconst =
blanchet@42568
   595
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   596
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   597
blanchet@42568
   598
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   599
  case strip_combterm_comb tm of
blanchet@42542
   600
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   601
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   602
  | _ => predicator tm
blanchet@42542
   603
blanchet@42544
   604
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   605
blanchet@42544
   606
fun explicit_app arg head =
blanchet@42544
   607
  let
blanchet@42562
   608
    val head_T = combtyp_of head
blanchet@42693
   609
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   610
    val explicit_app =
blanchet@42562
   611
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42693
   612
                 [arg_T, res_T])
blanchet@42544
   613
  in list_app explicit_app [head, arg] end
blanchet@42544
   614
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   615
blanchet@42565
   616
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   617
  let
blanchet@42544
   618
    fun aux tm =
blanchet@42544
   619
      case strip_combterm_comb tm of
blanchet@42544
   620
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   621
        args |> map aux
blanchet@42557
   622
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   623
             |>> list_app head
blanchet@42544
   624
             |-> list_explicit_app
blanchet@42544
   625
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   626
  in aux end
blanchet@38282
   627
blanchet@42753
   628
fun chop_fun 0 T = ([], T)
blanchet@42753
   629
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
   630
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
   631
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
   632
blanchet@42780
   633
fun filter_type_args _ _ _ [] = []
blanchet@42780
   634
  | filter_type_args thy s arity T_args =
blanchet@42834
   635
    let
blanchet@42834
   636
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42834
   637
      val U = if s = explicit_app_base then
blanchet@42834
   638
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
   639
              else
blanchet@42834
   640
                s |> Sign.the_const_type thy
blanchet@42834
   641
    in
blanchet@42781
   642
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
   643
        [] => []
blanchet@42781
   644
      | res_U_vars =>
blanchet@42781
   645
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
   646
          U_args ~~ T_args
blanchet@42781
   647
          |> map_filter (fn (U, T) =>
blanchet@42781
   648
                            if member (op =) res_U_vars (dest_TVar U) then
blanchet@42781
   649
                              SOME T
blanchet@42781
   650
                            else
blanchet@42781
   651
                              NONE)
blanchet@42781
   652
        end
blanchet@42780
   653
    end
blanchet@42780
   654
    handle TYPE _ => T_args
blanchet@42753
   655
blanchet@42753
   656
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42753
   657
  let
blanchet@42753
   658
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
   659
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
   660
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
   661
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   662
        let
blanchet@42701
   663
          val level = level_of_type_sys type_sys
blanchet@42701
   664
          val (T, T_args) =
blanchet@42701
   665
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   666
               anyway, by distinguishing overloads only on the homogenized
blanchet@42837
   667
               result type. Don't do it for lightweight type systems, though,
blanchet@42837
   668
               since it leads to too many unsound proofs. *)
blanchet@42701
   669
            if s = const_prefix ^ explicit_app_base andalso
blanchet@42726
   670
               length T_args = 2 andalso
blanchet@42836
   671
               not (is_type_sys_virtually_sound type_sys) andalso
blanchet@42837
   672
               heaviness_of_type_sys type_sys = Heavy then
blanchet@42701
   673
              T_args |> map (homogenized_type ctxt nonmono_Ts level)
blanchet@42701
   674
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42831
   675
                                    (T --> T, tl Ts)
blanchet@42701
   676
                                  end)
blanchet@42701
   677
            else
blanchet@42701
   678
              (T, T_args)
blanchet@42701
   679
        in
blanchet@42701
   680
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   681
             NONE => (name, T_args)
blanchet@42701
   682
           | SOME s'' =>
blanchet@42753
   683
             let
blanchet@42753
   684
               val s'' = invert_const s''
blanchet@42831
   685
               fun filtered_T_args false = T_args
blanchet@42831
   686
                 | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@42753
   687
             in
blanchet@42701
   688
               case type_arg_policy type_sys s'' of
blanchet@42831
   689
                 Explicit_Type_Args drop_args =>
blanchet@42831
   690
                 (name, filtered_T_args drop_args)
blanchet@42831
   691
               | Mangled_Type_Args drop_args =>
blanchet@42831
   692
                 (mangled_const_name (filtered_T_args drop_args) name, [])
blanchet@42753
   693
               | No_Type_Args => (name, [])
blanchet@42701
   694
             end)
blanchet@42701
   695
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   696
        end
blanchet@42753
   697
      | aux _ tm = tm
blanchet@42753
   698
  in aux 0 end
blanchet@42573
   699
blanchet@42701
   700
fun repair_combterm ctxt nonmono_Ts type_sys sym_tab =
blanchet@42565
   701
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   702
  #> introduce_predicators_in_combterm sym_tab
blanchet@42753
   703
  #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42701
   704
fun repair_fact ctxt nonmono_Ts type_sys sym_tab =
blanchet@42701
   705
  update_combformula (formula_map
blanchet@42701
   706
      (repair_combterm ctxt nonmono_Ts type_sys sym_tab))
blanchet@42573
   707
blanchet@42573
   708
(** Helper facts **)
blanchet@42573
   709
blanchet@42573
   710
fun ti_ti_helper_fact () =
blanchet@42573
   711
  let
blanchet@42573
   712
    fun var s = ATerm (`I s, [])
blanchet@42589
   713
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   714
  in
blanchet@42612
   715
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   716
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42573
   717
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   718
  end
blanchet@42573
   719
blanchet@42574
   720
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   721
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   722
    SOME mangled_s =>
blanchet@42573
   723
    let
blanchet@42573
   724
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   725
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42579
   726
      fun dub_and_inst c needs_some_types (th, j) =
blanchet@42579
   727
        ((c ^ "_" ^ string_of_int j ^ (if needs_some_types then "T" else ""),
blanchet@42640
   728
          Chained),
blanchet@42573
   729
         let val t = th |> prop_of in
blanchet@42753
   730
           t |> ((case general_type_arg_policy type_sys of
blanchet@42753
   731
                    Mangled_Type_Args _ => true
blanchet@42753
   732
                  | _ => false) andalso
blanchet@42573
   733
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   734
                ? (case typ of
blanchet@42573
   735
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   736
                   | NONE => I)
blanchet@42573
   737
         end)
blanchet@42573
   738
      fun make_facts eq_as_iff =
blanchet@42573
   739
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42589
   740
      val has_some_types = is_type_sys_fairly_sound type_sys
blanchet@42573
   741
    in
blanchet@42573
   742
      metis_helpers
blanchet@42579
   743
      |> maps (fn (metis_s, (needs_some_types, ths)) =>
blanchet@42573
   744
                  if metis_s <> unmangled_s orelse
blanchet@42589
   745
                     (needs_some_types andalso not has_some_types) then
blanchet@42573
   746
                    []
blanchet@42573
   747
                  else
blanchet@42573
   748
                    ths ~~ (1 upto length ths)
blanchet@42579
   749
                    |> map (dub_and_inst mangled_s needs_some_types)
blanchet@42579
   750
                    |> make_facts (not needs_some_types))
blanchet@42573
   751
    end
blanchet@42573
   752
  | NONE => []
blanchet@42573
   753
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   754
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   755
blanchet@42573
   756
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   757
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   758
blanchet@42709
   759
fun translate_formulas ctxt prem_kind type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   760
  let
blanchet@42573
   761
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   762
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   763
    val (facts, fact_names) =
blanchet@42573
   764
      rich_facts
blanchet@42573
   765
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   766
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   767
      |> ListPair.unzip
blanchet@42573
   768
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   769
       boost an ATP's performance (for some reason). *)
blanchet@42573
   770
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   771
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   772
    val all_ts = goal_t :: fact_ts
blanchet@42573
   773
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   774
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   775
    val tycons = type_consts_of_terms thy all_ts
blanchet@42709
   776
    val conjs = make_conjecture ctxt prem_kind (hyp_ts @ [concl_t])
blanchet@42573
   777
    val (supers', arity_clauses) =
blanchet@42589
   778
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   779
      else make_arity_clauses thy tycons supers
blanchet@42573
   780
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   781
  in
blanchet@42573
   782
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   783
  end
blanchet@42573
   784
blanchet@42573
   785
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   786
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   787
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   788
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   789
blanchet@42573
   790
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   791
blanchet@42878
   792
fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
blanchet@42834
   793
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T])
blanchet@42834
   794
           |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
blanchet@42573
   795
           tm)
blanchet@42573
   796
blanchet@42878
   797
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@42878
   798
  | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@42878
   799
    accum orelse (s = "equal" andalso member (op =) tms (ATerm (name, [])))
blanchet@42878
   800
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
blanchet@42878
   801
  | is_var_nonmonotonic_in_formula pos phi _ name =
blanchet@42878
   802
    formula_fold pos (var_occurs_positively_naked_in_term name) phi false
blanchet@42834
   803
blanchet@42829
   804
fun tag_with_type ctxt nonmono_Ts type_sys T tm =
blanchet@42829
   805
  CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42829
   806
  |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42829
   807
  |> term_from_combterm ctxt nonmono_Ts type_sys Top_Level
blanchet@42829
   808
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42829
   809
and term_from_combterm ctxt nonmono_Ts type_sys site u =
blanchet@42573
   810
  let
blanchet@42829
   811
    val (head, args) = strip_combterm_comb u
blanchet@42829
   812
    val (x as (s, _), T_args) =
blanchet@42829
   813
      case head of
blanchet@42829
   814
        CombConst (name, _, T_args) => (name, T_args)
blanchet@42829
   815
      | CombVar (name, _) => (name, [])
blanchet@42829
   816
      | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42829
   817
    val arg_site = if site = Top_Level andalso s = "equal" then Eq_Arg
blanchet@42829
   818
                   else Elsewhere
blanchet@42829
   819
    val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42829
   820
                      map (term_from_combterm ctxt nonmono_Ts type_sys arg_site)
blanchet@42829
   821
                          args)
blanchet@42829
   822
    val T = combtyp_of u
blanchet@42829
   823
  in
blanchet@42829
   824
    t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
blanchet@42829
   825
            tag_with_type ctxt nonmono_Ts type_sys T
blanchet@42829
   826
          else
blanchet@42829
   827
            I)
blanchet@42829
   828
  end
blanchet@42834
   829
and formula_from_combformula ctxt nonmono_Ts type_sys should_predicate_on_var =
blanchet@42829
   830
  let
blanchet@42878
   831
    val do_term = term_from_combterm ctxt nonmono_Ts type_sys Top_Level
blanchet@42573
   832
    val do_bound_type =
blanchet@42682
   833
      case type_sys of
blanchet@42722
   834
        Simple_Types level =>
blanchet@42682
   835
        SOME o mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42682
   836
      | _ => K NONE
blanchet@42878
   837
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@42834
   838
      if should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42878
   839
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@42834
   840
        CombVar (name, T)
blanchet@42878
   841
        |> type_pred_combterm ctxt nonmono_Ts type_sys T
blanchet@42878
   842
        |> do_term |> AAtom |> SOME
blanchet@42573
   843
      else
blanchet@42573
   844
        NONE
blanchet@42878
   845
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
   846
        let
blanchet@42878
   847
          val phi = phi |> do_formula pos
blanchet@42878
   848
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
   849
        in
blanchet@42834
   850
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
   851
                                        | SOME T => do_bound_type T)),
blanchet@42834
   852
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
   853
                      (map_filter
blanchet@42834
   854
                           (fn (_, NONE) => NONE
blanchet@42834
   855
                             | (s, SOME T) =>
blanchet@42878
   856
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
   857
                           xs)
blanchet@42834
   858
                      phi)
blanchet@42834
   859
        end
blanchet@42878
   860
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@42878
   861
      | do_formula _ (AAtom tm) = AAtom (do_term tm)
blanchet@42878
   862
  in do_formula o SOME end
blanchet@42573
   863
blanchet@42727
   864
fun bound_atomic_types type_sys Ts =
blanchet@42727
   865
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42727
   866
                (atp_type_literals_for_types type_sys Axiom Ts))
blanchet@42727
   867
blanchet@42680
   868
fun formula_for_fact ctxt nonmono_Ts type_sys
blanchet@42573
   869
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   870
  combformula
blanchet@42727
   871
  |> close_combformula_universally
blanchet@42727
   872
  |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42878
   873
                              is_var_nonmonotonic_in_formula true
blanchet@42727
   874
  |> bound_atomic_types type_sys atomic_types
blanchet@42573
   875
  |> close_formula_universally
blanchet@42573
   876
blanchet@42640
   877
fun useful_isabelle_info s = SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42640
   878
blanchet@42573
   879
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   880
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   881
   the remote provers might care. *)
blanchet@42680
   882
fun formula_line_for_fact ctxt prefix nonmono_Ts type_sys
blanchet@42640
   883
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   884
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   885
                     else string_of_int j ^ "_") ^
blanchet@42647
   886
           ascii_of name,
blanchet@42680
   887
           kind, formula_for_fact ctxt nonmono_Ts type_sys formula, NONE,
blanchet@42640
   888
           if generate_useful_info then
blanchet@42640
   889
             case locality of
blanchet@42640
   890
               Intro => useful_isabelle_info "intro"
blanchet@42640
   891
             | Elim => useful_isabelle_info "elim"
blanchet@42640
   892
             | Simp => useful_isabelle_info "simp"
blanchet@42640
   893
             | _ => NONE
blanchet@42640
   894
           else
blanchet@42640
   895
             NONE)
blanchet@42573
   896
blanchet@42573
   897
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@42573
   898
                                                       superclass, ...}) =
blanchet@42573
   899
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   900
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   901
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   902
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42573
   903
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   904
  end
blanchet@42573
   905
blanchet@42573
   906
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   907
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   908
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   909
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   910
blanchet@42573
   911
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@42573
   912
                                                ...}) =
blanchet@42577
   913
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   914
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42573
   915
                          o fo_literal_from_arity_literal) premLits)
blanchet@42573
   916
                    (formula_from_fo_literal
blanchet@42573
   917
                         (fo_literal_from_arity_literal conclLit))
blanchet@42573
   918
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   919
blanchet@42680
   920
fun formula_line_for_conjecture ctxt nonmono_Ts type_sys
blanchet@42573
   921
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   922
  Formula (conjecture_prefix ^ name, kind,
blanchet@42680
   923
           formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42878
   924
                                    is_var_nonmonotonic_in_formula false
blanchet@42573
   925
                                    (close_combformula_universally combformula)
blanchet@42573
   926
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   927
blanchet@42573
   928
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   929
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   930
               |> map fo_literal_from_type_literal
blanchet@42573
   931
blanchet@42573
   932
fun formula_line_for_free_type j lit =
blanchet@42577
   933
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   934
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   935
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   936
  let
blanchet@42573
   937
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   938
    val lits = fold (union (op =)) litss []
blanchet@42573
   939
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   940
blanchet@42573
   941
(** Symbol declarations **)
blanchet@42544
   942
blanchet@42677
   943
fun insert_type get_T x xs =
blanchet@42677
   944
  let val T = get_T x in
blanchet@42677
   945
    if exists (curry Type.raw_instance T o get_T) xs then xs
blanchet@42677
   946
    else x :: filter_out ((fn T' => Type.raw_instance (T', T)) o get_T) xs
blanchet@42677
   947
  end
blanchet@42677
   948
blanchet@42574
   949
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   950
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42753
   951
  not (String.isPrefix tptp_special_prefix s) andalso
blanchet@42834
   952
  ((case type_sys of
blanchet@42834
   953
      Simple_Types _ => true
blanchet@42837
   954
    | Tags (_, _, Light) => true
blanchet@42834
   955
    | _ => false) orelse not pred_sym)
blanchet@38282
   956
blanchet@42698
   957
fun sym_decl_table_for_facts type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
   958
  let
blanchet@42698
   959
    fun add_combterm in_conj tm =
blanchet@42574
   960
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   961
        (case head of
blanchet@42574
   962
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   963
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   964
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   965
               Symtab.map_default (s, [])
blanchet@42698
   966
                   (insert_type #3 (s', T_args, T, pred_sym, length args,
blanchet@42698
   967
                                    in_conj))
blanchet@42574
   968
             else
blanchet@42574
   969
               I
blanchet@42574
   970
           end
blanchet@42574
   971
         | _ => I)
blanchet@42698
   972
        #> fold (add_combterm in_conj) args
blanchet@42574
   973
      end
blanchet@42698
   974
    fun add_fact in_conj =
blanchet@42834
   975
      fact_lift (formula_fold NONE (K (add_combterm in_conj)))
blanchet@42698
   976
  in
blanchet@42698
   977
    Symtab.empty
blanchet@42698
   978
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
   979
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
   980
  end
blanchet@42533
   981
blanchet@42685
   982
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
   983
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42829
   984
fun add_combterm_nonmonotonic_types _ _  (SOME false) _ = I
blanchet@42829
   985
  | add_combterm_nonmonotonic_types ctxt level _
blanchet@42680
   986
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
   987
                  tm2)) =
blanchet@42680
   988
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
   989
     (case level of
blanchet@42829
   990
        Nonmonotonic_Types => not (is_type_surely_infinite ctxt T)
blanchet@42829
   991
      | Finite_Types => is_type_surely_finite ctxt T
blanchet@42829
   992
      | _ => true)) ? insert_type I T
blanchet@42829
   993
  | add_combterm_nonmonotonic_types _ _ _ _ = I
blanchet@42829
   994
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
blanchet@42829
   995
                                            : translated_formula) =
blanchet@42834
   996
  formula_fold (SOME (kind <> Conjecture))
blanchet@42829
   997
               (add_combterm_nonmonotonic_types ctxt level) combformula
blanchet@42680
   998
fun add_nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42829
   999
  let val level = level_of_type_sys type_sys in
blanchet@42836
  1000
    (case level of
blanchet@42836
  1001
       Nonmonotonic_Types => true
blanchet@42836
  1002
     | Finite_Types =>
blanchet@42837
  1003
       heaviness_of_type_sys type_sys = Light andalso
blanchet@42836
  1004
       polymorphism_of_type_sys type_sys <> Polymorphic
blanchet@42836
  1005
     | _ => false)
blanchet@42829
  1006
    ? (fold (add_fact_nonmonotonic_types ctxt level) facts
blanchet@42836
  1007
       (* We must add bool in case the helper "True_or_False" is added later.
blanchet@42836
  1008
          In addition, several places in the code rely on the list of
blanchet@42836
  1009
          nonmonotonic types not being empty. *)
blanchet@42829
  1010
       #> insert_type I @{typ bool})
blanchet@42829
  1011
  end
blanchet@42677
  1012
blanchet@42754
  1013
fun decl_line_for_sym ctxt nonmono_Ts level s (s', _, T, pred_sym, ary, _) =
blanchet@42754
  1014
  let
blanchet@42754
  1015
    val translate_type =
blanchet@42754
  1016
      mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42754
  1017
    val (arg_tys, res_ty) =
blanchet@42754
  1018
      T |> chop_fun ary |>> map translate_type ||> translate_type
blanchet@42754
  1019
  in
blanchet@42754
  1020
    Decl (sym_decl_prefix ^ s, (s, s'), arg_tys,
blanchet@42754
  1021
          if pred_sym then `I tptp_tff_bool_type else res_ty)
blanchet@42579
  1022
  end
blanchet@42579
  1023
blanchet@42592
  1024
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
  1025
blanchet@42829
  1026
fun formula_line_for_pred_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys n s j
blanchet@42829
  1027
                                   (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1028
  let
blanchet@42709
  1029
    val (kind, maybe_negate) =
blanchet@42709
  1030
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1031
      else (Axiom, I)
blanchet@42753
  1032
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42579
  1033
    val bound_names =
blanchet@42579
  1034
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1035
    val bounds =
blanchet@42579
  1036
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
  1037
    val bound_Ts =
blanchet@42592
  1038
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
  1039
                             else NONE)
blanchet@42579
  1040
  in
blanchet@42612
  1041
    Formula (sym_decl_prefix ^ s ^
blanchet@42709
  1042
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1043
             CombConst ((s, s'), T, T_args)
blanchet@42829
  1044
             |> fold (curry (CombApp o swap)) bounds
blanchet@42878
  1045
             |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
blanchet@42878
  1046
             |> AAtom
blanchet@42579
  1047
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42878
  1048
             |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42878
  1049
                                         (K (K (K (K true)))) true
blanchet@42727
  1050
             |> n > 1 ? bound_atomic_types type_sys (atyps_of T)
blanchet@42709
  1051
             |> close_formula_universally
blanchet@42709
  1052
             |> maybe_negate,
blanchet@42579
  1053
             NONE, NONE)
blanchet@42579
  1054
  end
blanchet@42579
  1055
blanchet@42852
  1056
fun formula_lines_for_tag_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys n s
blanchet@42852
  1057
                                  (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1058
  let
blanchet@42829
  1059
    val ident_base =
blanchet@42829
  1060
      sym_decl_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1061
    val (kind, maybe_negate) =
blanchet@42852
  1062
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1063
      else (Axiom, I)
blanchet@42829
  1064
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1065
    val bound_names =
blanchet@42829
  1066
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1067
    val bounds = bound_names |> map (fn name => ATerm (name, []))
blanchet@42829
  1068
    fun const args = ATerm ((s, s'), map fo_term_from_typ T_args @ args)
blanchet@42830
  1069
    val atomic_Ts = atyps_of T
blanchet@42834
  1070
    fun eq tms =
blanchet@42834
  1071
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@42834
  1072
       else AAtom (ATerm (`I "equal", tms)))
blanchet@42830
  1073
      |> bound_atomic_types type_sys atomic_Ts
blanchet@42830
  1074
      |> close_formula_universally
blanchet@42852
  1075
      |> maybe_negate
blanchet@42836
  1076
    val should_encode = should_encode_type ctxt nonmono_Ts All_Types
blanchet@42829
  1077
    val tag_with = tag_with_type ctxt nonmono_Ts type_sys
blanchet@42829
  1078
    val add_formula_for_res =
blanchet@42829
  1079
      if should_encode res_T then
blanchet@42852
  1080
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42834
  1081
                       eq [tag_with res_T (const bounds), const bounds],
blanchet@42829
  1082
                       NONE, NONE))
blanchet@42829
  1083
      else
blanchet@42829
  1084
        I
blanchet@42829
  1085
    fun add_formula_for_arg k =
blanchet@42829
  1086
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1087
        if should_encode arg_T then
blanchet@42829
  1088
          case chop k bounds of
blanchet@42829
  1089
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1090
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42834
  1091
                           eq [const (bounds1 @ tag_with arg_T bound ::
blanchet@42834
  1092
                                      bounds2),
blanchet@42834
  1093
                               const bounds],
blanchet@42829
  1094
                           NONE, NONE))
blanchet@42829
  1095
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1096
        else
blanchet@42829
  1097
          I
blanchet@42829
  1098
      end
blanchet@42829
  1099
  in
blanchet@42834
  1100
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1101
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1102
  end
blanchet@42829
  1103
blanchet@42836
  1104
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1105
blanchet@42709
  1106
fun problem_lines_for_sym_decls ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1107
                                (s, decls) =
blanchet@42682
  1108
  case type_sys of
blanchet@42754
  1109
    Simple_Types level => map (decl_line_for_sym ctxt nonmono_Ts level s) decls
blanchet@42829
  1110
  | Preds _ =>
blanchet@42574
  1111
    let
blanchet@42579
  1112
      val decls =
blanchet@42579
  1113
        case decls of
blanchet@42579
  1114
          decl :: (decls' as _ :: _) =>
blanchet@42592
  1115
          let val T = result_type_of_decl decl in
blanchet@42592
  1116
            if forall ((fn T' => Type.raw_instance (T', T))
blanchet@42592
  1117
                       o result_type_of_decl) decls' then
blanchet@42592
  1118
              [decl]
blanchet@42592
  1119
            else
blanchet@42592
  1120
              decls
blanchet@42592
  1121
          end
blanchet@42579
  1122
        | _ => decls
blanchet@42579
  1123
      val n = length decls
blanchet@42579
  1124
      val decls =
blanchet@42834
  1125
        decls
blanchet@42834
  1126
        |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
blanchet@42834
  1127
                   o result_type_of_decl)
blanchet@42574
  1128
    in
blanchet@42709
  1129
      (0 upto length decls - 1, decls)
blanchet@42829
  1130
      |-> map2 (formula_line_for_pred_sym_decl ctxt conj_sym_kind nonmono_Ts
blanchet@42829
  1131
                                               type_sys n s)
blanchet@42574
  1132
    end
blanchet@42837
  1133
  | Tags (_, _, heaviness) =>
blanchet@42837
  1134
    (case heaviness of
blanchet@42837
  1135
       Heavy => []
blanchet@42837
  1136
     | Light =>
blanchet@42829
  1137
       let val n = length decls in
blanchet@42829
  1138
         (0 upto n - 1 ~~ decls)
blanchet@42852
  1139
         |> maps (formula_lines_for_tag_sym_decl ctxt conj_sym_kind nonmono_Ts
blanchet@42852
  1140
                                                 type_sys n s)
blanchet@42829
  1141
       end)
blanchet@42579
  1142
blanchet@42709
  1143
fun problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1144
                                     sym_decl_tab =
blanchet@42709
  1145
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt conj_sym_kind
blanchet@42709
  1146
                                                        nonmono_Ts type_sys)
blanchet@42574
  1147
                  sym_decl_tab []
blanchet@42543
  1148
blanchet@42543
  1149
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
  1150
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
  1151
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
  1152
    fold add_tff_types_in_formula phis
blanchet@42543
  1153
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
  1154
blanchet@42562
  1155
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
  1156
    union (op =) (res_T :: arg_Ts)
blanchet@42577
  1157
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
  1158
    add_tff_types_in_formula phi
blanchet@42543
  1159
blanchet@42543
  1160
fun tff_types_in_problem problem =
blanchet@42543
  1161
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
  1162
blanchet@42545
  1163
fun decl_line_for_tff_type (s, s') =
blanchet@42568
  1164
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
  1165
blanchet@42837
  1166
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
blanchet@42831
  1167
    level = Nonmonotonic_Types orelse level = Finite_Types
blanchet@42831
  1168
  | should_add_ti_ti_helper _ = false
blanchet@42831
  1169
blanchet@42543
  1170
val type_declsN = "Types"
blanchet@42544
  1171
val sym_declsN = "Symbol types"
blanchet@41157
  1172
val factsN = "Relevant facts"
blanchet@41157
  1173
val class_relsN = "Class relationships"
blanchet@42543
  1174
val aritiesN = "Arities"
blanchet@41157
  1175
val helpersN = "Helper facts"
blanchet@41157
  1176
val conjsN = "Conjectures"
blanchet@41313
  1177
val free_typesN = "Type variables"
blanchet@41157
  1178
blanchet@41157
  1179
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
  1180
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
  1181
    if heading = needle then j
blanchet@41157
  1182
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
  1183
blanchet@42709
  1184
fun prepare_atp_problem ctxt conj_sym_kind prem_kind type_sys explicit_apply
blanchet@42709
  1185
                        hyp_ts concl_t facts =
blanchet@38282
  1186
  let
blanchet@41313
  1187
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42709
  1188
      translate_formulas ctxt prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1189
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42682
  1190
    val nonmono_Ts =
blanchet@42682
  1191
      [] |> fold (add_nonmonotonic_types_for_facts ctxt type_sys) [facts, conjs]
blanchet@42701
  1192
    val repair = repair_fact ctxt nonmono_Ts type_sys sym_tab
blanchet@42682
  1193
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1194
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1195
    val helpers =
blanchet@42682
  1196
      repaired_sym_tab |> helper_facts_for_sym_table ctxt type_sys |> map repair
blanchet@42680
  1197
    val sym_decl_lines =
blanchet@42731
  1198
      (conjs, helpers @ facts)
blanchet@42680
  1199
      |> sym_decl_table_for_facts type_sys repaired_sym_tab
blanchet@42709
  1200
      |> problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42522
  1201
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1202
       Flotter hack. *)
blanchet@38282
  1203
    val problem =
blanchet@42561
  1204
      [(sym_declsN, sym_decl_lines),
blanchet@42680
  1205
       (factsN, map (formula_line_for_fact ctxt fact_prefix nonmono_Ts type_sys)
blanchet@42180
  1206
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1207
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1208
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42680
  1209
       (helpersN, map (formula_line_for_fact ctxt helper_prefix nonmono_Ts
blanchet@42680
  1210
                                             type_sys)
blanchet@42563
  1211
                      (0 upto length helpers - 1 ~~ helpers)
blanchet@42831
  1212
                  |> should_add_ti_ti_helper type_sys
blanchet@42831
  1213
                     ? cons (ti_ti_helper_fact ())),
blanchet@42680
  1214
       (conjsN, map (formula_line_for_conjecture ctxt nonmono_Ts type_sys)
blanchet@42680
  1215
                    conjs),
blanchet@42545
  1216
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1217
    val problem =
blanchet@42561
  1218
      problem
blanchet@42682
  1219
      |> (case type_sys of
blanchet@42722
  1220
            Simple_Types _ =>
blanchet@42561
  1221
            cons (type_declsN,
blanchet@42561
  1222
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42682
  1223
          | _ => I)
blanchet@42646
  1224
    val (problem, pool) =
blanchet@42646
  1225
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@42778
  1226
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1227
      if min_ary > 0 then
blanchet@42755
  1228
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1229
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1230
        | NONE => I
blanchet@42755
  1231
      else
blanchet@42755
  1232
        I
blanchet@38282
  1233
  in
blanchet@38282
  1234
    (problem,
blanchet@38282
  1235
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1236
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1237
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1238
     fact_names |> Vector.fromList,
blanchet@42755
  1239
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1240
  end
blanchet@38282
  1241
blanchet@41313
  1242
(* FUDGE *)
blanchet@41313
  1243
val conj_weight = 0.0
blanchet@41770
  1244
val hyp_weight = 0.1
blanchet@41770
  1245
val fact_min_weight = 0.2
blanchet@41313
  1246
val fact_max_weight = 1.0
blanchet@42608
  1247
val type_info_default_weight = 0.8
blanchet@41313
  1248
blanchet@41313
  1249
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42734
  1250
  (not (is_atp_variable s) andalso s <> "equal" andalso
blanchet@42753
  1251
   not (String.isPrefix tptp_special_prefix s)) ? Symtab.default (s, weight)
blanchet@41313
  1252
  #> fold (add_term_weights weight) tms
blanchet@42577
  1253
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1254
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1255
  | add_problem_line_weights _ _ = I
blanchet@41313
  1256
blanchet@41313
  1257
fun add_conjectures_weights [] = I
blanchet@41313
  1258
  | add_conjectures_weights conjs =
blanchet@41313
  1259
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1260
      add_problem_line_weights conj_weight conj
blanchet@41313
  1261
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1262
    end
blanchet@41313
  1263
blanchet@41313
  1264
fun add_facts_weights facts =
blanchet@41313
  1265
  let
blanchet@41313
  1266
    val num_facts = length facts
blanchet@41313
  1267
    fun weight_of j =
blanchet@41313
  1268
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1269
                        / Real.fromInt num_facts
blanchet@41313
  1270
  in
blanchet@41313
  1271
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1272
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1273
  end
blanchet@41313
  1274
blanchet@41313
  1275
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1276
fun atp_problem_weights problem =
blanchet@42608
  1277
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1278
    Symtab.empty
blanchet@42608
  1279
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1280
    |> add_facts_weights (get factsN)
blanchet@42608
  1281
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1282
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1283
    |> Symtab.dest
blanchet@42608
  1284
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1285
  end
blanchet@41313
  1286
blanchet@38282
  1287
end;