src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Thu May 12 15:29:19 2011 +0200 (2011-05-12)
changeset 42754 b9d7df8c51c8
parent 42753 c9552e617acc
child 42755 4603154a3018
permissions -rw-r--r--
make sure "simple_types_query" and "simple_types_bang" symbols are declared with the proper types
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
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    Author:     Fabian Immler, TU Muenchen
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    Author:     Makarius
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    Author:     Jasmin Blanchette, TU Muenchen
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Translation of HOL to FOL for Sledgehammer.
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*)
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signature SLEDGEHAMMER_ATP_TRANSLATE =
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sig
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  type 'a fo_term = 'a ATP_Problem.fo_term
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  type formula_kind = ATP_Problem.formula_kind
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  type 'a problem = 'a ATP_Problem.problem
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  type locality = Sledgehammer_Filter.locality
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  datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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  datatype type_level =
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    All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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  datatype type_system =
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    Simple_Types of type_level |
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    Preds of polymorphism * type_level |
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    Tags of polymorphism * type_level
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  type translated_formula
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  val readable_names : bool Config.T
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  val fact_prefix : string
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  val conjecture_prefix : string
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  val predicator_base : string
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  val explicit_app_base : string
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  val type_pred_base : string
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  val tff_type_prefix : string
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  val type_sys_from_string : string -> type_system
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  val polymorphism_of_type_sys : type_system -> polymorphism
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  val level_of_type_sys : type_system -> type_level
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  val is_type_sys_virtually_sound : type_system -> bool
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  val is_type_sys_fairly_sound : type_system -> bool
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  val num_atp_type_args : theory -> type_system -> string -> int
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  val unmangled_const : string -> string * string fo_term list
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  val translate_atp_fact :
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    Proof.context -> bool -> (string * locality) * thm
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    -> translated_formula option * ((string * locality) * thm)
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  val prepare_atp_problem :
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    Proof.context -> formula_kind -> formula_kind -> type_system -> bool
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    -> term list -> term
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    -> (translated_formula option * ((string * 'a) * thm)) list
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    -> string problem * string Symtab.table * int * int
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       * (string * 'a) list vector
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  val atp_problem_weights : string problem -> (string * real) list
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end;
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structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
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struct
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open ATP_Problem
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open Metis_Translate
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open Sledgehammer_Util
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open Sledgehammer_Filter
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(* experimental *)
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val generate_useful_info = false
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(* Readable names are often much shorter, especially if types are mangled in
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   names. Also, the logic for generating legal SNARK sort names is only
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   implemented for readable names. Finally, readable names are, well, more
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   readable. For these reason, they are enabled by default. *)
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val readable_names =
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  Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
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val type_decl_prefix = "type_"
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val sym_decl_prefix = "sym_"
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val fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val class_rel_clause_prefix = "crel_";
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val arity_clause_prefix = "arity_"
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val tfree_prefix = "tfree_"
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val predicator_base = "hBOOL"
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val explicit_app_base = "hAPP"
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val type_pred_base = "is"
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val tff_type_prefix = "ty_"
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fun make_tff_type s = tff_type_prefix ^ ascii_of s
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
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datatype type_level =
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  All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
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datatype type_system =
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  Simple_Types of type_level |
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  Preds of polymorphism * type_level |
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  Tags of polymorphism * type_level
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fun try_unsuffixes ss s =
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  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
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fun type_sys_from_string s =
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  (case try (unprefix "poly_") s of
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     SOME s => (SOME Polymorphic, s)
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   | NONE =>
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     case try (unprefix "mono_") s of
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       SOME s => (SOME Monomorphic, s)
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     | NONE =>
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       case try (unprefix "mangled_") s of
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         SOME s => (SOME Mangled_Monomorphic, s)
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       | NONE => (NONE, s))
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  ||> (fn s =>
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          (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
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          case try_unsuffixes ["?", "_query"] s of
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            SOME s => (Nonmonotonic_Types, s)
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          | NONE =>
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            case try_unsuffixes ["!", "_bang"] s of
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              SOME s => (Finite_Types, s)
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            | NONE => (All_Types, s))
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  |> (fn (poly, (level, core)) =>
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         case (core, (poly, level)) of
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           ("simple_types", (NONE, level)) => Simple_Types level
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         | ("preds", (SOME Polymorphic, level)) =>
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           if level = All_Types then Preds (Polymorphic, level)
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           else raise Same.SAME
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         | ("preds", (SOME poly, level)) => Preds (poly, level)
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         | ("tags", (SOME Polymorphic, level)) =>
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           if level = All_Types orelse level = Finite_Types then
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             Tags (Polymorphic, level)
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           else
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             raise Same.SAME
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         | ("tags", (SOME poly, level)) => Tags (poly, level)
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         | ("args", (SOME poly, All_Types (* naja *))) =>
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           Preds (poly, Const_Arg_Types)
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         | ("erased", (NONE, All_Types (* naja *))) =>
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           Preds (Polymorphic, No_Types)
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         | _ => 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 is_type_level_virtually_sound level =
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  level = All_Types orelse level = Nonmonotonic_Types
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val is_type_sys_virtually_sound =
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  is_type_level_virtually_sound o level_of_type_sys
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fun is_type_level_fairly_sound level =
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  is_type_level_virtually_sound level orelse level = Finite_Types
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val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
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fun is_type_level_partial level =
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  level = Nonmonotonic_Types orelse level = Finite_Types
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fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
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  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
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  | formula_map f (AAtom tm) = AAtom (f tm)
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fun formula_fold pos f =
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  let
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    fun aux pos (AQuant (_, _, phi)) = aux pos phi
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      | aux pos (AConn (ANot, [phi])) = aux (Option.map not pos) phi
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      | aux pos (AConn (AImplies, [phi1, phi2])) =
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        aux (Option.map not pos) phi1 #> aux pos phi2
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      | aux pos (AConn (AAnd, phis)) = fold (aux pos) phis
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      | aux pos (AConn (AOr, phis)) = fold (aux pos) phis
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      | aux _ (AConn (_, phis)) = fold (aux NONE) phis
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      | aux pos (AAtom tm) = f pos tm
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  in aux (SOME pos) end
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type translated_formula =
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  {name: string,
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   locality: locality,
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   kind: formula_kind,
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   combformula: (name, typ, combterm) formula,
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   atomic_types: typ list}
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fun update_combformula f ({name, locality, kind, combformula, atomic_types}
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                          : translated_formula) =
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  {name = name, locality = locality, kind = kind, combformula = f combformula,
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   atomic_types = atomic_types} : translated_formula
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fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
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val boring_consts = [explicit_app_base, @{const_name Metis.fequal}]
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fun should_omit_type_args type_sys s =
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  s <> type_pred_base andalso s <> type_tag_name andalso
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  (s = @{const_name HOL.eq} orelse level_of_type_sys type_sys = No_Types orelse
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   (case type_sys of
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      Tags (_, All_Types) => true
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    | _ => polymorphism_of_type_sys type_sys <> Mangled_Monomorphic andalso
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           member (op =) boring_consts s))
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(* 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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(* FIXME: Find out whether and when erasing the non-result type arguments is
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   sound. *)
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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 (is_type_sys_virtually_sound type_sys)
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  else
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    Explicit_Type_Args (is_type_sys_virtually_sound type_sys)
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fun type_arg_policy type_sys s =
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  if should_omit_type_args type_sys s then No_Type_Args
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  else general_type_arg_policy type_sys
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fun num_atp_type_args thy type_sys s =
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  case type_arg_policy type_sys s of
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    Explicit_Type_Args keep_all =>
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    if keep_all then num_type_args thy s
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    else error "not implemented yet" (* FIXME *)
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  | _ => 0
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fun atp_type_literals_for_types type_sys kind Ts =
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  if level_of_type_sys type_sys = No_Types then
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    []
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  else
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    Ts |> type_literals_for_types
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       |> filter (fn TyLitVar _ => kind <> Conjecture
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                   | TyLitFree _ => kind = Conjecture)
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fun mk_anot phi = AConn (ANot, [phi])
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
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fun mk_aconns c phis =
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  let val (phis', phi') = split_last phis in
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    fold_rev (mk_aconn c) phis' phi'
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  end
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fun mk_ahorn [] phi = phi
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  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
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fun mk_aquant _ [] phi = phi
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  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
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    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
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  | mk_aquant q xs phi = AQuant (q, xs, phi)
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fun close_universally atom_vars phi =
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  let
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    fun formula_vars bounds (AQuant (_, xs, phi)) =
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        formula_vars (map fst xs @ bounds) phi
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      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
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      | formula_vars bounds (AAtom tm) =
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        union (op =) (atom_vars tm []
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                      |> filter_out (member (op =) bounds o fst))
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  in mk_aquant AForall (formula_vars [] phi []) phi end
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fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
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  | combterm_vars (CombConst _) = I
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  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
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fun close_combformula_universally phi = close_universally combterm_vars phi
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fun term_vars (ATerm (name as (s, _), tms)) =
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  is_atp_variable s ? insert (op =) (name, NONE)
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  #> fold term_vars tms
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fun close_formula_universally phi = close_universally term_vars phi
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fun fo_term_from_typ (Type (s, Ts)) =
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    ATerm (`make_fixed_type_const s, map fo_term_from_typ Ts)
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  | fo_term_from_typ (TFree (s, _)) =
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    ATerm (`make_fixed_type_var s, [])
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  | fo_term_from_typ (TVar ((x as (s, _)), _)) =
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    ATerm ((make_schematic_type_var x, s), [])
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(* This shouldn't clash with anything else. *)
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val mangled_type_sep = "\000"
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fun generic_mangled_type_name f (ATerm (name, [])) = f name
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  | generic_mangled_type_name f (ATerm (name, tys)) =
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    f name ^ "(" ^ commas (map (generic_mangled_type_name f) tys) ^ ")"
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val mangled_type_name =
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  fo_term_from_typ
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  #> (fn ty => (make_tff_type (generic_mangled_type_name fst ty),
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                generic_mangled_type_name snd ty))
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fun generic_mangled_type_suffix f g Ts =
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  fold_rev (curry (op ^) o g o prefix mangled_type_sep
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            o generic_mangled_type_name f) Ts ""
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fun mangled_const_name T_args (s, s') =
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  let val ty_args = map fo_term_from_typ T_args in
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    (s ^ generic_mangled_type_suffix fst ascii_of ty_args,
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     s' ^ generic_mangled_type_suffix snd I ty_args)
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  end
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val parse_mangled_ident =
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  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
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fun parse_mangled_type x =
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  (parse_mangled_ident
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   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
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                    [] >> ATerm) x
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and parse_mangled_types x =
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  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
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fun unmangled_type s =
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  s |> suffix ")" |> raw_explode
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    |> Scan.finite Symbol.stopper
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           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
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                                                quote s)) parse_mangled_type))
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    |> fst
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val unmangled_const_name = space_explode mangled_type_sep #> hd
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fun unmangled_const s =
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  let val ss = space_explode mangled_type_sep s in
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    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   316
  end
blanchet@42542
   317
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   318
fun introduce_proxies tm =
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   319
  let
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   320
    fun aux top_level (CombApp (tm1, tm2)) =
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   321
        CombApp (aux top_level tm1, aux false tm2)
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   322
      | aux top_level (CombConst (name as (s, s'), T, T_args)) =
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   323
        (case proxify_const s of
blanchet@42568
   324
           SOME proxy_base =>
blanchet@42568
   325
           if top_level then
blanchet@42568
   326
             (case s of
blanchet@42568
   327
                "c_False" => (tptp_false, s')
blanchet@42568
   328
              | "c_True" => (tptp_true, s')
blanchet@42568
   329
              | _ => name, [])
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   330
           else
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   331
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   332
          | NONE => (name, T_args))
blanchet@42574
   333
        |> (fn (name, T_args) => CombConst (name, T, T_args))
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   334
      | aux _ tm = tm
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   335
  in aux true tm end
blanchet@42568
   336
blanchet@42562
   337
fun combformula_from_prop thy eq_as_iff =
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   338
  let
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   339
    fun do_term bs t atomic_types =
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   340
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42568
   341
      |>> (introduce_proxies #> AAtom)
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   342
      ||> union (op =) atomic_types
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   343
    fun do_quant bs q s T t' =
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   344
      let val s = Name.variant (map fst bs) s in
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   345
        do_formula ((s, T) :: bs) t'
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   346
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
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   347
      end
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   348
    and do_conn bs c t1 t2 =
blanchet@38282
   349
      do_formula bs t1 ##>> do_formula bs t2
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   350
      #>> uncurry (mk_aconn c)
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   351
    and do_formula bs t =
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   352
      case t of
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   353
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
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   354
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   355
        do_quant bs AForall s T t'
blanchet@38282
   356
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   357
        do_quant bs AExists s T t'
haftmann@38795
   358
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   359
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   360
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   361
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   362
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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   363
      | _ => do_term bs t
blanchet@38282
   364
  in do_formula [] end
blanchet@38282
   365
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   366
fun presimplify_term ctxt =
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   367
  Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
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   368
  #> Meson.presimplify ctxt
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   369
  #> prop_of
blanchet@38282
   370
wenzelm@41491
   371
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
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   372
fun conceal_bounds Ts t =
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   373
  subst_bounds (map (Free o apfst concealed_bound_name)
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   374
                    (0 upto length Ts - 1 ~~ Ts), t)
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   375
fun reveal_bounds Ts =
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   376
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   377
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   378
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   379
fun extensionalize_term ctxt t =
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   380
  let val thy = Proof_Context.theory_of ctxt in
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   381
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
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   382
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   383
  end
blanchet@38608
   384
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   385
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   386
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   387
    if Meson.is_fol_term thy t then
blanchet@38491
   388
      t
blanchet@38491
   389
    else
blanchet@38491
   390
      let
blanchet@38491
   391
        fun aux Ts t =
blanchet@38491
   392
          case t of
blanchet@38491
   393
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   394
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   395
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   396
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   397
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   398
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   399
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   400
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   401
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   402
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   403
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   404
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   405
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   406
              $ t1 $ t2 =>
blanchet@38491
   407
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   408
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   409
                   t
blanchet@38491
   410
                 else
blanchet@38491
   411
                   t |> conceal_bounds Ts
blanchet@38491
   412
                     |> Envir.eta_contract
blanchet@38491
   413
                     |> cterm_of thy
blanchet@39890
   414
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   415
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   416
                     |> reveal_bounds Ts
blanchet@39370
   417
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   418
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   419
      handle THM _ =>
blanchet@38491
   420
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   421
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   422
             else HOLogic.true_const
blanchet@38491
   423
  end
blanchet@38282
   424
blanchet@38282
   425
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   426
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   427
fun freeze_term t =
blanchet@38282
   428
  let
blanchet@38282
   429
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   430
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   431
      | aux (Var ((s, i), T)) =
blanchet@38282
   432
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   433
      | aux t = t
blanchet@38282
   434
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   435
blanchet@40204
   436
(* making fact and conjecture formulas *)
blanchet@42640
   437
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   438
  let
wenzelm@42361
   439
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   440
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   441
              |> transform_elim_term
blanchet@41211
   442
              |> Object_Logic.atomize_term thy
blanchet@42563
   443
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   444
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@42742
   445
              |> Raw_Simplifier.rewrite_term thy
blanchet@42742
   446
                     (Meson.unfold_set_const_simps ctxt) []
blanchet@42747
   447
              |> extensionalize_term ctxt
blanchet@42750
   448
              |> presimp ? presimplify_term ctxt
blanchet@38282
   449
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   450
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   451
              |> kind <> Axiom ? freeze_term
blanchet@42562
   452
    val (combformula, atomic_types) =
blanchet@42562
   453
      combformula_from_prop thy eq_as_iff t []
blanchet@38282
   454
  in
blanchet@42640
   455
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   456
     atomic_types = atomic_types}
blanchet@38282
   457
  end
blanchet@38282
   458
blanchet@42640
   459
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   460
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   461
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   462
    NONE
blanchet@41990
   463
  | (_, formula) => SOME formula
blanchet@42561
   464
blanchet@42709
   465
fun make_conjecture ctxt prem_kind ts =
blanchet@38613
   466
  let val last = length ts - 1 in
blanchet@42709
   467
    map2 (fn j => fn t =>
blanchet@42709
   468
             let
blanchet@42709
   469
               val (kind, maybe_negate) =
blanchet@42709
   470
                 if j = last then
blanchet@42709
   471
                   (Conjecture, I)
blanchet@42709
   472
                 else
blanchet@42709
   473
                   (prem_kind,
blanchet@42709
   474
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   475
                    else I)
blanchet@42709
   476
              in
blanchet@42709
   477
                make_formula ctxt true true (string_of_int j) Chained kind t
blanchet@42709
   478
                |> maybe_negate
blanchet@42709
   479
              end)
blanchet@38613
   480
         (0 upto last) ts
blanchet@38613
   481
  end
blanchet@38282
   482
blanchet@42682
   483
(** Finite and infinite type inference **)
blanchet@42682
   484
blanchet@42682
   485
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   486
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   487
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   488
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   489
blanchet@42682
   490
fun should_encode_type _ _ All_Types _ = true
blanchet@42682
   491
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   492
  | should_encode_type _ nonmono_Ts Nonmonotonic_Types T =
blanchet@42682
   493
    exists (curry Type.raw_instance T) nonmono_Ts
blanchet@42682
   494
  | should_encode_type _ _ _ _ = false
blanchet@42682
   495
blanchet@42682
   496
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level)) T =
blanchet@42682
   497
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   498
  | should_predicate_on_type _ _ _ _ = false
blanchet@42682
   499
blanchet@42682
   500
fun should_tag_with_type ctxt nonmono_Ts (Tags (_, level)) T =
blanchet@42682
   501
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   502
  | should_tag_with_type _ _ _ _ = false
blanchet@42682
   503
blanchet@42682
   504
val homo_infinite_T = @{typ ind} (* any infinite type *)
blanchet@42682
   505
blanchet@42682
   506
fun homogenized_type ctxt nonmono_Ts level T =
blanchet@42682
   507
  if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
blanchet@42682
   508
blanchet@42573
   509
(** "hBOOL" and "hAPP" **)
blanchet@41313
   510
blanchet@42574
   511
type sym_info =
blanchet@42563
   512
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   513
blanchet@42574
   514
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   515
  let
blanchet@42558
   516
    fun aux top_level tm =
blanchet@42558
   517
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   518
        (case head of
blanchet@42563
   519
           CombConst ((s, _), T, _) =>
blanchet@42558
   520
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   521
             I
blanchet@42558
   522
           else
blanchet@42563
   523
             let val ary = length args in
blanchet@42558
   524
               Symtab.map_default
blanchet@42558
   525
                   (s, {pred_sym = true,
blanchet@42563
   526
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   527
                        max_ary = 0, typ = SOME T})
blanchet@42563
   528
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   529
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   530
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   531
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   532
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   533
            end
blanchet@42558
   534
         | _ => I)
blanchet@42558
   535
        #> fold (aux false) args
blanchet@42558
   536
      end
blanchet@42558
   537
  in aux true end
blanchet@42674
   538
fun add_fact_syms_to_table explicit_apply =
blanchet@42680
   539
  fact_lift (formula_fold true (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   540
blanchet@42675
   541
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   542
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   543
   (make_fixed_const predicator_base,
blanchet@42563
   544
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   545
  ([tptp_false, tptp_true]
blanchet@42563
   546
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   547
blanchet@42544
   548
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   549
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   550
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   551
blanchet@42558
   552
fun min_arity_of sym_tab s =
blanchet@42558
   553
  case Symtab.lookup sym_tab s of
blanchet@42574
   554
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   555
  | NONE =>
blanchet@42558
   556
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   557
      SOME s =>
blanchet@42570
   558
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   559
        if s = predicator_base then 1
blanchet@42547
   560
        else if s = explicit_app_base then 2
blanchet@42547
   561
        else if s = type_pred_base then 1
blanchet@42557
   562
        else 0
blanchet@42547
   563
      end
blanchet@42544
   564
    | NONE => 0
blanchet@38282
   565
blanchet@38282
   566
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   567
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   568
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   569
   arguments and is used as a predicate. *)
blanchet@42558
   570
fun is_pred_sym sym_tab s =
blanchet@42558
   571
  case Symtab.lookup sym_tab s of
blanchet@42574
   572
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   573
    pred_sym andalso min_ary = max_ary
blanchet@42558
   574
  | NONE => false
blanchet@38282
   575
blanchet@42568
   576
val predicator_combconst =
blanchet@42568
   577
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   578
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   579
blanchet@42568
   580
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   581
  case strip_combterm_comb tm of
blanchet@42542
   582
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   583
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   584
  | _ => predicator tm
blanchet@42542
   585
blanchet@42544
   586
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   587
blanchet@42544
   588
fun explicit_app arg head =
blanchet@42544
   589
  let
blanchet@42562
   590
    val head_T = combtyp_of head
blanchet@42693
   591
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   592
    val explicit_app =
blanchet@42562
   593
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42693
   594
                 [arg_T, res_T])
blanchet@42544
   595
  in list_app explicit_app [head, arg] end
blanchet@42544
   596
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   597
blanchet@42565
   598
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   599
  let
blanchet@42544
   600
    fun aux tm =
blanchet@42544
   601
      case strip_combterm_comb tm of
blanchet@42544
   602
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   603
        args |> map aux
blanchet@42557
   604
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   605
             |>> list_app head
blanchet@42544
   606
             |-> list_explicit_app
blanchet@42544
   607
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   608
  in aux end
blanchet@38282
   609
blanchet@42753
   610
fun chop_fun 0 T = ([], T)
blanchet@42753
   611
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
   612
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
   613
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
   614
blanchet@42753
   615
fun filter_type_args thy s arity T_args =
blanchet@42573
   616
  let
blanchet@42753
   617
    val U = s |> Sign.the_const_type thy (* may throw "TYPE" *)
blanchet@42753
   618
    val res_U = U |> chop_fun arity |> snd
blanchet@42753
   619
    val res_U_vars = Term.add_tvarsT res_U []
blanchet@42753
   620
    val U_args = (s, U) |> Sign.const_typargs thy
blanchet@42753
   621
  in
blanchet@42753
   622
    U_args ~~ T_args
blanchet@42753
   623
    |> map_filter (fn (U, T) =>
blanchet@42753
   624
                      if member (op =) res_U_vars (dest_TVar U) then SOME T
blanchet@42753
   625
                      else NONE)
blanchet@42753
   626
  end
blanchet@42753
   627
  handle TYPE _ => T_args
blanchet@42753
   628
blanchet@42753
   629
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42753
   630
  let
blanchet@42753
   631
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
   632
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
   633
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
   634
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   635
        let
blanchet@42701
   636
          val level = level_of_type_sys type_sys
blanchet@42701
   637
          val (T, T_args) =
blanchet@42701
   638
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   639
               anyway, by distinguishing overloads only on the homogenized
blanchet@42701
   640
               result type. *)
blanchet@42701
   641
            if s = const_prefix ^ explicit_app_base andalso
blanchet@42726
   642
               length T_args = 2 andalso
blanchet@42701
   643
               not (is_type_sys_virtually_sound type_sys) then
blanchet@42701
   644
              T_args |> map (homogenized_type ctxt nonmono_Ts level)
blanchet@42701
   645
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42753
   646
                                    (T --> T, tl Ts) (* ### FIXME: need tl? *)
blanchet@42701
   647
                                  end)
blanchet@42701
   648
            else
blanchet@42701
   649
              (T, T_args)
blanchet@42701
   650
        in
blanchet@42701
   651
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   652
             NONE => (name, T_args)
blanchet@42701
   653
           | SOME s'' =>
blanchet@42753
   654
             let
blanchet@42753
   655
               val s'' = invert_const s''
blanchet@42753
   656
               fun filtered_T_args true = T_args
blanchet@42753
   657
                 | filtered_T_args false = filter_type_args thy s'' arity T_args
blanchet@42753
   658
             in
blanchet@42701
   659
               case type_arg_policy type_sys s'' of
blanchet@42753
   660
                 Explicit_Type_Args keep_all => (name, filtered_T_args keep_all)
blanchet@42753
   661
               | Mangled_Type_Args keep_all =>
blanchet@42753
   662
                 (mangled_const_name (filtered_T_args keep_all) name, [])
blanchet@42753
   663
               | No_Type_Args => (name, [])
blanchet@42701
   664
             end)
blanchet@42701
   665
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   666
        end
blanchet@42753
   667
      | aux _ tm = tm
blanchet@42753
   668
  in aux 0 end
blanchet@42573
   669
blanchet@42701
   670
fun repair_combterm ctxt nonmono_Ts type_sys sym_tab =
blanchet@42565
   671
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   672
  #> introduce_predicators_in_combterm sym_tab
blanchet@42753
   673
  #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42701
   674
fun repair_fact ctxt nonmono_Ts type_sys sym_tab =
blanchet@42701
   675
  update_combformula (formula_map
blanchet@42701
   676
      (repair_combterm ctxt nonmono_Ts type_sys sym_tab))
blanchet@42573
   677
blanchet@42573
   678
(** Helper facts **)
blanchet@42573
   679
blanchet@42573
   680
fun ti_ti_helper_fact () =
blanchet@42573
   681
  let
blanchet@42573
   682
    fun var s = ATerm (`I s, [])
blanchet@42589
   683
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   684
  in
blanchet@42612
   685
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   686
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42573
   687
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   688
  end
blanchet@42573
   689
blanchet@42574
   690
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   691
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   692
    SOME mangled_s =>
blanchet@42573
   693
    let
blanchet@42573
   694
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   695
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42579
   696
      fun dub_and_inst c needs_some_types (th, j) =
blanchet@42579
   697
        ((c ^ "_" ^ string_of_int j ^ (if needs_some_types then "T" else ""),
blanchet@42640
   698
          Chained),
blanchet@42573
   699
         let val t = th |> prop_of in
blanchet@42753
   700
           t |> ((case general_type_arg_policy type_sys of
blanchet@42753
   701
                    Mangled_Type_Args _ => true
blanchet@42753
   702
                  | _ => false) andalso
blanchet@42573
   703
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   704
                ? (case typ of
blanchet@42573
   705
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   706
                   | NONE => I)
blanchet@42573
   707
         end)
blanchet@42573
   708
      fun make_facts eq_as_iff =
blanchet@42573
   709
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42589
   710
      val has_some_types = is_type_sys_fairly_sound type_sys
blanchet@42573
   711
    in
blanchet@42573
   712
      metis_helpers
blanchet@42579
   713
      |> maps (fn (metis_s, (needs_some_types, ths)) =>
blanchet@42573
   714
                  if metis_s <> unmangled_s orelse
blanchet@42589
   715
                     (needs_some_types andalso not has_some_types) then
blanchet@42573
   716
                    []
blanchet@42573
   717
                  else
blanchet@42573
   718
                    ths ~~ (1 upto length ths)
blanchet@42579
   719
                    |> map (dub_and_inst mangled_s needs_some_types)
blanchet@42579
   720
                    |> make_facts (not needs_some_types))
blanchet@42573
   721
    end
blanchet@42573
   722
  | NONE => []
blanchet@42573
   723
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   724
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   725
blanchet@42573
   726
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   727
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   728
blanchet@42709
   729
fun translate_formulas ctxt prem_kind type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   730
  let
blanchet@42573
   731
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   732
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   733
    val (facts, fact_names) =
blanchet@42573
   734
      rich_facts
blanchet@42573
   735
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   736
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   737
      |> ListPair.unzip
blanchet@42573
   738
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   739
       boost an ATP's performance (for some reason). *)
blanchet@42573
   740
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   741
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   742
    val all_ts = goal_t :: fact_ts
blanchet@42573
   743
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   744
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   745
    val tycons = type_consts_of_terms thy all_ts
blanchet@42709
   746
    val conjs = make_conjecture ctxt prem_kind (hyp_ts @ [concl_t])
blanchet@42573
   747
    val (supers', arity_clauses) =
blanchet@42589
   748
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   749
      else make_arity_clauses thy tycons supers
blanchet@42573
   750
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   751
  in
blanchet@42573
   752
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   753
  end
blanchet@42573
   754
blanchet@42573
   755
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   756
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   757
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   758
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   759
blanchet@42573
   760
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   761
blanchet@42701
   762
fun type_pred_combatom ctxt nonmono_Ts type_sys T tm =
blanchet@42573
   763
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T]),
blanchet@42573
   764
           tm)
blanchet@42753
   765
  |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42573
   766
  |> AAtom
blanchet@42573
   767
blanchet@42680
   768
fun formula_from_combformula ctxt nonmono_Ts type_sys =
blanchet@42573
   769
  let
blanchet@42589
   770
    fun tag_with_type type_sys T tm =
blanchet@42589
   771
      CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42753
   772
      |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42589
   773
      |> do_term true
blanchet@42589
   774
      |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42589
   775
    and do_term top_level u =
blanchet@42573
   776
      let
blanchet@42573
   777
        val (head, args) = strip_combterm_comb u
blanchet@42574
   778
        val (x, T_args) =
blanchet@42573
   779
          case head of
blanchet@42574
   780
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42573
   781
          | CombVar (name, _) => (name, [])
blanchet@42573
   782
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42574
   783
        val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42573
   784
                          map (do_term false) args)
blanchet@42574
   785
        val T = combtyp_of u
blanchet@42573
   786
      in
blanchet@42680
   787
        t |> (if not top_level andalso
blanchet@42680
   788
                should_tag_with_type ctxt nonmono_Ts type_sys T then
blanchet@42589
   789
                tag_with_type type_sys T
blanchet@42573
   790
              else
blanchet@42573
   791
                I)
blanchet@42573
   792
      end
blanchet@42573
   793
    val do_bound_type =
blanchet@42682
   794
      case type_sys of
blanchet@42722
   795
        Simple_Types level =>
blanchet@42682
   796
        SOME o mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42682
   797
      | _ => K NONE
blanchet@42573
   798
    fun do_out_of_bound_type (s, T) =
blanchet@42680
   799
      if should_predicate_on_type ctxt nonmono_Ts type_sys T then
blanchet@42701
   800
        type_pred_combatom ctxt nonmono_Ts type_sys T (CombVar (s, T))
blanchet@42573
   801
        |> do_formula |> SOME
blanchet@42573
   802
      else
blanchet@42573
   803
        NONE
blanchet@42573
   804
    and do_formula (AQuant (q, xs, phi)) =
blanchet@42573
   805
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42574
   806
                                      | SOME T => do_bound_type T)),
blanchet@42573
   807
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42573
   808
                    (map_filter
blanchet@42573
   809
                         (fn (_, NONE) => NONE
blanchet@42574
   810
                           | (s, SOME T) => do_out_of_bound_type (s, T)) xs)
blanchet@42573
   811
                    (do_formula phi))
blanchet@42573
   812
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42573
   813
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42573
   814
  in do_formula end
blanchet@42573
   815
blanchet@42727
   816
fun bound_atomic_types type_sys Ts =
blanchet@42727
   817
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42727
   818
                (atp_type_literals_for_types type_sys Axiom Ts))
blanchet@42727
   819
blanchet@42680
   820
fun formula_for_fact ctxt nonmono_Ts type_sys
blanchet@42573
   821
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   822
  combformula
blanchet@42727
   823
  |> close_combformula_universally
blanchet@42727
   824
  |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42727
   825
  |> bound_atomic_types type_sys atomic_types
blanchet@42573
   826
  |> close_formula_universally
blanchet@42573
   827
blanchet@42640
   828
fun useful_isabelle_info s = SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42640
   829
blanchet@42573
   830
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   831
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   832
   the remote provers might care. *)
blanchet@42680
   833
fun formula_line_for_fact ctxt prefix nonmono_Ts type_sys
blanchet@42640
   834
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   835
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   836
                     else string_of_int j ^ "_") ^
blanchet@42647
   837
           ascii_of name,
blanchet@42680
   838
           kind, formula_for_fact ctxt nonmono_Ts type_sys formula, NONE,
blanchet@42640
   839
           if generate_useful_info then
blanchet@42640
   840
             case locality of
blanchet@42640
   841
               Intro => useful_isabelle_info "intro"
blanchet@42640
   842
             | Elim => useful_isabelle_info "elim"
blanchet@42640
   843
             | Simp => useful_isabelle_info "simp"
blanchet@42640
   844
             | _ => NONE
blanchet@42640
   845
           else
blanchet@42640
   846
             NONE)
blanchet@42573
   847
blanchet@42573
   848
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@42573
   849
                                                       superclass, ...}) =
blanchet@42573
   850
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   851
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   852
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   853
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42573
   854
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   855
  end
blanchet@42573
   856
blanchet@42573
   857
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   858
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   859
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   860
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   861
blanchet@42573
   862
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@42573
   863
                                                ...}) =
blanchet@42577
   864
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   865
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42573
   866
                          o fo_literal_from_arity_literal) premLits)
blanchet@42573
   867
                    (formula_from_fo_literal
blanchet@42573
   868
                         (fo_literal_from_arity_literal conclLit))
blanchet@42573
   869
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   870
blanchet@42680
   871
fun formula_line_for_conjecture ctxt nonmono_Ts type_sys
blanchet@42573
   872
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   873
  Formula (conjecture_prefix ^ name, kind,
blanchet@42680
   874
           formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42573
   875
                                    (close_combformula_universally combformula)
blanchet@42573
   876
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   877
blanchet@42573
   878
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   879
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   880
               |> map fo_literal_from_type_literal
blanchet@42573
   881
blanchet@42573
   882
fun formula_line_for_free_type j lit =
blanchet@42577
   883
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   884
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   885
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   886
  let
blanchet@42573
   887
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   888
    val lits = fold (union (op =)) litss []
blanchet@42573
   889
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   890
blanchet@42573
   891
(** Symbol declarations **)
blanchet@42544
   892
blanchet@42677
   893
fun insert_type get_T x xs =
blanchet@42677
   894
  let val T = get_T x in
blanchet@42677
   895
    if exists (curry Type.raw_instance T o get_T) xs then xs
blanchet@42677
   896
    else x :: filter_out ((fn T' => Type.raw_instance (T', T)) o get_T) xs
blanchet@42677
   897
  end
blanchet@42677
   898
blanchet@42574
   899
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   900
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42753
   901
  not (String.isPrefix tptp_special_prefix s) andalso
blanchet@42722
   902
  ((case type_sys of Simple_Types _ => true | _ => false) orelse not pred_sym)
blanchet@38282
   903
blanchet@42698
   904
fun sym_decl_table_for_facts type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
   905
  let
blanchet@42698
   906
    fun add_combterm in_conj tm =
blanchet@42574
   907
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   908
        (case head of
blanchet@42574
   909
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   910
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   911
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   912
               Symtab.map_default (s, [])
blanchet@42698
   913
                   (insert_type #3 (s', T_args, T, pred_sym, length args,
blanchet@42698
   914
                                    in_conj))
blanchet@42574
   915
             else
blanchet@42574
   916
               I
blanchet@42574
   917
           end
blanchet@42574
   918
         | _ => I)
blanchet@42698
   919
        #> fold (add_combterm in_conj) args
blanchet@42574
   920
      end
blanchet@42698
   921
    fun add_fact in_conj =
blanchet@42698
   922
      fact_lift (formula_fold true (K (add_combterm in_conj)))
blanchet@42698
   923
  in
blanchet@42698
   924
    Symtab.empty
blanchet@42698
   925
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
   926
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
   927
  end
blanchet@42533
   928
blanchet@42677
   929
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42677
   930
    String.isPrefix bound_var_prefix s
blanchet@42677
   931
  | is_var_or_bound_var (CombVar _) = true
blanchet@42677
   932
  | is_var_or_bound_var _ = false
blanchet@42677
   933
blanchet@42685
   934
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
   935
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42680
   936
fun add_combterm_nonmonotonic_types _ (SOME false) _ = I
blanchet@42680
   937
  | add_combterm_nonmonotonic_types ctxt _
blanchet@42680
   938
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
   939
                  tm2)) =
blanchet@42680
   940
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42680
   941
     not (is_type_surely_infinite ctxt T)) ? insert_type I T
blanchet@42680
   942
  | add_combterm_nonmonotonic_types _ _ _ = I
blanchet@42680
   943
fun add_fact_nonmonotonic_types ctxt ({kind, combformula, ...}
blanchet@42680
   944
                                      : translated_formula) =
blanchet@42680
   945
  formula_fold (kind <> Conjecture) (add_combterm_nonmonotonic_types ctxt)
blanchet@42680
   946
               combformula
blanchet@42680
   947
fun add_nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42680
   948
  level_of_type_sys type_sys = Nonmonotonic_Types
blanchet@42731
   949
  ? (fold (add_fact_nonmonotonic_types ctxt) facts
blanchet@42731
   950
     (* in case helper "True_or_False" is included *)
blanchet@42731
   951
     #> insert_type I @{typ bool})
blanchet@42677
   952
blanchet@42753
   953
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42579
   954
blanchet@42754
   955
fun decl_line_for_sym ctxt nonmono_Ts level s (s', _, T, pred_sym, ary, _) =
blanchet@42754
   956
  let
blanchet@42754
   957
    val translate_type =
blanchet@42754
   958
      mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42754
   959
    val (arg_tys, res_ty) =
blanchet@42754
   960
      T |> chop_fun ary |>> map translate_type ||> translate_type
blanchet@42754
   961
  in
blanchet@42754
   962
    Decl (sym_decl_prefix ^ s, (s, s'), arg_tys,
blanchet@42754
   963
          if pred_sym then `I tptp_tff_bool_type else res_ty)
blanchet@42579
   964
  end
blanchet@42579
   965
blanchet@42592
   966
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
   967
blanchet@42709
   968
fun formula_line_for_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys n s j
blanchet@42698
   969
                              (s', T_args, T, _, ary, in_conj) =
blanchet@42579
   970
  let
blanchet@42709
   971
    val (kind, maybe_negate) =
blanchet@42709
   972
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
   973
      else (Axiom, I)
blanchet@42753
   974
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42579
   975
    val bound_names =
blanchet@42579
   976
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42579
   977
    val bound_tms =
blanchet@42579
   978
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
   979
    val bound_Ts =
blanchet@42592
   980
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
   981
                             else NONE)
blanchet@42579
   982
  in
blanchet@42612
   983
    Formula (sym_decl_prefix ^ s ^
blanchet@42709
   984
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
   985
             CombConst ((s, s'), T, T_args)
blanchet@42579
   986
             |> fold (curry (CombApp o swap)) bound_tms
blanchet@42701
   987
             |> type_pred_combatom ctxt nonmono_Ts type_sys res_T
blanchet@42579
   988
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42680
   989
             |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42727
   990
             |> n > 1 ? bound_atomic_types type_sys (atyps_of T)
blanchet@42709
   991
             |> close_formula_universally
blanchet@42709
   992
             |> maybe_negate,
blanchet@42579
   993
             NONE, NONE)
blanchet@42579
   994
  end
blanchet@42579
   995
blanchet@42709
   996
fun problem_lines_for_sym_decls ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
   997
                                (s, decls) =
blanchet@42682
   998
  case type_sys of
blanchet@42754
   999
    Simple_Types level => map (decl_line_for_sym ctxt nonmono_Ts level s) decls
blanchet@42682
  1000
  | _ =>
blanchet@42574
  1001
    let
blanchet@42579
  1002
      val decls =
blanchet@42579
  1003
        case decls of
blanchet@42579
  1004
          decl :: (decls' as _ :: _) =>
blanchet@42592
  1005
          let val T = result_type_of_decl decl in
blanchet@42592
  1006
            if forall ((fn T' => Type.raw_instance (T', T))
blanchet@42592
  1007
                       o result_type_of_decl) decls' then
blanchet@42592
  1008
              [decl]
blanchet@42592
  1009
            else
blanchet@42592
  1010
              decls
blanchet@42592
  1011
          end
blanchet@42579
  1012
        | _ => decls
blanchet@42579
  1013
      val n = length decls
blanchet@42579
  1014
      val decls =
blanchet@42680
  1015
        decls |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42579
  1016
                         o result_type_of_decl)
blanchet@42574
  1017
    in
blanchet@42709
  1018
      (0 upto length decls - 1, decls)
blanchet@42709
  1019
      |-> map2 (formula_line_for_sym_decl ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1020
                                          n s)
blanchet@42574
  1021
    end
blanchet@42579
  1022
blanchet@42709
  1023
fun problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1024
                                     sym_decl_tab =
blanchet@42709
  1025
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt conj_sym_kind
blanchet@42709
  1026
                                                        nonmono_Ts type_sys)
blanchet@42574
  1027
                  sym_decl_tab []
blanchet@42543
  1028
blanchet@42543
  1029
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
  1030
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
  1031
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
  1032
    fold add_tff_types_in_formula phis
blanchet@42543
  1033
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
  1034
blanchet@42562
  1035
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
  1036
    union (op =) (res_T :: arg_Ts)
blanchet@42577
  1037
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
  1038
    add_tff_types_in_formula phi
blanchet@42543
  1039
blanchet@42543
  1040
fun tff_types_in_problem problem =
blanchet@42543
  1041
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
  1042
blanchet@42545
  1043
fun decl_line_for_tff_type (s, s') =
blanchet@42568
  1044
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
  1045
blanchet@42543
  1046
val type_declsN = "Types"
blanchet@42544
  1047
val sym_declsN = "Symbol types"
blanchet@41157
  1048
val factsN = "Relevant facts"
blanchet@41157
  1049
val class_relsN = "Class relationships"
blanchet@42543
  1050
val aritiesN = "Arities"
blanchet@41157
  1051
val helpersN = "Helper facts"
blanchet@41157
  1052
val conjsN = "Conjectures"
blanchet@41313
  1053
val free_typesN = "Type variables"
blanchet@41157
  1054
blanchet@41157
  1055
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
  1056
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
  1057
    if heading = needle then j
blanchet@41157
  1058
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
  1059
blanchet@42709
  1060
fun prepare_atp_problem ctxt conj_sym_kind prem_kind type_sys explicit_apply
blanchet@42709
  1061
                        hyp_ts concl_t facts =
blanchet@38282
  1062
  let
blanchet@41313
  1063
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42709
  1064
      translate_formulas ctxt prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1065
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42682
  1066
    val nonmono_Ts =
blanchet@42682
  1067
      [] |> fold (add_nonmonotonic_types_for_facts ctxt type_sys) [facts, conjs]
blanchet@42701
  1068
    val repair = repair_fact ctxt nonmono_Ts type_sys sym_tab
blanchet@42682
  1069
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1070
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1071
    val helpers =
blanchet@42682
  1072
      repaired_sym_tab |> helper_facts_for_sym_table ctxt type_sys |> map repair
blanchet@42680
  1073
    val sym_decl_lines =
blanchet@42731
  1074
      (conjs, helpers @ facts)
blanchet@42680
  1075
      |> sym_decl_table_for_facts type_sys repaired_sym_tab
blanchet@42709
  1076
      |> problem_lines_for_sym_decl_table ctxt conj_sym_kind nonmono_Ts type_sys
blanchet@42522
  1077
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1078
       Flotter hack. *)
blanchet@38282
  1079
    val problem =
blanchet@42561
  1080
      [(sym_declsN, sym_decl_lines),
blanchet@42680
  1081
       (factsN, map (formula_line_for_fact ctxt fact_prefix nonmono_Ts type_sys)
blanchet@42180
  1082
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1083
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1084
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42680
  1085
       (helpersN, map (formula_line_for_fact ctxt helper_prefix nonmono_Ts
blanchet@42680
  1086
                                             type_sys)
blanchet@42563
  1087
                      (0 upto length helpers - 1 ~~ helpers)
blanchet@42579
  1088
                  |> (case type_sys of
blanchet@42589
  1089
                        Tags (Polymorphic, level) =>
blanchet@42687
  1090
                        is_type_level_partial level
blanchet@42589
  1091
                        ? cons (ti_ti_helper_fact ())
blanchet@42579
  1092
                      | _ => I)),
blanchet@42680
  1093
       (conjsN, map (formula_line_for_conjecture ctxt nonmono_Ts type_sys)
blanchet@42680
  1094
                    conjs),
blanchet@42545
  1095
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1096
    val problem =
blanchet@42561
  1097
      problem
blanchet@42682
  1098
      |> (case type_sys of
blanchet@42722
  1099
            Simple_Types _ =>
blanchet@42561
  1100
            cons (type_declsN,
blanchet@42561
  1101
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42682
  1102
          | _ => I)
blanchet@42646
  1103
    val (problem, pool) =
blanchet@42646
  1104
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@38282
  1105
  in
blanchet@38282
  1106
    (problem,
blanchet@38282
  1107
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1108
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1109
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
  1110
     fact_names |> Vector.fromList)
blanchet@38282
  1111
  end
blanchet@38282
  1112
blanchet@41313
  1113
(* FUDGE *)
blanchet@41313
  1114
val conj_weight = 0.0
blanchet@41770
  1115
val hyp_weight = 0.1
blanchet@41770
  1116
val fact_min_weight = 0.2
blanchet@41313
  1117
val fact_max_weight = 1.0
blanchet@42608
  1118
val type_info_default_weight = 0.8
blanchet@41313
  1119
blanchet@41313
  1120
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42734
  1121
  (not (is_atp_variable s) andalso s <> "equal" andalso
blanchet@42753
  1122
   not (String.isPrefix tptp_special_prefix s)) ? Symtab.default (s, weight)
blanchet@41313
  1123
  #> fold (add_term_weights weight) tms
blanchet@42577
  1124
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42680
  1125
    formula_fold true (K (add_term_weights weight)) phi
blanchet@42528
  1126
  | add_problem_line_weights _ _ = I
blanchet@41313
  1127
blanchet@41313
  1128
fun add_conjectures_weights [] = I
blanchet@41313
  1129
  | add_conjectures_weights conjs =
blanchet@41313
  1130
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1131
      add_problem_line_weights conj_weight conj
blanchet@41313
  1132
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1133
    end
blanchet@41313
  1134
blanchet@41313
  1135
fun add_facts_weights facts =
blanchet@41313
  1136
  let
blanchet@41313
  1137
    val num_facts = length facts
blanchet@41313
  1138
    fun weight_of j =
blanchet@41313
  1139
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1140
                        / Real.fromInt num_facts
blanchet@41313
  1141
  in
blanchet@41313
  1142
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1143
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1144
  end
blanchet@41313
  1145
blanchet@41313
  1146
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1147
fun atp_problem_weights problem =
blanchet@42608
  1148
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1149
    Symtab.empty
blanchet@42608
  1150
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1151
    |> add_facts_weights (get factsN)
blanchet@42608
  1152
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1153
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1154
    |> Symtab.dest
blanchet@42608
  1155
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1156
  end
blanchet@41313
  1157
blanchet@38282
  1158
end;